id
stringlengths 14
15
| text
stringlengths 5
9.93k
| source
stringlengths 56
69
|
|---|---|---|
1a5e23fee427-3
|
Glacial isostatic adjustment (GIA):
response of the solid Earth to mass redistribution during a glacial cycle; isostasy refers to a concept whereby deformation takes place in an attempt to return the Earth to a state of equilibrium; GIA refers to isostatic deformation related to ice and water loading during a glacial cycle
Sediment compaction:
reduction in the volume of sediments caused by a decrease in pore space, which has the effect of lowering the height of the solid Earth surface; can occur naturally or due to the anthropogenic extraction of fluids (such as water and fossil fuels) from the pore space.
Mantle dynamic topography (MDT):
differences in the height of the surface of the solid Earth caused by density-driven flow within the Earth’s mantle.
Past and current observations of sea-level change
Reconstructions of Relative Sea Levels from Proxy Data
Geological reconstructions of RSL are derived from sea-level proxies, the formation of which was controlled by the past position of sea level (76). Sea-level proxies, which have a systematic and qunatifiable relationship with contemporary tides (77), include sedimentary, geomorphic, archeological, and fixed biological indicators, as well as coral reefs, coral microatolls, salt-marsh flora, and salt-marsh fauna (Figure 1b). The relationship of a proxy to sea level is deÞned by its “indicative meaning,” which describes the central tendency (reference water level) and vertical range (indicative range) of its relationship with tidal level(s).
Under the uniformitarian assumption that the indicative meaning is constant in time, the indicative meaning can be determined empirically by direct measurement of modern analogs. The reconstruction begins with Þeld measurement of the elevation of a paleo sea-level proxy with respect to a common datum (e.g., mean tide level). The vertical uncertainty of a RSL reconstruction is primarily related to the indicative range of the sea-level proxy (Figure 1b). For proxies that form in intertidal settings, including most sedimentary, fixed biological, and geomorphic indicators, vertical uncertainties are proportional to the magnitude of local tidal range. In contrast, the vertical distribution of corals varies among species and is driven by light attenuation, along with a host of other factors (78). Although vertical RSL uncertainties are not systematically larger for older reconstructions, paleo-tidal range change (see, e.g., 79) or variations in the relationship of a proxy to sea level over time may introduce unquantifiable uncertainties.
Paleo sea-level proxies are dated to provide a chronology for past RSL changes. The method used to date a proxy dictates the age range over which it may be used (Figure 1b). Sea-level proxies can be dated directly using radiometric methods. Radiocarbon dating is used to obtain chronologies over decades to the last .50,000 years, whereas methods such as U-series or luminescence dating can be used over hundreds of thousands of years (80). Sea-level proxies may also be dated by correlation with marine oxygen isotope stages, magnetic reversals, or other chronologies using bio-or chemostratigraphy. The age uncertainties of RSL reconstructions increase over time (e.g., 8, 68).
Three geological intervals have been the particular focus of attention for sea-level reconstructions, because they provide analogues for future predicted changes: the Mid-Pliocene Warm Period (MPWP), the LIG stage, and the Holocene.
Sea-level proxy:
any physical, biological, or chemical feature with a systematic and quantifiable relationship to sea level at its time of formation.
Mid-Pliocene Warm Period (~3.2 to 3.0 million years ago)
The MPWP is the most recent period in geologic time with temperatures comparable to those projected for the twenty-first century (e.g., 81). The period is characterized by a series of 41-kyr, orbitally paced climate cycles marked by three abrupt shifts in the stacked oxygen isotope record (82, 83). During this time, atmospheric CO2 ranged between approximately 350 and 450 ppm, and the configuration of oceans and continents was similar to todayÕs, which permits feasible comparison of oceanic and atmospheric conditions in models of Pliocene and modern climate (84, 85). Global climate model simulations estimate peak global mean surface temperatures between 1.9-3.6 C above preindustrial (86).
Both modeling and field evidence suggest that polar ice sheets were smaller during the MPWP, but constraints on the magnitude of GMSL maxima are highly uncertain. Early reconstructions of Pliocene sea levels have been derived from estimates of global ice volume from the temperature-corrected oxygen isotope composition of foraminifera and ostracods (e.g., 87), although the analytical uncertainties (~±10 m) and the uncertainties associated with separating the ice volume, temperature, and diagenetic signals may be greater than the estimated magnitude of GMSL change from the present (8). Therefore, attention has focused on geomorphic proxy reconstructions from paleoshoreline deposits (e.g., 88, 89) or erosional features caused by sea-level fluctuations such as disconformities on atolls (e.g., 90). Estimating GMSL during the Pliocene is complicated by the amount of time elapsed since the formation of sea-level proxies, which allows processes operating over long timescales, such as tectonic uplift or MDT, to create differences between RSL and GMSL of up to tens of meters (e.g., 74). The uncertain contribution of RSL change from MDT makes reconstructions from this period highly challenging, although increasing the number and spatial distribution of RSL reconstructions from the Pliocene may help to derive a GMSL estimate consistent with model predictions of GIA and MDT that use a unique and internally consistent set of physical conditions (7).
Last Interglacial (~129,000-116,000 years ago)
During the LIG, global mean surface temperature was comparable to or slightly warmer than present, although the peak LIG CO2 concentration of .285 ppm (e.g., 91) was considerably less than that of the present (.400 ppm). Global mean sea-surface temperature was .0.5 ± 0.3.C above its late nineteenth-century level (92). Model simulations indicate little global mean surface temperature change during the Last Inter.glacial stage, whereas combined land and ocean proxy data imply .1.C of warming, but with possible spatio-temporal sampling biases (93). Due to higher orbital eccentricity during the LIG, polar warming was more extreme (94). Greenland surface temperatures peaked .5-8.C above preindustrial levels (95), and Antarctic temperatures were .3-5.C warmer (96), both comparable to late twenty-first-century projections under Representative Concentration Pathway (RCP) 8.5 (97).
LIG RSL reconstructions are much more abundant than those for the MPWP (e.g., 4, 6, 68, 78, 98; see also Figure 3c). Geomorphic (marine terraces, shore platforms, beachrock, beach deposits and ridges, abrasion and tidal notches, and cheniers), sedimentary (lagoonal deposits), coral reef, and geochemical sea-level proxies are used to reconstruct RSL changes during this period (e.g., 68). Compilations of RSL data combined with spatio-temporal statistical and GIA modeling indicate that peak GMSL was extremely likely >6 m but unlikely >9 m above present (6, 99). These estimates are in agreement with site-speciÞc, GIA-corrected coastal records in the Seychelles at 7.6 ± 1.7 m (4) and in Western Australia at 9 m (100) above present (Figure 3c).
GMSL during the LIG may have experienced multiple peaks, possibly associated with orbitally driven, asynchronous land-ice minima at the two poles (e.g., 8, 99). A significant fraction of the Greenland ice sheet remained intact throughout the LIG period, with recent alternative reconstructions limiting the peak Greenland GMSL contribution to .2 m (95) or 4-6 m (101) of the ice sheetÕs total 7-m sea-level equivalent mass. Thermal expansion and the melting of mountain glaciers together likely contributed .1 m (102, 103). This implies a significant contribution to LIG GMSL from Antarctic ice melt. However, there is little direct observational evidence of mass loss from the Antarctic region. Additional constraints from RSL reconstructions in mid-to high-latitude regions may help to partition contributions from Greenland and Antarctica (104).
Estimates of LIG GMSL have not yet incorporated the effects of MDT, which may contribute as much as 4 ± 7m(1.) to RSL change in some regions (e.g., Southwestern Australia) (73). In contrast to MPWP, the magnitudes of RSL change due to GIA and MDT are roughly the same order, although the spatial pattern associated with the two processes should be distinct (e.g., 4, 73). Whether a formal accounting for MDT would significantly alter the estimated height of the LIG highstand is unknown.
Representative Concentration Pathway (RCP):
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-4
|
GMSL during the LIG may have experienced multiple peaks, possibly associated with orbitally driven, asynchronous land-ice minima at the two poles (e.g., 8, 99). A significant fraction of the Greenland ice sheet remained intact throughout the LIG period, with recent alternative reconstructions limiting the peak Greenland GMSL contribution to .2 m (95) or 4-6 m (101) of the ice sheetÕs total 7-m sea-level equivalent mass. Thermal expansion and the melting of mountain glaciers together likely contributed .1 m (102, 103). This implies a significant contribution to LIG GMSL from Antarctic ice melt. However, there is little direct observational evidence of mass loss from the Antarctic region. Additional constraints from RSL reconstructions in mid-to high-latitude regions may help to partition contributions from Greenland and Antarctica (104).
Estimates of LIG GMSL have not yet incorporated the effects of MDT, which may contribute as much as 4 ± 7m(1.) to RSL change in some regions (e.g., Southwestern Australia) (73). In contrast to MPWP, the magnitudes of RSL change due to GIA and MDT are roughly the same order, although the spatial pattern associated with the two processes should be distinct (e.g., 4, 73). Whether a formal accounting for MDT would significantly alter the estimated height of the LIG highstand is unknown.
Representative Concentration Pathway (RCP):
one of a set of four standardized pathways, developed by the global climate modeling and integrated assessment modeling communities, describing possible future pathways of climate forcing over the twenty-first century; Extended Concentration Pathways extended the RCPs to the end of the twenty-third century
Figure 3: Reconstructions of global mean sea level (GMSL) and relative sea level (RSL) (6, 25, 119) from (a) the instrumental period, (b)the Holocene, and (c) the Last Interglacial. (a) GMSL estimates during the Instrumental Period from Dangendorf et al. (2017) (118) (green), Hay et al. (2015; Gaussian process regression (GPR)) (119) (dark blue), Hay et al. (2015; Kalman smoothing (KS)) (119) (light blue), Jevrejeva et al. (2014) (117) (orange), and Church & White (2011) (116) (purple), as well as individual RSL records from tide gauges obtained from the Permanent Service for Mean Sea Level (PSMSL). (b) GMSL (and sea-level equivalent signal) derived from far-field data (purple: Lambeck et al. (2014) (46), with 2-sigma uncertainty range) and from GIA models [ICE-5G (Peltier 2004) (52) (red); ICE-6G (Peltier et al. 2015) (42) (blue); Bradley et al. 2016 (111) (black)]. RSL data from Southern Disko Bugt (175, 176); Arisaig, Scotland (177); West Guangdong, southern China (178); Northeastern Brazil (179); South Shetland Island, Antarctica (180); and Langebaan Lagoon, South Africa (181). (c) GMSL estimate from Kopp et al. (6) and RSL reconstructions from Barbados (182-192) interpreted using coral depth distributions presented in Hibbert et al. (78), the Netherlands (193) as interpreted by Kopp et al. (6), the Red Sea continuous delta-18O record (green crosses) with probabilistic model and 95% confidence interval shown (green shading) (194), the Seychelles (195), and Western Australia (100, 196-206) where coral data are interpreted as a lower limit on RSL. Unless otherwise indicated, model uncertainties are 1-sigma, whereas data uncertainties are 2-sigma. Error bars cross at the median of the vertical probability distribution and midpoint of the age distribution of each data point. U-series data are screened following guidelines presented in Hibbert et al. (2016) (78) or Dutton et al. (2015) (195). With the exception of the Red Sea dataset, RSL reconstructions have not been corrected for tectonic motion. To demonstrate the potential inßuence of tectonics on RSL reconstructions, we plot data from Barbados (C1) using uncorrected elevations (solid lines) and elevations corrected for tectonic uplift (dashed lines).
The Holocene (11,700 years ago to present)
A global temperature reconstruction for the early to middle Holocene (from ~9.5-5.5 ka), derived from both marine and terrestrial proxies, suggests a global mean surface temperature ~0.8C higher than preindustrial temperatures (105). This estimate, however, conflicts with climate models that simulate a warming trend through the Holocene. The discrepancy may be due to uncertainties in both the seasonality of proxy reconstructions and the sensitivity of climate models to orbital forcing (106). Recent evidence suggests that estimates of global temperatures may be biased by sub-seasonal sensitivity of marine and coastal temperature estimates from the North Atlantic, with pollen records from North America and Europe instead suggesting a later period of peak warmth from .5.5-3.5 ka and temperatures .0.6.C warmer than the late nineteenth century (107).
The Holocene has more abundant and highly resolved RSL reconstructions than previous interglacial periods (Figure 3b, 45). These reconstructions are sourced from sedimentary (wet.land, deltaic, estuarine, lagoonal facies), geomorphic (beachrock, tidal and abrasional notches), archaeological, coral reef, coral microatoll, and other biological sea-level proxies. The abundance of RSL data from this period, combined with the preservation of near-Þeld glacial deposits, has contributed to the development of a relatively well-constrained history of ice-sheet retreat, particularly in the Northern Hemisphere (108). However, questions remain about Antarctic and Greenland contributions to GMSL (e.g., 109, 110), the timing of when (prior to the twentieth century rise) land-ice contributions to GMSL ceased (e.g., 46, 111, 112), and the magnitude and timescale of internal variability in glaciers, ice sheets, and the ocean.
Given the resolution of Holocene data, detailed sea-level reconstructions from this period are important for constraining local to regional processes and providing estimates of rates of change. GIA is the dominant process driving spatial variability during the Holocene (45). Records from locations formerly covered by ice sheets (near-field regions such as Antarctica, Greenland, Canada, Sweden, and Scotland) reveal a complex pattern of RSL fall from a maximum marine limit due to the net effect of inputs from melting of land-based ice sheets and glacio-isostatic uplift. Rates of RSL fall in near-field regions during the early Holocene were up to -69 ± 9 m/ka (45). Regions near the periphery of ice sheets (intermediate-field locations such as the mid-Atlantic and Pacific coasts of the United States, and northwestern Europe and the Caribbean) display fast rates of RSL rise (up to 10 ± 1 m/ka) in the early Holocene in regions near the center of forebulge collapse. Regions far from ice sheets exhibit a mid-Holocene highstand, the timing (between 8 and 4 ka) and magnitude (between <1 and 6 m) of which vary among South American, African, Asian, and Oceania regions. With diminishing contributions from GIA and melting of land-based ice sheets during the past several millennia, lower amplitude local-to regional-scale processes, such as steric effects or ocean dynamics, are manifested in RSL records (22).
Although the past two millennia (the Common Era) may not be a direct analog for future changes, semi-empirical relationships between high-resolution RSL reconstruction can be paired with temperature reconstructions (e.g., 113) that show periods of both warming (e.g., Medieval Climate Anomaly) and cooling (e.g., Little Ice Age) to show climate forcing on timescales (multi.decadal to multicentennial) and magnitudes relevant to future climate and sea-level scenarios (e.g., 25). The more complete geologic record in the Common Era permits the reconstruction of continuous time series of decimeter-scale RSL change over this period using salt-marsh sequences and coral microatolls (5). The resolution of reconstructions is comparable to future sea-level changes over the next decades to centuries, which enables an examination of regional dynamic variability in sea level that is not possible for earlier periods (24). In addition, the GIA signal is approximately linear over the Common Era and, therefore, it is easier to quantify its contribution to RSL.
Tide gauge:
device for measuring the height of the sea surface with respect to a reference height fixed to the solid Earth.
Reconstructions of Relative Sea Level from Instrumental Data
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-5
|
Although the past two millennia (the Common Era) may not be a direct analog for future changes, semi-empirical relationships between high-resolution RSL reconstruction can be paired with temperature reconstructions (e.g., 113) that show periods of both warming (e.g., Medieval Climate Anomaly) and cooling (e.g., Little Ice Age) to show climate forcing on timescales (multi.decadal to multicentennial) and magnitudes relevant to future climate and sea-level scenarios (e.g., 25). The more complete geologic record in the Common Era permits the reconstruction of continuous time series of decimeter-scale RSL change over this period using salt-marsh sequences and coral microatolls (5). The resolution of reconstructions is comparable to future sea-level changes over the next decades to centuries, which enables an examination of regional dynamic variability in sea level that is not possible for earlier periods (24). In addition, the GIA signal is approximately linear over the Common Era and, therefore, it is easier to quantify its contribution to RSL.
Tide gauge:
device for measuring the height of the sea surface with respect to a reference height fixed to the solid Earth.
Reconstructions of Relative Sea Level from Instrumental Data
Tide-gauge measurements of RSL date back to at least the eighteenth century, with archived records available for Amsterdam beginning in 1700, Liverpool beginning in 1768, and Stockholm beginning in 1774 (114). Originally put in place to monitor tides for shipping purposes, most of the earliest records are located in northern Europe and along the coasts of North America, and many contain persistent data gaps through time. It was not until the mid-twentieth century that most of the current tide-gauge network, which includes tide gauges in the Southern Hemisphere and the Arctic Ocean, became operational (115). Contained in each tide-gauge record is the combined effect of local, regional, and global sea-level processes that take place over timescales ranging from minutes to centuries. The Permanent Service for Mean Sea Level compiles the worldÕs tide-gauge records into two databases: raw unprocessed time series are contained in the metric database; and the revised local reference database contains the time series referenced to a common datum (1).
Today, sea levels are on a long-term rising trend along a large majority of coastlines (Figure 3a; see also 26, 115, 116). Rates of RSL change derived from tide-gauge data varied both spatially and temporally during the twentieth century, and decadal rates of GMSL rise show large variations throughout this period (116). Dense tide-gauge records along the US Atlantic coast have resulted in numerous studies that show rates of RSL rise exceeding GMSL rise. This sea-level rise has been attributed to the combination of GIA, ocean dynamics, and land-based ice melt (20, 49). Tide-gauge records from Alaska, northern Canada, and Fennoscandia illustrate the impact of GIA on local and regional sea level (Figure 3b). These regions, which were covered by ice during the Last Glacial Maximum, are experiencing RSL changes that are dominated by ongoing postglacial rebound of the solid Earth. As the land uplifts at rates >10 mm/year, the result is a RSL fall (48).
Given the regional variability in sea level, and the spatio-temporal sparsity of the tide-gauge network, inferring GMSL over the nineteenth and twentieth centuries is a difficult task. The first attempts to compute GMSL involved regional averaging of small subsets of tide gauges (2). The tide gauges included in these subsets had to satisfy multiple criteria, including being located far from regions experiencing significant sea-level changes due to GIA and having at least 60 years of observations with minimal data gaps. Resulting subsets ranged from 9 to 22 sites and estimates of GMSL fall in the range of 1.7-1.8 mm/year. Extending the simple regional averaging technique, Jevrejeva et al. (115, 117) used a “virtual station” approach that sequentially averages pairs of tide gauges to produce a single virtual tide gauge in each region. This approach, with a GMSL estimate over the twentieth century of 1.9 ± 0.3 mm/year and 3.1 ± 0.6 mm/year over 1993-2009 (Figure 4), produces a more robust estimate of the uncertainty than the simple averaging technique by better addressing the spatial sparsity in the tide-gauge network. More recently, Dangendorf et al. (118) extended the virtual station approach. They simulated local geoid changes and observations of vertical land motion to correct the tide gauges for local sea level effects, resulting in a 1901-1990 GMSL estimate of 1.1 ± 0.3 mm/year and a 1993-2012 estimate of 3.1 ± 1.4 mm/year.
Figure 4: Rates of sea-level rise, and the 1-sigma uncertainty range, over the twentieth century (green dots) and over the satellite altimetry era (blue dots) derived from tide-gauge and satellite altimetry observations. The time windows for reach reconstruction are as follows: (a) 1993-2014 (VM2; 127); (b) 1993-2014 (VM1; 127);(c) 1993-2010 (125); (d) 1993-2009 (117); (e) 1901-1990, 1993-2012 (118); ( f ) 1901-1990 (GPR; 119); (g) 1901-1990, 1993-2010 (KS; 119); (h) 1900-1999, 1993-2009 (117); (i) 1900-2009 (121); ( j) 1901-1990, 1993-2009 (116); (k) 1992-2010 (120); (l) 1993-2010 (26); (m) 1904-2003 (3); (n) 1880-1990 (207).
Tackling the problem of spatio-temporal sparsity differently, Hay et al. (119) combined the tide-gauge records with process-based models of the underlying physics driving global and regional sea-level change using two techniques: a multi-model Kalman smoother and Gaussian process regression. These two methodologies estimate GMSL by first estimating, from the tide-gauge record, the magnitudes of the individual processes contributing to local and global sea level, then summing the individual contributors to produce GMSL estimates. During 1901-1990, the Kalman smoother and Gaussian process regression techniques produced GMSL rise estimates of 1.2 ± 0.2 mm/year and 1.1 ± 0.4 mm/year, respectively. During the altimetry era, from 1993-2010, the Kalman smoother technique estimates that GMSL rose at 3.0 ± 0.7 mm/year (Figure 4).
Satellite altimetry:
measurement of the height of the sea surface through satellite-based techniques such as radar altimetry.
Since 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately ± 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the worldÕs coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.
Accurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 ± 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 ± 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-6
|
Satellite altimetry:
measurement of the height of the sea surface through satellite-based techniques such as radar altimetry.
Since 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately ± 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the worldÕs coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.
Accurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 ± 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 ± 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).
As the satellite altimetry record length grows, so does the satellite-derived time series of (near) global mean sea surface height (123, 124). These estimates of 2.6-3.2 mm/year (125-127) are obtained by computing area weighted averages of the near global sea surface height fields. It is now possible to use the 25-year altimetry record to estimate the acceleration in GMSL since 1993. This acceleration of 0.084 ± 0.025 mm/year^2 (128) represents a starting point for putting recent GMSL estimates into historical context. Developing new statistically robust methodologies to combine the satellite altimetry data with the tide gauge observations is an important and daunting task, and it is necessary in order to quantify local and regional accelerations over the twentieth century.
Attribution of Twentieth-Century Global Mean Sea-Level Change
Attribution studies focus on the extent to which twentieth (and early twenty-first) century GMSL can be affirmatively tied to the effects of human-caused warming (129). These studiesÑrelying on a variety of both physical modeling and statistical techniquesÑgenerally agree that a large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming (25, 130-132).
For example, Slangen et al. (132) used a suite of physical models of global climate and land-ice surface mass balance, together with correction terms for omitted factors, to compare GMSL with and without natural forcing. They found that natural forcing could account for approximately 50% of the modeled historical GMSL change from 1900-2005, and only approximately 10% of modeled historical GMSL change from 1970-2005. Kopp et al. (25) calibrated a statistical model to the relationship between temperature and rate of sea-level change over the past two millennia, and found thatÑhad the twentieth-century global mean surface temperature been the same as the average over 500-1800 CEÑtwentieth-century GMSL rise would have been approximately 35% (90% probable range: .13 to +59%) of its instrumental value.
Projections of future sea-level rise
Our knowledge of past and present changes in sea level can help us understand and predict its future evolution. Methods used to project sea-level changes in the future can be categorized along two basic axes: (1) the degree to which they disaggregate the different drivers of sea-level change, and (2) the extent to which they attempt to characterize probabilities of future outcomes (Figure 5). The former axis separates projections that tabulate individual processes - including projections focused on central ranges, scenarios attempting to assess upper bounds of plausible sea-level rise, and probabilistic bottom-up projections - from semi-empirical approaches based on global climate and sea-level statistics, as well as some expert judgement-based approaches. The latter axis separates approaches focused on assessing either central or extreme outcomes from fully probabilistic approaches.
Figure 5: Taxonomy of sea-level rise projections methods. The horizontal axis separates methods based on the degree to which they disaggregate the different drivers of sea-level change. The vertical axis separates methods based on the extent to which they attempt to characterize probabilities of future outcomes.
Sea-level rise projections published in the past several years have largely been conditional on different RCPs (133). The RCPs represent a range of possible future climate forcing path.ways, including a high-emission pathway with continued growth of CO2 emissions (RCP8.5), a moderate-emission pathway with stabilized emissions (RCP4.5), and a low-emission pathway consistent with the Paris AgreementÕs goal (134) of net-zero CO2 emissions in the second half of this century (RCP2.6). The use of the RCPs enables comparisons among projections from different studies and different methods (135-142).
Bottom-Up Approaches
Most projections are based on a bottom-up accounting of contributions from different driving factors of global and regional sea-level change. Estimates of different contributing factors may be based on a quantitative or semi-quantitative literature meta-analysis. For example, climate models such as those included in the Coupled Model Intercomparison Projection Phase 5 are often used to inform projections of thermal expansion and dynamic sea-level change as well as to drive models of glacier surface mass balance. Alternatively, estimates of factors that contribute to sea-level rise may also be based on the output of a single model study of complex processes such as marine-ice sheet dynamics [e.g., the use of DeConto & Pollard (143) in Kopp et al. (144)] or on simpliÞed models that capture the core dynamics of a process such as ocean heat uptake in response to climate forcing (135, 142). Estimates of sea-level contributions may also be based on heuristic judgements, for example, of the plausible acceleration of ice ßow through outlet glaciers (145).
Central-range estimates
In the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, deÞned by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.
High-end estimates
High-end (sometimes referred to as “worst-case”) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & PollardÕs (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.
Probabilistic approaches
Probabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-7
|
Central-range estimates
In the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, deÞned by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.
High-end estimates
High-end (sometimes referred to as “worst-case”) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & PollardÕs (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.
Probabilistic approaches
Probabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.
The first published probabilistic GMSL projections were developed by Titus & Narayanan (149) for the US Environmental Protection Agency, based on a suite of coupled simple physical models with parameters informed by structured expert elicitation. Probabilistic approaches experienced a resurgence in the past half-decade, in part because of concerns regarding the adequacy of communication about high-end uncertainty in IPCC AR5 sea-level projections (126, 137, 138, 140). Probabilistic studies have been largely constrained to use the climate scenarios run by large model intercomparison projects. However, some more recent probabilistic studies rely on simple coupled models of different components, allowing for more flexible simulations (135, 136, 141, 142, 150).
Top-Down Approaches
Top-down approaches for estimating GMSL focus on comprehensive metrics of change, rather than a bottom-up accounting of individual driving factors. Most top-down studies are semi-empirical in nature.
Semi-empirical approaches
Semi-empirical approaches rely on historical statistical relationships between GMSL change and driving factors such as temperature. One of the earliest GMSL projections (151) used such a relationship, fitting approximated GMSL as a lagged linear function of global mean surface temperature; their relationship (roughly 16 cm/ûC) would yield a likely twenty-first century GMSL rise of approximately 0.2-0.3 m under RCP2.6, and 0.4-0.8 m under RCP8.5. They noted, however, the potential for rapid loss of marine-based ice in Antarctica to raise their projections significantly. This particular study did not formally account for uncertainty in the relationship between temperature and sea level, and thus would fall at the lower end of our probabilistic axis. However, uncertainty analysis is straightforward with simple parametric approaches, and subsequent semi-empirical studies have generally been highly probabilistic.
The current generation of semi-empirical approaches began with Rahmstorf (152), who fitted the historical rate of GMSL change as a function of temperature disequilibrium. Combining a semi-empirical approach that includes uncertainty estimates on key parameters with probabilistic projections of the global mean surface temperature response to different forcing scenarios can yield formally complete probability distributions of future GMSL rise. Such projections are, however, sensitive to the choice of calibration data setÑan additional level of uncertainty not typically formally quantified within a single studyÑpreventing a formal probabilistic evaluation. These choices can have a significant impact. For example, Kopp et al. (144), using a calibration based on reconstructions of temperature and GMSL over the past two millennia, project a rise of 0.3-0.9 m (at the 90% confidence level) over the twenty-first century under RCP4.5, whereas Schaeffer et al. (153), using a calibration based on a single geological reconstruction from North Carolina (5), project 0.6-1.2 m.
Expert judgement
In the course of scientific practice, experts integrate many streams of information to revise their assessments of the world and the way it behaves; Bayes’ theorem, as used in formal statistical analyses, is a formalization of this process. On some level, all projections of future change are based on expert judgement, frequently expressed within the deliberative context of a scientific publication or assessment panel.
A variety of approaches - some relatively informal, others based on more rigorous social scientific practices - use this integration process executed by individuals as an object of study in its own right, and extract from it estimates of the likelihood of different future outcomes. In the sea-level realm, structured expert elicitationÑa formal method in which experts are guided in the interpretation of probabilities in a workshop setting before having their responses weighted based on their performance on calibration questionsÑhas been used to assess the probability distribution of future ice-sheet changes (154). Less structured, more informal expert surveys have also been used to assess the response of GMSL as a whole to different forcing scenarios (155).
Methods of Using Sea-Level Rise Projections
The approaches described above are “science-first” approaches Ñ focused on integrating a variety of lines of information to produce a scientific judgement about future global and/or regional sea-level changes. These approaches are not generally designed to produce projections that can be directly used in a decision process. Yet, in the absence of ongoing dialogue between scientists and decision makers, this distinction can give rise to confusion. For example, approaches focused exclusively on central ranges omit information about high-end outcomes that can be crucial for risk management, whereas approaches focused exclusively on high-end estimates could lead to excessively costly and overly cautious decisions. Bottom-up probabilistic approaches and semi-empirical approaches can provide self-consistent information about both central tendencies and high-end outcomes, but relying on results from a single estimated probability distribution can mask ambiguity and potentially provide a false sense of security about the (un)likelihood of extreme outcomes (156). Caveats expressed in primary scientific literature are frequently lost in the translation to assessment reports.
Scenario approaches
One approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated “plausible variations in GMSL rise,” spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.
Probabilistic approaches and deep uncertainty
One motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, beneÞt-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-8
|
Scenario approaches
One approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated “plausible variations in GMSL rise,” spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.
Probabilistic approaches and deep uncertainty
One motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, beneÞt-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).
Sea-level rise projections, particularly for the second half of this century and beyond, exhibit ambiguity. Projections have no uniquely specifiable probability distribution, and different approaches yield distributions that differ considerably. The Þeld of decision making under un.certainty has developed several approaches to cope with ambiguity (e.g., 161). Some approaches rely on employing multiple probability distributions, which can reveal the robustness (or lack thereof ) of a probability-based judgement to the underlying uncertainty in scientific knowledge that may not be captured within a single probability distribution. Possibility theory (162) provides one approach for combining multiple lines of evidence to produce a “probability box” that bounds the upper and lower limits of different quantiles of a probability distribution, revealing areas of relatively low and relatively high ambiguity. We apply a simpler but related approach below, summarizing literature projections for different scenarios in “very likely” ranges that are constructed from the minima of 5th-percentile projections and maxima of 95th-percentile projections.
Deep uncertainty:
also known as ambiguity or Knightian uncertainty; describes uncertainties for which it is not possible to develop a single, well-characterized probability distribution
Sea-Level Rise Projections
We summarize recent literature projections of GMSL rise for 2050, 2100, 2150, and 2300, as well as recent studies on multi-millennial sea-level rise commitments (Table 1, Figure 6a). Most of these studies are based on the RCPs, which allow the quantile projections produced by different studies to be directly compared to one another.
Sea-level rise projections conditional on different RCPs do not, however, align with the differ.ent temperature targets laid out in the 2015 Paris Agreement, which aims to hold “the increase in the global average temperature to well below 2 C above pre-industrial levels and [pursue] efforts to limit the temperature increase to 1.5.C above pre-industrial levels” (134, paragraph 2-1a). Among the RCPs, both the 2.0C and 1.5C Paris Agreement temperature targets are most consistent with RCP2.6, although some RCP4.5 projections are consistent with 2.0.C. Thus, there has also been a recent set of studies focused on different scenarios consistent with these goals, providing another point for cross-study comparison (163-166).
In order to compare values across different studies that use different temporal baselines, we have normalized sea-level projections:
SLR_{Adj} = SLR left(frac{t}{(Y-Y_0)} right), (1)
where SLR_{Adj} is the normalized sea-level rise projection, SLR is the sea-level rise reported in the study, t is the time range in years (e.g., in the case of 2050 projections, t = 50), Y is the study end year, and Y_0 is the study baseline year. In cases where a range of years is used for either the study endpoint, or for the study baseline, we use the central year from the range for Equation 1 above.
Table 1: Global mean sea-level rise projections (median, 17th to 83rd percentile range, and 5th to 95th percentile range). Studies have been categorized as probabilistic (projections that sample uncertainty for different driving factors and present multiple quantiles in the original study), semi-empirical (projections made with a model that uses a statistical relationship between global mean temperature and GMSL, without computing individual factors), or central range (projections that are either not semi-empirical and also do not sample uncertainty for different driving factors, or that focus the original study exclusively on a central, low, and high quantile). Probabilistic models include Kopp14 (140), Grinsted15 (137), Jackson16 (138), Kopp17 (144), Nauels17a (142), Jackson18 (164), and Rasmussen18 (165). Semi-empirical models include Jevrejeva12 (139), Schaeffer12 (153), Kopp16 (25), Bittermann17 (163), and Jackson18 (164). Central range models include Perrette13 (208), Slangen14 (147), Mengel16 (141), Schleussner16 (166), Bakker17 (135), Goodwin17 (136), Nauels17b (209), and Wong17 (150).
Year
Percentile range projections
50 (median)
17-83
5-95
Probabilistic projections
Kopp14
RCP8.5
2050
0.29
0.24-0.34
0.21-0.38
2100
0.79
0.62-1.00
0.52-1.21
2150
1.30
1.00-1.80
0.80-2.30
2300
3.18
1.75-5.16
0.98-7.37
RCP4.5
2050
0.26
0.21-0.31
0.18-0.35
2100
0.59
0.45-0.77
0.36-0.93
2150
0.90
0.60-1.30
0.40-1.70
2300
1.92
0.70-3.49
0.00-5.31
RCP2.6
2050
0.25
0.21-0.29
0.18-0.33
2100
0.50
0.37-0.65
0.29-0.82
2150
0.70
0.50-1.10
0.30-1.50
2300
1.42
0.32-2.88
0.22-4.70
Grinsted15 - RCP8.5
2100
0.80
0.58-1.20
0.45-1.83
Jackson16 - RCP8.5 High-end
2050
0.27
0.20-0.34
0.17-0.44
2100
0.80
0.60-1.16
0.49-1.60
Jackson16 - RCP8.5
2100
0.72
0.52-0.94
0.35-1.13
Jackson16 - RCP4.5
2100
0.52
0.34-0.69
0.21-0.81
Kopp17 - RCP8.5
2050
0.31
0.22-0.40
0.17-0.48
2100
1.46
1.09-2.09
0.83-2.43
2150
4.09
3.17-5.47
2.92-5.98
2300
11.69
9.80-14.09
9.13-15.52
Kopp17 - RCP4.5
2050
0.26
0.18-0.36
0.14-0.43
2100
0.91
0.66-1.25
0.50-1.58
2150
1.72
1.21-2.72
0.90-3.22
2300
4.21
2.75-5.95
2.11-6.96
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-9
|
0.90
0.60-1.30
0.40-1.70
2300
1.92
0.70-3.49
0.00-5.31
RCP2.6
2050
0.25
0.21-0.29
0.18-0.33
2100
0.50
0.37-0.65
0.29-0.82
2150
0.70
0.50-1.10
0.30-1.50
2300
1.42
0.32-2.88
0.22-4.70
Grinsted15 - RCP8.5
2100
0.80
0.58-1.20
0.45-1.83
Jackson16 - RCP8.5 High-end
2050
0.27
0.20-0.34
0.17-0.44
2100
0.80
0.60-1.16
0.49-1.60
Jackson16 - RCP8.5
2100
0.72
0.52-0.94
0.35-1.13
Jackson16 - RCP4.5
2100
0.52
0.34-0.69
0.21-0.81
Kopp17 - RCP8.5
2050
0.31
0.22-0.40
0.17-0.48
2100
1.46
1.09-2.09
0.83-2.43
2150
4.09
3.17-5.47
2.92-5.98
2300
11.69
9.80-14.09
9.13-15.52
Kopp17 - RCP4.5
2050
0.26
0.18-0.36
0.14-0.43
2100
0.91
0.66-1.25
0.50-1.58
2150
1.72
1.21-2.72
0.90-3.22
2300
4.21
2.75-5.95
2.11-6.96
Figure 6: (a) Near-term (2050; left), mid-term (2100; center), and long-term (2300; right) sea-level rise projections for RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively, as well as for scenarios stabilizing global mean temperature at 1.5 C (Stab1.5) and 2.0.C (Stab2.0) above preindustrial levels. Shown are the 5th-95th percentile ranges (thin bars), 17th-83rd percentile ranges (thick bars), and median (circles) global mean sea-level (GMSL) rise projections (in meters). The AR5 “likely” ranges of 2050 and 2100 sea-level rise for each RCP scenario are shown by colored shading on the left and center panels, respectively. Gray shading on the right-most panel represents the range of IPCC AR5 2300 sea-level rise projections. (b) Decomposition of uncertainty in GMSL projections, following the DP16 projections of Kopp et al. (144). Red represents within-scenario variance due to the Antarctic ice sheet (AIS), cyan the variance due to the Greenland ice sheet (GIS), blue the variance due to glaciers and ice caps (GIC), green the variance due to thermal expansion (TE), and purple the variance due to land-water storage (LWS). The yellow line represents the total variance, pooling across RCP2.6, RCP4.5, and RCP8.5 (Scen). Until the 2040s, cross-scenario variance is negligible, leading to a total variance across RCPs that is slightly smaller than the variance within RCP4.5 (represented by the sum of all other contributions). In the second half of the twenty-first century, across-scenario variance grows to dominate uncertainty.
Projections for 2050
Near-term projections (through 2050) exhibit minimal sensitivity to emission pathways and a relatively small spread among studies (135, 138-141, 144, 150, 163). Across various RCPs and temperature scenarios, median GMSL projections in these studies range from 0.2-0.3 m. A conservative interpretation of these different studies would place the very likely GMSL rise between 2000 and 2050, across possible forcing pathways, at 0.1-0.5 m, with the beneÞt of transitioning from rapid emission growth to rapid emission decline being <0.1 m (Table 1, Figure 6a).
Projections for 2100
In the second half of the century and beyond, the spread in projections grows substantially due to both alternative methods and emissions uncertainty. Within a single forcing pathway, uncertainty in the response of the polar ice sheets to climate changes becomes increasingly dominant (Figure 6b), but uncertainty across scenarios becomes at least as large and often larger. Across RCPs and studies, median projections for total twenty-first-century GMSL rise range from as low as 0.4 m under RCP2.6 (25, 141) to as high as 1.5 m under RCP8.5 in simulations allowing for an aggressively unstable Antarctic ice sheet (150). Scenario choice exerts a great deal of influence, with median projections ranging from 0.4 to 0.8 m under RCP2.6, 0.5 to 0.9 m under RCP4.5, and 0.7 to 1.5 m under RCP8.5 (25, 135-142, 144, 147, 150). Assessing across studies yields a very likely GMSL rise of 0.2-1.0 m under RCP2.6, 0.2-1.6 m under RCP4.5, and 0.4-2.4 m under RCP8.5 (Table 1, Figure 6a).
Studies attempting to assess the difference in GMSL rise between 1.5C and 2.0C warmer worlds that are consistent with goals of the Paris Agreement largely occupy the space of RCP2.6 and the cooler fraction of RCP4.5 projections. Excluding one older semi-empirical study (153), normalized projections of median 2100 sea-level rise range from 0.4-0.6 m under a scenario in which global average temperatures stabilize at 1.5.C (163) and from 0.5-0.7 m under a scenario in which global average temperatures stabilize at 2.0.C (164). Across studies, very likely ranges are 0.2-1.0 m under 1.5.C stabilization and 0.2-1.1 m under 2.0.C stabilization (163-166).
Projections for 2150
Across the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.
Among studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.
Projections for 2300
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-10
|
Projections for 2150
Across the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.
Among studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.
Projections for 2300
The same three studies providing 2150 RCP projections (140, 142, 144) also provide projections through 2300, the temporal endpoint of the extensions of the RCPs. [Kopp et al.’s (140) projections are extended to 2300 in Kopp et al. (144).]. One semi-empirical study (167) also provides projections on this timescale. Unsurprisingly, the difference among scenarios is extremely large by 2300 Ñ by which time, the extension of RCP2.6 is characterized by an atmospheric CO2 concentration lower than today, whereas the extension of RCP8.5 is characterized by a CO2 concentration of nearly 2,000 ppm. Median estimates of GMSL rise between 2000 and 2300 range from 1.0-2.0 m under RCP2.6, 1.7-4.2 m under RCP4.5, and 3.2-11.7 m under RCP8.5. Across studies, very likely ranges are .0.2 to 4.7 m under RCP2.6, 0.0 to 7.0 m under RCP4.5, and 1.0 to 15.5 m under RCP8.5 (Figure 6a).
Kopp et al. (144) provide two sets of projections, one (labeled K14), based on an extension of Kopp et al. (140) that, for ice sheets, is largely consistent with the IPCC AR5, and one (labeled DP16) incorporating results from the Antarctic ice-sheet model of DeConto & Pollard (143). The difference between these two projections highlights the importance of Antarctic ice-sheet behavior on this timescale. In K14, the 90% credible projections are -0.2 to 4.7 m under RCP2.6, 0.0 to 5.3 m under RCP4.5, and 1.0 to 7.4 m under RCP8.5. In DP16, the corresponding projections are 0.5-3.0 m under RCP2.6, 2.1-7.0 m under RCP4.5, and 9.1-15.6 m under RCP8.5. The incorporation of the results of a mechanistic model for the Antarctic ice sheet narrows the projection range under low emissions but shifts and fattens it under high emissions.
Multi-millennial projections
The effects of climate change on sea level are not felt instantaneously; rather, due to the slow response time of deep ocean heat uptake and the sluggish response of ice sheets, they play out over millennia. The long-term sea-level response to a given emission future is sometimes called a “sea-level commitment” (168). Levermann et al. (168) use a combination of physical models for ocean warming, glaciers, ice caps, and ice-sheet contributions to assess the sea-level change arising from two millennia of exposure to a constant temperature. Over 2,000 years, they find a sea-level commitment of approximately 2.3 m/C of warming. They note, however, that over longer time periods Greenland exhibits an abrupt threshold of ice loss between 0.8 and 2.2.C that ultimately adds approximately 6 m to GMSL. Incorporating this abrupt threshold yields a relationship, they conclude, that is consistent with paleo-sea-level constraints from the LIG, the MPWP, and Marine Isotope Stage 11 (approximately 411-401 thousand years ago). Over two millennia, they project a commitment of 1.4-5.2 m from 1.C of warming, 3.0- 7.7 m from 2.C of warming, and 6.0-12.1 m from 4.C of warming. Over ten millennia, these numbers increase to 1.5-10.9 m, 3.5-13.5 m, and 12.0-16.0 m. Clark et al. (169) use physical models to consider not only the translation between temperature and long-term sea-level change, but also the translation between emissions and temperature. For a scenario in which 1,280 Gt C are emitted after the year 2000 - roughly comparable to RCP4.5, and leading to a peak warming of approximately 2.5.C above preindustrial levels - they find a 10,000-year sea-level commitment in excess of 20 m. They estimate that historical CO2 emissions have already locked in 1.2-2.2 m of sea-level rise, and phasing emissions down to zero over the course of the next .90 years will lock in another ~9m.
A few additional studies have focused on individual drivers of sea-level rise and the possible long-term contributions to sea level from specific mechanisms. Numerous studies have used Earth system models of intermediate complexity to assess the long-term thermal expansion contribution to GMSL rise, which amounts to approximately 0.2-0.6 m/.C (11). Zickfeld et al. (170) found that the slow response time of the oceans is important even for their response to short-lived climate forcers. For example, if CH4 emissions cease, 75% of the CH4-induced thermal expansion persists for 100 years, and approximately 40% persists for 500 years.
In addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.
Marine Isotope Stages:
warm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.
Synthesis
Bayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to reÞned future projections.
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-11
|
In addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.
Marine Isotope Stages:
warm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.
Synthesis
Bayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to reÞned future projections.
Probabilistic projections allow the identification of the major drivers of variance and, thus, the areas where investigation has the potential to yield the greatest reduction in that variance. For example, the DP16 of Kopp et al. (144), RSL projections in New Jersey (Figure 7) and Singapore (Figure 8) both are highly sensitive to the fate of the Antarctic ice sheet. Physical uncertainty in the Antarctic response (distinct from scenario uncertainty) accounts for at least ~25% of projection variance at both sites throughout the twenty-first century. In Singapore, the second largest contributor to projection variance for much of the century is the geological background (e.g., land subsidence), and the third largest contributor is atmosphere/ocean dynamics. By contrast, in New Jersey, atmosphere/ocean dynamics are the dominant contributor to variance through most of the century, whereas uncertainty in the geological background is negligible. This analysis would, thus, guide research to improve RSL projections in both localities toward the Antarctic, but it also highlights the importance of the geological background in Singapore and of a better characterization of North Atlantic atmosphere/ocean dynamics (Figures 7 and 8).
Figure 7: (a) Geological reconstruction of past relative sea level (RSL) in Atlantic City, New Jersey. Red boxes indicate sea-level index points. The yellow-orange curve indicates annual tide-gauge data. The gray curve is a prediction of past RSL at Atlantic City from a spatio-temporal empirical hierarchical model (25) Þt to a database of western North Atlantic sea-level proxies and tide-gauge data. (b) Projections of RSL change in Atlantic City, New Jersey, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of the uncertainty in the RSL projections of b. Wedges indicate the fractional contributions of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.
Figure 8: (a) Geological reconstruction of past relative sea level (RSL) in Singapore. Red boxes indicate sea-level index points. The orange curve indicates annual tide-gauge data at Raffles Light House, and the gray curve is a prediction of past RSL from an empirical hierarchical model (25) Þt to the proxy and tide-gauge data. (b) Projections of future RSL change at Rafßes Light House, Singapore, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of uncertainty in the RSL projections in panel b. Wedges indicate the fractional contribution of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.
The deep uncertainty regarding the behavior of marine-based parts of the Antarctic ice sheet has been noted since the earliest days of modern GMSL rise projections (e.g., 151), based on geological considerations. The Antarctic response during past warm periods serves as an important diagnostic of the performance of models used to project ice-sheet behavior in future warm cli.mates. For example, DeConto & PollardÕs (143) estimates of the Antarctic contribution to GMSL during the LIG (3.6-7.4 m) and MPWP (5-15 m) serve as a filter on ensemble members viewed as having reasonable physical parameterizations. Under both high-and low-emissions scenarios, LIG behavior correlates with sea-level contributions in 2100 (r = 0.52 for RCP2.6 and r = 0.35 for RCP8.5), whereas Pliocene behavior correlates strongly (r = 0.67) with behavior under RCP8.5. The Pliocene correlation is even stronger (r = 0.83) for RCP8.5 in 2500, as is the LIG correlation for RCP2.6 (r = 0.61). These modeling results support the heuristic idea that the LIG provides information relevant to the long-term future in a low-emission world and that the Pliocene and other warmer past periods provide information relevant to a higher-emission world. Unfortunately, whereas significant progress may be possible over the next decade in understanding the LIG, knowledge about sea level during earlier periods may be problematic in light of the potentially major contributions from MDT (73).
The variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 ± 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signiÞcant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 ± 1.5 mm/year to 0.0 ± 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-12
|
The variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 ± 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signiÞcant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 ± 1.5 mm/year to 0.0 ± 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).
Another regionally important factor indicated by the variance decomposition is atmosphere/ ocean dynamics, estimated to contribute 1 ± 5 cm to RSL change between 2000 and 2050 for Singapore. As with the geological component, the precise quantitative value should be viewed with caution. The global climate models used to estimate RSL do not resolve the details of atmospheric and ocean circulation in the Java Sea and through the Singapore Strait. The potential importance of this contribution should motivate studies with regional ocean models. Indeed, geological reconstructions also suggest the potential significance of this term. Meltzner et al. (172) found coral microatoll evidence at Belitung, in the Java Sea, for mid-Holocene ±60-cm swings in RSL, with peak rates of change reaching 13 ± 4 mm/year for roughly half a century. Were such a swing to happen over the next half century, it would dwarf other drivers of RSL change. This finding emphasizes the value of understanding the relevant physical processes and ensuring the models used to project future RSL changes can reasonably reproduce them.
A similar example arises in New Jersey. In 2050 under RCP4.5, the central 90% projection for total RSL is 19-65 cm, to which atmosphere/ocean dynamics contribute -7 to 18 cm (Figure 7c). Eliminating atmosphere/ocean dynamics uncertainty would reduce the range to 26-60 cm (a 26% reduction in width). This broad range is driven primarily by the uncertain response of the Gulf Stream, the North Atlantic Oscillation, the AMOC, and possibly El Nino-Southern Oscillation to warming. On shorter timescales, dynamics involving these systems are likely responsible for the migrating “hot spots” of sea-level change observed along the US Atlantic Coast (e.g., 31). The uncertain atmosphere/ocean dynamics contribution motivates paleo-sea level studies focused on understanding multidecadal-scale and centennial-scale variability along the Atlantic coast of North America. Studies of RSL change over the past millennium suggest variability of more than a decimeter (173). The spatial pattern of this past variability along the coast suggests the same atmosphere/ocean dynamics factors that are involved in future projections (rather than, for example, land-ice changes) are the most likely drivers (22, 24). This variability thus provides a historical test case for the coupled climate models used to project future atmosphere/ocean dynamic RSL change.
Conclusion
With 11% of the world population living in coastal areas less than 10 m above sea level (174), rising seas represent one of the main sources of future economic and ecological risk. Although records from the instrumental era provide useful information in constraining the future evolution of sea level, the geological record presents us with a history of climatic changes under a wide range of different boundary conditions (e.g., paleogeographic configurations) and climatic forcings (e.g., atmospheric CO2 levels and orbital regimes). To better constrain the response of the climate system to current and future anthropogenic greenhouse forcing, it is necessary to study these geological periods. Given the serious risks associated with sea-level rise, reconstructions of RSL are particularly important. However, claims of ties between past changes and future projections are not always formally established. It is only if both geological reconstructions and projections are made cognizant of uncertainty and spatial variability that a range of specific connections between past and future changes can be made and turned into useful information for planners and decision makers. Although projections of future sea level will always remain uncertain, greater interconnections between the two sub-disciplines could lead to significant progress in constraining their characteristics.
Summary Points
Relative sea level (RSL) differs from global mean sea level (GMSL), because driving processesÑsuch as atmosphere/ocean dynamics, the static-equilibrium effects of ocean/cryosphere/hydrosphere mass redistribution on the height of the geoid and the EarthÕs surface, glacio-isostatic adjustment (GIA), sediment compaction, tectonics, and mantle dynamic topography (MDT)Ñare spatially variable and cause RSL change to vary in rate and magnitude among regions.
Geological reconstructions of RSL are derived from sea-level proxies, the formation of which were controlled by the past position of sea level. We summarize the response of sea level to past climatic changes during three geological intervals that provide analogues for future predicted changes: the Mid-Pliocene Warm Period, the Last Interglacial, and the Holocene.
Estimates of GMSL rise over the twentieth century (1.1-1.9 mm/year) are derived from the temporally and spatially sparse tide gauge network, whereas more recent estimates (2.6-3.2 mm/year) are also obtained using satellite altimetry observations of sea surface height.
A large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming.
Methods used to project sea-level changes in the future vary both in the degree to which they disaggregate the different drivers of sea-level change and the extent to which they attempt to characterize probabilities of future outcomes.
A review of recent GMSL rise projections shows that, across methodologies and emission scenarios, median values of future sea-level range from 0.2-0.3 m (2050), 0.4-1.5 m (2100), 0.6-4.1 m (2150), and 1.0-11.69 m (2300), with 95th percentile projections for RCP8.5 (a high-emission scenario) reaching as high as 2.4 m in 2100, and 15.5 m in 2300.
Future Issues
Increasing the spatial and temporal distribution, improving the resolution, and incorporating geological sea-level reconstructions into uniÞed, freely accessible databases may improve insights into the relative contribution of climatic and geophysical processes into present and future sea-level change.
Recognition of the sizable contributions of MDT to RSL change over millions of years has complicated reconstruction of sea level during the Pliocene, the last time global mean temperatures were as high as projected for this century. Reducing uncertainty of MDT may allow more useful constraints on future sea level.
Characterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.
More rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.
In order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.
Sustained dialogue between scientists and decision-makers, not just “science-first” assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.
References
Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. New data systems and products at the permanent service for mean sea level. J. Coast. Res. 29:493-504
Douglas BC. 1991. Global sea level rise. J. Geophys. Res. Oceans 96(C4):6981-92
Holgate SJ. 2007. On the decadal rates of sea level change during the twentieth century. Geophys. Res. Lett. 34(1):L01602
Dutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96
Kemp AC, Horton BP, Donnelly JP, Mann ME, Vermeer M, Rahmstorf S. 2011. Climate related sea-level variations over the past two millennia. PNAS 108(27):11017-22
Kopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2009. Probabilistic assessment of sea level during the Last Interglacial Stage. Nature 462(7275):863-67
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-13
|
Characterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.
More rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.
In order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.
Sustained dialogue between scientists and decision-makers, not just “science-first” assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.
References
Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. New data systems and products at the permanent service for mean sea level. J. Coast. Res. 29:493-504
Douglas BC. 1991. Global sea level rise. J. Geophys. Res. Oceans 96(C4):6981-92
Holgate SJ. 2007. On the decadal rates of sea level change during the twentieth century. Geophys. Res. Lett. 34(1):L01602
Dutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96
Kemp AC, Horton BP, Donnelly JP, Mann ME, Vermeer M, Rahmstorf S. 2011. Climate related sea-level variations over the past two millennia. PNAS 108(27):11017-22
Kopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2009. Probabilistic assessment of sea level during the Last Interglacial Stage. Nature 462(7275):863-67
Raymo ME, Mitrovica JX, OÕLeary MJ, DeConto RM, Hearty PJ. 2011. Departures from eustasy in Pliocene sea-level records. Nat. Geosci. 4(5):328-32
Dutton A, Carlson AE, Long AJ, Milne GA, Clark PU, et al. 2015. Sea-level rise due to polar ice-sheet mass loss during past warm periods. Science 349(6244):aaa4019
Milne GA, Gehrels WR, Hughes CW, Tamisiea ME. 2009. Identifying the causes of sea-level change. Nat. Geosci. 2(7):471-78
Sweet WV, Kopp RE, Weaver CP, Obeysekera J, Horton R, et al. 2017. Global and regional sea level rise scenarios for the United States. Tech. Rep. NOS CO-OPS 083, Nat. Oceanic Atmos. Admin., US Dep. Comm.
Church JA, Clark PU, Cazenave A, Gregory JM, Jevrejeva S, et al. 2013. Sea level change. In Climate Change 2013: The Physical Science Basis, ed. TF Stocker, D Qin, G-K Plattner, M Tignor, SK Allen, et al., pp. 1137-216. Cambridge, UK: Cambridge Univ. Press
Cahill N, Kemp AC, Horton BP, Parnell AC. 2015. Modeling sea-level change using errors-in-variables integrated Gaussian processes. Ann. Appl. Stat. 9(2):547-71
Hinkel J, Jaeger C, Nicholls RJ, Lowe J, Renn O, Peijun S. 2015. Sea-level rise scenarios and coastal risk management. Nat. Clim. Change 5(3):188-90
Slangen ABA, Meyssignac B, Agosta C, Champollion N, Church JA, et al. 2017. Evaluating model simulations of twentieth-century sea level rise. Part I: Global mean sea level change. J. Clim. 30(21):8539-63
Marzeion B, Jarosch AH, Hofer M. 2012. Past and future sea-level change from the surface mass balance of glaciers. Cryosphere 6(6):1295-1322
Shepherd A, Ivins ER, Geruo A, Barletta VR, Bentley MJ, et al. 2012. A reconciled estimate of ice-sheet mass balance. Science 338(6111):1183-89
Konikow LF. 2011. Contribution of global groundwater depletion since 1900 to sea-level rise. Geophys. Res. Lett. 38(17):L17401
MerriÞeld MA, Thompson PR, Lander M. 2012. Multidecadal sea level anomalies and trends in the western tropical PaciÞc. Geophys. Res. Lett. 39(13):L13602
Ezer T, Atkinson LP, Corlett WB, Blanco JL. 2013. Gulf StreamÕs induced sea level rise and variability along the U.S. mid-Atlantic coast. J. Geophys. Res. Oceans 118(2):685-97
Kopp RE. 2013. Does the mid-Atlantic United States sea level acceleration hot spot reßect ocean dynamic variability? Geophys. Res. Lett. 40(15):3981-85
Little CM, Piecuch CG, Ponte RM. 2017. On the relationship between the meridional overturning circulation, alongshore wind stress, and United States East Coast sea level in the Community Earth System Model Large Ensemble. J. Geophys. Res. Oceans 122(6):4554-68
Kemp AC, Bernhardt CE, Horton BP, Kopp RE, Vane CH. 2014. Late Holocene sea-and land-level change on the U.S. southeastern Atlantic coast. Mar Geol. 357:90-100
Kemp AC, Hawkes AD, Donnelly JP, Vane CH, Horton BP. 2015. Relative sea-level change in Con.necticut (USA) during the last 2200 yrs. Earth Planet. Sci. Lett. 428:217-229
Kopp RE, Hay CC, Little CM, Mitrovica JX. 2015. Geographic variability of sea-level change. Curr. Clim. Change Rep. 1(3):192-204
Kopp RE, Kemp AC, Bittermann K, Horton BP, Donnelly JP. 2016. Temperature-driven global sea-level variability in the Common Era. PNAS 113(11):1434-41
Nerem RS, Chambers DP, Choe C, Mitchum GT. 2010. Estimating mean sea level change from the TOPEX and Jason Altimeter missions. Mar. Geod. 33(sup1):435-46
Hamlington BD, Cheon SH, Thompson PR, MerriÞeld MA, Nerem RS, et al. 2016. An ongoing shift in PaciÞc Ocean sea level. J. Geophys. Res. Oceans 121(7):5084-97
McGregor S, Gupta AS, England MH. 2012. Constraining wind stress products with sea surface height observations and implications for PaciÞc Ocean sea level trend attribution. J. Clim. 25(23):8164-76
Yin J, Goddard PB. 2013. Oceanic control of sea level rise patterns along the East Coast of the United States. Geophys. Res. Lett. 40(20):5514-20
Taylor KE, Stouffer RJ, Meehl GA. 2012. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93(4):485-98
Valle-Levinson A, Dutton A, Martin JB. 2017. Spatial and temporal variability of sea level rise hot spots over the eastern United States. Geophys. Res. Lett. 44(15):7876-82
Clark JA, Lingle CS. 1977. Future sea-level changes due to West Antarctic ice sheet fluctuations. Nature 269(5625):206-9
Mitrovica JX, Gomez N, Morrow E, Hay C, Latychev K, Tamisiea ME. 2011. On the robustness of predictions of sea level Þngerprints. Geophys. J. Int. 187(2):729-42
Mitrovica JX, Tamisiea ME, Davis JL, Milne GA. 2001. Recent mass balance of polar ice sheets inferred from patterns of global sea-level change. Nature 409(6823):1026-29
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-14
|
Nerem RS, Chambers DP, Choe C, Mitchum GT. 2010. Estimating mean sea level change from the TOPEX and Jason Altimeter missions. Mar. Geod. 33(sup1):435-46
Hamlington BD, Cheon SH, Thompson PR, MerriÞeld MA, Nerem RS, et al. 2016. An ongoing shift in PaciÞc Ocean sea level. J. Geophys. Res. Oceans 121(7):5084-97
McGregor S, Gupta AS, England MH. 2012. Constraining wind stress products with sea surface height observations and implications for PaciÞc Ocean sea level trend attribution. J. Clim. 25(23):8164-76
Yin J, Goddard PB. 2013. Oceanic control of sea level rise patterns along the East Coast of the United States. Geophys. Res. Lett. 40(20):5514-20
Taylor KE, Stouffer RJ, Meehl GA. 2012. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93(4):485-98
Valle-Levinson A, Dutton A, Martin JB. 2017. Spatial and temporal variability of sea level rise hot spots over the eastern United States. Geophys. Res. Lett. 44(15):7876-82
Clark JA, Lingle CS. 1977. Future sea-level changes due to West Antarctic ice sheet fluctuations. Nature 269(5625):206-9
Mitrovica JX, Gomez N, Morrow E, Hay C, Latychev K, Tamisiea ME. 2011. On the robustness of predictions of sea level Þngerprints. Geophys. J. Int. 187(2):729-42
Mitrovica JX, Tamisiea ME, Davis JL, Milne GA. 2001. Recent mass balance of polar ice sheets inferred from patterns of global sea-level change. Nature 409(6823):1026-29
Hsu C-W, Velicogna I. 2017. Detection of sea level Þngerprints derived from GRACE gravity data. Geophys. Res. Lett. 44(17):8953-61
Mitrovica JX, Hay CC, Kopp RE, Harig C, Latychev K. 2018. Quantifying the sensitivity of sea level change in coastal localities to the geometry of polar ice mass ßux. J. Clim. 31:3702-9
Larour E, Ivins ER, Adhikari S. 2017. Should coastal planners have concern over where land ice is melting? Sci. Adv. 3(11):e1700537
Wu P, Peltier WR. 1984. Pleistocene deglaciation and the EarthÕs rotation: a new analysis. Geophys. J. R. Astron. Soc. 76(3):753-91
Farrell WE, Clark JA. 1976. On postglacial sea level. Geophys. J. R. Astron. Soc. 46(3):647-67
Clark JA, Farrell WE, Peltier WR. 1978. Global changes in postglacial sea level: a numerical calculation. Quat. Res. 9:265-87
Mitrovica JX, Milne GA. 2003. On post-glacial sea level: I. General theory. Geophys. J. Int. 154(2):253-67
Peltier WR, Argus DF, Drummond R. 2015. Space geodesy constrains ice age terminal deglaciation: the global ICE-6G_C (VM5a) model. J. Geophys. Res. Solid Earth 120(1):450-87
Kendall R, Mitrovica JX, Milne GA. 2005. On post-glacial sea level: II. Numerical formulation and comparative results on spherically symmetric models. Geophys. J. Int. 161:679-706
Hay CC, Lau HCP, Gomez N, Austermann J, Powell E, et al. 2017. Sea level Þngerprints in a region of complex Earth structure: the case of WAIS. J. Clim. 30(6):1881-92
Khan NS, Ashe E, Shaw TA, Vacchi M, Walker J. 2015. Holocene relative sea-level changes from near-, intermediate-, and far-Þeld locations. Curr. Clim. Change Rep. 1:247-62
Lambeck K, Rouby H, Purcell A, Sun Y, Sambridge M. 2014. Sea level and global ice volumes from the Last Glacial Maximum to the Holocene. PNAS 111(43):15296-303
Milne GA. 2015. Glacial isostatic adjustment. In Handbook of Sea-Level Research, ed. I Shennan, AJ Long, BP Horton, pp. 419-37. Chichester, UK: Wiley
Roy K, Peltier WR. 2017. Space-geodetic and water level gauge constraints on continental uplift and tilting over North America: regional convergence of the ICE-6G_C (VM5a/VM6) models. Geophys. J. Int. 210(2):1115-42
Engelhart SE, Horton BP, Douglas BC, Peltier WR, T¬ornqvist TE. 2009. Spatial variability of late Holocene and 20th century sea-level rise along the Atlantic coast of the United States. Geology 37(12):1115-18
Milne GA, Long AJ, Bassett SE. 2005. Modelling Holocene relative sea-level observations from the Caribbean and South America. Quat.Sci.Rev. 24(10):1183-1202
Mitrovica JX, Milne GA. 2002. On the origin of late Holocene sea-level highstands within equatorial ocean basins. Quat. Sci. Rev. 21(20):2179-90
Peltier WR. 2004. Global glacial isostasy and the surface of the ice-age Earth: the ICE-5G (VM2) model and GRACE. Annu. Rev. Earth Planet. Sci. 32(1):111-49
Abe-Ouchi A, Saito F, Kageyama M, Braconnot P, Harrison SP, et al. 2015. Ice-sheet conÞguration in the CMIP5/PMIP3 Last Glacial Maximum experiments. Geosci. Model. Dev. 8(11):3621-37
Horton BP, Shennan I. 2009. Compaction of Holocene strata and the implications for relative sealevel change on the east coast of England. Geology 37(12):1083-86
Miller KG, Kopp RE, Horton BP, Browning JV, Kemp AC. 2013. A geological perspective on sea-level rise and its impacts along the U.S. mid-Atlantic coast. Earths Future 1(1):3-18
Johnson CS, Miller KG, Browning JV, Kopp RE, Khan NS, et al. 2018. The role of sediment compaction and groundwater withdrawal in local sea-level rise, Sandy Hook, New Jersey, USA. Quat. Sci. Rev. 181:30- 42
Tornqvist TE, Wallace DJ, Storms JEA, Wallinga J, van Dam RL, et al. 2008. Mississippi Delta subsi.dence primarily caused by compaction of Holocene strata. Nat. Geosci. 1(3):173-76
Kolker AS, Allison MA, Hameed S. 2011. An evaluation of subsidence rates and sea-level variability in the northern Gulf of Mexico. Geophys. Res. Lett. 38(21):L21404
Syvitski JPM, Kettner AJ, Overeem I, Hutton EWH, Hannon MT, et al. 2009. Sinking deltas due to human activities. Nat. Geosci. 2(10):681-86
Allison M, Yuill B, T¬ornqvist T, Amelung F, Dixon T, et al. 2016. Global risks and research priorities for coastal subsidence. Eos Trans. Am. Geophys. Union 97:22-27
van de Plassche O, Wright AJ, Horton BP, Engelhart SE, Kemp AC, et al. 2014. Estimating tectonic uplift of the Cape Fear Arch (southeast-Atlantic coast, USA) using reconstructions of Holocene relative sea level. J. Quat. Sci. 29(8):749-59
Meltzner AJ, Sieh K, Abrams M, Agnew DC, Hudnut KW, et al. 2006. Uplift and subsidence associated with the great Aceh-Andaman earthquake of 2004. J. Geophys. Res. Solid Earth 111:B02407
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-15
|
Miller KG, Kopp RE, Horton BP, Browning JV, Kemp AC. 2013. A geological perspective on sea-level rise and its impacts along the U.S. mid-Atlantic coast. Earths Future 1(1):3-18
Johnson CS, Miller KG, Browning JV, Kopp RE, Khan NS, et al. 2018. The role of sediment compaction and groundwater withdrawal in local sea-level rise, Sandy Hook, New Jersey, USA. Quat. Sci. Rev. 181:30- 42
Tornqvist TE, Wallace DJ, Storms JEA, Wallinga J, van Dam RL, et al. 2008. Mississippi Delta subsi.dence primarily caused by compaction of Holocene strata. Nat. Geosci. 1(3):173-76
Kolker AS, Allison MA, Hameed S. 2011. An evaluation of subsidence rates and sea-level variability in the northern Gulf of Mexico. Geophys. Res. Lett. 38(21):L21404
Syvitski JPM, Kettner AJ, Overeem I, Hutton EWH, Hannon MT, et al. 2009. Sinking deltas due to human activities. Nat. Geosci. 2(10):681-86
Allison M, Yuill B, T¬ornqvist T, Amelung F, Dixon T, et al. 2016. Global risks and research priorities for coastal subsidence. Eos Trans. Am. Geophys. Union 97:22-27
van de Plassche O, Wright AJ, Horton BP, Engelhart SE, Kemp AC, et al. 2014. Estimating tectonic uplift of the Cape Fear Arch (southeast-Atlantic coast, USA) using reconstructions of Holocene relative sea level. J. Quat. Sci. 29(8):749-59
Meltzner AJ, Sieh K, Abrams M, Agnew DC, Hudnut KW, et al. 2006. Uplift and subsidence associated with the great Aceh-Andaman earthquake of 2004. J. Geophys. Res. Solid Earth 111:B02407
Feng L, Hill EM, Banerjee P, Hermawan I, Tsang LLH, et al. 2015. A uniÞed GPS-based earthquake catalog for the Sumatran plate boundary between 2002 and 2013. J. Geophys. Res. Solid Earth 120(5):3566- 98
Horton B, Milker Y, Dura T, Wang K, Bridgeland W, et al. 2017. Microfossil measures of rapid sea-level rise: timing of response of two microfossil groups to a sudden tidal-ßooding experiment in Cascadia. Geology 45(6):535-38
Herman F, Seward D, Valla PG, Carter A, Kohn B, et al. 2013. Worldwide acceleration of mountain erosion under a cooling climate. Nature 504(7480):423-26
Woo HB, Panning MP, Adams PN, Dutton A. 2017. Karst-driven ßexural isostasy in North-Central Florida. Geochem. Geophys. Geosyst. 18(9):3327-39
Creveling JR, Mitrovica JX, Hay CC, Austermann J, Kopp RE. 2015. Revisiting tectonic corrections applied to Pleistocene sea-level highstands. Quat.Sci.Rev. 111:72-80
Rovere A, Raymo ME, Vacchi M, Lorscheid T, Stocchi P, et al. 2016. The analysis of Last Interglacial (MIS 5e) relative sea-level indicators: reconstructing sea-level in a warmer world. Earth-Sci. Rev. 159:404-27
Flament N, Gurnis M, M ¬uller RD. 2013. A review of observations and models of dynamic topography. Lithosphere 5(2):189-210
Hoggard MJ, White N, Al-Attar D. 2016. Global dynamic topography observations reveal limited in.ßuence of large-scale mantle ßow. Nat. Geosci. 9(6):456-63
Husson L, Conrad CP. 2006. Tectonic velocities, dynamic topography, and relative sea level. Geophys. Res. Lett. 33(18):L18303
Conrad CP, Husson L. 2009. Inßuence of dynamic topography on sea level and its rate of change. Lithosphere 1(2):110-20
Austermann J, Mitrovica JX, Huybers P, Rovere A. 2017. Detection of a dynamic topography signal in last interglacial sea-level records. Sci. Adv. 3(7):e1700457
Rowley DB, Forte AM, Moucha R, Mitrovica JX, Simmons NA, Grand SP. 2013. Dynamic topography change of the Eastern United States since 3 million years ago. Science 340(6140):1560-63
Austermann J, Pollard D, Mitrovica JX, Moucha R, Forte AM, et al. 2015. The impact of dynamic topog.raphy change on Antarctic ice sheet stability during the mid-Pliocene warm period. Geology 43(10):927-30
Shennan I. 2015. Handbook of Sea-Level Research: framing research questions. In Handbook of Sea-Level Research, ed. I Shennan, AJ Long, BP Horton, pp. 3-25. Chichester, UK: Wiley
van de Plassche O, ed. 1986. Sea-Level Research: A Manual for the Collection and Evaluation of Data. Dordrecht, Neth.: Springer
Hibbert FD, Rohling EJ, Dutton A, Williams FH, Chutcharavan PM, et al. 2016. Coral indicators of past sea-level change: a global repository of U-series dated benchmarks. Quat. Sci. Rev. 145:1-56
Wilmes S-B, Green JAM, Gomez N, Rippeth TP, Lau H. 2017. Global tidal impacts of large-scale ice sheet collapses. J. Geophys. Res. Oceans 122(11):8354-70
Walker MJC. 2005. Quaternary Dating Methods. Chichester, UK: Wiley
Haywood AM, Chandler MA, Valdes PJ, Salzmann U, Lunt DJ, Dowsett HJ. 2009. Comparison of mid-Pliocene climate predictions produced by the HadAM3 and GCMAM3 General Circulation Models. Glob. Planet. Change 66(3):208-24
Kemp AC, Dutton A, Raymo ME. 2015. Paleo constraints on future sea-level rise. Curr. Clim. Change Rep. 1(3):205-15
Lisiecki LE, Raymo ME. 2005. A Pliocene-Pleistocene stack of 57 globally distributed benthic .18O records. Paleoceanography 20(1):PA1003
Dowsett H, Dolan A, Rowley D, Moucha R, Forte AM, et al. 2016. The PRISM4 (mid-Piacenzian) paleoenvironmental reconstruction. Clim. Past. 12(7):1519-38
Haywood AM, Dowsett HJ, Dolan AM, Rowley D, Abe-Ouchi A, et al. 2016. The Pliocene Model Intercomparison Project (PlioMIP) Phase 2: ScientiÞc objectives and experimental design. Clim. Past. 12(3):663-75
Haywood AM, Hill DJ, Dolan AM, Otto-Bliesner BL, Bragg F, et al. 2013. Large-scale features of Pliocene climate: results from the Pliocene Model Intercomparison Project. Clim. Past. 9(1):191-209
Kennett JP, Hodell DA. 1995. Stability or instability of Antarctic ice sheets during warm climates of the Pliocene. GSA Today 5(1):9-13
Dowsett HJ, Cronin T. 1990. High eustatic sea level during the middle Pliocene: evidence from the southeastern U.S. Atlantic Coastal Plain. Geology 18:435-38
Rovere A, Hearty PJ, Austermann J, Mitrovica JX, Gale J, et al. 2015. Mid-Pliocene shorelines of the US Atlantic Coastal PlainÑan improved elevation database with comparison to Earth model predictions. Earth-Sci. Rev. 145:117-31
Wardlaw BR, Quinn TM. 1991. The record of Pliocene sea-level change at Enewetak Atoll. Quat. Sci. Rev. 10(2):247-58
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-16
|
Kemp AC, Dutton A, Raymo ME. 2015. Paleo constraints on future sea-level rise. Curr. Clim. Change Rep. 1(3):205-15
Lisiecki LE, Raymo ME. 2005. A Pliocene-Pleistocene stack of 57 globally distributed benthic .18O records. Paleoceanography 20(1):PA1003
Dowsett H, Dolan A, Rowley D, Moucha R, Forte AM, et al. 2016. The PRISM4 (mid-Piacenzian) paleoenvironmental reconstruction. Clim. Past. 12(7):1519-38
Haywood AM, Dowsett HJ, Dolan AM, Rowley D, Abe-Ouchi A, et al. 2016. The Pliocene Model Intercomparison Project (PlioMIP) Phase 2: ScientiÞc objectives and experimental design. Clim. Past. 12(3):663-75
Haywood AM, Hill DJ, Dolan AM, Otto-Bliesner BL, Bragg F, et al. 2013. Large-scale features of Pliocene climate: results from the Pliocene Model Intercomparison Project. Clim. Past. 9(1):191-209
Kennett JP, Hodell DA. 1995. Stability or instability of Antarctic ice sheets during warm climates of the Pliocene. GSA Today 5(1):9-13
Dowsett HJ, Cronin T. 1990. High eustatic sea level during the middle Pliocene: evidence from the southeastern U.S. Atlantic Coastal Plain. Geology 18:435-38
Rovere A, Hearty PJ, Austermann J, Mitrovica JX, Gale J, et al. 2015. Mid-Pliocene shorelines of the US Atlantic Coastal PlainÑan improved elevation database with comparison to Earth model predictions. Earth-Sci. Rev. 145:117-31
Wardlaw BR, Quinn TM. 1991. The record of Pliocene sea-level change at Enewetak Atoll. Quat. Sci. Rev. 10(2):247-58
Petit J, Jouzel R, Raynaud D, Barkov NI, Barnola JA, et al. 1999. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 1999(399):429-36
Hoffman JS, Clark PU, Parnell AC, He F. 2017. Regional and global sea-surface temperatures during the last interglaciation. Science 355(6322):276-79
Otto-Bliesner BL, Rosenbloom N, Stone EJ, McKay NP, Lunt DJ, et al. 2013. How warm was the last interglacial? New model-data comparisons. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 371:20130097
Otto-Bliesner BL, Marshall SJ, Overpeck JT, Miller GH, Hu A, CAPE Last Interglacial Project Mem.bers. 2006. Simulating arctic climate warmth and iceÞeld retreat in the Last Interglaciation. Science 311:1751-53
NEEM Community Members. 2013. Eemian interglacial reconstructed from a Greenland folded ice core. Nature 493:489-94
Jouzel J, Masson-Delmotte V, Cattani O, Dreyfus G, Falourd S. 2007. Orbital and Millennial Antarctic climate variability over the past 800,000 years. Science 317(5839):793-96
Christensen JH, Kanikicharla KK, Aldrian E, An S-I, Cavalcanti IFA, et al. 2013. Climate phenomena and their relevance for future regional climate change. In Climate Change 2013: The Physical Science Basis, ed. TF Stocker, D Qin, G-K Plattner, M Tignor, SK Allen, et al., pp. 1217-1308. Cambridge, UK: Cambridge Univ. Press
Pedoja K, Husson L, Johnson ME, Melnick D, Witt C, et al. 2014. Coastal staircase sequences reßecting sea-level oscillations and tectonic uplift during the Quaternary and Neogene. Earth-Sci. Rev. 132:13-38
Kopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2013. A probabilistic assessment of sea level variations within the last interglacial stage. Geophys. J. Int. 193(2):711-16
OÕLeary MJ, Hearty PJ, Thompson WG, Raymo ME, Mitrovica JX, Webster JM. 2013. Ice sheet collapse following a prolonged period of stable sea level during the last interglacial. Nat. Geosci. 6(9):796-800
Yau AM, Bender ML, Robinson A, Brook EJ. 2016. Reconstructing the last interglacial at Summit, Greenland: insights from GISP2. PNAS 113(35):9710-15
McKay NP, Overpeck JT, Otto-Bliesner BL. 2011. The role of ocean thermal expansion in Last Inter.glacial sea level rise. Geophys. Res. Lett. 38:14605
Radic V, Hock R. 2010. Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data. J. Geophys. Res. Earth Surf. 115:01010
Kemp AC, Dutton A, Raymo ME. 2015. Paleo constraints on future sea-level rise. Curr. Clim. Change Rep. 1(3):205-15
Marcott SA, Shakun JD, Clark PU, Mix AC. 2013. A reconstruction of regional and global temperature for the past 11,300 years. Science 339(6124):1198-201
Liu Z, Zhu J, Rosenthal Y, Zhang X, Otto-Bliesner BL. 2014. The Holocene temperature conundrum. PNAS 111(34):3501-5
Marsicek J, Shuman BN, Bartlein PJ, Shafer SL, Brewer S. 2018. Reconciling divergent trends and millennial variations in Holocene temperatures. Nature 554(7690):92-96
Carlson AE, Clark PU. 2012. Ice sheet sources of sea level rise and freshwater discharge during the last deglaciation. Rev. Geophys. 50(4):RG4007
Johnson JS, Bentley MJ, Smith JA, Finkel RC, Rood DH, et al. 2014. Rapid thinning of Pine Island Glacier in the Early Holocene. Science 343:999-1001
Lecavalier BS, Milne GA, Simpson MJR, Wake L, Huybrechts P, et al. 2014. A model of Greenland ice sheet deglaciation constrained by observations of relative sea level and ice extent. Quat.Sci.Rev. 102:54-84
Bradley SL, Milne GA, Horton BP, Zong Y. 2016. Modelling sea level data from China and Malay-Thailand to estimate Holocene ice-volume equivalent sea level change. Quat. Sci. Rev. 137:54-68
Roy K, Peltier WR. 2018. Relative sea level in the Western Mediterranean basin: a regional test of the ICE-7G_NA (VM7) model and a constraint on Late Holocene Antarctic deglaciation. Quat.Sci.Rev. 183:76-87
Mann ME, Zhang Z, Hughes MK, Bradley RS, Miller SK, et al. 2008. Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. PNAS 105(36):13252-57
Ekman M. 1988. The worldÕs longest continuous series of sea level observations. Pure Appl. Geophys. 127:73-77
Jevrejeva S, Moore JC, Grinsted A, Woodworth PL. 2008. Recent global sea level acceleration started over 200 years ago? Geophys. Res. Lett. 35(8):L08715
Church JA, White NJ. 2011. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32(4-5):585-602
Jevrejeva S, Moore JC, Grinsted A, Matthews AP, Spada G. 2014. Trends and acceleration in global and regional sea levels since 1807. Glob. Planet. Change 113:11-22
Dangendorf S, Marcos M, W ¬oppelmann G, Conrad CP, Frederikse T, Riva R. 2017. Reassessment of 20th century global mean sea level rise. PNAS 114(23):5946-51
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-17
|
Lecavalier BS, Milne GA, Simpson MJR, Wake L, Huybrechts P, et al. 2014. A model of Greenland ice sheet deglaciation constrained by observations of relative sea level and ice extent. Quat.Sci.Rev. 102:54-84
Bradley SL, Milne GA, Horton BP, Zong Y. 2016. Modelling sea level data from China and Malay-Thailand to estimate Holocene ice-volume equivalent sea level change. Quat. Sci. Rev. 137:54-68
Roy K, Peltier WR. 2018. Relative sea level in the Western Mediterranean basin: a regional test of the ICE-7G_NA (VM7) model and a constraint on Late Holocene Antarctic deglaciation. Quat.Sci.Rev. 183:76-87
Mann ME, Zhang Z, Hughes MK, Bradley RS, Miller SK, et al. 2008. Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. PNAS 105(36):13252-57
Ekman M. 1988. The worldÕs longest continuous series of sea level observations. Pure Appl. Geophys. 127:73-77
Jevrejeva S, Moore JC, Grinsted A, Woodworth PL. 2008. Recent global sea level acceleration started over 200 years ago? Geophys. Res. Lett. 35(8):L08715
Church JA, White NJ. 2011. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32(4-5):585-602
Jevrejeva S, Moore JC, Grinsted A, Matthews AP, Spada G. 2014. Trends and acceleration in global and regional sea levels since 1807. Glob. Planet. Change 113:11-22
Dangendorf S, Marcos M, W ¬oppelmann G, Conrad CP, Frederikse T, Riva R. 2017. Reassessment of 20th century global mean sea level rise. PNAS 114(23):5946-51
Hay CC, Morrow E, Kopp RE, Mitrovica JX. 2015. Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517(7535):481-84
Cazenave A, Llovel W. 2010. Contemporary sea level rise. Annu. Rev. Mar. Sci. 2(1):145-73
Ray RD, Douglas BC. 2011. Experiments in reconstructing twentieth-century sea levels. Prog. Oceanogr. 91(4):496-515
Calafat FM, Chambers DP, Tsimplis MN. 2014. On the ability of global sea level reconstructions to determine trends and variability. J. Geophys. Res. Oceans 119(3):1572-92
Ablain M, Cazenave A, Larnicol G, Balmaseda M, Cipollini P, et al. 2015. Improved sea level record over the satellite altimetry era (1993-2010) from the Climate Change Initiative project. Ocean. Sci. 11(1):67-82
Legeais J-F, Ablain M, Zawadzki L, Zuo H, Johannessen JA, et al. 2017. An accurate and homogeneous altimeter sea level record from the ESA climate change initiative. Earth Syst. Sci. Data Discuss.10:281-301
Church JA, Monselesan D, Gregory JM, Marzeion B. 2013. Evaluating the ability of process based models to project sea-level change. Environ. Res. Lett. 8(1):014051
Jevrejeva S, Grinsted A, Moore JC. 2014. Upper limit for sea level projections by 2100. Environ. Res. Lett. 9(10):104008
Watson CS, White NJ, Church JA, King MA, Burgette RJ, Legresy B. 2015. Unabated global mean sea-level rise over the satellite altimeter era. Nat. Clim. Change 5(6):565-68
Nerem RS, Beckley BD, Fasullo JT, Hamlington BD, Masters D, Mitchum GT. 2018. Climate-change- driven accelerated sea-level rise. PNAS 1152022-25
Marcos M, Marzeion B, Dangendorf S, Slangen ABA, Palanisamy H, Fenoglio-Marc L. 2017. Internal variability versus anthropogenic forcing on sea level and its components. Surv. Geophys. 38(1):329-48
Dangendorf S, Marcos M, Muller A, Zorita E, Riva R, et al. 2015. Detecting anthropogenic footprints in sea level rise. Nat. Commun. 6:7849
Jevrejeva S, Grinsted A, Moore JC. 2009. Anthropogenic forcing dominates sea level rise since 1850. Geophys. Res. Lett. 36(20):L20706
Slangen ABA, Church JA, Agosta C, Fettweis X, Marzeion B, Richter K. 2016. Anthropogenic forcing dominates global mean sea-level rise since 1970. Nat. Clim. Change 6:701-5
Van Vuuren DP, Edmonds J, Kainuma M, Riahi K, Thomson A, et al. 2011. The Representative Con.centration Pathways: an overview. Clim. Change 109:5-31
UNFCCC. 2015. Paris Agreement.NewYork:U.N. https://unfccc.int/process-and-meetings/the.paris-agreement/the-paris-agreement
Bakker AMR, Wong TE, Ruckert KL, Keller K. 2017. Sea-level projections representing the deeply uncertain contribution of the West Antarctic ice sheet. Sci. Rep. 7(1):3880
Goodwin P, Haigh ID, Rohling EJ, Slangen A. 2017. A new approach to projecting 21st century sea-level changes and extremes. Earths Future 5(2):240-53
Grinsted A, Jevrejeva S, Riva REM, Dahl-Jensen D. 2015. Sea level rise projections for Northern Europe under RCP8.5. Clim. Res. 64:15-23
Jackson LP, Jevrejeva S. 2016. A probabilistic approach to 21st century regional sea-level projections using RCP and high-end scenarios. Glob. Planet. Change 146:179-89
Jevrejeva S, Moore JC, Grinsted A. 2012. Sea level projections to AD2500 with a new generation of climate change scenarios. Glob. Planet. Change 80-81:14-20
Kopp RE, Horton RM, Little CM, Mitrovica JX, Oppenheimer M, et al. 2014. Probabilistic 21st and 22nd century sea-level projections at a global network of tide gauge sites. Earths Future 2:383-406
Mengel M, Levermann A, Frieler K, Robinson A, Marzeion B, Winkelmann R. 2016. Future sea level rise constrained by observations and long-term commitment. PNAS 113(10):2597-602
Nauels A, Meinshausen M, Mengel M, Lorbacher K, Wigley TML. 2017. Synthesizing long-term sea level rise projectionsÑthe MAGICC sea level model v2.0. Geosci. Model. Dev. 10(6):2495-524
DeConto RM, Pollard D. 2016. Contribution of Antarctica to past and future sea-level rise. Nature 531(7596):591-97
Kopp RE, DeConto RM, Bader DA, Horton RM, Hay CC, et al. 2017. Evolving understanding of Antarctic ice-sheet physics and ambiguity in probabilistic sea-level projections. Earths Future 5:1217-33
Pfeffer WT, Harper JT, OÕNeel S. 2008. Kinematic constraints on glacier contributions to 21st-century sea-level rise. Science 321(5894):1340-43
Church JA, Clark PU, Cazenave A, Gregory JM, Jevrejeva S, et al. 2013. Sea-level rise by 2100. Science 342(6165):1445
Slangen ABA, Carson M, Katsman CA, van de Wal RSW, Kohl A, et al. 2014. Projecting twenty-Þrst century regional sea-level changes. Clim. Change 124:317-32
Sriver RL, Urban NM, Olson R, Keller K. 2012. Toward a physically plausible upper bound of sea-level rise projections. Clim. Change 115(3-4):893-902
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-18
|
Kopp RE, Horton RM, Little CM, Mitrovica JX, Oppenheimer M, et al. 2014. Probabilistic 21st and 22nd century sea-level projections at a global network of tide gauge sites. Earths Future 2:383-406
Mengel M, Levermann A, Frieler K, Robinson A, Marzeion B, Winkelmann R. 2016. Future sea level rise constrained by observations and long-term commitment. PNAS 113(10):2597-602
Nauels A, Meinshausen M, Mengel M, Lorbacher K, Wigley TML. 2017. Synthesizing long-term sea level rise projectionsÑthe MAGICC sea level model v2.0. Geosci. Model. Dev. 10(6):2495-524
DeConto RM, Pollard D. 2016. Contribution of Antarctica to past and future sea-level rise. Nature 531(7596):591-97
Kopp RE, DeConto RM, Bader DA, Horton RM, Hay CC, et al. 2017. Evolving understanding of Antarctic ice-sheet physics and ambiguity in probabilistic sea-level projections. Earths Future 5:1217-33
Pfeffer WT, Harper JT, OÕNeel S. 2008. Kinematic constraints on glacier contributions to 21st-century sea-level rise. Science 321(5894):1340-43
Church JA, Clark PU, Cazenave A, Gregory JM, Jevrejeva S, et al. 2013. Sea-level rise by 2100. Science 342(6165):1445
Slangen ABA, Carson M, Katsman CA, van de Wal RSW, Kohl A, et al. 2014. Projecting twenty-Þrst century regional sea-level changes. Clim. Change 124:317-32
Sriver RL, Urban NM, Olson R, Keller K. 2012. Toward a physically plausible upper bound of sea-level rise projections. Clim. Change 115(3-4):893-902
Titus JG, Narayanan VK. 1995. The Probability of Sea Level Rise, Vol. 95. Wash., DC: Environ. Protect. Agency, Off. Policy, Plann., Eval., Clim. Change Div., Adapt. Branch
Wong TE, Bakker AMR, Keller K. 2017. Impacts of Antarctic fast dynamics on sea-level projections and coastal ßood defense. Clim. Change 144(2):347-64
Gornitz V, Lebedeff S, Hansen J. 1982. Global sea level trend in the past century. Science 215(4540):1611-14
Rahmstorf S. 2007. A semi-empirical approach to projecting future sea-level rise. Science 315(5810):368-70
Schaeffer M, Hare W, Rahmstorf S, Vermeer M. 2012. Long-term sea-level rise implied by 1.5.Cand 2.C warming levels. Nat. Clim. Change 2:867-70
Bamber JL, Aspinall WP. 2013. An expert judgement assessment of future sea level rise from the ice sheets. Nat. Clim. Change 3:424-27
Horton BP, Rahmstorf S, Engelhart SE, Kemp AC. 2014. Expert assessment of sea-level rise by AD 2100 and AD 2300. Quat. Sci. Rev. 84:1-6
Behar DH, Kopp RE, DeConto RM, Weaver CP, White KD, et al. 2017. Planning for sea level rise: an AGU talk in the form of a co-production experiment exploring recent science. Presented at Am. Geophys. Union, Fall Meeting, New Orleans. https://www.wucaonline.org/assets/pdf/pubs-agu-consensus.statement.pdf
National Research Council. 1987. Responding to Changes in Sea Level: Engineering Implications. Wash., DC: Nat. Acad. Press
National Academies of Sciences, Engineering, and Medicine. 2017. Valuing Climate Damages: Updating Estimation of the Social Cost of Carbon Dioxide. Wash., DC: Nat. Acad. Press
Buchanan MK, Oppenheimer M, Kopp RE. 2017. AmpliÞcation of ßood frequencies with local sea level rise and emerging ßood regimes. Environ. Res. Lett. 12:064009
Garner AJ, Mann ME, Emanuel KA, Kopp RE, Ling N, et al. 2017. Impact of climate change on New York CityÕs coastal ßood hazard: Increasing ßood heights from the preindustrial to 2300 CE. PNAS 114:11861-66
Heal G, Millner A. 2014. Uncertainty and decision making in climate change economics. Rev. Environ. Econ. Policy 8(1):120-37
Le Cozannet G, Nicholls RJ, Hinkel J, Sweet WV, McInnes KL, et al. 2017. Sea level change and coastal climate services: the way forward. J. Mar. Sci. Eng. 5(4):49
Bittermann K, Rahmstorf S, Kopp RE, Kemp AC. 2017. Global mean sea-level rise in a world agreed upon in Paris. Environ. Res. Lett. 12(12):124010
Jackson LP, Grinsted A, Jevrejeva S. 2018. 21st century sea-level rise in line with the Paris Accord. Earths Future 6:213-29
Rasmussen DJ, Bittermann K, Buchanan MK, Kulp S, Strauss BH, Kopp RE, Oppenheimer M. 2018. Extreme sea level implications of 1.5.C, 2.0.C, and 2.5.C temperature stabilization targets in the 21st and 22nd century. Environ. Res Lett. 13(3):034040
Schleussner C-F, Lissner TK, Fischer EM, Wohland J, Perrette M, et al. 2016. Differential climate impacts for policy-relevant limits to global warming: the case of 1.5.Cand 2.C. Earth Syst. Dynam. 7(2):327-51
Schaeffer M, Hare W, Rahmstorf S, Vermeer M. 2012. Long-term sea-level rise implied by 1.5.Cand 2.C warming levels. Nat. Clim. Change 2:867-70
Levermann A, Clark PU, Marzeion B, Milne GA, Pollard D, et al. 2013. The multimillennial sea-level commitment of global warming. PNAS 110(34):13745-50
Clark PU, Shakun JD, Marcott SA, Mix AC, Eby M. 2016. Consequences of twenty-Þrst-century policy for multi-millennial climate and sea-level change. Nat. Clim. Change 6:360-69
Zickfeld K, Solomon S, Gilford DM. 2017. Centuries of thermal sea-level rise due to anthropogenic emissions of short-lived greenhouse gases. PNAS 114(4):657-62
Golledge NR, Kowalewski DE, Naish TR, Levy RH, Fogwill CJ, Gasson EGW. 2015. The multi-millennial Antarctic commitment to future sea-level rise. Nature 526(7573):421-25
Meltzner AJ, Switzer AD, Horton BP, Ashe E, Qiu Q, et al. 2017. Half-metre sea-level ßuctuations on centennial timescales from mid-Holocene corals of Southeast Asia. Nat. Commun. 8:14387
Kopp RE, Horton BP, Kemp AC, Tebaldi C. 2015. Past and future sea-level rise along the coast of North Carolina, USA. Clim. Change 132(4):693-707
Neumann B, Vafeidis AT, Zimmermann J, Nicholls RJ. 2015. Future coastal population growth and exposure to sea-level rise and coastal ßoodingÑa global assessment. PLOS ONE 10(6):e0131375
Long AJ, Roberts DH, Rasch M. 2003. New observations on the relative sea level and deglacial history of Greenland from Innaarsuit, Disko Bugt. Quat. Res. 60(2):162-71
Long AJ, Roberts DH. 2003. Late Weichselian deglacial history of Disko Bugt, West Greenland, and the dynamics of the Jakobshavns Isbrae ice stream. Boreas 32(1):208-26
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-19
|
Levermann A, Clark PU, Marzeion B, Milne GA, Pollard D, et al. 2013. The multimillennial sea-level commitment of global warming. PNAS 110(34):13745-50
Clark PU, Shakun JD, Marcott SA, Mix AC, Eby M. 2016. Consequences of twenty-Þrst-century policy for multi-millennial climate and sea-level change. Nat. Clim. Change 6:360-69
Zickfeld K, Solomon S, Gilford DM. 2017. Centuries of thermal sea-level rise due to anthropogenic emissions of short-lived greenhouse gases. PNAS 114(4):657-62
Golledge NR, Kowalewski DE, Naish TR, Levy RH, Fogwill CJ, Gasson EGW. 2015. The multi-millennial Antarctic commitment to future sea-level rise. Nature 526(7573):421-25
Meltzner AJ, Switzer AD, Horton BP, Ashe E, Qiu Q, et al. 2017. Half-metre sea-level ßuctuations on centennial timescales from mid-Holocene corals of Southeast Asia. Nat. Commun. 8:14387
Kopp RE, Horton BP, Kemp AC, Tebaldi C. 2015. Past and future sea-level rise along the coast of North Carolina, USA. Clim. Change 132(4):693-707
Neumann B, Vafeidis AT, Zimmermann J, Nicholls RJ. 2015. Future coastal population growth and exposure to sea-level rise and coastal ßoodingÑa global assessment. PLOS ONE 10(6):e0131375
Long AJ, Roberts DH, Rasch M. 2003. New observations on the relative sea level and deglacial history of Greenland from Innaarsuit, Disko Bugt. Quat. Res. 60(2):162-71
Long AJ, Roberts DH. 2003. Late Weichselian deglacial history of Disko Bugt, West Greenland, and the dynamics of the Jakobshavns Isbrae ice stream. Boreas 32(1):208-26
Shennan I, Lambeck K, Horton B, Innes J, Lloyd J, et al. 2000. Late Devensian and Holocene records of relative sea-level changes in northwest Scotland and their implications for glacio-hydro-isostatic modelling. Quat.Sci.Rev. 19(11):1103-35
Zong Y. 2004. Mid-Holocene sea-level highstand along the Southeast Coast of China. Quat. Int. 117(1):55-67
Boski T, Bezerra FHR, de F«atima Pereira L, Souza AM, Maia RP, Lima-Filho FP. 2015. Sea-level rise since 8.2 ka recorded in the sediments of the Potengi-Jundiai Estuary, NE Brasil. Mar. Geol. 365:1-13
Watcham EP, Bentley MJ, Hodgson DA, Roberts SJ, Fretwell PT, et al. 2011. A new Holocene relative sea level curve for the South Shetland Islands, Antarctica. Quat.Sci.Rev. 30(21):3152-70
Compton JS. 2001. Holocene sea-level ßuctuations inferred from the evolution of depositional environ.ments of the southern Langebaan Lagoon salt marsh, South Africa. Holocene 11(4):395-405
Gallup CD, Edwards RL, Johnson RG. 1994. The timing of high sea levels over the past 200,000 years. Science 263(5148):796-800
Gallup CD, Cheng H, Taylor FW, Edwards RL. 2002. Direct determination of the timing of sea level change during termination II. Science 295(5553):310-13
Speed RC, Cheng H. 2004. Evolution of marine terraces and sea level in the last interglacial, Cave Hill, Barbados. GSA Bull. 116(1-2):219-32
Cutler KB, Edwards RL, Taylor FW, Cheng H, Adkins J, et al. 2003. Rapid sea-level fall and deep-ocean temperature change since the last interglacial period. Earth Planet. Sci. Lett. 206(3):253-71
Thompson WG, Spiegelman MW, Goldstein SL, Speed RC. 2003. An open-system model for U-series age determinations of fossil corals. Earth Planet. Sci. Lett. 210(1):365-81
Bard E, Hamelin B, Fairbanks RG, Zindler A. 1990. Calibration of the 14C timescale over the past 30,000 years using mass spectrometric U-Th ages from Barbados corals. Nature 345(6274):405-10
Hamelin B, Bard E, Zindler A, Fairbanks RG. 1991. 234U/238U mass spectrometry of corals: How accurate is the UTh age of the last interglacial period? Earth Planet. Sci. Lett. 106(1):169-80
Edwards RL, Cheng H, Murrell MT, Goldstein SJ. 1997. Protactinium-231 dating of carbonates by ther.mal ionization mass spectrometry: implications for quaternary climate change. Science 276(5313):782-86
Edwards RL, Chen JH, Ku T-L, Wasserburg GJ. 1987. Precise timing of the last interglacial period from mass spectrometric determination of thorium-230 in corals. Science 236(4808):1547-53
Blanchon P, Eisenhauer A. 2000. Multi-stage reef development on Barbados during the Last Interglacia.tion. Quat. Sci. Rev. 20(10):1093-112
Potter E-K, Esat TM, Schellmann G, Radtke U, Lambeck K, McCulloch MT. 2004. Suborbital-period sea-level oscillations during marine isotope substages 5a and 5c. Earth Planet. Sci. Lett. 225(1):191-204
Zagwin WH. 1983. Sea-level changes in the Netherlands during the Eemian. Geol. Mijnb. 62:437-50
Grant KM, Rohling EJ, Bar-Matthews M, Ayalon A, Medina-Elizalde M, et al. 2012. Rapid coupling between ice volume and polar temperature over the past 150 kyr. Nature 491:744-47
Dutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96
Hearty PJ, Hollin JT, Neumann AC, OÕLeary MJ, McCulloch M. 2007. Global sea-level fluctuations during the Last Interglaciation (MIS 5e). Quat.Sci.Rev. 26(17):2090-112
Stirling CH, Esat TM, McCulloch MT, Lambeck K. 1995. High-precision U-series dating of corals from Western Australia and implications for the timing and duration of the Last Interglacial. Earth Planet.Sci.Lett. 135(1):115-30
Stirling CH, Esat TM, Lambeck K, McCulloch MT. 1998. Timing and duration of the Last Interglacial: evidence for a restricted interval of widespread coral reef growth. Earth Planet. Sci. Lett. 160(3):745-62
Stirling CH, Esat TM, Lambeck K, McCulloch MT, Blake SG, et al. 2001. Orbital forcing of the Marine Isotope Stage 9 Interglacial. Science 291(5502):290-93
McCulloch MT, Mortimer G. 2008. Applications of the 238U-230Th decay series to dating of fossil and modern corals using MC-ICPMS. Aust. J. Earth Sci. 55:955-65
Zhu ZR, Wyrwoll K-H, Collins LB, Chen JH, Wasserburg GJ, Eisenhauer A. 1993. High-precision U-series dating of Last Interglacial events by mass spectrometry: Houtman Abrolhos Islands, western Australia. Earth Planet. Sci. Lett. 118(1):281-93
Eisenhauer A, Zhu ZR, Collins LB, Wyrwoll KH, Eichst¬atter R. 1996. The Last Interglacial sea level change: new evidence from the Abrolhos islands, West Australia. Geol. Rundsch. 85(3):606-14
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
1a5e23fee427-20
|
Hearty PJ, Hollin JT, Neumann AC, OÕLeary MJ, McCulloch M. 2007. Global sea-level fluctuations during the Last Interglaciation (MIS 5e). Quat.Sci.Rev. 26(17):2090-112
Stirling CH, Esat TM, McCulloch MT, Lambeck K. 1995. High-precision U-series dating of corals from Western Australia and implications for the timing and duration of the Last Interglacial. Earth Planet.Sci.Lett. 135(1):115-30
Stirling CH, Esat TM, Lambeck K, McCulloch MT. 1998. Timing and duration of the Last Interglacial: evidence for a restricted interval of widespread coral reef growth. Earth Planet. Sci. Lett. 160(3):745-62
Stirling CH, Esat TM, Lambeck K, McCulloch MT, Blake SG, et al. 2001. Orbital forcing of the Marine Isotope Stage 9 Interglacial. Science 291(5502):290-93
McCulloch MT, Mortimer G. 2008. Applications of the 238U-230Th decay series to dating of fossil and modern corals using MC-ICPMS. Aust. J. Earth Sci. 55:955-65
Zhu ZR, Wyrwoll K-H, Collins LB, Chen JH, Wasserburg GJ, Eisenhauer A. 1993. High-precision U-series dating of Last Interglacial events by mass spectrometry: Houtman Abrolhos Islands, western Australia. Earth Planet. Sci. Lett. 118(1):281-93
Eisenhauer A, Zhu ZR, Collins LB, Wyrwoll KH, Eichst¬atter R. 1996. The Last Interglacial sea level change: new evidence from the Abrolhos islands, West Australia. Geol. Rundsch. 85(3):606-14
O’Leary MJ, Hearty PJ, McCulloch MT. 2008. U-series evidence for widespread reef development in Shark Bay during the last interglacial. Palaeogeogr. Palaeoclimatol. Palaeoecol. 259(4):424-35
O’Leary MJ, Hearty PJ, McCulloch MT. 2008. Geomorphic evidence of major sea-level ßuctuations during marine isotope substage-5e, Cape Cuvier, Western Australia. Geomorphology 102(3):595-602
Stirling CH, Esat TM, McCulloch MT, Lambeck K. 1995. High-precision U-series dating of corals from Western Australia: implications for Last Interglacial sea levels. Earth Planet. Sci. Lett. 135:115-30
Andersen MB, Stirling CH, Potter E-K, Halliday AN, Blake SG, et al. 2010. The timing of sea-level high-stands during Marine Isotope Stages 7.5 and 9: constraints from the uranium-series dating of fossil corals from Henderson Island. Geochim. Cosmochim. Acta 74(12):3598-620
Douglas BC. 1997. Global sea rise: a redetermination. Surv. Geophys. 18(2-3):279-92
Perrette M, Landerer F, Riva R, Frieler K, Meinshausen M. 2013. A scaling approach to project regional sea level rise and its uncertainties. Earth Syst. Dyn. 4:11-29
Nauels A, Rogelj J, Schleussner C-F, Meinshausen M, Mengel M. 2017. Linking sea level rise and socioeconomic indicators under the Shared Socioeconomic Pathways. Environ. Res Lett. 12(11):114002
|
https://sealeveldocs.readthedocs.io/en/latest/horton18.html
|
bccc98a2faca-0
|
Hallberg et al. (2013)
Title:
Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation
Corresponding author:
Robert Hallberg
Keywords:
Sea level, Climate change, Ocean models
Citation:
Hallberg, R., Adcroft, A., Dunne, J. P., Krasting, J. P., & Stouffer, R. J. (2013). Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation. Journal of Climate, 26(9), 2947Ð2956. doi: 10.1175/jcli-d-12-00506.1
URL:
https://journals.ametsoc.org/view/journals/clim/26/9/jcli-d-12-00506.1.xml
Abstract
Two comprehensive Earth system models (ESMs), identical apart from their oceanic components, are used to estimate the uncertainty in projections of twenty-first-century sea level rise due to representational choices in ocean physical formulation. Most prominent among the formulation differences is that one (ESM2M) uses a traditional z-coordinate ocean model, while the other (ESM2G) uses an isopycnal-coordinate ocean. As evidence of model fidelity, differences in twentieth-century global-mean steric sea level rise are not statistically significant between either model and observed trends. However, differences between the two models’ twenty-first-century projections are systematic and both statistically and climatically significant. By 2100, ESM2M exhibits 18% higher global steric sea level rise than ESM2G for all four radiative forcing scenarios (28-49 mm higher), despite having similar changes between the models in the near-surface ocean for several scenarios. These differences arise primarily from the vertical extent over which heat is taken up and the total heat uptake by the models (9% more in ESM2M than ESM2G). The fact that the spun-up control state of ESM2M is warmer than ESM2G also contributes by giving thermal expansion coefficient that are about 7% larger in ESM2M than ESM2G. The differences between these models provide a direct estimate of the sensitivity of twenty-first-century sea level rise to ocean model formulation, and, given the span of these models across the observed volume of the ventilated thermocline, may also approximate the sensitivities expected from uncertainties in the characterization of interior ocean physical processes.
Introduction
Global-mean sea level has been rising throughout the twentieth century, with increased rates in recent decades (Church et al. 2011). The leading contributors have been documented as the melting of land ice (snow, mountain glaciers, and ice sheets) and the steric rise in sea level due to a warming and expanding ocean (Church et al. 2011), with smaller contributions from climatic and anthropogenic changes in land-water storage (Milly et al. 2003). Projecting twenty-first-century sea level rise (SLR) is of great societal importance but is subject to uncertainties in our understanding of the underlying physical processes. The dynamic response of marine-terminated ice sheets to warming oceans is poorly understood and has the potential to contribute to SLR at rates with a plausible order of magnitude of 10 mm yr^{-1} (Holland et al. 2008; Pfeffer et al. 2008). Because the response of clouds under changing climate is a leading order uncertainty in the earth’s changing radiative budget, and because of the close connection between this budget, ocean heat uptake, and SLR, the cloud response is another substantial cause of uncertainty in SLR. Similarly, uncertainties in the radiative forcing due to aerosols and the overall sensitivity of the feedbacks in the coupled system generally can also contribute to un.certainty in projections of SLR.
The ocean contribution to SLR is closely related to its net uptake of heat, although the properties of the water taking up that heat are of leading order importance to SLR. Additionally, interior ocean mixing of heat and salinity generally cause seawater to contract because of nonlinearities of the equation of state, even though they do not alter the net heat content of the ocean (Griffies and Greatbatch 2012). Changes in ocean circulation play a leading order role in determining where the temperature will increase because of the ocean circulation response to climate change, and hence in detecting steric sea level rise (e.g., Gnanadesikan et al. 2007a; Winton et al. 2013). Interior ocean diapycnal mixing and ocean mixed layer processes play a major role in regulating the ocean’s long-term uptake of heat (e.g., Dalan et al. 2005), but the explicit specification of diapycnal mixing in climate models remains largely empirical. Ocean models can also exhibit numerical artifacts, such as spurious diapycnal mixing (Griffies et al. 2000) or excessive entrainment in overflows (Legg et al. 2006), that can complicate their ability to project SLR for the real world. There is also evidence that representation of the rectified effects of ocean mesoscale eddies are an important source of uncertainty in the ocean circulation response to climate change (Hallberg and Gnanadesikan 2006; Farneti et al. 2010), and hence potentially for heat uptake and SLR. With such a broad range of processes contributing, it is worthwhile to estimate the overall magnitude of the contributions of oceanic uncertainties to uncertainties in projections of steric sea level rise.
This study examines global-mean steric sea level rise (GSSLR) from four climate change scenarios from two Earth system models (ESMs) that are identical apart from their ocean components. We utilize this framework to identify and quantify the uncertainties in GSSLR attributable to limitations in our understanding of the physics of the ocean and the numerical portrayal of the ocean’s dynamics. This approach is thus different than the typical ensemble survey of coupled model inter-comparison for uncertainty estimation, as it allows us to roughly distinguish ocean-derived GSSLR differences from atmospherically forced GSSLR differences, be.cause it avoids convolving issues relating to drift in sea level and overweighting z-coordinate ocean models (with very similar lineages and algorithmic choices) in the ensemble. This study finds systematic 18% differences in GSSLR between the two models. While these differences are large enough to warrant a more thorough study, they do not fundamentally alter previous estimates of sea level rise that can be expected to occur in the twenty-fist century.
The earth system models
This study uses two comprehensive earth system models with identical atmospheric, land surface, sea ice, and ocean ecosystem components, differing only in their physical ocean components (Dunne et al. 2012). The ESM2M uses a 50-level z*-coordinate ocean model, built with the Modular Ocean Model, version 4.1 (MOM4p1) code (Griffies 2009). The ESM2G uses a 63-layer isopycnal-coordinate version of the Generalized Ocean Layer Dynamics (GOLD) ocean model (Hallberg and Adcroft 2009). Both use nominal horizontal resolutions of 1˚ with a tripolar fold over the Arctic. Both have comprehensive sets of physical parameterizations representative of the state-of-the-art z-coordinate and isopycnal-coordinate ocean climate models, as described in Dunne et al. (2012). Both ocean models conserve heat, salt, and mass to numerical round off, and both use proper freshwater mass flux surface boundary conditions, instead of artificially converting them into virtual salt fluxes. Neither model’s atmosphere was changed or retuned from the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model, version 2.1 (CM2.1) (Anderson et al. 2004). The runs presented here use the temporally evolving concentrations of well-mixed radiatively active gases and aerosols (Lamarque et al. 2010) prescribed by phase 5 of the Coupled Model Intercomparison Project (CMIP5) for the historical period up to 2005, and the four standardized Representative Concentration Pathways (RCPs) (Moss et al. 2010; Taylor et al. 2012). The RCP scenarios are labeled with the approximate global-mean radiative forcing anomalies due to well-mixed gases at the end of the twenty-first century (e.g., RCP8.5 has about an 8.5 W m 22 radiative heating anomaly relative to the preindustrial control in 1850). The various RCP scenarios are based on plausible choices for anthropogenic emissions. The atmospheric concentrations of CO2 differ, particularly in the latter half of the twenty-first century. While the radiative forcing for RCP8.5 increases strongly throughout the twenty-first century, the radiative forcing in RCP2.6 peaks in midcentury before declining. RCP4.5 and RCP6.0 have radiative forcing in the twenty-first century between RCP8.5 and RCP2.6.
|
https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html
|
bccc98a2faca-1
|
Both models have been spun up with 1860 radiative forcing for over 1000 years (2560 years for ESM2M and 1160 years for ESM2G), until their global-mean heat budgets were well balanced before starting their respective control runs. The ESM2M control runs exhibit a slight warming averaged over the volume of the ocean (dT/dt = -0.038˚C century^{-1} averaged over a 500-yr-long control run), while ESM2G has an even smaller cooling (dT/dt = -0.010˚C century^{-1}). The ocean heat (and steric sea level) budgets for the control runs of these models are thus much closer to balance than in most coupled climate models of this resolution (Sen Gupta et al. 2012). The 500-yr-long 1860 control run of ESM2G has an average steric sea level drop of 0.023 mm yr^{-1}, while ESM2M’s has an average steric sea level rise of 0.074 mm yr^{-1}. In these runs, the standard deviation of the detrended annual-mean global-mean steric sea level anomaly is 2.3 mm for ESM2G and 1.8 mm for ESM2M, and they are used as uncertainty estimates in the figures presented later.
There are some pertinent differences in the spun-up ocean control states of the two models, both in the ocean interior and at the surface. As shown in Figure 1, the main thermocline extends too deeply in ESM2M and is too shallow in ESM2G relative to observations (see also Dunne et al. 2012). While the models use explicit diapycnal diffusivities of similar magnitudes in the main thermocline, ESM2M includes both parameterizations that indirectly enhance diapycnal mixing (e.g., Gnanadesikan et al. 2007b) and numerically induced diapycnal mixing (Ilicak et al. 2012; Griffies et al. 2000). The overly sharp thermocline in ESM2G may indicate that it is underrepresenting mixing processes in the thermocline. Below the thermocline, ESM2G uses an enhanced diapycnal diffusivity relative to ESM2M, following the prescription of Gargett (1984), while both models use similar abyssal tidal mixing parameterizations following Simmons et al. (2004). Under historical climate forcing, ESM2M is an average of 1˚C warmer relative to the observed climatology for 1980-2000, while ESM2G is 0.25˚C cooler than the climatology (Figure 1, middle). The root-mean-square (RMS) temperature errors relative to climatology for ESM2G are substantially smaller than for ESM2M below 500 m, while ESM2M has smaller RMS errors above 500 m, converging to similar RMS errors at the surface (Figure 1, right). Differences in the parameterizations of other processes, such as eddy mixing, could also contribute substantially to differences in both the oceans’ mean states and to GSSLR. The annual-mean near-surface temperatures in 1980-2000 of the historical simulations average 0.4˚C colder in ESM2G than ESM2M, with smaller differences in midlatitudes and zonal-mean differences exceeding 1.5˚C between 50˚ and 75˚N. The northern sea ice is more extensive than observed, especially in ESM2G, and the southern sea ice is less extensive than observed, especially in ESM2M (Dunne et al. 2012). These differences between the spun-up mean states of the two models figure prominently in their differing projections of GSSLR.
Figure 1: (left) Horizontal-mean potential temperatures from ESM2M (red) and ESM2G (blue) averaged over years 1981-2000 of the historical runs, along with the observed horizontal-mean temperature from the World Ocean Atlas, 2001 (WOA2001) (dashed) (Conkright et al. 2002). (middle) As in (left), but for horizontal-mean temperature bias from ESM2M and ESM2G relative to observed. (right) As in (left), but for horizontal RMS temperature errors for ESM2M and ESM2G. The WOA2001 dataset was chosen as a reference because most of the observations are from the 1980s and 1990s, giving a consistent comparison with this time average from the models.
Projected global steric sea level rise
The GSSLR for the historical and twenty-first-century projections under the four RCP scenarios are shown in Figure 2. This figure includes both thermosteric and halosteric contributions, although the focus here is on exploring the thermosteric differences, since the global-mean differences in the halosteric sea level rise are relatively small. The two models are statistically similar through.out the twentieth century, including responses of similar magnitudes to major volcanic eruptions such as Krakatoa (1883), Agung (1963), and Pinatubo (1991). The mean rate of GSSLR in the latter twentieth century in both models (1.16 mm yr^{-1} for ESM2M and 1.10 mm yr^{-1} for ESM2G) is slightly higher than observational estimates of sea level rise from thermal expansion of 0.8 ± 0.15 mm yr^{-1} for 1972Ð2008 (Church et al. 2011), while observed global-mean halosteric sea level rise is much smaller, just 0.04 ± 0.02 mm yr^{-1} averaged from 1955 to 2003 (Ishii et al. 2006), and not as well constrained observationally.
Figure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 ± 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.
In the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.
|
https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html
|
bccc98a2faca-2
|
Figure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 ± 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.
In the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.
The first reason for the higher GSSLR in ESM2M than in ESM2G is simply because it takes up more heat. This is readily evident in Fig. 3 (bottom), where ESM2M warms substantially more than comparable ESM2G simulations, with volume-mean temperature increasing about 9% more in ESM2M than in ESM2G. These differences in heat uptake are primarily found over the broad depth range from 200 to 2000 m (Fig. 4, left). The warming itself is much more strongly surface intensified in both models than are the differences between the models, and it is quite similar at the surface (apart from RCP2.6, where near-surface temperatures start diverging around 2050, as seen in Fig. 3); this point is discussed further below. To leading order, the heat is being taken up primarily in the thermocline of both models, but the main thermocline is deeper in ESM2M than in ESM2G, giving a greater volume of water to warm. As shown in Fig. 4 (middle left), the density changes contributing to the differences in GSSLR between the models are broadly distributed over the top 2500 m of the models, with roughly equal contributions coming from the depth ranges of 0–600 m, 600–1200 m, and 1200–2500 m. By contrast, well over half the total GSSLR comes from the topmost 600 m in all the cases. Differences in salinity changes compensate or augment the GSSLR differences because of differences in thermal changes at varying depths (Fig. 4, right), but when vertically integrated, the differences in salinity changes between the models contribute less than 0.2 mm to the difference in GSSLR. The larger heat uptake in ESM2M than ESM2G accounts for about half the difference in GSSLR between the models.
Figure 3: (top) Time series of global-mean SST, relative to the mean for 1880–1920, from ESM2M (red) and ESM2G (blue) for ensembles of historical runs and the four CMIP5 radiative scenarios. The values on the right are projections to 2100 from linear fits over the last 40 years, with error bars indicating the variance from these trends over the same 40-yr period. (bottom) Time series of globally integrated heat content anomalies, expressed as volume-mean ocean temperature anomalies in degrees Celsius.
Figure 4: (left) Vertical profiles of the horizontal-mean temperature change for ESM2M (red) and ESM2G (blue) averaged over a 40-yr period relative to 1861–1900. The historical intervals are a century apart (1961–2000), while for RCP2.6 and RCP8.5, the intervals are two centuries apart (2061–2100). (middle left) Vertical profiles of the horizontal-mean contributions to GSSLR (spatially integrated density anomalies divided by the ocean’s surface area and a mean density) from the same runs. (middle right) Profiles of the difference in contribution to GSSLR, ESM2M minus ESM2G. (right) Vertical profiles of the dominant terms in the differences between ESM2M and ESM2G in GSSLR contributions for RCP8.5. The average of the models’ temperature changes acting on the difference between the models’ thermal expansion coefficient differences (blue) and the differences in water-mass property changes acting on the mean thermal expansion and haline contraction coefficients of the two models (solid black) explain almost the entire signal shown in the third panel. The dashed and dotted lines show the separate profiles of GSSLR contributions from the temperature and salinity change differences, respectively, acting on the mean of the models’ thermal expansion and haline contraction coefficients.
A second factor in the differing GSSLR between these two models is the difference in the thermal expansion coefficients where the heating occurs; the thermal expansion coefficient is a strongly increasing function of temperature and pressure, so the two models could be taking up similar amounts of heat, but in different locations, leading to differing amounts of GSSLR (see, e.g., Griffies and Greatbatch 2012). This effect is evident in Fig. 4 (left and middle-left panels), where the contributions to GSSLR are relatively concentrated in the warmer near-surface waters compared with the heat uptake, and it is explicitly diagnosed for RCP8.5 in Fig. 4 (right). ESM2G has a sharper thermocline than ESM2M, and is, on average, about 1.25°C colder than ESM2M at the same depths below the topmost few hundred meters (Fig. 1, middle), with differences in thermal expansion coefficients based on the horizontal-mean temperatures peaking at about 750-m depth, where it is 14% larger in the ESM2M historical run than in ESM2G (and 8% larger than for observed temperatures; in ESM2G it is 6% smaller than observed). The thermal expansion coefficients have smaller relative differences above 750 m because the water is warmer, on average, and they have smaller relative differences below 1000 m because of the effects of pressure. Averaged over the whole volume of the ocean, the simulated thermal expansion coefficient averaged from 1981 to 2000 is 1.1% smaller than observed in ESM2G and 6.6% larger than observed in ESM2M. For RCP8.5, between 1870 and 2090 the volume-mean thermal expansion coefficient increases by about 2.8% in both cases. When weighted by the models’ temperature changes, the mean thermal expansion coefficients are 4% smaller than observed for ESM2G and 3.1% larger than observed for ESM2M for 1981–2000 and increase in the simulations by 10.4% and 11.0% between 1870 and 2090 for RCP8.5. The fact that the warming of the top 2000 m occurs, on average, some 40 m deeper in ESM2M than ESM2G (Fig. 4) also tends to give larger GSSLR in ESM2M than ESM2G, but only by about 0.5%, and it is a minor contributor to the GSSLR differences between the models. The simple fact that the thermal expansion coefficient is a strong function of temperature, and that the control state of ESM2M is warmer than ESM2G, accounts for a roughly 7% larger GSSLR in ESM2M than ESM2G.
|
https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html
|
bccc98a2faca-3
|
Nonoceanic factors that might affect GSSLR, such as atmospheric feedbacks and differences in sea ice that have confounded previous attribution efforts (see Bindoff et al. 2007), do not contribute directly in this study, since those components are identical. However, surface differences in the spun-up mean state of the coupled models can lead to different responses in the atmosphere or sea ice. For instance, the global-mean SSTs in the ESM2G RCP2.6 simulation cool substantially in the latter half of the twenty-first century (Fig. 3, top), tracking the decline in the radiative forcing of RCP2.6, as high-latitude haloclines form in both the Northern and Southern Hemispheres and the sea ice expands. These ice-covered haloclines locally limit the otherwise large ocean heat loss, and the ocean’s warming (Fig. 3, bottom) is not greatly slowed by this global-mean near-surface cooling, even as the lower-latitude surface cooling slows the uptake of heat by warmer waters and sea level rise slows (Fig. 2). Other scenarios exhibit somewhat similar behavior, although they figure less prominently in the differences between the two models’ projections of GSSLR than in RCP2.6.
The RCP8.5 simulations are particularly intriguing, in that the sea surface temperature anomalies exhibit strikingly similar histories throughout the twenty-first century (Fig. 3, top), and by the end of the twenty-first century, summertime sea ice is too limited to do much in either model, but there are still 9% differences in integrated heat uptake (Fig. 3) and 18% differences in GSSLR (Fig. 2). In the near-surface waters (an average from 0 to 400 m is shown in Figs. 5a,b), which dominate the GSSLR signals, both models exhibit temperature changes that are remarkably similar both in magnitude (ESM2M warms just 4% more than ESM2G) and in their spatial patterns. These near-surface temperature changes include both contributions that are directly forced by the uptake of heat from the atmosphere and internal redistributions of heat tied to circulation changes, such as the spinup of the Antarctic Circumpolar Current and the weakening of the Gulf Stream. Some of the heating differences between the models may reflect a deeper rapidly ventilated thermocline in ESM2M than in ESM2G. The volume of water between 50°N and 50°S that is ventilated within 50 years (as measured by a passive “ideal age” tracer) is roughly 20% larger in ESM2M than ESM2G (172-m versus 141-m average thicknesses in 1981–2000). If the surface warming signal is partly acting as a Dirichlet boundary condition for the ocean’s interior temperature, this greater volume of rapidly ventilated water would lead to a larger heat uptake and GSSLR. These relative differences in the volumes of ventilated water are similar to the differences in the volumes of water warmer that some temperatures appropriate to the thermocline (e.g., 12°C). Whether the differences in ventilation drive the differences in near-surface stratification (see Fig. 1) or whether it is the reverse is beyond the scope of this paper; certainly, there is a connection between them and with the amount of heat that the upper ocean can take up on time scales of decades. However, these near-surface heating differences are not the dominant driver of GSSLR differences in the RCP8.5 simulations.
Figure 5: Temperature change for RCP8.5 averaged over the years 2081–2100, relative to 1861–1900 and corrected for long-term mean drifts, for (left) ESM2G and (right) ESM2M and averaged over the depth ranges of (a),(b) 0–400 m and (c),(d) 800–1200 m. The horizontal-mean temperature changes are 1.59°, 1.66°, 0.56°, and 0.73°C in (a)–(d), respectively. Between 0 and 400 m, the average warming is 4% larger in ESM2M than ESM2G, but between 800 and 1200 m, the average warming is 29% larger in ESM2M than ESM2G.
At a depth of 800–1200 m in the RCP8.5 scenario (Figs. 5c,d), the heat uptake is of profoundly different magnitude between the models (the temperature increase is 29% larger in ESM2M than ESM2G), but still with very similar patterns. This depth is chosen for greater scrutiny because there is a peak in the difference in SLR contributions from water-mass changes between the models at about 1000 m (Fig. 4, right). Both exhibit warming (and an increase in salinity) in the western Atlantic because of a slowdown of the Atlantic meridional overturning circulation with a somewhat stronger warming signal in ESM2M than ESM2G. The Pacific is comparable to the Atlantic in the integrated heat change difference between the models in the 800–1200-m depth range and actually dominates the horizontally averaged steric sea level rise difference because there is no compensating salinity signal. The North Pacific signal is too deep for any of the water involved to have been directly influenced by the surface heat flux anomalies; instead, it is due to circulation changes. The broad warming of the eastern Pacific in both models is consistent with a broad downward displacement of the isopycnals of approximately 100 m in both models. The cooling signals on the western side of the Pacific basin are consistent with a vertical contraction of the subtropical gyres as the overlying waters become more strongly stratified. The temperature signal at about 1000 m in the Pacific is much larger in ESM2M than ESM2G, primarily because the vertical temperature gradients at this depth are much larger in ESM2M than ESM2G (Fig. 1). These deep temperature signals, which make up a large portion of the overall GSSLR difference, illustrate the importance of the ocean’s initial state in determining the details of its forced GSSLR signal.
Discussion and summary
This study examines the differences between the GSSLR projected by two earth system models, which differ only in their ocean components, in order to estimate the uncertainties in twenty-first-century GSSLR projections arising solely from uncertainties in the numerical representation of ocean dynamics and parameterizations of physical processes in the ocean. The interior ocean–mean states of these two models have water-mass biases that broadly straddle the observed properties of the ocean, and their ocean components might be considered cutting-edge geopotential- and isopycnal-coordinate ocean climate models. ESM2G exhibits twenty-first-century GSSLR that is consistently 18% smaller than in ESM2M for all four radiative forcing scenarios. Differences in the amount of heat taken up by the two models would account for a 9% difference in GSSLR, while differences in the thermal expansion coefficient due to different control states would account for a 7% difference. While these differences are highly statistically significant, they are also small enough to suggest that uncertainties in the ocean do not qualitatively alter the expected magnitude of twenty-first-century GSSLR.
There are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., Böning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models’ very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models’ dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models’ identical pre-spin-up initial conditions.
The regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean’s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.
|
https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html
|
bccc98a2faca-4
|
There are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., Böning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models’ very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models’ dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models’ identical pre-spin-up initial conditions.
The regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean’s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.
The fact that it is the lower thermocline that dominates the GSSLR differences between the models, and not the upper main thermocline that dominates GSSLR itself, suggests that differences in the processes that set and alter the interior ocean water-mass properties in these density ranges may largely explain the differences between these two models. Formation of mode waters and intermediate waters are problematic for many of the coupled models that are included in CMIP5 (e.g., Downes et al. 2011) and are a focus of ongoing development. The two models also represent very differently the overflows (e.g., Legg et al. 2006) that are an integral part of the ocean’s overturning circulation and the formation of water masses that are found at this depth. Increasing diapycnal diffusion is well known to broaden the lower thermocline. Ilicak et al. (2012) diagnose that ESM2M has spurious (numerically induced) diapycnal mixing that is about a third of the size of the explicitly parameterized intended mixing, while that in ESM2G is only about an eighth as large. While this global diagnostic cannot say where this spurious mixing is occurring, it could help explain both the greater breadth of the main thermocline and the deeper penetration of heat in ESM2M compared to ESM2G. Greater scrutiny of the models’ representation of the processes that control the water-mass structure and location of the lower main thermocline might be of particular value for further reducing the oceanic uncertainty in projections of GSSLR.
The biggest uncertainties in projecting twenty-first-century sea level rise are in how much mass the Antarctic and Greenland ice sheets will lose dynamically. Twenty-first-century SLR due to ice sheet dynamics is unknown to within about 1 m of sea level rise (e.g., Pfeffer et al. 2008); while recent rates of observed ice sheet mass loss would only contribute approximately 130 ± 40 mm in the twenty-first century, this increases to between 450 and 700 mm if observed accelerations in ice sheet mass loss continue (Rignot et al. 2011). A second major source of uncertainty is what radiative forcing scenario humans will collectively choose for our planet, here differing between the highest and lowest CMIP5 scenarios by about 125 mm of GSSLR by 2100. Uncetainties in the representation of the dynamics of the ocean and atmosphere and of key physical processes, such as clouds or small-scale ocean mixing, also map significantly onto uncertainties in projected GSSLR. The various coupled climate models used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report give 5% and 95% estimates of twenty-first-century GSSLR that differ by ±42% from the mean for a given forcing scenario (Meehl et al. 2007), or a range of about 190 mm. Since these IPCC models are largely independent, this value is likely to be dominated by atmospheric differences, especially in changing cloud distributions, although ocean differences will also contribute. The comparison presented here suggests that the uncertainty in twenty-first-century steric sea level rise due only to the ocean model formulation and physical processes in the ocean is approximately 28–49 mm (depending on the forcing scenario).
To put these results into the long-term perspective, it is important to recognize that the uncertainties in twenty-first-century GSSLR arising from the ocean (of order 0.05 m) are small compared with the potential sea level rise stemming from interactions between the oceans and ice sheets (of order 1 m). While additional work to improve our ability to capture the physics and dynamics of the ocean in numerical models will be useful, and the role of ocean eddies in modulating GSSLR is largely unexplored, by far the most prominent open questions regarding the ocean’s role in sea level rise center on the interactions between the oceans and ice sheets and how they will evolve in coming centuries.
|
https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html
|
8e1a60b11d1e-0
|
Dangendorf et al. (2021)
Title:
Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level
Key Points:
Regional coastal sea levels are largely dominated by sterodynamic sea-level variations
Steric sea level signals originate from open ocean regions often thousands of kilometers away
Better understanding of sterodynamic sea-level variations is key for robust near-term coastal sea-level estimates
Keywords:
steric dynamic sea level, coastal sea level, tide gauge, Empirical Orthogonal Functions
Corresponding author:
Dangendorf
Citation:
Dangendorf, S., Frederikse, T., Chafik, L., Klinck, J. M., Ezer, T., & Hamlington, B. D. (2021). Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level. Nature Climate Change, 11(6), 514–520. doi:10.1038/s41558-021-01046-1
URL:
https://www.nature.com/articles/s41558-021-01046-1
Abstract
Understanding historical and projected coastal sea-level change is limited because the impact of large-scale ocean dynamics is not well constrained. Here, we use a global set of tide-gauge records over nine regions to analyse the relationship between coastal sea-level variability and open-ocean steric height, related to density fluctuations. Interannual-to-decadal sea-level variability follows open-ocean steric height variations along many coastlines. We extract their common modes of variability and reconstruct coastal sterodynamic sea level, which is due to ocean density and circulation changes, based on steric height observations. Our reconstruction, tested in Earth system models, explains up to 91% of coastal sea-level variability. Combined with barystatic components related to ocean mass change and vertical land motion, the reconstruction also permits closure of the coastal sea-level budget since 1960. We find ocean circulation has dominated coastal sea-level budgets over the past six decades, reinforcing its importance in near-term predictions and coastal planning.
Introduction
The ability to predict and estimate future coastal sea-level changes depends on a thorough understanding of the observational record. Recent studies provide evidence that the global sea-level budget — the comparison of observed sea-level rise with the sum of individual contributions — can be reasonably closed with independent observations from remote sensing techniques and Argo floats since 2005 (refs. 1,2,3) but also with a combination of observations and reanalysis estimates since 1900 (ref. 4). This points to notable progress since the 2013 fifth assessment report of the Intergovernmental Panel on Climate Change [5]. The budget has also been closed regionally for larger areas off the coast since 2005 (refs. 6,7) and at basin scales since the 1950s [4,8]. However, at the coast, where information is most needed, budget assessments have higher uncertainty due to the number of additional processes that cancel out in the global mean. These include: changes in the sterodynamic component [9], due to ocean circulation change and steric (density-driven) expansion; gravitational, rotational and deformational effects accompanying global barystatic (ocean mass-driven) sea-level changes; and vertical land motion induced by glacial isostatic adjustment, tectonics or local subsidence.
For barystatic sea level and vertical land motion, a number of observations and model estimates now provide constraints at decadal [10] to century scales11. Specifically, the barystatic estimates due to ice-mass loss, terrestrial water storage and glacier melting and their representation at individual locations have considerably improved [4,8].
However, the role of steric sea-level changes and their signature along shallow coastlines is still poorly understood [12,13]. The steric component, defined as the depth integral of density changes in the ocean, is the dominant driver of sea-level variability in the (deep) open ocean (Fig. 1a) with mostly minor contributions coming from ocean-bottom pressure14 (Fig. 1b). In contrast, at the coast where the ocean’s depth decreases to zero, the resulting steric contribution vanishes as well (Fig. 1a). Thus, changes in ocean density will necessarily lead to larger expansion and contraction of the water column in the deep ocean than at the shallow coast15, driving a sea-surface height gradient between the two. This gradient needs to be balanced and hence forces changes in ocean-bottom pressure, with the latter becoming the dominant contributor to sea-level variability at the coast (Fig. 1b). However, due to a wide variety of ocean dynamic processes, coastal sea-level variability cannot be directly derived from steric sea-level changes in the nearby open ocean12,16,17 (Fig. 1c). Due to the lack of this direct relation between the open-ocean steric effects and coastal sea level, both the geographical origin and the underlying processes of the resulting coastal sterodynamic sea-level variations (hereafter SDSL) are poorly understood, inhibiting their proper quantification6,18. Particularly challenging in many coastal regions is the presence of strong boundary currents and coastally trapped waves that mediate open-ocean steric effects to the coast and introduce, due to their coast-parallel flow and propagation, substantial alongshore coherence in sea level often extending over thousands of kilometres17. Indeed, sea-level signals at the continental coasts often originate from perturbations at remote locations13,16, hindering the simple across-shelf integration of steric height from the nearby deep ocean as previously described by ref. 12. While global ocean reanalyses should provide a physically consistent solution for simulating coastal SDSL, they currently face challenges such as drifts and biases due to air–sea fluxes and ocean mixing errors, coarse model resolution or the assimilation of observations that become sparse back in time19. As a consequence, they poorly reproduce observations at the coast20,21 (particularly spatial trends; Extended Data Fig. 1). These knowledge and modelling gaps about past SDSL changes are critical to resolve given that sea-level information is most needed at the coast. Together with the improved information about non-steric processes, these factors call for an alternative, and ideally data-driven, approach for estimating SDSL in the coastal zone.
Fig. 1: Relative roles of ocean-bottom pressure and steric components for coastal SDSL. a,b, Shown is the explained SDSL variance through steric height (a) and ocean-bottom pressure (b) in a historical ocean simulation with the CNRM-CM6-1-HR ESM. c, Schematic of the relationship between deep-ocean steric expansion and ocean-bottom pressure changes on the shallow shelf. The exchange is largely controlled by boundary currents and coastally trapped waves.
Here, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.
Identification of regions of common variability
We start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000 m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P ≤ 0.05) with the corresponding regional mean of SDSLTG.
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-1
|
Here, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.
Identification of regions of common variability
We start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000 m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P ≤ 0.05) with the corresponding regional mean of SDSLTG.
Fig. 2: Origin and reconstruction of coastal SDSL changes. a, Spatial correlation patterns between the detrended SDSL residuals at tide gauges (SDSLTG, grey dots) and detrended steric height from the open ocean for nine coastal regions. Only significant correlations (P ≤ 0.05) are shown. Note that in some regions, correlation patterns of different regions may overlap. b, Illustration of the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR ESM, bottom) for the Northwest Atlantic south of Cape Hatteras. Shadings represent the 95% confidence intervals (CI) from all Monte-Carlo samples. c, Correlation and trend differences between reconstructed SDSLEOF and the a priori known SDSLTG in the validation experiments with 12 ESMs. Also shown is the correlation between SDSLEOF and SDSLTG in actual observations (orange dots). TG, tide gauge; NW, northwest; NE, northeast; NCH, north of Cape Hatteras; SCH, south of Cape Hatteras.
For all regions, significant correlations are widely spread over the oceans and often extend thousands of kilometres away from the tide-gauge sites (Fig. 2a globally and Extended Data Fig. 3 for expanded views into each region). Along eastern boundaries the correlation patterns range from the (sub)tropics to high latitudes with narrowing bands of high correlations along the continental slope moving poleward. In the Atlantic (Extended Data Fig. 3a), steric sea-level variations near the Strait of Gibraltar have recently been linked to both local wind forcing and Atlantic Meridional Overturning Circulation changes16,25, while further north along the Portuguese coastline, sea-level variability is tightly connected to longshore wind forcing13,26,27,28. The along-shelf coherence (Extended Data Fig. 3a) is consistent with the hypothesis that coastally trapped waves communicate SDSL variations from the eastern boundary into the North Sea16,17,28. A similar, but much more pronounced, correlation pattern can be found in the Northeast Pacific, where the largest correlations, r > 0.9, occur around the Equator and off the California coast (Extended Data Fig. 3d). This is consistent with ref. 29, who demonstrated that coastal sea levels along the Californian coastline vary in concert with fluctuations in equatorial trade winds and longshore winds generated around the Aleutian Low. Westerlies in the western and central Pacific generate equatorial Kelvin waves, which first propagate eastward along the Equator and then, after being reflected at the eastern boundary, travel northward as coastal Kelvin waves16,30.
For the western regions in the Atlantic and Pacific, correlations indicate a dynamic connection to the western boundary currents (Kuroshio and Gulf Stream), although with an interesting distinction in the Atlantic north and south of Cape Hatteras31 (Extended Data Fig. 3b,c). North of Cape Hatteras the correlation pattern follows the continental slope into the Labrador Sea and the Subpolar Gyre. This agrees with ref. 23, who provided evidence that Labrador Sea density anomalies (driven by both atmospheric processes in the upper layers and variations in the Deep Western Boundary Current at intermediate and deeper levels) propagate southward as coastally trapped waves32. South of Cape Hatteras, however, highest correlations are directly centred on the Gulf Stream pathway. This is consistent with the suggestion that coastal sea-level variability in this region is linked to a fast barotropic response of the coastal ocean to (overturning-related) large-scale heat divergence in the open ocean33,34 and/or subtle variations in the strength and position of the Gulf Stream35.
In the Indo-Pacific regions (West Australia and Western Pacific), coastal SDSL variations are highly coherent even between widely separated regions leading to overlapping correlation patterns extending from the Bay of Bengal into the Central Pacific (Extended Data Fig. 3g,i). These signals are linked to the El Niño/Southern Oscillation and primarily driven by equatorial trade winds36. These trade winds induce westward propagating equatorial Rossby waves, which first cross the Indonesian throughflow region and then travel poleward as coastally trapped waves along the west coast of Australia37,38. The coasts of New Zealand show coherence with the larger South Pacific Gyre region as well as the warm subtropical currents in the Tasman Sea extending onto the southwestern Australian continental shelves. Sasaki39 used an eddy-resolving ocean general circulation model to show that long baroclinic Rossby waves, forced by wind stress curl over the subtropical gyre, are an important driver of New Zealand’s decadal sea-level variability. For gauges at Hawaii, a typical example of an open-ocean site surrounded by steeply sloping topography, highest correlations are pronounced locally northeast of the islands, indicating a more local control of coastal sea-level variations.
In summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.
Reconstruction of SDSL at the coast
The large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-2
|
In summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.
Reconstruction of SDSL at the coast
The large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.
To test the robustness of the reconstruction against overfitting and to assess uncertainties, we use ocean simulations from 12 Earth system models (ESM) over the period 1850–2012 with historical forcing (Supplementary Table 2). In the ESMs coastal SDSL, open-ocean steric height and ocean-bottom pressure variations are a priori known and therefore form an ideal testbed for the EOF approach (using source regions similarly determined in each ESM as for the observational record; Methods). We extract in total 12,000 realizations of 53-yr periods to calibrate the reconstruction (with randomly varied model parameters; Methods) and use an independent, random 53-yr period (from the remaining model years) for validation. The resulting time series are displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. In all model runs, the EOF reconstruction mimics coastal SDSL variations reasonably well, which is reflected in significant correlation coefficients over all models and subsamples providing only subtle differences between calibration and validation periods (Fig. 2c). EOF reconstructions in tropical and subtropical coastal regions with known links to the El Niño/Southern Oscillation show slightly larger correlations (median r ≥ 0.86, P ≤ 0.05) than those at higher latitudes (for example, the Northwest Atlantic north of Cape Hatteras) or in large continental shelf seas (for example, the North Sea) (median r = 0.64–0.77, P ≤ 0.05). This is probably related to increased and atmospherically forced barotropic variability in these records, which might mask the remotely forced and density induced SDSL variations28,41,42. Similarly well reconstructed are linear trends in the ESMs (Fig. 2d). These usually agree with the model internal true coastal SDSL signal within a range ±0.7 mm yr–1 in all subsamples and regions and show little evidence for systematic trend biases (median trend differences are of the order of ±0.06 mm yr–1 over both calibration and validation periods) (Fig. 2d). Overall, this demonstrates the skill of the EOF approach in reconstructing coastal SDSL from open-ocean steric height and motivates its application to observations.
The SDSLEOF reconstructions based on open-ocean steric height observations from the source regions are again displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. We generated an ensemble of 5,000 SDSLEOF reconstructions at each site, which is based on varying barystatic sea-level corrections at tide-gauge records (Methods) and randomly varied parameter choices in the EOF approach (Methods). In agreement with the ESM experiments, the ensemble SDSLEOF reconstructions show significant median correlations to SDSLTG that range from r = 0.62 (P ≤ 0.05) in the Northwest Atlantic south of Cape Hatteras to r = 0.95 (P ≤ 0.05) in the Western Pacific (Fig. 2c). In the three regions that are directly influenced by western boundary currents (Northwest Atlantic south of Cape Hatteras, Japan Sea and New Zealand), SDSLEOF displays slightly lower (but still good) agreement with coastal residual sea level than in the other regions. This is probably related to the more complex dynamics involving mesoscale eddy activity and slowly propagating Rossby waves39,43,44 that are hard to capture in the EOF approach without any consideration of time lags. Such time lags seem to play a minor role in regions dominated by coastally trapped waves, which typically have travel times below a month from the source regions to the coasts26,30. Overall, the EOF reconstructions display an encouraging performance in transferring open-ocean steric height signals toward the coast that exceeds those from standard reanalysis products (Extended Data Fig. 1) and even holds for longer timescales as further discussed in the budget assessment below.
Implications for the coastal sea-level budget
Taking advantage of the improved representation of SDSL variability at the coast, we finally reassess the total coastal sea-level budget for each region by adding the barystatic component back to the reconstructed SDSL component and comparing it to the vertical land motion corrected coastal sea level in each region. This budget is displayed in Fig. 3 for linear (Fig. 3a,b and Table 1) and nonlinear trends (Fig. 3c) during 1960 to 2012. In all regions the trend budget can be closed within the respective uncertainties (Fig. 3b and Table 1) that are, particularly in Northern Europe and North America, dominated by vertical land motion (Fig. 3b). Median differences to observations are everywhere within a range ±0.2 mm yr–1. The only exception is Hawaii, where the median trend is overestimated by 0.4 mm yr–1. We note, however, that there are also substantial uncertainties in the underlying steric products (Extended Data Fig. 5 and Methods) that may account for these differences. At all locations, except Hawaii and the Japan Sea, SDSL components explain the major fraction of the total trend budget (Fig. 3a).
Fig. 3: Coastal sea-level budget over 1950 to 2012. a, Shown are (as pie diagrams for each region) the fractions of the coastal trend budget that are explained by SDSLEOF and barystatic components. b, The linear trend budget of coastal sea level for nine regions after correcting each tide gauge for glacial isostatic adjustment and residual vertical land motion. Blue bars represent regional averages, while the stacked blue/orange bars represent the budget estimated with SDSLEOF and barystatic sea level. c, The rates derived from a nonlinear trend for each component and region. All shadings and error bars represent 95% CI derived from the 5,000-member ensemble.
Table 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.
Region
Observations
(mm yr–1)
Budget
(mm yr–1)
SDSLMEFOF
(mm yr–1)
Barystatic GRD
(mm yr–1)
North Sea
2.01 (1.30;2.76)
2.09 (1.58;2.52)
1.73 (1.28;2.09)
0.36 (0.17;0.56)
NW Atlantic
NCH
1.43 (0.78;2.40)
1.42 (1.02;1.87)
0.76 (0.50;1.14)
0.65 (0.39;0.87)
NW Atlantic
SCH
1.40 (0.52;2.32)
1.48 (1.12;1.80)
0.76 (0.56;0.98)
0.72 (0.42;0.97)
NE Pacific
1.23 (0.20;2.26)
1.40 (0.97;1.80)
1.02 (0.89;1.20)
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-3
|
Table 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.
Region
Observations
(mm yr–1)
Budget
(mm yr–1)
SDSLMEFOF
(mm yr–1)
Barystatic GRD
(mm yr–1)
North Sea
2.01 (1.30;2.76)
2.09 (1.58;2.52)
1.73 (1.28;2.09)
0.36 (0.17;0.56)
NW Atlantic
NCH
1.43 (0.78;2.40)
1.42 (1.02;1.87)
0.76 (0.50;1.14)
0.65 (0.39;0.87)
NW Atlantic
SCH
1.40 (0.52;2.32)
1.48 (1.12;1.80)
0.76 (0.56;0.98)
0.72 (0.42;0.97)
NE Pacific
1.23 (0.20;2.26)
1.40 (0.97;1.80)
1.02 (0.89;1.20)
0.38 (–0.02;0.71)
Hawaii
1.55 (1.24;1.89)
1.18 (0.71;1.58)
0.47 (0.27;0.67)
0.71 (0.31;1.05)
Japan Sea
1.29 (0.89;1.75)
1.13 (0.64;1.60)
0.48 (0.12;0.81)
0.65 (0.35;0.96)
West Australia
1.48 (1.11;1.85)
1.60 (1.10;2.04)
0.89 (0.61;1.19)
0.71 (0.34;1.03)
New Zealand
1.74 (1.16;2.35)
1.66 (1.12;2.11)
0.99 (0.64;1.25)
0.66 (0.32;0.99)
The budget terms also explain the observed interannual variability, which is expressed by an explained variance ranging from 38% at sites in the Northwest Atlantic south of Cape Hatteras to 91% along the Californian coast in the Northeast Pacific (Fig. 2c and Extended Data Fig. 4). The temporal variability is largely dominated by the SDSL component at all sites (Fig. 3c), although barystatic sea level through ice-mass loss and natural and anthropogenic terrestrial water storage variations (Methods) adds an accelerating signal to the rates. Largest accelerations in barystatic sea level are found around the Hawaiian Islands, where rates have been increasing from close to 0 to >2 mm yr–1 since the late 1990s. However, in the total budget, this acceleration has been reversed by strong negative anomalies in the SDSL components since the early 2000s (Fig. 3c). In contrast, Northern European coastlines only exhibit a small barystatic sea-level signal with an average rate of 0.4 (0.2; 0.6) mm yr–1 over 1960 to 2012 but this is (despite the large uncertainties in different steric products) counterbalanced by the largest average SDSL rates of all sites (Fig. 3b). In the Northeast Pacific, SDSL shows the well-known sea-level suppression since the 1970s45, while at gauges in the Western Pacific and West Australia, SDSL is characterized by a sustained acceleration from close-to-zero rates before the 1980s to >14 mm yr–1 in the 2010s (in an opposite direction to the negative SDSL rates at Hawaii); a value that is six times larger than the simultaneous barystatic sea-level rise. This acceleration has previously been attributed to anthropogenic forcing46 and represents the most pronounced SDSL sea-level change signal of all sites. Further accelerations in the SDSL terms can be seen in the Japan Sea and New Zealand since the early 1980s and along the coasts of Northeast America north of Cape Hatteras since the 1990s but their magnitudes are far smaller than those seen in the tropical Indo-Pacific regions and an attribution to natural and anthropogenic forcing has not yet been achieved.
The large site-specific rates also suggest substantial regional SDSL deviations from the simultaneous global mean (Fig. 4b) that are considerably larger than the spatial variations that have been contributed by barystatic sea level. Such deviations are important for coastal planning purposes, particularly at engineering-relevant timescales of a few decades. To generalize the potential of coastal SDSL variations to deviate from the global mean at varying timescales, we calculate moving trends for window sizes between 10 and 53 yr for both coastal SDSL and global mean steric sea level and assess their respective ratio (Fig. 4). At decadal timescales (~10 yr), local variations can be several hundred times larger or smaller than the global mean in any region considered here. This number decreases with increasing timescale but regional deviations can still be as large as ten, six and three times the simultaneous global mean for periods of 20, 30 and 50 yr, respectively. Given the dominance of SDSL variations at these timescales (Fig. 3c), this indicates that the key to more robust near-term coastal sea-level estimates for the coming decades clearly lies in a better understanding of SDSL variations and their geographical origin.
Fig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53 yr. Three periods at 20, 30 and 50 yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10 yr, are shown in b.
Our results represent a notable advance in estimating drivers of regional coastal sea level over the past 53 yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.
Methods
Tide-gauge data and corrections
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-4
|
Fig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53 yr. Three periods at 20, 30 and 50 yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10 yr, are shown in b.
Our results represent a notable advance in estimating drivers of regional coastal sea level over the past 53 yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.
Methods
Tide-gauge data and corrections
We make use of a set of 89 annual tide-gauge records from nine coastal regions taken from the online portal of the Permanent Service for Mean Sea Level in Liverpool49 and listed in Supplementary Table 1. The nine coastal regions have been selected on the basis of previous studies demonstrating that their tide-gauge records show similar dynamic sea-level variability4,21,25,29,36,39,43. In each region, individual records have been chosen on the basis of criteria such as data availability (>75%, except of a few exceptions primarily in the Indo-Pacific) and homogeneity (visual inspections and data flags). The individual records, together with their corresponding virtual stations and a cross-correlation matrix, are shown in Extended Data Fig. 2. Nine clusters of pronounced positive correlations appear, thus underpinning the coherence within each region. Existing data gaps have been filled with the local realizations from the hybrid sea-level reconstruction from ref. 50. The local realizations from the hybrid reconstruction include a local residual process from the Kalman Smoother that accounts for local effects such as vertical land motion (but does not contribute to the sea-level fields in the ocean and the corresponding global mean sea level) and therefore almost perfectly mimics their long-term trends50,51. They are also highly correlated with the real tide gauges (Supplementary Table 1). The gap-filling is a requirement for the EOF approach outlined below and avoids issues with benchmark differences when being merged to regional means52. We note, however, that the median percentage of data gaps is only 6% over all sites (Supplementary Table 1) and thus has a negligible influence on our results. Our major aim here is to investigate the SDSL variability in each of these regions. A challenge in this regard stems from the fact that tide-gauge records are affected by numerous different additional processes (vertical land motion and barystatic sea level) that may mask the actual SDSL signals. To isolate the SDSL variability at each site, we therefore initially remove vertical land motion and barystatic components. Each of these corrections comes with notable uncertainties. These uncertainties are considered here and build the basis for a probabilistic ensemble assessment with 5,000 members.
The first correction corresponds to vertical land motion, which primarily affects coastal sea level at lowest frequencies and induces spatially varying trends between individual locations. To correct for vertical land motion, we fit a linear trend to the differences between each tide-gauge record (before the gap-filling) and the nearest-neighbour time series from the hybrid reconstruction (that does not include the residual component and is corrected for its median glacial isostatic adjustment field) from ref. 50, which combines a process-based Kalman Smoother51 with ordinary EOF reconstructions53. As the Kalman Smoother aligns a series of predescribed processes (barystatic fingerprints, dynamic sea-level changes from climate models and 161 glacial isostatic adjustment models but excluding non-climatic local vertical land motion; ref. 51) to a global set of tide gauges, the difference between the hybrid reconstruction and tide gauges should, next to model errors, predominantly be driven by local vertical land motion51. The basic idea is similar to the Gaussian process approach used in ref. 54 for future projections and estimates based on the difference between tide-gauge records and satellite altimetry10 but it has the advantage of providing much longer residual series covering the entire length of tide-gauge records back to 1900 (that is, the period over which the hybrid reconstruction is available). As a preliminary cross-validation, we compare our estimates to the vertical land motion dataset from ref. 4. Their dataset is based on Global Navigation Satellite System observations and differences between tide gauges and nearby satellite altimetry but corrected for the nonlinear crustal components of present-day barystatic sea-level change and, therefore, is directly comparable to ours. The corrections are only available at 65 out of our 89 tide-gauge sites. Both datasets are significantly correlated (r = 0.78, P ≤ 0.05) with a root mean square difference of 0.8 mm yr–1 (which is substantially smaller than that from satellite altimetry minus tide gauge (1.22 mm yr–1); ref. 55) but vertical land motion estimates from the hybrid reconstruction show a higher correlation to linear trends from tide-gauge observations (r = 0.91, P ≤ 0.05) than those from ref. 4 (r = 0.67, P ≤ 0.05) (Extended Data Fig. 6). For this reason, as well as the fact that the hybrid reconstruction provides vertical land motion estimates at more stations than the ref. 4 dataset, we proceed with the hybrid reconstruction-based vertical land motion estimates. The largest uncertainty in the hybrid reconstruction-based vertical land motion estimates stems from the 161 glacial isostatic adjustment models used in the Kalman Smoother from ref. 53 that consider different solid-Earth parameters (lithosphere thickness and mantle viscosity) and varying global deglaciation histories over the past 20,000 yr. The second uncertainty in the vertical land motion estimates is related to fitting of the linear trend to noisy data. This uncertainty has been modelled considering that the residuals are normally distributed but temporally correlated. To consider both uncertainties in the budget assessment, we perturb the vertical land motion estimates with random noise from the fitting uncertainty as well as the uncertainty from the 161 glacial isostatic adjustment models (considering their spatial correlation). This results in a 5,000-member ensemble of plausible vertical land motion corrections at each site.
The next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-5
|
The next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.
In addition to vertical land motion and barystatic effects, tide-gauge records are also affected by the barotropic response of the ocean to atmospheric forcing. This consists of barotropic wind forcing and the inverted barometer response to sea-level pressure fluctuations over the oceans and represents a dominant fraction of the sea-level spectrum from intra-annual to decadal scales42. While the barotropic wind forcing term is usually considered as an inherent process of SDSL, it may introduce large variability of opposite sign at different locations27,28 and mask the actual SDSL variability seen by a tide gauge41. The latter may particularly be the case, when SDSL signals have, for instance, been initiated by wind forcing in remote regions affected by different atmospheric circulation systems than those responsible for the local barotropic signals. For this reason, we initially remove these wind and pressure effects from each tide-gauge record for the correlation and EOF analyses. Note, however, that we later add this component back to SDSL for the overall validation and the budget assessment. Thus, the SDSLEOF components shown in Figs. 1–3 in fact represent SDSL plus atmospheric pressure effects. As an estimate of these effects, we use the outputs from barotropic simulations with the MIT global circulation model forced with atmospheric reanalysis winds and sea-level pressure from the twentieth century reanalysis66 over the period 1871–2012. Further details on the model configuration and detailed validations can be found in refs. 21,42. The wind and pressure components are most important at higher latitudes, where stratification is weak, and they introduce both spatially varying temporal trends as well as pronounced intra-annual to decadal variability [42].
Steric height data
We estimate steric changes from a gridded temperature24 and salinity reconstruction67 on the basis of hydrographic profiles covering the upper 2,000 m of the ocean over the 1960 to 2012 period using the TEOS-10 GSW software for MATLAB68. This temperature and salinity reconstruction is based on an optimal interpolation approach, which uses the CMIP5 multimodel ensemble to derive correlation scales and to set the initial field. We note that there are many other gridded temperature and salinity datasets available that use different mapping methods than ref. 24. Three of these datasets have additionally been analysed here: ref. 69 and EN4 (EN4.2.1.)70 with two different mechanical bathythermograph (MBT) and expendable bathythermograph (XBT) bias corrections schemes following refs. 71,72. There are notable differences in linear trends calculated from each of the steric height datasets over 1960 to 2012 (Extended Data Fig. 5a–d) that are particularly pronounced in areas of major ocean circulation systems (>2 mm yr–1)73. These large differences between individual products may be partly related to the distinct mesoscale eddy activity that is not resolved by hydrographic observations as well as the different mapping approaches in each reconstruction24. They also feed in the SDSLEOF reconstruction (that essentially covers information from these circulation systems) when applied to each dataset individually (Extended Data Fig. 5e,f). However, the SDSLEOF reconstruction based on the ref. 24 dataset has the smallest trend differences to the SDSLTG in most regions (Extended Data Fig. 5) and also provides the best representation of variability (Extended Data Fig. 5f). It is interesting to note that regions with the largest interproduct trend spread also show the largest spread in correlations to SDSLTG with ref. 24 data providing far better agreement than all other products. For this reason, and since the dataset from ref. 24 has been shown to represent a methodological improvement over former reconstructions, we limit our analysis in the main paper to this particular dataset.
EOF reconstruction
The EOF approach assumes that two or more sets of variables share a certain degree of similar variability, which can be expressed by distinct spatial patterns (EOF modes) for each individual variable (here, steric height from the open ocean and SDSLTG at the coast) and a common principal component (PC) corresponding to each spatial pattern. In the literature, similar approaches (but using canonical correlation analysis74 or cyclostationary EOFs40) have been used to reconstruct sparse/short climatic data (for example, precipitation) on the basis of covariates covering much longer periods than the variable of interest (for example, sea-level pressure or sea-surface temperature). Here, we use this approach to transfer steric height estimates from the source regions (identified with the correlation patterns in Fig. 2a) to the coast represented by the tide-gauge residuals after removing vertical land motion, barystatic sea level and (barotropic) wind and pressure effects (SDSLTG). This is done in three steps:
We calculate EOFs over the 1960–2012 period between detrended and smoothed (using a randomly chosen smoothing window between 3 and 5 yr) steric height and SDSLTG. This produces several different modes with variable-specific spatial patterns and common PCs. In our reconstruction, we only use a subsample of these modes that share a certain degree of variance in each region. We randomly varied the corresponding threshold, such that only those modes are considered that cumulatively explain between 92 and 98% of the variance of the entire coupled field. On average, this resulted in the consideration of five (West Pacific) to nine (North Sea) modes in the different regions.
The spatial pattern of the steric height from the EOF analysis is then projected back onto the entire (1960–2012) non-detrended and non-smoothed steric height fields from the source region to produce a series of each PC.
Finally, the PCs from step 2, now solely based on steric height from the open ocean, are projected onto the spatial patterns from tide-gauge residuals (SDSLTG), which produces an EOF-based SDSL reconstruction (SDSLEOF) over the entire 1960–2012 period at each site.
The SDSLEOF reconstructions are then evaluated as spatial averages over all sites in each region. By using varying barystatic corrections and by considering randomly varied parameter choices, we produce 5,000 ensemble members that are used to assess uncertainties of the EOF reconstruction. The EOF approach has two major advantages compared to simple field averages over the source region as formerly used in refs. 22,23 While a simple area average assumes that the steric signal from the open ocean is one on one transferred toward the coast, there are factors at play that may dampen or amplify the signal while propagating from the open ocean toward the coast. The regression character of the EOF approach explicitly takes this into account and scales the signal to match the variability seen at tide gauges. Furthermore, EOF analysis decomposes a field into common modes. As typical for many other atmospheric or oceanographic time series, most of the variance of the entire field is contained in the first few modes, while local effects move as noise into lower EOFs. Thus, the EOF approach is robust against local outliers. To test the stability of the EOF reconstruction against increasing data uncertainties in the steric products before the 1980s, we also calculated a second 5,000-member ensemble on the basis of PCs calculated since solely 1980 (Extended Data Fig. 7). We do not find any significant differences in the reconstructions based on PCs calculated over the entire period or only since 1980. Correlations are, in all cases, >0.98 with the only exception being the three western boundary currents where the correlation coefficients are between 0.92 and 0.94. The trends are also not significantly different between the two ensembles (Extended Data Fig. 7b).
Earth system models
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-6
|
The spatial pattern of the steric height from the EOF analysis is then projected back onto the entire (1960–2012) non-detrended and non-smoothed steric height fields from the source region to produce a series of each PC.
Finally, the PCs from step 2, now solely based on steric height from the open ocean, are projected onto the spatial patterns from tide-gauge residuals (SDSLTG), which produces an EOF-based SDSL reconstruction (SDSLEOF) over the entire 1960–2012 period at each site.
The SDSLEOF reconstructions are then evaluated as spatial averages over all sites in each region. By using varying barystatic corrections and by considering randomly varied parameter choices, we produce 5,000 ensemble members that are used to assess uncertainties of the EOF reconstruction. The EOF approach has two major advantages compared to simple field averages over the source region as formerly used in refs. 22,23 While a simple area average assumes that the steric signal from the open ocean is one on one transferred toward the coast, there are factors at play that may dampen or amplify the signal while propagating from the open ocean toward the coast. The regression character of the EOF approach explicitly takes this into account and scales the signal to match the variability seen at tide gauges. Furthermore, EOF analysis decomposes a field into common modes. As typical for many other atmospheric or oceanographic time series, most of the variance of the entire field is contained in the first few modes, while local effects move as noise into lower EOFs. Thus, the EOF approach is robust against local outliers. To test the stability of the EOF reconstruction against increasing data uncertainties in the steric products before the 1980s, we also calculated a second 5,000-member ensemble on the basis of PCs calculated since solely 1980 (Extended Data Fig. 7). We do not find any significant differences in the reconstructions based on PCs calculated over the entire period or only since 1980. Correlations are, in all cases, >0.98 with the only exception being the three western boundary currents where the correlation coefficients are between 0.92 and 0.94. The trends are also not significantly different between the two ensembles (Extended Data Fig. 7b).
Earth system models
To test the performance of the EOF technique, we apply it to the historical runs of 11 ESMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5) [75], which are all listed in Supplementary Table 2. As CMIP5 models usually have a horizontal resolution that barely exceeds one degree, we additionally included one eddy-permitting model (CNRM-CM6-1-HR; ref. 76) from the HighResMIP initiative. CNRM-CM6-1-HR has a resolution of 25 km, providing a more realistic representation of the coastal zone than its CMIP5 counterparts and many ocean reanalyses19. We decided to use ESMs rather than ocean reanalyses because the latter suffer from (regionally varying) drifts due to sparse data assimilation, uncertainties in air–sea fluxes and mixing errors19, while ESMs are entirely consistent without data assimilation. All simulations have been linearly de-drifted using the pre-industrial control run (PiControl). ESMs have the advantage of providing predescribed components of the sea-surface height (‘zos’), ocean-bottom pressure (‘pbl’) and global mean thermosteric sea-level changes (‘zostoga’). As the ESMs are volume- rather than mass-conserving, we sum zos and zostoga and subsequently subtract pbl to derive steric height from each model (one might also estimate steric height from temperature and salinity profiles in each model, which is, however, more time consuming). We sample coastal sea-level (zos + zostoga) at the grid points closest to the tide-gauge locations and perform a similar correlation analysis with steric height to identify the source regions. Then the EOF technique is applied in a similar fashion (with 1,000 randomly varied smoothing factors and mode-selection thresholds) as for observations. We compare the reconstruction to both the available 53-yr calibration periods as well as a randomly selected and independent validation period of 53 consecutive years that have not been used for calibration. There are three factors to keep in mind when using ESMs as a testbed for the EOF approach. First, the resolution of ESMs is, even in CNRM-CM6-1-HR, still too coarse to fully resolve coastal processes. Second, the model provides ‘perfect observations’ at each location without gaps and measurement errors. Third, we do not have corrections for barotropic wind forcing available for the ESMs as we apply for real observations. While the first two factors spatially smooth the observations and therefore tend to increase the covariance compared to real observations, the missing barotropic correction may lead to a slightly degraded performance in high latitude regions compared to reality.
Statistics
All correlations and regressions were performed after removing linear trends. Statistical significance and error estimates for the correlation analyses are computed using Fisher’s z-transform77. While the test does not account for temporal correlations in the data, it is much more time-efficient and leads to barely different source regions than with repeated simulations using autoregressive processes. Uncertainties of linear trends are calculated assuming that the residuals are temporally correlated following an autoregressive process of the order one. Nonlinear trends in the different budget components have been calculated by a singular spectrum analysis with an embedding dimension of ten using the MATLAB package from ref. 78.
Extended data
Extended Data Fig. 1: Performance of ocean reanalysis in simulating SDSL variability and trends. Shown are linear trends of SDSL as simulated by the a SODAsi.378, b SODA 2.2.480, c ORA S481, d ORA20C82,83, and e GECCO214 reanalysis over the common period from 1960 to 2012. For all reanalysis systems, the model internal global average has been replaced by ref. 24. In b and d, data is only available until 2008 and 2009, respectively. Grey dots show the 89 tide-gauge locations used in this study. f Linear trends in SDSLTG from the virtual stations of the nine coastal regions (grey bars) are compared to trends calculated from SDSL as simulated by the five ocean reanalysis systems (nearest-neighbour series). d, Correlations between detrended SDSLTG and SDSL from the five ocean reanalysis systems. The grey shadings separate the different regions from each other.
Extended Data Fig. 2: Tide-gauge coherence and virtual stations for each region. a, Cross-Correlation matrix for the 89 tide-gauge records ordered by region. Black boxes mark the locations of the selected tide-gauge records for each region. b, The observed tide-gauge records (corrected for vertical land motion; coloured lines) together with the virtual station for each region (thick black line) that has been built based on gap-filled records (see Methods). The percentage of total data availability in each region is given in brackets.
Extended Data Fig. 3: Origin of coastal SDSL changes. Spatial correlation patterns between the SDSL residuals at tide gauges (SDSLTG, grey dots) and steric height24 from the open ocean used to assemble Fig. 1a but for each of the nine coastal regions separately. Only significant correlations (P ≤ 0.05) are shown. a, North Sea, b NW Atlantic north of Cape Hatteras, c NW Atlantic south of Cape Hatteras, d NE Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.
Extended Data Fig. 4: Reconstruction of coastal SDSL changes. Extension of Fig. 2b illustrating the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR, bottom) for each of the nine coastal regions. a, North Sea, b Northwest Atlantic north of Cape Hatteras, c Northwest Atlantic south of Cape Hatteras, d Northeast Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.
Extended Data Fig. 5: Linear trends in steric height and comparison of different observational products. Shown are the linear trends in steric height calculated over the upper 2000m for different gridded observational products. a, ref. 24 and 67, b ref. 68, c EN469 with ref. 70 corrections, and d EN4 with ref. 71 corrections. The grey dots mark the locations of tide-gauge records used in this study. e, Linear trends for the SDSLEOF reconstructions in each region using the four different data products (grey bars = ref. 24 and67; blue = ref. 68; turquoise = EN469 with ref. 70 corrections; yellow = EN469 with ref. 71 corrections. f, Same as e but showing the correlation between SDSLEOF based on the different products and SDSLTG.
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
8e1a60b11d1e-7
|
Extended Data Fig. 3: Origin of coastal SDSL changes. Spatial correlation patterns between the SDSL residuals at tide gauges (SDSLTG, grey dots) and steric height24 from the open ocean used to assemble Fig. 1a but for each of the nine coastal regions separately. Only significant correlations (P ≤ 0.05) are shown. a, North Sea, b NW Atlantic north of Cape Hatteras, c NW Atlantic south of Cape Hatteras, d NE Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.
Extended Data Fig. 4: Reconstruction of coastal SDSL changes. Extension of Fig. 2b illustrating the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR, bottom) for each of the nine coastal regions. a, North Sea, b Northwest Atlantic north of Cape Hatteras, c Northwest Atlantic south of Cape Hatteras, d Northeast Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.
Extended Data Fig. 5: Linear trends in steric height and comparison of different observational products. Shown are the linear trends in steric height calculated over the upper 2000m for different gridded observational products. a, ref. 24 and 67, b ref. 68, c EN469 with ref. 70 corrections, and d EN4 with ref. 71 corrections. The grey dots mark the locations of tide-gauge records used in this study. e, Linear trends for the SDSLEOF reconstructions in each region using the four different data products (grey bars = ref. 24 and67; blue = ref. 68; turquoise = EN469 with ref. 70 corrections; yellow = EN469 with ref. 71 corrections. f, Same as e but showing the correlation between SDSLEOF based on the different products and SDSLTG.
Extended Data Fig. 6: Validation of the vertical land motion (VLM) correction. Comparison between observed trends (after the removal of barystatic gravitation, rotation and deformation terms) and residual VLM plus Glacial Isostatic Adjustment from the difference between tide gauges and the hybrid reconstruction from ref. 50 as well as the observed trends and residual VLM from Global Navigation Satellite System plus Glacial Isostatic Adjustment and the difference between tide-gauge and satellite altimetry as calculated by ref. 4 (Fred).
Extended Data Fig. 7: Validation of the EOF approach. a, Shown are the time series of SDSLEOF based on reconstructions using principal components that have been calculated and regressed on the steric height from the open-ocean over the entire 1960 to 2012 period (and as used in the main paper) as well as those based on principal components that have been calculated (and regressed on the steric height from the open-ocean) over the period from 1980–2012. The grey shading marks the corresponding validation period from 1960–1979. b, The corresponding linear trends of SDSLEOF over the common period from 1960–2012. Shadings and error bars represent the 95% confidence intervals.
|
https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html
|
9435f63cacce-0
|
Chen and Tung (2018)
Title:
Global surface warming enhanced by weak Atlantic overturning circulation
Key Points:
The role of AMOC has shifted its primary role from transporting surface heat northwards to storing heat in the deeper Atlantic, thereby buffering global surface warming.
During an accelerating phase from the mid-1990s to the early 2000s, the AMOC stored about half of the global excess heat, contributing to a slowdown in global warming.
Changes in the AMOC since the 1940s are best explained by multidecadal variability, rather than a trend forced by human activities.
Recently, the AMOC and oceanic heat uptake have weakened, suggesting a period of rapid global surface warming.
Keywords:
Atlantic meridional overturning circulation, Global surface warming, Ocean heat storage, Multidecadal variability, Climate change, Oceanic heat uptake
Corresponding author:
Ka-Kit Tung
Citation:
Chen, X., & Tung, K.-K. (2018). Global surface warming enhanced by weak Atlantic overturning circulation. Nature, 559(7714), 1–14. doi:10.1038/s41586-018-0320-y
URL:
https://www.nature.com/articles/s41586-018-0320-y
Abstract
Evidence from palaeoclimatology suggests that abrupt Northern Hemisphere cold events are linked to weakening of the Atlantic Meridional Overturning Circulation (AMOC) [1], potentially by excess inputs of fresh water [2]. But these insights — often derived from model runs under preindustrial conditions — may not apply to the modern era with our rapid emissions of greenhouse gases. If they do, then a weakened AMOC, as in 1975–1998, should have led to Northern Hemisphere cooling. Here we show that, instead, the AMOC minimum was a period of rapid surface warming. More generally, in the presence of greenhouse-gas heating, the AMOC’s dominant role changed from transporting surface heat northwards, warming Europe and North America, to storing heat in the deeper Atlantic, buffering surface warming for the planet as a whole. During an accelerating phase from the mid-1990s to the early 2000s, the AMOC stored about half of excess heat globally, contributing to the global-warming slowdown. By contrast, since mooring observations began [3,4,5] in 2004, the AMOC and oceanic heat uptake have weakened. Our results, based on several independent indices, show that AMOC changes since the 1940s are best explained by multidecadal variability [6], rather than an anthropogenically forced trend. Leading indicators in the subpolar North Atlantic today suggest that the current AMOC decline is ending. We expect a prolonged AMOC minimum, probably lasting about two decades. If prior patterns hold, the resulting low levels of oceanic heat uptake will manifest as a period of rapid global surface warming.
Main
As an analogy of the flow of energy in our climate system, consider the filling of a bucket of water from a tap at the top. The feed rate of the tap is an analogue of the top-of-atmosphere radiative imbalance—the net heating—of our planet, with the water level in the bucket analogous to surface warming. The sink at the bucket bottom drains into a larger bucket below (the deeper oceans). If the drain rate is the same as the feed rate from the tap at the top, the water level in the bucket does not rise (hiatus of surface warming). If the drain is plugged, the water level will rise rapidly in the bucket (rapid surface warming). AMOC controls about half of the variation of this ‘drain rate’.
Figure 1 quantifies the energy budget of our climate system, using the subsurface ocean heat content (OHC) measured mostly by a system of autonomous profiling Argo floats, during a period, 2000–2014, when the ‘drain rate’ was large. The total OHC, as approximated by that in the upper 1,500 m of the oceans, is increasing at a rate of about 0.42 ± 0.02 W m−2, consistent with radiative imbalance7. The upper 200 m roughly corresponds to the mixed layer globally. Through wind and turbulent mixing, variations of sea surface temperature (SST) and mixed-layer OHC are highly statistically correlated (r = 0.82 in 13-month running mean). Figure 1 shows that both were in a warming slowdown for this period. Why the upper 200 m OHC was in a warming slowdown is clear: the increase in heat storage below 200 m, about 89 zettajoules (1 ZJ = 1021 J). This amount of heat is equivalent to 180 years of the world’s energy consumption at the current rate, and any future variation even within this observed range will have important consequences for the surface temperature.
Figure 1: Quantifying the global heat budget and the partition among ocean basins in the two periods 2000–2004 and 2005–2014. The SST from ERSST.v4 is shown as a black curve and the 0−200-m OHC from the ISHII and Scripps datasets (see Methods) is shown as an orange curve, showing that they co-vary and that both are in a warming slowdown, while the total OHC, as approximated by the 0−1,500-m OHC (red curve), is increasing at the regressed linear rate of 0.42 W m−2 (red dashed straight line). This excess heat from forcing is sequestered below 200 m. The orange-shaded region represents the additional amount of heat stored in the 200−1,500 m layer since 2000, about 89 ZJ. One zettajoule is equivalent to twice the world’s annual energy consumption. If this additional storage were absent, the upper 200 m would have increased at the rapid rate of the red curve. We adjusted the data for the Southern Ocean to remove a possible artefact due to the rapid transition from no-Argo to the Argo observing platform around 2002−200328. The inset shows the division of the 89 ZJ of global ocean increase in heat storage in the 200−1,500 m layer into the four ocean basins and two periods. 35° S marks the northern boundary of the Southern Ocean and the southern boundary of the Atlantic, Pacific and Indian oceans. The error bars are one-standard-deviation errors of the linear regression.
If the radiative imbalance and the heat storage below 200 m were to remain the same, the 0–1,500 m OHC would still increase at the same rate as the radiative imbalance, but the 0–200 m OHC curve would lie on the 0–1,500 m curve, increasing at the same rate, or about 0.23 °C per decade. Our best estimate for the next two decades, allowing for some increase in ocean storage, is 70% of that rate, at 0.16 °C per decade (see Methods), close to the 25-year trend of 0.177 °C per decade of the last rapid warming period in the twentieth century [8].
The inset of Figure 1 shows how the global increase in OHC storage between 200 m and 1,500 m are partitioned among the various oceans. The Pacific and the Indian oceans dominate the horizontal exchanges of heat in the upper 300 m [9,10], and the Atlantic and the Southern oceans dominate the vertical redistribution11. They accounted for about 70% of the global heat storage increase in the 200–1,500 m layer during 2000–2014, divided between the North Atlantic, which is dominant before 2005, and the Southern Ocean after 2005. The subsurface warming in the Southern Ocean started in 1993 according to the data available (see below), and was attributed to the southward displacement and intensification of the circumpolar jet [8], caused in large part by the Antarctic ozone hole [12]. The North Atlantic’s role appears to be cyclic on decadal timescales, with AMOC in an accelerating phase before 2005.
AMOC transports warm saline surface water found in the subtropical Atlantic to the subpolar Atlantic, where heat loss to the cold atmosphere increases its density. Aided by its high salinity it sinks and returns southward at depth. When AMOC is stronger (weaker), more (less) of the warm and saline water is found in the subpolar Atlantic, and subsequent sinking subducts more (less) heat there, as demonstrated in Figure 2. The contrast is dramatic between periods when AMOC is increasing and when it is decreasing. Why AMOC sometimes accelerates or declines is more complicated. It could be responding to external forcing, for example, such as the freshening of the subpolar waters from melting ice at the end of the Little Ice Age [13]. Or, AMOC could be part of a natural, multidecadal variability involving feedbacks between the density effect of salinity on deep convection in Labrador and the Nordic Seas, and the subsequent induced northward transport of surface salinity reinforcing the deep convection [14].
|
https://sealeveldocs.readthedocs.io/en/latest/chentung18.html
|
9435f63cacce-1
|
The inset of Figure 1 shows how the global increase in OHC storage between 200 m and 1,500 m are partitioned among the various oceans. The Pacific and the Indian oceans dominate the horizontal exchanges of heat in the upper 300 m [9,10], and the Atlantic and the Southern oceans dominate the vertical redistribution11. They accounted for about 70% of the global heat storage increase in the 200–1,500 m layer during 2000–2014, divided between the North Atlantic, which is dominant before 2005, and the Southern Ocean after 2005. The subsurface warming in the Southern Ocean started in 1993 according to the data available (see below), and was attributed to the southward displacement and intensification of the circumpolar jet [8], caused in large part by the Antarctic ozone hole [12]. The North Atlantic’s role appears to be cyclic on decadal timescales, with AMOC in an accelerating phase before 2005.
AMOC transports warm saline surface water found in the subtropical Atlantic to the subpolar Atlantic, where heat loss to the cold atmosphere increases its density. Aided by its high salinity it sinks and returns southward at depth. When AMOC is stronger (weaker), more (less) of the warm and saline water is found in the subpolar Atlantic, and subsequent sinking subducts more (less) heat there, as demonstrated in Figure 2. The contrast is dramatic between periods when AMOC is increasing and when it is decreasing. Why AMOC sometimes accelerates or declines is more complicated. It could be responding to external forcing, for example, such as the freshening of the subpolar waters from melting ice at the end of the Little Ice Age [13]. Or, AMOC could be part of a natural, multidecadal variability involving feedbacks between the density effect of salinity on deep convection in Labrador and the Nordic Seas, and the subsequent induced northward transport of surface salinity reinforcing the deep convection [14].
Fig. 2: The OHC linear trend in the Atlantic basin. The trend is zonally averaged over two periods, when AMOC is increasing (a) and decreasing (b). The two periods are chosen according to the observed AMOC trends in Fig. 3a. ISHII data are used in the first period and Scripps data are used in the second period. Stippling indicates areas of statistical significance at the 95% confidence level. The linear trend is unreliable in the Southern Ocean prior to 2005, and so that region is masked.
AMOC is commonly believed to be slowing on centennial timescales owing to global warming. The RAPID/MOCHA mooring array, deployed in 20043 off the coast of Florida to monitor AMOC, soon afterwards recorded its weakening4. The decadal decline, however, is ten times larger than the predicted forced response5, causing concerns about its long-term trend and possible deficiencies of the models used. Figure 3a, constructed from various independent proxies from 1945 to the present (see Extended Data Fig. 1 for unfiltered time series and Extended Data Fig. 2 for error bars), shows that it is dominated instead by reversing phases. The weakening AMOC, by 3.7 Sverdrups (Sv) since 2005 measured by the RAPID/MOCHA array, was actually preceded by an acceleration15,16. Altimetry data of sea-surface heights (SSH) available since 199317 were used to deduce18 via geostrophic balance that at 41° N AMOC sped up by 4 Sv from the early 1990s to 2005, consistent with Zhang’s subsurface fingerprint proxy6. We use multiple independent proxies to infer subpolar AMOC strength back in time to 1945. Many of the proxies used here have been validated by models: Zhang’s subsurface temperature fingerprint was highly coherent with AMOC strength6,19,20 at low frequencies in the model (GFDL CM2.1) at mid-latitudes. The subpolar gyre SST proxy21, and the upper ocean subpolar salinity proxy20 were also model-validated. Along with the long record of tide gauges along the east coast of the USA22, these proxies consistently indicate a period of low AMOC from the mid-1970s to the 1990s. The shading in Fig. 3 shows that this period coincided with a period of rapid surface warming. See also Extended Data Fig. 3 for the coincidence of Atlantic OHC change and global surface warming. See Methods for model–observation reconciliation.
Figure 3: AMOC and GSTA variations. a, Mid and subpolar latitude AMOC strength, as calculated at 41° N using altimetry measurements, from ref. 18 (red, two-year running mean, Sverdrup scale shown on the right); inferred from integrated subpolar salinity in 0–1,500 m and 45–65° N in the Atlantic as a proxy, using the ISHII (dark blue) and Scripps (purple) datasets, with a two-year running mean. The green curve is the subpolar salinity, similarly calculated but using EN4. The AMOC fingerprint6 (dark blue) and the accumulated sea-level index (turquoise) calculated from historical tide gauge measurements22 were smoothed with 10-year and 7-year low-pass filters, respectively, from their sources. The subpolar gyre SST index21 in orange is also a two-year running mean. See Methods for details. The inset shows RAPID-measured AMOC at 26° N. b, Shown are GSTA from HadCRUT4.6 (black), the nonlinear secular trend (close to the 100-year linear trend) (brown) and variation about the trend for timescales longer than decadal (multidecadal variability (MDV), red). The inset shows the SST spatial pattern associated with MDV obtained by regressing SST onto its time series. The blue curve is the smoothed version of GSTA obtained as the sum of the secular trend and MDV. The faint lines around the solid lines are from 100 ensemble members of the HadCRUT4.6, which assess the range of uncertainty of the data used in the solid lines.
We call AMOC+ (AMOC–) the phase when the AMOC strength is above (below) climatology (based on the subpolar salinity, which has a long record with no trend). The high (+) phase consists of two rapid subphases. The increasing subphase (AMOCup) started in 1993, from the low point in AMOC–, first slowly and then rapidly, peaking in 2005. It is then followed by a rapid decreasing subphase (AMOCdown) (2005 to the present) (Fig. 3a). At low values of overturning (AMOC–) the strength is relatively level even though there are short-term fluctuations, because a slower poleward transport of saline water from the tropical Atlantic makes it difficult to speed up the sinking in the subpolar North Atlantic except through slower processes: The surface water could slowly become more saline through the reduction of fresh water outflow from land glaciers and from the Arctic Ocean23. The northward transport of warm and saline water increased more rapidly since 1999, and started a negative feedback as the warm surface water increased glacier melt and freshwater outflow. The previous AMOCdown subphase of 1965–1974 started with the gradual freshening of the north Atlantic waters, as can be inferred from the decreasing salinity in the subpolar region, braking the AMOC. Incidentally, both SSH at 41° N and RAPID at 26° N showed a simultaneous, short-lived 30% drop in AMOC strength in 2009–20105, partially caused by an extreme negative episode of atmospheric North Atlantic Oscillation that affected the wind field5 over both areas.
Water masses in the subpolar and subtropical gyres are different and transports across gyre boundaries need not be continuous14. For vertical heat subduction, it is mainly the subpolar AMOC that is our focus in Fig. 3a. Signals from salinity proxies at the subpolar Atlantic have almost reached the previous low. The subpolar gyre SST has started to warm. The deep Labrador Sea density, which is known to lead by 7–10 years changes in wider basin AMOC15,16, has stopped declining since 2014 (Extended Data Fig. 4). The subtropical region is more prone to higher-frequency perturbations14, and the RAPID time series is experiencing its short-term oscillations (two so far) after the recovery from the large dip in 2010 so the decadal trend may be difficult to see. Nevertheless, it appears to have stabilized at that latitude. Previously, when AMOC reached its lowest AMOC– value after 1975, that level phase lasted two and a half decades. Although we have data only for one cycle, its observed non-sinusoidal pattern characterized by a prolonged flat minimum separated by steep peaks is as expected from the physical arguments presented above.
|
https://sealeveldocs.readthedocs.io/en/latest/chentung18.html
|
9435f63cacce-2
|
Water masses in the subpolar and subtropical gyres are different and transports across gyre boundaries need not be continuous14. For vertical heat subduction, it is mainly the subpolar AMOC that is our focus in Fig. 3a. Signals from salinity proxies at the subpolar Atlantic have almost reached the previous low. The subpolar gyre SST has started to warm. The deep Labrador Sea density, which is known to lead by 7–10 years changes in wider basin AMOC15,16, has stopped declining since 2014 (Extended Data Fig. 4). The subtropical region is more prone to higher-frequency perturbations14, and the RAPID time series is experiencing its short-term oscillations (two so far) after the recovery from the large dip in 2010 so the decadal trend may be difficult to see. Nevertheless, it appears to have stabilized at that latitude. Previously, when AMOC reached its lowest AMOC– value after 1975, that level phase lasted two and a half decades. Although we have data only for one cycle, its observed non-sinusoidal pattern characterized by a prolonged flat minimum separated by steep peaks is as expected from the physical arguments presented above.
The longer Global-mean Surface Temperature Anomaly (GSTA) record shown in Fig. 3b, together with its low-frequency variation24,25, consists of a secular trend and a multidecadal variability (MDV), defined to be on timescales that are decadal or longer. The spatial pattern associated with MDV (inset to Fig. 3b) has the pattern of an interhemispheric seesaw in the Atlantic, with the North Atlantic being the centre of action, consistent with model results26. When the MDV is increasing it doubles the GSTA warming rate over the 100-year trend of 0.08 K per decade, and is associated with a period of rapid warming in the late and also the early twentieth century. That secular trend of 0.08 K per decade, statistically significant at over 95% confidence level against a second-order autoregressive (AR(2)) red noise, has been attributed to the underlying anthropogenic global warming trend27. The regressed spatial pattern associated with the secular trend resembles the model-predicted response from greenhouse warming24,25. The MDV in the GSTA is related to the Atlantic Multidecadal Oscillation (AMO) (see Methods), the latter having a record extending back several hundred years.
The previous period of low overturning in the AMOC− phase, from 1975 to the 1990s, coincided with a period of rapid global warming at the surface. This is more than a coincidence because the energy budget involved can be quantified. We do not have reliable subsurface data for the period when the surface warming was rapid. However, the change from that period can be quantified so that an estimate can be made for what would happen if that change were absent. During 2000–2005, in the AMOCup subphase, 52% of the global increase between 200 m and 1,500 m is sequestered in the Atlantic. Together with the heat sequestrated in the Southern Ocean, it contributed to a period of global warming slowdown. When this additional heat storage is absent, a period of rapid surface warming is expected to reoccur.
Although the Argo programme was launched around 2000, its coverage in the Southern Ocean did not become adequate until 2005. To validate the data on OHC we compare satellite SSH* (the asterisk indicates the deviation of SSH from its global mean) available since 1993 (Fig. 4a and b) to the thermosteric sea level rise (due to thermal expansion of the water column) (Fig. 4c and d) calculated using OHC above 1,500 m. The comparison is surprisingly good north of 35° S. Notable exceptions are as expected; they include areas with no Argo measurements: shallow maritime areas west of the Caribbean islands, and the deep mid-Atlantic Ocean below 1,500 m, which was not included in our OHC. South of 35° S the linear trend in the Argo data is not reliable across 2003 during the transition from no-Argo to Argo measurements28. The two datasets consistently show that in the subpolar Atlantic there is increasing (decreasing) heat storage when AMOC is increasing (decreasing). The southward (northward) displacement of the Gulf Stream at mid-latitudes created some compensating cooling (warming)21. In the AMOC’s rapidly decreasing subphase, some heat is entrained in the subtropical gyre. The Southern Hemisphere north of 35° S is mostly featureless. South of 35° S, mesoscale patterns of warming can be seen in SSH*, which is also reflected in the OHC after 2004, but not before, owing to data quality. These mesoscale eddies in the linear trend occurring south of the Antarctic Circumpolar Current may be due to its recent strengthening, and its increased baroclinic instability [29].
Figure 4: Contrasting thermosteric SSH* patterns for increasing and decreasing AMOC. a, c, Linear SSH* trend when AMOC is increasing; b, d, Linear SSH* trend when AMOC is decreasing. a and b show SSH* from remote sensing, compared with the steric sea level calculated using OHC in c and d. SSH* is SSH with its global mean subtracted, reflecting mostly the thermosteric part of SSH (see Methods).
The increased sea level (Fig. 4b) and warmer SST (Extended Data Fig. 5d) in the western subtropical Atlantic may have led to strong hurricanes and their destructive power, and the surprising string of category-5 hurricanes making landfall towards the end of the decreasing phase of the AMOC, instead of at the peak of the AMOC, when the mean SST of the entire North Atlantic is the warmest and the basin-wide hurricane number is the highest30.
Climate-model runs under preindustrial conditions demonstrated the existence of multidecadal variation in AMOC, and its associated Atlantic SST variation: the AMOC+ (AMOC−) phase corresponds to warm (cold) SST and Northern Hemisphere mean surface temperature6,19. This prevailing paradigm has permeated popular perceptions about the future climate consequence of an AMOC weakened by global warming, similar to the abrupt switch back into icy conditions of the Younger Dryas during the last deglaciation2. Over the past few decades, however, there is a positive trend of warmer subsurface water in the subpolar Atlantic (Extended Data Fig. 6), rendering the mean state lighter (see the temperature–salinity diagram in Extended Data Fig. 7). Deep convections can now carry more heat downward. In the presence of greenhouse heating from above and warmer SSTs, AMOC’s role in sequestering heat becomes important in the current global surface energy budget (Fig. 1). When AMOC is more constant, as in the AMOC− phase, little additional heat is sequestered in the Atlantic, contributing to a more rapid surface warming as more heat from radiative imbalance remains on the surface and the upper 200 m of the global oceans. We note, however, that we have discussed here only one component of a complex system: global heat balance is maintained by the combined ocean and atmosphere systems and a change in the transport of one regional component may affect the partitioning of change between other parts of the ocean or of the atmosphere, depending on the timescales involved.
Methods
Updated AMOC indices
We reproduced the unfiltered monthly AMOC indices (Extended Data Fig. 1). Their correlation coefficient with Zhang’s unfiltered AMOC fingerprint is listed on the right. All correlations are statistically significant at over 95% confidence level.
AMOC indices in Fig.3a
Extended Data Fig. 1 shows that all unfiltered AMOC proxies used in Fig. 3a are correlated with Zhang’s fingerprint AMOC proxy at over 95% confidence level. Zhang showed20 that in the Geophysical Fluid Dynamics Laboratory model the fingerprint proxy is highly coherent with the model AMOC Index, defined as the zonal integrated maximum Atlantic overturning at 40° N, at decadal and multidecadal scales. This is the reason that the fingerprint is shown smoothed with a 10-year low-pass filter. This fingerprint is calculated using the detrended 400-m subsurface temperature. (It was updated to 2017 by the author with permission to use.)
Our subpolar upper ocean salinity index is defined as the average over 45°–65° N in the Atlantic basin and integrated over 0–1,500 m. The two undetrended salinity indices shown in Fig. 3 and Extended Data Fig. 1 are from three data sources. The first index is based on ISHII and Scripps. ISHII data have not been updated since 2012 and Scripps data are only available since 2004; they are connected at 2012 when calculating the correlation coefficient with Zhang’s fingerprint AMOC proxy. The data source for the second salinity index is from EN4 (version 4.2.1).
|
https://sealeveldocs.readthedocs.io/en/latest/chentung18.html
|
9435f63cacce-3
|
Methods
Updated AMOC indices
We reproduced the unfiltered monthly AMOC indices (Extended Data Fig. 1). Their correlation coefficient with Zhang’s unfiltered AMOC fingerprint is listed on the right. All correlations are statistically significant at over 95% confidence level.
AMOC indices in Fig.3a
Extended Data Fig. 1 shows that all unfiltered AMOC proxies used in Fig. 3a are correlated with Zhang’s fingerprint AMOC proxy at over 95% confidence level. Zhang showed20 that in the Geophysical Fluid Dynamics Laboratory model the fingerprint proxy is highly coherent with the model AMOC Index, defined as the zonal integrated maximum Atlantic overturning at 40° N, at decadal and multidecadal scales. This is the reason that the fingerprint is shown smoothed with a 10-year low-pass filter. This fingerprint is calculated using the detrended 400-m subsurface temperature. (It was updated to 2017 by the author with permission to use.)
Our subpolar upper ocean salinity index is defined as the average over 45°–65° N in the Atlantic basin and integrated over 0–1,500 m. The two undetrended salinity indices shown in Fig. 3 and Extended Data Fig. 1 are from three data sources. The first index is based on ISHII and Scripps. ISHII data have not been updated since 2012 and Scripps data are only available since 2004; they are connected at 2012 when calculating the correlation coefficient with Zhang’s fingerprint AMOC proxy. The data source for the second salinity index is from EN4 (version 4.2.1).
The sea-level index was obtained as in ref. 22 by calculating the sea-level difference between the average of a group of linearly detrended, deseasonalized tide-gauge measurements south of 35° N and that to the north. It is accumulated in time, shifted to the right by 4.8 years and smoothed with a 7-year lowpass filter.
The subpolar gyre SST index was obtained by ‘detrending’ the subpolar gyre SST by the subtraction of the global mean SST. It is averaged over the subpolar gyre region, defined by ref. 21.
Willis’ AMOC strength at 41° N was calculated [18] using altimetry SSH measurements and geostrophic approximation for the zonal-mean northward velocity vertically integrated above 1,130 m. It is not detrended or accumulated.
Error bars for data used in Fig. 3
The error bars for the salinity time series used in Fig. 3a are plotted in Extended Data Fig. 2. The uncertainty at each gridpoint is provided by each data source: ISHII, Scripps and EN4. The error bar of the salinity time series at each time is computed as the combination of the gridpoint uncertainty and one standard deviation due to the averaging in space. The uncertainty of the SSH-deduced AMOC strength was given by ref. 18. The measurement and sampling errors at each time gridpoint were ±12%. The uncertainty of tide-gauge data was discussed by ref. 22, and that of Zhang’s fingerprint proxy by ref. 30. The uncertainty of the global surface temperature data from HadCRUT4.6 was assessed by the data source using 100 ensemble members that span the uncertainty range of the data.
Calculation of warming scenarios
We emphasize that this is not a prediction, but a scenario calculation. In our current climate system, the OHC in the upper 1,500 m of the global oceans increases at the rate of 0.42 W m−2, which is approximately the top-of-atmosphere radiative imbalance. Apart from short-term variations of radiative imbalance such as those due to volcanic eruptions, it is reasonable to assume that for the next two decades there will not be an appreciable change in radiative imbalance, barring an unexpected development of carbon sequestration technology.
Scenario 1
If the OHC storage below 200 m remains the same (no increases), then the radiative imbalance of the 0.42 W m−2 heats only the top 200 m of the global oceans. That is, the increase of OHC in the top 200 m of the oceans is responsible for the increase in the entire 1,500 m of the column. The top 200 m of the global ocean then warms at the rate calculated as: 0.42 W m−2 divided by the heat capacity of 200 m of the ocean = 0.23 °C per decade. This is equivalent to that obtained for a ‘slab’ ocean of 200 m thick.
Scenario 2
As for Scenario 1 except that only the Atlantic and the Southern oceans’ heat content below 200 m remain the same for the next two decades. The Pacific and the Indian oceans continue to increase their OHC at the current rate. The warming rate is 70% of that for Scenario 1 because at present the Atlantic and the Southern oceans together are responsible for 70% of the OHC increase in the upper 1,500 m of the oceans. This is probably the more likely scenario because we have argued in the main text that AMOC is likely to remain relatively constant during the next two decades. The subsurface Southern Ocean has been warming since at least 1993, caused by the southward displacement and intensification of the westerly jet, which cannot continue much longer, first because the proposed cause (the ozone hole) has diminished in importance as the ozone hole heals, and second because there is not much more room for the jet’s southward displacement. So the increase in warming will probably stop.
Model AMOC and reconciliation with recent observations
Observational results in Fig. 3a show that there was a positive trend from 1993 to 1999, with a small peak in 1996. The rapid rising trend from 1999 to 2005 is statistically significant at the over 95% confidence level. This is seen in all proxies, most clearly in the less smoothed data (SSH and subpolar salinity). This claim is supported by observation of SSH-deduced AMOC strength, tide-gauges, the subpolar salinity proxy, and also the Zhang fingerprint proxy. (The last proxy, because of 10-year smoothing, does not show the smaller peak in the mid-1990s). A model reanalysis also showed an acceleration prior to 2005 followed by a decline at 26° N, and a peak in the mid-1990s as well as one in 2005 at 45° N16. AMOC in models is sensitive to resolution and subgrid parameterization31, resulting in little consensus among reanalysis (and hindcast) products. With one exception16 these products do not agree with the RAPID observation at 26° N. The exception is the GloSea5 model, which has a higher, eddy-permitting resolution than previous reanalyses. Supplementary figure 1 of ref. 16 shows two peaks, one at 1995 and one at 2005. The 1995 peak is slightly higher than the 2005 peak, and is referred to thus in the main text of ref. 16: “The AMOC at 45° N is representative of the changes in the subpolar gyre, with the AMOC decreasing from a maximum in the mid-1990s, followed by a slight increase (Fig. 1d)”. The peak in 2005 was not mentioned. However, the result on the 1995 peak should be treated with care, as the authors themselves stated in the supplementary information of ref. 16: “It is likely that there will be a period of spinup, where the deep ocean (where there are few observational constraints) adjusts, which may explain the divergence in trend. Hence we disregard the first few years of each experiment. There is also a shock in 1992 when the altimeter data is introduced, which may contribute to the increase in AMOC strength between 1989 and 1995. Hence we choose the period to analyse starting from January 1995, and join the two analyses in January 2002.” The relative magnitude of the 1995 peak and the 2005 peak may be unreliable as it was obtained by joining two reanalyses, one starting from 1989 and one from 1995 with “divergence in trend”16.
The observed SSH data since 1992 can be used to deduce AMOC strength using geostrophic approximation, bypassing the problems of shock and subsequent adjustment when the same SSH data were introduced in model assimilation.
SST changes during different phases of AMOC
|
https://sealeveldocs.readthedocs.io/en/latest/chentung18.html
|
9435f63cacce-4
|
The observed SSH data since 1992 can be used to deduce AMOC strength using geostrophic approximation, bypassing the problems of shock and subsequent adjustment when the same SSH data were introduced in model assimilation.
SST changes during different phases of AMOC
The upper branch of the climatological AMOC brings warm and saline surface water from the subtropical North Atlantic to its subpolar latitudes. When the overturning is stronger, more of this warm water is found in the subpolar northern latitudes. In the Southern Hemisphere, more of the cold water from the region of the Antarctic Circumpolar Current is brought northward into the Southern subtropics. Consequently a characteristic signature in the Atlantic SST is an opposite-signed multidecadal anomaly, with warming to the north and smaller cooling to the south when the overturning is stronger (AMOC+), and the reverse pattern when it is weaker (AMOC–) (Extended Data Fig. 5a, b). This ocean-induced SST variability is centered in the subpolar North Atlantic20. The observed tendency during the last two subphases of the AMOC is as expected (Extended Data Fig. 5c, d): As AMOC slows after 2005, the SST tends towards a cooler North Atlantic and warmer subtropics. Accompanying the strong cooling in the subpolar gyre is an interesting intense warming after 2005 in the northwest Atlantic, centered in the Gulf of Main, which was recently simulated in a high-resolution climate model32 as due to the northward displacement of the Gulf Stream when AMOC slows. The inverse relationship between Gulf Stream’s northward displacement and AMOC strength was found6 to be caused by the Labrador Current retreat and the bottom vortex stretching33.
AMO
In long coupled atmosphere–ocean model runs under preindustrial conditions (without increasing greenhouse gases) the AMO is the SST manifestation of AMOC variations, and the two time series are approximately in phase19. The definition of AMO in ref. 19 is the mean of Atlantic SST north of 45° N, which may lead the subtropical SST anomaly by two years. A more traditional definition of AMO is the mean Atlantic SST north of the Equator34, with an approximately one-year phase difference. It has been shown24, using the space-time perspective of rotated empirical orthogonal function analysis, that the AMO is mainly responsible for the observed global mean surface temperature variation on multidecadal timescales. The two are in phase during the industrial era. Since the AMOC and the global mean surface temperature variation are not in phase (as shown in Fig. 3), it follows that during the industrial era, AMOC and AMO are off phase, possibly by a quarter cycle, although AMOC’s time series is too short for an accurate determination of the phase information.
During the positive phase of AMO, SST is warm in the North Atlantic and surrounding continents. Therefore, Northern Hemisphere mean surface temperature is warm during the positive phase and cool during the negative phase of the AMO. Using multiproxy data in the Northern Hemisphere the AMO time series can be extended back several hundred years35. The longest instrumental temperature record exists in central England, and it was used27 to reconstruct the AMO timeseries back to the Little Ice Ages. An even longer record of ice cores in Greenland, in the northern Atlantic, exists, and a statistically significant at the over 95% confidence level AMO signal can be found36 extending back to 800 AD that is coherent with the instrumental record of central England27 during their overlapping period. It appears that AMO is a recurrent phenomenon of period around 65–70 years and that it is robust in the preindustrial era, with the Atlantic and the surrounding areas warm during the positive phase and cold during the negative phase. From climate model preindustrial control runs, it seems that AMO is a surface manifestation of AMOC variation. Furthermore, based on palaeoclimate evidence of cold events when AMOC slows down abruptly, a common perception is that a slowdown in AMOC would lead to a cold Northern Hemisphere. The mechanism relies on the dominant role of AMOC (and its Gulf Stream) in horizontally transporting surface heat from the tropics to the mid- and high-latitude Atlantic, where it releases some heat to the cold atmosphere before sinking in the subpolar Atlantic. The heat released to the atmosphere makes Europe warmer (when wind blows in that direction) than it should be for its latitude.
Calculating SSH* from altimetry data
SSH* is SSH with its global mean subtracted. SSH contains both the thermosteric part (due to thermal expansion of the entire water column) and the ocean water mass addition that is due to melting land ice. It is known that the ocean will adjust to any change in ocean mass rapidly through the propagation of gravity waves, and will reach a new equilibrium globally within a couple of months37. Therefore, the subtraction of the global mean largely removes the mass contribution from SSH.
Extended data figures and tables
Extended Data Fig. 1: Unfiltered AMOC proxy time series in monthly resolution. The thick solid lines are 13-month running means. The numbers to the right of each time series show the correlation coefficient with the unfiltered AMOC subsurface temperature fingerprint of Zhang. Data are taken from refs 20,21,22. All of the correlation coefficients are above 95% confidence level. The accumulated sea-level index is shifted to the right by 4.8 years in this figure. Without the time shift, its correlation with the AMOC proxy is practically zero (r = 0.06).
Extended Data Fig. 2: Error bars for the three salinity time series shown in Fig. 1. The colour lines are monthly values of uncertainty, superimposed on the 13-month means of the time series. psu, practical salinity units.
Extended Data Fig. 3: Coincidence of the three AMOC phases with global warming slowdown and acceleration. a, Global mean surface temperature. b, OHC north of 45° N in the Atlantic. c, Salinity north of 45° N in the Atlantic.
Extended Data Fig. 4: Deep Labrador Sea density. Average density in the 1,000–1,500 m layer of the Labrador Sea, regionally averaged over the ocean area shown in the inset, from the three data sources given. A leading signal for stronger AMOC is the increased deep Labrador Sea salinity (and hence density). The signal propagates southward along the western boundary at depth, changing the cross-basin zonal gradient, and hence the geostrophic southward velocity13. The return flow then strengthens the upper branch of AMOC with a lag of 7–10 years15,16.
Extended Data Fig. 5: SST patterns during different AMOC phases. a, When AMOC is below climatology. b, When AMOC is above climatology, SST detrended. c, SST linear trend when AMOC is increasing. d, When AMOC is decreasing.
Extended Data Fig. 6: Linear trends, from 1950 to 2017, of temperature, salinity and density. a–c, Trends in temperature (a), salinity (b) and density (c) as a function of depth. Solid curves indicate where the trend is statistically significant at 95% confidence level.
Extended Data Fig. 7: Temperature–salinity diagram. The subpolar Atlantic Ocean (45°–65° N) for each depth between 300 m and 1,500 m for the two periods, with the mean of 2000–2016 in red and the mean of 1920–1940 in blue. The dots shown are the five winter month values (NDJFM). At these depths the seasonal cycle is very small [38].
|
https://sealeveldocs.readthedocs.io/en/latest/chentung18.html
|
e85a386fd775-0
|
Zika et al. (2021)
Title:
Recent Water Mass Changes Reveal Mechanisms of Ocean Warming
Corresponding author:
Zika
Citation:
Zika, J. D., Gregory, J. M., McDonagh, E. L., Marzocchi, A., & Clement, L. (2021). Recent Water Mass Changes Reveal Mechanisms of Ocean Warming. Journal of Climate, 34(9), 3461-3479. doi: 10.1175/jcli-d-20-0355.1
Keywords:
Ocean, Water masses/storage, Climate change, Heat budgets/fluxes, Climate variability, Trends
Abstract
Over 90% of the buildup of additional heat in the Earth system over recent decades is contained in the ocean. Since 2006, new observational programs have revealed heterogeneous patterns of ocean heat content change. It is unclear how much of this heterogeneity is due to heat being added to and mixed within the ocean leading to material changes in water mass properties or is due to changes in circulation that redistribute existing water masses. Here we present a novel diagnosis of the “material” and “redistributed” contributions to regional heat content change between 2006 and 2017 that is based on a new “minimum transformation method” informed by both water mass transformation and optimal transportation theory. We show that material warming has large spatial coherence. The material change tends to be smaller than the redistributed change at any geographical location; however, it sums globally to the net warming of the ocean, whereas the redistributed component sums, by design, to zero. Material warming is robust over the time period of this analysis, whereas the redistributed signal only emerges from the variability in a few regions. In the North Atlantic Ocean, water mass changes indicate substantial material warming while redistribution cools the subpolar region as a result of a slowdown in the meridional overturning circulation. Warming in the Southern Ocean is explained by material warming and by anomalous southward heat transport of 118 ± 50 TW through redistribution. Our results suggest that near-term projections of ocean heat content change and therefore sea level change will hinge on understanding and predicting changes in ocean redistribution.
Introduction
Over the past 50 years, as atmospheric greenhouse gas concentrations have increased, the ocean has absorbed more than 10 times as much heat as all other components of the climate system combined (Rhein et al. 2013). This warming showed substantial spatial variability between 1993 and 2005, being up to 10 times as much in some regions as the global average (Zhang and Church 2012). It is unclear whether this variability is due to geographical variation in the interior propagation of surface warming versus redistribution of existing heat within the ocean.
Ocean warming is an important issue because ocean thermal expansion is the largest projected contribution to global mean sea level rise in the twenty-first century (Church et al. 2013). Numerical climate models disagree on the pattern and amplitude of ocean heat content (OHC) change and hence on sea level rise under anthropogenic greenhouse warming (Gregory et al. 2016). Understanding how heat has been taken up and redistributed by the ocean is essential for predicting future changes in sea level.
Numerical ocean models forced with historical atmospheric conditions have proved to be useful tools in quantifying how variability in atmospheric forcing can set variability in OHC (Drijfhout et al. 2014) and sea level (Penduff et al. 2011) at interannual to decadal time scales. However, such models can be unrealistic for simulating multidecadal climate change because of model drift and inaccuracies in long-term changes in atmospheric forcing, particularly global mean heat fluxes (GrifÞes et al. 2009). On the other hand, coupled ocean atmosphere climate models are routinely used to capture the effect of long-term climate forcing. But such models only accurately simulate past unforced variability in regional OHC when, by chance, their internal variability is in phase with the observed system.
An advance in terms of numerical ocean climate modeling has come from the separation of OHC change into an “added” and a “redistributed” component in climate model simulations, where the former is due to change in the surface heat flux, and the latter due to rearrangement of existing OHC because of altered ocean heat transports (Banks and Gregory 2006). This decomposition is analogous to the “anthropogenic” and “natural” decomposition that has revolutionized our under standing of oceanic carbon records (Khatiwala et al. 2013). Here we will present a novel method to diagnose the “material” component of OHC change, which we will show is closely related to the “added” component introduced by Banks and Gregory (2006).
Recent work has aimed to reconstruct the drivers of OHC change based on observationally derived airÐsea boundary conditions. Zanna et al. (2019) for example used surface temperature anomalies combined with a tracer-based approach to reconstruct the role of anomalous surface heat fluxes in centennial heat content change. Roberts et al. (2017) estimated the contribution of airÐsea heat flux changes in setting mixed layer and full-depth-integrated OHC budgets over recent decades and inferred the role of ocean circulation as a residual. Here we aim to circumvent reliance on such boundary conditions and infer the mechanisms of ocean heat content change directly based on water mass changes.
Water mass-based methods have been used to decompose local temperature and salinity changes into a dynamic “heave” component and an apparently material component at constant density based on a one-dimensional view of the water column (Bindoff and McDougall 1994). However, their analysis did not distinguish between material processes and horizontal advection, insofar as they affect the water mass properties of an individual water column.
Here we introduce a new method based on water mass theory, called the minimum transformation method, which we use to estimate recent drivers of three-dimensional OHC change. In section 2 we will review water mass theory and establish the relationship between changes in water masses as deÞned by their temperature and salinity and material changes in seawater temperature. We will describe in section 3 how this theory is translated into a practical method to estimate material changes in water masses and map these into geographical space. We present an application of this minimum transformation method to recent data over the Argo period in section 4 and give results in section 5. We discuss the results and compare them with existing work in section 6, and we give conclusions in section 7.
Water mass theory
Water mass analysis has long been used in physical oceanography to trace the origin of waters (Montgomery 1958). In the latter half of the twentieth century a quantitative framework emerged to describe the relationship between water masses, airÐsea fluxes, and mixing [Walin 1982; see the review by Groeskamp et al. (2019)]. Recent work has seen this framework advanced in two ways specifically relevant to our work here: to multiple tracer dimensions to understand the thermodynamics of ocean circulation (Nycander et al. 2007; Zika et al. 2012; Doos et al. 2012; Groeskamp et al. 2014; Hieronymus et al. 2014) and to unsteady problems to understand the oceanÕs role in transient climate change (Palmer and Haines 2009; Evans et al. 2014; Zika et al. 2015a,b; Evans et al. 2017, 2018).
An example of the utility of the water mass transformation framework in understanding transient change is provided by Zika et al. (2015a). They demonstrate that the distribution of water in salinity coordinates is influenced by the water cycle and turbulent mixing, the latter only being able to collapse the range of salinities the ocean covers. This means that changes in the width of the salinity distribution indicate an enhancement of the water cycle and/or a reduction in that rate at which salt is mixed. In this project we extend this concept to consider how changes in the temperature-salinity distribution relate to material changes in water masses.
Material changes in Conservative Temperature Theta (hereinafter simply “temperature” or T) following the motion of an incompressible fluid are related to Eulerian changes and advection by
frac{DT}{Dt} = frac{partial T}{partial t} + bf{u} cdot nabla{T}, (1)
where bf{u} is the 3D velocity vector and frac{DT}{Dt} is the material derivative, which is related to sources and sinks of heat and irreversible mixing. Conservative Temperature is used here since it is a more accurate “heat” variable than potential temperature (McDougall 2003), although the later is still routinely used in ocean models, including the one analyzed in section a of appendix A.
Even if a perfect record of frac{partial T}{partial t} were available at a fixed location, we would not know the relative roles of advection (bf{u} cdot nabla{T}) and material processes (frac{DT}{Dt}). To separate them, we consider the water mass perspective as an alternative to the Eulerian perspective. The following theory draws directly from Hieronymus et al. (2014).
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-1
|
An example of the utility of the water mass transformation framework in understanding transient change is provided by Zika et al. (2015a). They demonstrate that the distribution of water in salinity coordinates is influenced by the water cycle and turbulent mixing, the latter only being able to collapse the range of salinities the ocean covers. This means that changes in the width of the salinity distribution indicate an enhancement of the water cycle and/or a reduction in that rate at which salt is mixed. In this project we extend this concept to consider how changes in the temperature-salinity distribution relate to material changes in water masses.
Material changes in Conservative Temperature Theta (hereinafter simply “temperature” or T) following the motion of an incompressible fluid are related to Eulerian changes and advection by
frac{DT}{Dt} = frac{partial T}{partial t} + bf{u} cdot nabla{T}, (1)
where bf{u} is the 3D velocity vector and frac{DT}{Dt} is the material derivative, which is related to sources and sinks of heat and irreversible mixing. Conservative Temperature is used here since it is a more accurate “heat” variable than potential temperature (McDougall 2003), although the later is still routinely used in ocean models, including the one analyzed in section a of appendix A.
Even if a perfect record of frac{partial T}{partial t} were available at a fixed location, we would not know the relative roles of advection (bf{u} cdot nabla{T}) and material processes (frac{DT}{Dt}). To separate them, we consider the water mass perspective as an alternative to the Eulerian perspective. The following theory draws directly from Hieronymus et al. (2014).
We characterize water masses by their T and Absolute Salinity S_A (IOC/SCOR/IAPSO 2010; hereinafter simply “salinity” or S). The volume v of water per unit temperature and salinity and at temperature T^* and salinity S^* is
v(T^*, S^*) = frac{partial^2}{partial T partial S} int_{T<T^*, S<S^*}dV, (2)
where the integral is over elements dV of ocean volume that are cooler than T^* and fresher than S^*. An estimate of v that is based on recent observational analysis is given in Fig. 1a. (These data are described in detail in section 4.)
Figure 1: Portrait of changing ocean water masses: (a) inventory of ocean volume in Conservative Temperature vs Absolute Salinity coordinates (mean of 2006-17 inclusive) and (b) change in water mass volume between the early half and late half of the period divided by the six years (Sv). According to water mass theory, changes in air-sea heat and freshwater fluxes and/or changes in rates of diffusion are required for these changes to occur.
Considering all of the water in the ocean and retaining the incompressibility assumption, the only way v can change is via transformation - that is, by making water parcels warmer, colder, saltier, or fresher as described by the following continuity equation [derived formally in Hieronymus et al. (2014)]:
frac{partial v}{partial t} + frac{partial}{partial T} (v dot{T}) + frac{partial}{partial S} (v dot{S}) = 0, (3)
where dot{T} is the average material derivative of T within a water mass. That is,
dot{T}(T^*, S^*) = frac{1}{v} frac{partial^2}{partial T partial S} int_{T<T^*, S<S^*}frac{DT}{Dt} dV, (4)
and likewise dot{S} is the average material derivative of S. An estimate of recent changes in v is given in Figure 1b.
In Eq. (3) the terms vdot{T} and vdot{S} are the transformation rates in the temperature direction (Sv g^{-1} kg^{-1}; 1 Sv = 10^6 m^3 s^{-1}) and salinity direction (Sv C˚^{-1}) respectively. Equation (3) states that the amount of water between two closely spaced isotherms (T and T + partial T) and isohalines (S and S + partial S) will go up if more water is made warmer at T than at T + partial T and/or more water is made saltier at S than at S + partial S.
When the system is in a statistically steady state the water mass distribution v remains constant such that
frac{partial}{partial T} overline{v dot{T}} + frac{partial}{partial S} overline{v dot{S}} = 0, (5)
where the overbar represents a sufficiently long time average. In this steady case, the vector field described by overline{v dot{T}} and overline{v dot{S}} can be characterized by a thermohaline streamfunction (Zika et al. 2012; Groeskamp et al. 2014).
Here, we will not attempt to estimate this steady-state component of water mass transformation [e.g., as Groeskamp et al. (2017) have done]. Rather we will attempt to quantify only the component required to explain changes in v. That is, we aim to quantify the anomaly in the transformation rate (v dot{T})’ such that v dot{T} = overline{v dot{T}} + (v dot{T})’, and likewise for (v dot{S})’, with
frac{partial v}{partial t} + frac{partial}{partial T} (v dot{T})’ + frac{partial}{partial S} (v dot{S})’ = 0, (6)
Note that a steady-state component like Eq. (5) can always be added to (v dot{T})’ and (v dot{S})’ such that Eq. (6) is still satisfied. Hwever, we seek only the net change in water mass transformation required to explain changes in v and therefore seek the smallest (in a root-mean-square sense) values of dot{T}’ and dot{S}’ that satisfy Eq. (6). That is, we seek the smallest change in air-sea heat and freshwater fluxes and mixing - in a net sense - that can explain changes in water masses. We call this the minimum transformation.
Here we will use changes in v to infer the minimum transformation and therefore estimate v dot{T}’. This will allow us to estimate the material processes influencing ocean temperature change.
The minimum transformation method
We now apply water mass theory to understand changes in a discrete set of water masses describing the ocean over two time periods. We will then describe the application of a minimum transformation method that exploits an “earth moverÕs distance” (EMD) algorithm to estimate the amount of material warming required to affect changes in those water masses.
Discrete water masses
Consider the set of N discrete water masses with the ith water mass defined by the limits [T_i^{min}, S_i^{min}, mathbf{x}_i^{min}] and [T_i^{max}, S_i^{max}, mathbf{x}_i^{max}]. Essentially, our water masses are hypercubes in TÐSÐxÐyÐz space (more arbitrary space-and tim-dependent regions can be defined without affecting the method described below). To indicate whether water is within the ith water mass we define a boxcar function Pi_i such that
begin{equation}
Pi_i(mathbf{x}, t) = begin{cases}1, & T_i^{min} leq T(mathbf{x}, t) < T_i^{max}, S_i^{min} leq S(mathbf{x}, t) < S_i^{max} text{and} mathbf{x}_i^{min} leq mathbf{x} < mathbf{x}_i^{max}\
0, & text{otherwise}. end{cases}
end{equation}
The volume of water in the ith water mass at time t is then iiint{Pi_i(mathbf{x}, t) dV}.
We consider two time periods: an early period (t_0 - Delta t leq t < t_0) and a late period (t_0 leq t < t_0 + Delta t). The average volume of the ith water mass over the early period is V1_i and the average volume of the jth water mass over the late period is V2_j such that
V1_i = frac{1}{Delta t} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) dV dt
and
V2_j = frac{1}{Delta t} int_{t_0}^{t_0 + Delta t} iiint Pi_i(mathbf{x}, t) dV dt, (8)
and the average temperature and salinity of water within V1_i is
T1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) T(mathbf{x}, t) dV dt
and
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-2
|
Discrete water masses
Consider the set of N discrete water masses with the ith water mass defined by the limits [T_i^{min}, S_i^{min}, mathbf{x}_i^{min}] and [T_i^{max}, S_i^{max}, mathbf{x}_i^{max}]. Essentially, our water masses are hypercubes in TÐSÐxÐyÐz space (more arbitrary space-and tim-dependent regions can be defined without affecting the method described below). To indicate whether water is within the ith water mass we define a boxcar function Pi_i such that
begin{equation}
Pi_i(mathbf{x}, t) = begin{cases}1, & T_i^{min} leq T(mathbf{x}, t) < T_i^{max}, S_i^{min} leq S(mathbf{x}, t) < S_i^{max} text{and} mathbf{x}_i^{min} leq mathbf{x} < mathbf{x}_i^{max}\
0, & text{otherwise}. end{cases}
end{equation}
The volume of water in the ith water mass at time t is then iiint{Pi_i(mathbf{x}, t) dV}.
We consider two time periods: an early period (t_0 - Delta t leq t < t_0) and a late period (t_0 leq t < t_0 + Delta t). The average volume of the ith water mass over the early period is V1_i and the average volume of the jth water mass over the late period is V2_j such that
V1_i = frac{1}{Delta t} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) dV dt
and
V2_j = frac{1}{Delta t} int_{t_0}^{t_0 + Delta t} iiint Pi_i(mathbf{x}, t) dV dt, (8)
and the average temperature and salinity of water within V1_i is
T1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) T(mathbf{x}, t) dV dt
and
S1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) S(mathbf{x}, t) dV dt, (9)
respectively; likewise for V2_j we have
T2_j = frac{1}{Delta t V2_j} int_{t_0}^{t_0 + Delta t} iiint Pi_j(mathbf{x}, t) T(mathbf{x}, t) dV dt
and
S2_j = frac{1}{Delta t V2_j} int_{t_0}^{t_0 + Delta t} iiint Pi_j(mathbf{x}, t) S(mathbf{x}, t) dV dt. (10)
To change the set of volumes V1_i into the set of volumes V2_j requires a transformation of water in T-S space. When water transforms, it changes its T and S and can also move geographically.
To understand how water is transformed from the physical location and physical properties of one water mass to another we use the shorthand tilde{x}(t+Delta t | mathbf{x}, t) for the position of a water parcel at time t + Delta t conditional on it previously being at position mathbf{x} at time t. That is,
tilde{x}(t+Delta t | mathbf{x}, t) = mathbf{x} + int_t^{t+Delta t} mathbf{u}[tilde{x}(t^* | mathbf{x}, t), t^*] dt^*, (11)
where, as previously, mathbf{u} is the 3D velocity vector. We describe the transformation rate between the early and late water masses with the matrix mathbf{g}. The ith column and jth row of this matrix g_{ij} correspond to the average rate of transformation of water from early water mass i to late water mass j such that
g_{ij} = frac{1}{Delta t^2} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t]dV dt. (12)
In Eq. (12) the term Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t] isolates water that was in the ith water mass at time t and was subsequently in the jth water mass at some time Delta t later. The quantity g_{ij} is therefore the average rate (m^3 s^{-1}) at which water in the ith early water mass is transformed into the jth late water mass.
Since the total volume of water is conserved between the early and late periods all the water from the early water masses (V1_i) must be transformed into late water masses. Likewise, all water masses from the late period (V2_j) are made from water masses of the early period. That is,
V1_i = Delta t sum_{j=1}^N g_{ij}
and
V2_j = Delta t sum_{i=1}^N g_{ij}. (13)
The average temperature change of water that transforms from V1_i to V2_j is then
Delta T_{ij} = frac{1}{Delta t^2 g_{ij}} int_{t_0-Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t]{T[tilde{x}(t + Delta t | mathbf{x}, t),t]-T(mathbf{x}, t)} dV dt, (14)
where the temperature change of individual parcel is related to the Lagrangian derivative by
T[tilde{x}(t + Delta t | mathbf{x}, t),t] - T(mathbf{x}, t) = int_t^{t + Delta t} frac{DT}{Dt}[tilde{x}(t^*|mathbf{x},t),t^*]dt^*. (15)
We can write Eq. (14) as
Delta T_{ij} = mathcal{T}2_{ji} - mathcal{T}1_{ij}, (16)
where mathcal{T}2_{ji} is the volume-weighted average temperature of the water in the jth late water mass that was previously in the ith early water mass and mathcal{T}1_{ij} is the volume-weighted average temperature of the water in the ith early water mass that is later in the jth late water mass.
The transformation g_{ij} involves a range of water parcels with a range of temperatures T(mathbf{x}, t), whose mean is mathcal{T}1_{ij},in the early period moving to a range of temperatures T[tilde{x}(t + Delta t | mathbf{x}, t),t], whose mean is mathcal{T}2_{ji}, in the late period. To simplify this problem, we assume that in both periods the water masses are well mixed. This means that we expect that the mean temperature of any sample of water parcels from water mass i in the early period will equal the mean temperature of the water mass as a whole, and in particular this is true for the sample of parcels that ends up in water mass j in the late period. Thus mathcal{T}1_{ij} = T1_i with this assumption. By a similar argument, mathcal{T}2_{ji} = T2_j, and hence the average T and S change of water transforming from the ith early to the jth late water mass as the difference of the average T and S of the two water masses. That is, Delta T_{ij} = T2_j - T1_j and Delta S_{ij} = S2_j - S1_j.
This above approximation preserves the following equality relating the change in global volume-weighted temperature to the transformation matrix:
sum_{j=1}^N V2_j T2_j - sum_{i=1}^N V1_i T1_i = Delta t sum_{i=1}^Nsum_{j=1}^N g_{ij} (T2_j - T1_i), (17)
and likewise for the volume-weighted salinity.
We have effectively discretized the continuum of trajectories from early to late water masses into a finite set of discrete trajectories. This discretization clearly leads to some information loss; however, such losses are unavoidable in any computationally feasible inverse method.
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-3
|
where mathcal{T}2_{ji} is the volume-weighted average temperature of the water in the jth late water mass that was previously in the ith early water mass and mathcal{T}1_{ij} is the volume-weighted average temperature of the water in the ith early water mass that is later in the jth late water mass.
The transformation g_{ij} involves a range of water parcels with a range of temperatures T(mathbf{x}, t), whose mean is mathcal{T}1_{ij},in the early period moving to a range of temperatures T[tilde{x}(t + Delta t | mathbf{x}, t),t], whose mean is mathcal{T}2_{ji}, in the late period. To simplify this problem, we assume that in both periods the water masses are well mixed. This means that we expect that the mean temperature of any sample of water parcels from water mass i in the early period will equal the mean temperature of the water mass as a whole, and in particular this is true for the sample of parcels that ends up in water mass j in the late period. Thus mathcal{T}1_{ij} = T1_i with this assumption. By a similar argument, mathcal{T}2_{ji} = T2_j, and hence the average T and S change of water transforming from the ith early to the jth late water mass as the difference of the average T and S of the two water masses. That is, Delta T_{ij} = T2_j - T1_j and Delta S_{ij} = S2_j - S1_j.
This above approximation preserves the following equality relating the change in global volume-weighted temperature to the transformation matrix:
sum_{j=1}^N V2_j T2_j - sum_{i=1}^N V1_i T1_i = Delta t sum_{i=1}^Nsum_{j=1}^N g_{ij} (T2_j - T1_i), (17)
and likewise for the volume-weighted salinity.
We have effectively discretized the continuum of trajectories from early to late water masses into a finite set of discrete trajectories. This discretization clearly leads to some information loss; however, such losses are unavoidable in any computationally feasible inverse method.
Note that, even if the ith water mass for the early period has the same temperature and salinity bounds as the ith water mass of the late period, the distribution of properties within the water mass can change. That is, in general T1_j ≠ T2_i and S1_j ≠ S2_i, so g_{ij} is always a transformation, even with i = j. For example, assume the ith water mass has temperature bounds 1˚ and 2˚C and that the water between those bounds is on average at 1.9˚C in the early period and 1.1˚C in the late period. Groeskamp et al. (2014) called this a “local effect” and included it as a separate term in their formulation. Here, we find it convenient to consider the transformation from the ith early water mass at 1.9˚C to the ith late water mass at 1.1˚C to be yet another transformation - no different than between any other pair of water masses.
We relate the transformation rate to the average material temperature tendency required to warm the ith early water mass to form the range of destination water masses it arrives at in the late period. That is,
dot{T}_i = frac{1}{V1_i} sum_{j=1}^N (T2_j - T1_i) g_{ij}. (18)
We use dot{T} to define a 3D material temperature change field Delta T_{material} such that
Delta T_{material}(mathbf{x}) = int_{t_0-Delta t}^{t_0} sum_{i=1}^N Pi_i(mathbf{x}, t) dot{T}_i dt
approx frac{1}{Delta t} int_{t_0-Delta t}^{t_0} left{int_t^{t + Delta t}frac{DT’}{Dt}[tilde{x}(t^*|mathbf{x},t),t^*]dt^*right} dt. (19)
Note here that we are relating dot{T}_i only to the anomaly of the Lagrangian tendency (i.e., frac{DT’}{Dt} rather than frac{DT}{Dt}) as it appears in Eq. (19). This is because our dot{T}_i describes only the changes in the transformation rate required to explain changes in the water mass distribution [as in Eq. (6)]. There can be (and indeed is) an additional “mean” transformation rate that leads to cycles of water in T-S space but does not lead to any changes in water mass inventories with time (Groeskamp et al. 2014). Implicit in Eq. (19) is the assumption that the anomalous warming of a particular water mass occurred evenly (in a volume-and time-weighted sense) over the regions and times during which that water mass existed in the early period.
We will contrast the inferred material warming at one location mathbf{x} against the total warming
Delta T(mathbf{x}) = int_{t_0 - Delta t}^{t_0} T(mathbf{x}, t + Delta t) - T(mathbf{x}, t) dt/Delta t,
with the residual of the two being a redistribution component such that
Delta T_{material} = Delta T - Delta T_{redistribution}.
By construction, Delta T_{redistribution} accounts for the advective redistribution of temperature (mathbf{u} cdot nabla{T}), which does not affect the underlying water masses and therefore is not accounted for in Delta T_{material}.
Finding the minimum transformation using an EMD algorithm
Our goal now is to estimate the transformation matrix mathbf{g}. Out of the inÞnite number of choices that could satisfy Eq. (13),we will look for the smallest (in a least squares sense) possible transformation required to change the distribution. We call this the minimum transformation.
Previous studies have diagnosed transformation rates from time-dependent changes in water mass distributions by searching for a minimum least squares solution on a regular T-S (Evans et al. 2014) or density-spiciness grid (Portela et al. 2020). Because of the dramatic variations in volume per unit temperature and salinity of the World Ocean (Fig. 1b) we choose to describe the distribution in an unstructured way. Furthermore, we exploit recent advances in the area of “optimal transportation theory” - in particular, the EMD algorithm that is mentioned at the beginning of section 3 (Pele and Werman 2008, 2009).
The EMD solves the hypothetical problem of moving earth from a set of mounds, each with varying amounts of earth, into a set of holes with varying amounts of empty space to be filled, where the total volume of the mounds is equal to that of the holes. In our case the “mounds” are the early water masses and the “holes” are the late water masses. The optimization problem is to find the set of transfers (from a mound to a hole, or the early to late water masses) that gives the smallest possible total of mass-weighted distance (the product of the mass and the distance of a transfer) that needs to be traveled in order to empty the mounds and fill the holes. For the EMD algorithm, we require a distance metric mathbf{d} ,which is a matrix whose ith column and jth row d_{ij} is the cost of moving water from the ith early water mass to the jth late water mass. The EMD algorithm then estimates mathbf{g} such that Eq. (13) is satisÞed and the following total mass-weighted “distance” is minimized:
sum_{j=1}^Nsum_{i=1}^N g_{ij} d_{ij}. (21)
We use the following distance metric:
d_{ij} = (T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2 + delta_{ij}, (22)
where temperature and salinity differences are squared so that the distance is positive definite and long trajectories in TÐS space are penalized more than short ones and a is a constant that scales the salinity change relative to the temperature change and whose choice is described in the next section. The intent of delta_{ij} is to permit movement between water masses that are adjacent geographically without additional penalty but at the same time to stop direct exchange between geographically disconnected water masses, for example between water masses in the Southern Ocean and the Arctic. To achieve this we set delta_{ij} = 0 where the ith and jth water masses are in the same or adjacent geographical regions and delta_{ij} >> max{(T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2} otherwise (in practice we use delta_{ij} = 10^6 in the latter case). Regions that share a meridional or zonal boundary are considered to be adjacent. The Arctic and North PaciÞc Oceans are not considered to be adjacent, whereas the Indian Ocean and equatorial PaciÞc regions are considered to be adjacent.
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-4
|
sum_{j=1}^Nsum_{i=1}^N g_{ij} d_{ij}. (21)
We use the following distance metric:
d_{ij} = (T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2 + delta_{ij}, (22)
where temperature and salinity differences are squared so that the distance is positive definite and long trajectories in TÐS space are penalized more than short ones and a is a constant that scales the salinity change relative to the temperature change and whose choice is described in the next section. The intent of delta_{ij} is to permit movement between water masses that are adjacent geographically without additional penalty but at the same time to stop direct exchange between geographically disconnected water masses, for example between water masses in the Southern Ocean and the Arctic. To achieve this we set delta_{ij} = 0 where the ith and jth water masses are in the same or adjacent geographical regions and delta_{ij} >> max{(T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2} otherwise (in practice we use delta_{ij} = 10^6 in the latter case). Regions that share a meridional or zonal boundary are considered to be adjacent. The Arctic and North PaciÞc Oceans are not considered to be adjacent, whereas the Indian Ocean and equatorial PaciÞc regions are considered to be adjacent.
Our motivation for using EMD is simply to find the smallest amount of transformation (in a least squares sense) required to explain observed water mass change. If T-S changes in the ocean could be explained purely by adiabatic redistribution of existing water masses, then our method would prioritize this solution. Our initial guess is therefore this adiabatic solution (i.e., where g_{ij} = 0 for all i and j). The EMD algorithm finds the smallest deviation possible from this adiabatic case. We cannot rule out larger compensating transformations having taken place. In principle, solutions given different initial guesses (e.g., an initial guess for mathbf{g} that is based on a numerical simulation) could be explored. We leave this to future work.
Figure 2 summarizes the minimum transformation method schematically. In the schematic just four early and four late water masses are deÞned with two in one geographical area and two in another. The minimum transformation moves water from the ith early to the ith late water masses in all four cases (i.e., g_{ii} ≠ 0 for all i). In addition, a substantial amount of water is moved from the second early water mass to the first late water mass (g_{21}) and from the third early water mass to the fourth late water mass (g_{34}). The observed change in temperature is therefore explained by a material warming of 2˚ and 1˚C of the two warmer shallower water masses and of 0.5˚C for the cooler deeper water masses. The remainder of the Eulerian pattern of temperature change is explained by redistribution. This schematic representation is vastly simplified as compared to our actual implementation of the minimum transformation method, which is described in the next section.
Figure 2: Schematic describing a simplified hypothetical implementation of the minimum transformation method. (left) Between a late and an early period, surface waters warm, especially to the south, where the ocean is fresher and the upper ocean layer becomes thicker. (center) The ocean is split into a southern region containing water masses 1 and 3 and a northern region containing water masses 2 and 4. Between the early and late periods, water masses 1 and 4 increase in volume and 2 and 3 reduce in volume. Taking into account the changing temperatures, salinities, and volumes of the early and late water masses, the “minimum transformations” g_{ij} are found using the EMD algorithm. These suggest modest warming of each water mass with some of early water mass 2 transforming to become late water mass 1 (g_{21}) and some of early water mass 3 transforming to become late water mass 4 (g_{34}). (right) The total temperature change is heterogeneous. A warming of 2˚C explains changes in water mass 1, a warming of 1˚C explains changes in water mass 2, and a warming of 0.5˚C explains changes in water masses 3 and 4. This warming is projected onto the location of those water masses in the early period to show the “material change.” The residual of the total and material changes is then explained by a “redistribution” that involves intense subsurface warming in the southern region and intense subsurface cooling in the northern region.
Data and application of the minimum transformation method
Observational estimates of T and S come from the objective analysis provided by the Enact Ensemble (V4.0, hereinafter EN4; Good et al. 2013). EN4 has a 1˚-by-1˚ horizontal resolution with 42 vertical levels. We analyze each month between 2006 and 2017 inclusive. We split these data into two time periods: an early period between 2006 and 2011 inclusive and a late period between 2012 and 2017 inclusive (i.e., t_0 = 0000 1 January 2007 and Delta t = 6 years).
We then define a discrete set of water masses for each time period by splitting the ocean into nine geographical regions and within each region by splitting up the ocean according to T-S bins. Our nine geographical regions are the Southern Ocean south of 35˚S, the subtropical Pacific and Atlantic Oceans between 35˚ and 10˚S, the Indian Ocean north of 35˚S, the tropical Pacific and Atlantic Oceans between 10˚S and 10˚N, the North Pacific north of 10˚N, the Atlantic Ocean between 10˚ and 40˚N, and the Atlantic and Arctic Ocean north of 40˚N. To avoid discontinuities in our resulting analysis we transition linearly from one region to another over a 10˚ band (Figure 5).
We define T and S bin boundaries ([T_{min}, T_{max}] and [S_{min}, S_{max}] respectively) using a quadtree. The quadtree starts with a single (obviously oversized) bin with T boundaries [-6.4˚,96˚C] and S boundaries [-5.2, 46 g kg^{-1}] in which the entirety of the ocean’s seawater resides. The single bin is then split into four equally sized bins with the same aspect ratio as the original bin. The same process of splitting into four is repeated for any bin whose volume change is greater than a threshold of 62 times 10^{12} m^3 (equivalent to the volume of a 5˚ longitude by 5˚ latitude region at the equator with a depth of 200 m) or until the bin size is 0.4˚C by 0.2 g kg^{-1}. Average volumes for each water mass are shown in Figure 3. In the supplementary text we show that changing the size of these bins by a factor of 2 does not substantially change our results. The quadtree is applied within each region and for the change between the late and early periods. This results in bin edges defining N = 1447 water masses. These bins are then used to dedine both the early water masses and the late water masses.
Figure 3: Gray lines show Conservative Temperature T and Absolute Salinity S bounds of each water mass (or “bin”) generated using a quadtree for each geographical region. The average T and S of the water found within each bin are shown by the location of each marker, and the volume is represented by the color scale (log10m3). Inventories and mean T and S values represent the entire period (2006-17 inclusive). Inset panels show masks associated with each geographical region.
We choose the constant a to be the ratio of a typical haline contraction coefficient to a typical thermal expansion coefficient (a = beta_0/alpha_0 = 4.28). This does not mean that transformations along density surfaces are necessarily preferred; rather, the squares in Eq. (22) mean that density-compensated changes in T and S are penalized as much as changes of the same magnitude where one of the signs is reversed. The inferred Delta T_{material} for each water mass is shown in Figure 4. We have tested the sensitivity of our method to varying a by a factor of 2 and found only negligible changes in inferred warming (see section b of appendix A).
Figure 4: Each symbol shows Delta T_{material}, the average warming required for each early water mass in order to transform them into the set of late water masses.
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-5
|
Figure 3: Gray lines show Conservative Temperature T and Absolute Salinity S bounds of each water mass (or “bin”) generated using a quadtree for each geographical region. The average T and S of the water found within each bin are shown by the location of each marker, and the volume is represented by the color scale (log10m3). Inventories and mean T and S values represent the entire period (2006-17 inclusive). Inset panels show masks associated with each geographical region.
We choose the constant a to be the ratio of a typical haline contraction coefficient to a typical thermal expansion coefficient (a = beta_0/alpha_0 = 4.28). This does not mean that transformations along density surfaces are necessarily preferred; rather, the squares in Eq. (22) mean that density-compensated changes in T and S are penalized as much as changes of the same magnitude where one of the signs is reversed. The inferred Delta T_{material} for each water mass is shown in Figure 4. We have tested the sensitivity of our method to varying a by a factor of 2 and found only negligible changes in inferred warming (see section b of appendix A).
Figure 4: Each symbol shows Delta T_{material}, the average warming required for each early water mass in order to transform them into the set of late water masses.
In section a of appendix A, we compare the results of our method applied to synthetic data from a climate model simulation with an added-heat variable explicitly simulated by the model. We find good agreement between added heat and our inferred Delta T_{material} and between simulated redistributed heat and our inferred Delta T_{redistributed} when ocean temperature and salinity are fed in as “data” to the method. Section b of appendix A also explores sensitivity of our results to parameter choices. The uncertainties we place on OHC change are ±2 standard deviations of a bootstrap ensemble, also described in section c of appendix A.
To produce maps of the total, material and redistributed contributions to the heat content we multiply the density and heat capacity of seawater by the respective temperature change and vertically integrate these through the entire water column. Our method also produces a material salinity change. We leave discussion of those data to future work.
Results
Patterns of total OHC change between early and late periods are heterogeneous (Figure 5a). There are basin-scale patches of decreasing heat content in the western equatorial and tropical Pacific, in the Pacific sector of the Southern Ocean, in the subtropical south Indian Ocean, and in the subpolar North Atlantic. Warming is seen most strongly in the tropical eastern Pacific, South Atlantic Ocean, and subtropical North Atlantic. These changes are highly sensitive to the specific observation years chosen and the length of the epochs reflecting the regional time scale of variability associated with the redistributed component. Uncertainty is far larger than the signal in the majority of regions (stippling in Figure 5a) and coincident with previously identified regions of large sea level anomaly variability (Penduff et al. 2011).
Figure 5: Heterogeneous pattern of total and redistributed heat content change contrast against robust material heat content change: (a) change in depth-integrated ocean heat content between 2006-11 and 2012-17 inclusive, (b) inferred redistributed heat, and (c) inferred material heat content change based on changing water masses for the same period. Regions where the magnitude of the signal is less significant (less than 2 standard deviations of a bootstrap ensemble) are stippled.
However, there are a few regions (e.g., patches of the Southern Ocean and North Atlantic) where the regional redistributed signal is robust and emerges from the uncertainty (Figure 5b). The patterns of redistributed heat observed in the Pacific are consistent with interdecadal Pacific oscillation (IPO)-driven thermosteric sea level variability (Lyu et al. 2017). The IPO was typically positive in the late period and negative in the early period (see https://psl.noaa.gov/gcos_wgsp/Timeseries/ for these data).
Material heat content change shows a smaller amplitude but more coherent signal than redistributed heat (Figures 5b,c). Material warming is seen across almost the entirety of the globe, with maxima in the Southern Hemisphere and Atlantic subtropical convergence zones (Maximenko et al. 2009), consistent with model simulations of passive ocean heat uptake due to anthropogenic greenhouse warming (Gregory et al. 2016). In such model simulations, anomalous heat fluxes into the ocean predominate at mid-to high latitudes and this heat is distributed throughout the ocean largely passively via subduction (downwelling) in the North Atlantic and the Southern Ocean (Marshall et al. 2015).
Strikingly, the uncertainty in material heat content change is far smaller than that of total OHC change (stippling in Figure 5c). This suggests that heat was added to and distributed within the ocean persistently over the Argo period and that this warming is not an artifact of a particularly warm year or years.
Zonally integrating the net OHC change reveals a signal of roughly the same magnitude as its uncertainty at all latitudes (Figure 6a). Zonally integrated redistributed heat likewise has a small signal to uncertainty ratio except in the Southern Ocean (Figure 6a). Accumulating the redistributed heat contribution from north to south gives the meridional heat transport due to redistribution. Broadly, heat is redistributed from north to south with a southward cross-equatorial transport of 73 ± 60 TW between the two epochs (Figure 6c).
Figure 6: Material heat content change is accumulating in the tropics and subtropics, whereas existing heat is being redistributed southward. (a) Total heat content change (gray), redistribution contribution (blue), and material contribution (red). (b) Contributions to material heat content change from the Indian (green), Pacific (orange), and Atlantic (yellow) Oceans. (c) Meridional heat transport due to redistribution in the Southern Ocean (blue), Atlantic (cyan), and Indian plus Pacific Oceans (magenta). Shaded areas represent ±2 standard deviations of a bootstrap ensemble.
Material heat content change (Figure 6a) is larger than its uncertainty at most latitudes and shows a peak at 35˚S and at 15˚ and 35˚N. The material heat content change peaks at 35˚S and 35˚N are collocated with climatological wind stress curl minima, where material warming due to anomalous surface heat fluxes may be accumulating due to convergence of surface Ekman transport.
Table 1 shows material, redistributed, and total heat content changes by ocean basin. Material heat content change is distributed among the Indian, South Pacific, and South Atlantic basins approximately according to their area. However, the tropical and subtropical North Atlantic stores close to 20% of the global ocean’s material heat content change despite representing less than 10% of its area (Table 1). An outsized role for the North Atlantic in storing material heat content change in the climate system has also been foreseen in numerical modeling studies (Lee et al. 2011).
Table 1: Material, redistribution, and total contributions to heat content change by ocean basin in terawatts and area as fraction of global ocean area. Heat content change estimates are based on differences between the periods 2006–11 and 2012–17 inclusive. Uncertainties are ±2 standard deviations. The Southern Ocean is defined as the entire ocean south of 32˚S. The South Pacific, South Atlantic, and Indian Ocean estimates exclude the ocean south of 32S. The North Atlantic is split into a region south of and a region north of 44˚N. The latter includes the Arctic Ocean.
Material
Redistributed
Total
Area fraction
Southern Ocean
90 ± 18
118 ± 50
208 ± 63
0.27
South Pacific
53 ± 16
226 ± 22
28 ± 22
0.15
North Pacific
82 ± 25
261 ± 55
21 ± 54
0.23
Indian Ocean
45 ± 10
213 ± 25
32 ± 30
0.12
South Atlantic
34 ± 11
6 ± 7
40 ± 7
0.06
North Atlantic (<44˚N)
75 ± 33
20 ± 17
95 ± 46
0.10
North Atlantic (>44˚N)
19 ± 6
240 ± 13
220 ± 16
0.08
Global Ocean
398 ± 81
0
398 ± 81
1.00
We identify robust redistributed warming signals in the subtropical North Atlantic and Southern Ocean. Warming in the subtropical North Atlantic is compensated by cooling in the subpolar North Atlantic consistent with a 40 ± 13 TW southward transport of heat across 44˚N (Figure 6c). Southward heat redistribution across 32S brings 118 ± 50 TW into the Southern Ocean.
Discussion
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
e85a386fd775-6
|
Table 1: Material, redistribution, and total contributions to heat content change by ocean basin in terawatts and area as fraction of global ocean area. Heat content change estimates are based on differences between the periods 2006–11 and 2012–17 inclusive. Uncertainties are ±2 standard deviations. The Southern Ocean is defined as the entire ocean south of 32˚S. The South Pacific, South Atlantic, and Indian Ocean estimates exclude the ocean south of 32S. The North Atlantic is split into a region south of and a region north of 44˚N. The latter includes the Arctic Ocean.
Material
Redistributed
Total
Area fraction
Southern Ocean
90 ± 18
118 ± 50
208 ± 63
0.27
South Pacific
53 ± 16
226 ± 22
28 ± 22
0.15
North Pacific
82 ± 25
261 ± 55
21 ± 54
0.23
Indian Ocean
45 ± 10
213 ± 25
32 ± 30
0.12
South Atlantic
34 ± 11
6 ± 7
40 ± 7
0.06
North Atlantic (<44˚N)
75 ± 33
20 ± 17
95 ± 46
0.10
North Atlantic (>44˚N)
19 ± 6
240 ± 13
220 ± 16
0.08
Global Ocean
398 ± 81
0
398 ± 81
1.00
We identify robust redistributed warming signals in the subtropical North Atlantic and Southern Ocean. Warming in the subtropical North Atlantic is compensated by cooling in the subpolar North Atlantic consistent with a 40 ± 13 TW southward transport of heat across 44˚N (Figure 6c). Southward heat redistribution across 32S brings 118 ± 50 TW into the Southern Ocean.
Discussion
Recent anomalous southward heat transport in the North Atlantic has been well documented and has been attributed to a downturn in the Atlantic meridional overturning circulation (Smeed et al. 2014; Bryden et al. 2020). Observed heat transport anomalies equate to a downturn in meridional heat transport equivalent to -23 ± 60 TW for the period 2006-11 versus 2012–17 at 26˚N in the Atlantic [see appendix B for details of this calculation, which is based on data from Bryden et al. (2020)], which is consistent with our estimate of the change in redistribution heat transport of -23 ± 19 TW (Figure 6; uncertainties are ±2 standard deviations).
The large apparent meridional heat transport we have identified in the Southern Ocean was previously identified by Roberts et al. (2017) based on the residual of observed OHC change and estimates of air-sea heat fluxes. Their approach captures additional heat in the system where it is fluxed into the ocean while our approach estimates how that heat is distributed. Nonetheless, the correspondence between our results and theirs is reassuring and perhaps not surprising if the redistribution signal is large as both approaches indicate.
The approach of Zanna et al. (2019) is more directly comparable to ours. They reconstruct the passive contribution to ocean warming since 1850 by propagating SST anomalies into the ocean interior using Green’s functions. They report changes for a much longer time frame (1955-2017 as opposed to our 2006-17), and therefore magnitudes of warming estimates are not comparable, but a comparison of patterns of change is relevant. In terms of our zonally averaged material warming and their “passive warming” the two datasets share peaks at approximately 35˚S and 35˚N potentially attributable to surface Ekman convergence (see their Fig. 3).
Zanna et al. (2019) report relatively small amounts of passive warming at low-latitude regions while we report a peak in material warming there. This may suggest that the material warming we estimate at low latitudes is in fact related to interannual to decadal variability. An explanation of this may be that the lower low-latitude SST corresponds to a predominance of a negative IPO (Lyu et al. 2017), leading to anomalous ocean heat uptake over our study period. This is a commonly cited explanation for the so-called global warming hiatus discussed in the 2010s (Whitmarsh et al. 2015).
Zanna et al. (2019) compare their inferred passive warming between 1955 and 2017 to the warming observed in situ. Based on this they find evidence of a southward redistribution of heat in the Northern Hemisphere but no substantial southward redistribution in the Southern Hemisphere. This suggests that the southward redistribution of heat inferred by both Roberts et al. (2017) and this study in the Southern Hemisphere may be a more recent occurrence. Indeed, two recent studies have shown that the Southern Hemisphere dominance of ocean heat content change during the twenty-first century is not consistently represented in historical climate simulations and is likely linked to internal variability (Bronselaer and Zanna 2020; Rathore et al. 2020).
Here we have exclusively analyzed the Hadley Centre’s EN4 dataset. Sensitivity to observational coverage is mitigated in part by our consideration of data during the Argo observing period (2006-17). We consider uncertainties to have been reasonably estimated based on our bootstrapping approach, which subsamples those years (see section c of appendix A). Because of EN4’s mapping approach, however, regions where minimal observations were made (e.g., the marginal ice zones in the Southern Hemisphere and below 2000 m) will likely have muted trend estimates. This issue will require special attention when our method is applied to the pre-Argo period and in particular with regard to salinity observations, which are less numerous than temperature observations (Clement et al. 2020).
Conclusions
In summary we have shown the following:
Water mass changes between 2006-11 and 2012-17 can be interpreted in terms of material warming across the globe and with the highest concentrations in the tropical and subtropical North Atlantic Ocean, consistent with simulations of the addition of heat into the ocean due to greenhouse forcing.
The majority of the variance in ocean heat content change at scales of 1˚-by-1˚ over that period can be explained by a redistribution of existing water masses within the ocean.
The inferred redistribution indicates a downturn in northward meridional heat transport into the subpolar North Atlantic of 40 ± 13 TW and an anomalous southward heat transport into the Southern Ocean of 118 ± 50 TW.
The material warming signal that we have inferred is generally weaker than redistribution, but the signal is far less sensitive to changes in the years over which the analysis was carried out. This suggests that material warming may be giving a robust indication of slow thermodynamic changes in the ocean. This could be a result of anthropogenic forcing, although that would be remarkable since the midpoints of the early and late periods are only 6 years apart.
We expect the strength of the material warming signal to increase into the future as the ocean warms. However, since the redistribution signal is so large, circulation changes and variability must be understood if near-term ocean temperature variability and regional sea level change are to be projected accurately.
|
https://sealeveldocs.readthedocs.io/en/latest/zika21.html
|
a4e559be412f-0
|
Hughes et al. (2010)
Title:
Identification of jets and mixing barriers from sea level and vorticity measurements using simple statistics
Key Points:
Skewness and kurtosis in sea level data can be used to identify oceanic fronts and mixing barriers.
Regions indicative of strong jets are associated with zero skewness and low kurtosis.
Geostrophic relative vorticity was the preferred variable to represent local dynamics.
Keywords:
skewness, kurtosis, sea level, vorticity, jet, meander, mixing, AVISO, altimetry
Corresponding author:
Chris W. Hughes
Citation:
Hughes, C. W., Thompson, A. F., & Wilson, C. (2010). Identification of jets and mixing barriers from sea level and vorticity measurements using simple statistics. Ocean Modelling, 32(1–2), 44–57. doi:10.1016/j.ocemod.2009.10.004
URL:
https://doi.org/10.1016/j.ocemod.2009.10.004
Abstract
The probability density functions (PDFs) of sea level and geostrophic relative vorticity are examined using satellite altimeter data. It is shown that departures from a Gaussian distribution can generally be repre.sented by two functions, and that the spatial distribution of these two functions is closely linked to the skewness and kurtosis of the PDF. The patterns indicate that strong jets tend to be identified by a zero contour in skewness coinciding with a low value of kurtosis. A simple model of the statistics of a mean.dering frontal region is presented which reproduces these features. Comparisons with mean currents and sea surface temperature gradients confirm the identification of these features as jets, and confirm the existence of several Southern Ocean jets unresolved by drifter data. Diagnostics from a range of idealized eddying model simulations show that there is a strong, simple relationship between kurtosis of potential vorticity and effective diffusivity. This suggests that kurtosis may provide a simple method of mapping mixing barriers in the ocean.
Introduction
More than a decade of precise satellite altimeter measurements has produced long time series of sea level h, over most of the global ocean. As a way of representing the different variations seen in different regions, it is common to plot the root-mean-square devi.ation of sea level from its mean, r.h., or the geostrophic eddy kinetic energy (EKE), large values of which tend to be associated with strong, eddying currents. More recently, Thompson and Demirov (2006) noted that there is further interesting information in the skewness $S(h)$ of the sea level distribution, which tends to be positive on the poleward side of strong eastward currents, and negative on the equatorward side. They interpreted this as indica.tive of the intermittent passage of warm core eddies or warm meanders across points poleward of a jet, and of cold core eddies or meanders on the equatorward side.
This prompts the question of whether higher moments of variability contain further information, and how those moments might be interpreted. More generally, what is the spatial variation in the PDF of sea level, and what causes that variation? In considering this question, we found that sea level, being a non-local variable from a dynamical point of view, is sometimes more difficult to interpret than the more localized relative vorticity, so in much of the work presented here we focus on the PDF of relative vorticity $zeta$.
We show below that, in fact, maps of skewness $S$ and kurtosis $K$ contain most of the information which can be reliably extracted from PDFs at each position. These are defined as
$$ S(chi) = frac{frac{1}{n}sum_nchi^3}{(frac{1}{n}sum_nchi^2)^{frac{3}{2}}} $$, (1)
$$ K(chi) = frac{frac{1}{n}sum_nchi^4}{(frac{1}{n}sum_nchi^2)^2} $$, (2)
P3=2 ;
1 x2
n Pn
where $chi$ is the deviation of some quantity from its mean value. Skewness is a measure of asymmetry of the PDF. Where rare, large events predominantly have one sign, this is the sign of the skewness; a Gaussian distribution is symmetric and therefore has a skewness of zero. Kurtosis is traditionally described as a measure of ‘‘peakiness” of the PDF. High kurtosis means that rare, large amplitude events occur more frequently than would be expected for a Gaussian distribution, producing a more sharply peaked PDF with broader tails than a Gaussian. Low kurtosis means that events much larger than typical are rarer than would be expected from a Gaussian distribution, and the associated PDF tends to be flat near its peak, or even bimodal, and drops to small values faster than a Gaussian. The smallest possible kurtosis is 1, and this results from a variable taking only two possible values, with equal probability. A Gaussian distribution leads to a kurtosis of 3. For this reason, the quantity $K - 3$ is often used, sometimes termed excess ‘‘kurtosis” and sometimes simply ‘‘kurtosis” . We will use the definition given above and, when 3 is subtracted, this will be stated explicitly.
Our dataset consists of the AVISO gridded sea level anomaly (corrected for tides and inverse barometer effect) supplied weekly on a 1/3 degree Mercator grid. While the grid is 1/3 degree, the spacing between altimeter tracks is 0.72 degrees of longitude for ERS/Envisat, and 2.78 degrees for Topex or Jason, so we should not expect to resolve all features less than about 100 km across. We use the ‘‘reference” version of the data in which sampling is always from two altimeters (Topex/Poseidon or Jason 1 and ERS or Envisat) in the same two orbits, and consider 690 weeks spanning the period 5th April 1995–11th June 2008 which follows the period when ERS-1 was not in the standard 35-day repeat orbit. Geostrophic relative vorticity anomalies are calculated by first-order centered differencing of the sea level to give geostrophic velocity, and the same form of differencing to then give vorticity at the same grid points as the sea level data. These are divided by the local Coriolis parameter $f$ so that positive values represent cyclonic, and negative values anti-cyclonic, relative vorticity.
As we are interested in the shape of the PDFs rather than their widths, we consider only time series which have had their means removed and have been divided by their standard deviations. In fact, we also subtract an annual and semiannual cycle and a linear trend, simultaneously Þt to each time series. It is also worth noting a limitation of the geostrophic relative vorticity calculation. The effect of nonlinear terms in the momentum equation is such that the geostrophic velocity (and hence vorticity) is an underestimate in cyclonic vortices, and an overestimate in anticyclonic vortices. This potential bias should be kept in mind, although it is not particularly important for the main issue we consider here, which focuses on the step-like structure in jets.
Binning the resulting normalized PDFs from each grid point into bins 0.01 standard deviations wide, and averaging over the globe (excluding the band within 5 degrees of the equator in the case of vorticity, to avoid the equatorial singularity), produces the average PDFs shown on both logarithmic and linear scales in Fig. 1. The dashed lines show the corresponding Gaussian PDF for reference. We see that the average shape of the PDF for both sea level and relative vorticity is fairly close to Gaussian, but significantly above Gaussian in the wings and centre of the distribution (and below Gaussian in between). Gille and Sura (submitted for publication) look at the overall global relationship between skewness and kurtosis seen from such PDFs, and similar characterization of the velocity PDFs from altimetry has been investigated by Schorghofer and Gille (2002) and Gille and Llewellyn-Smith (2000). This average shape, however, conceals a large geographic variation. Characterization of this spatial variability is the subject of the next section.
Fig. 1: Global average, normalized PDF of (left) sea level, and (right) geostrophic relative vorticity $zeta/f$f from gridded altimetry. The same data are shown on (top) logarithmic and (bottom) linear scales. In each panel, the dotted line is the corresponding Gaussian PDF.
Spatial variations of the PDFs
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-1
|
As we are interested in the shape of the PDFs rather than their widths, we consider only time series which have had their means removed and have been divided by their standard deviations. In fact, we also subtract an annual and semiannual cycle and a linear trend, simultaneously Þt to each time series. It is also worth noting a limitation of the geostrophic relative vorticity calculation. The effect of nonlinear terms in the momentum equation is such that the geostrophic velocity (and hence vorticity) is an underestimate in cyclonic vortices, and an overestimate in anticyclonic vortices. This potential bias should be kept in mind, although it is not particularly important for the main issue we consider here, which focuses on the step-like structure in jets.
Binning the resulting normalized PDFs from each grid point into bins 0.01 standard deviations wide, and averaging over the globe (excluding the band within 5 degrees of the equator in the case of vorticity, to avoid the equatorial singularity), produces the average PDFs shown on both logarithmic and linear scales in Fig. 1. The dashed lines show the corresponding Gaussian PDF for reference. We see that the average shape of the PDF for both sea level and relative vorticity is fairly close to Gaussian, but significantly above Gaussian in the wings and centre of the distribution (and below Gaussian in between). Gille and Sura (submitted for publication) look at the overall global relationship between skewness and kurtosis seen from such PDFs, and similar characterization of the velocity PDFs from altimetry has been investigated by Schorghofer and Gille (2002) and Gille and Llewellyn-Smith (2000). This average shape, however, conceals a large geographic variation. Characterization of this spatial variability is the subject of the next section.
Fig. 1: Global average, normalized PDF of (left) sea level, and (right) geostrophic relative vorticity $zeta/f$f from gridded altimetry. The same data are shown on (top) logarithmic and (bottom) linear scales. In each panel, the dotted line is the corresponding Gaussian PDF.
Spatial variations of the PDFs
Skewness and kurtosis are the first two in an infinite series of moments which characterize the shape of the PDF, following the mean and standard deviation which characterize its position and width. However, it is not immediately clear that these are the parameters best suited to describing the spatial variations in shape. Furthermore, as kurtosis is particularly sensitive to rogue large values in a dataset (it is sometimes used as an indicator of bad data), it is quite possible for much of the shape of the PDF to be invisible to the kurtosis in cases where one particularly large value occurs. For this reason, we seek to characterize the typical variations in shape of the PDF, ignoring the very extreme wings of the distribution.
To do this, we use empirical orthogonal function (EOF) analysis. This is often used to calculate spatial patterns associated with the principal modes of variability of time series given at each grid point. Here, instead of time, we are using the x-axis of the normalized PDF graph at each grid point. Rather than calculate EOFs of the complete PDF, we choose fist to subtract the Gaussian PDF so that we will clearly be mapping departures from Gaussian behavior. We obtain a set of orthonormal eigenvectors, the first of which explains the largest possible amount of spatial variability in the PDF, the second of which describes as much as possible of the remaining variability after removing the effect of the first mode, and so on. The associated eigenvalues give the amount of variance explained by each mode.
There are not enough points in a time series at one point to produce a PDF with such high resolution as in Fig. 1, so here we increase the bin size to 0.1 standard deviations, and consider only the 80 points between -4 and +4 standard deviations (this avoids the inclusion of any very extreme values). The analysis was also repeated with a bin size of 0.4 standard deviations, and only 20 points per PDF, with very similar results to those presented here.
The first 15 eigenvalues of the resulting EOFs are plotted in Fig. 2, as percentages of the total variance (diamonds for the sea level EOFs and crosses for relative vorticity). In both cases, the first two eigenvalues stand clearly above the background continuum, together explaining 28.8% of the sea level variance and 22.7% of relative vorticity variance. In the case of sea level, the second two EOFs may also plausibly be said to stand above the background. Inspection of the associated eigenvectors clearly shows the remaining EOFs to be associated with statistical noise, representing simply the exchange of probability between neighbouring bins (using coarser bins reduces the amplitude of this noise, leaving the first two EOFs to account for 61.7% of variance for sea level and 60.6% for relative vorticity, but does not lead to identification of any more significant modes).
Fig. 2: Eigenvalues of the first 15 EOFs of the PDFs for (diamonds) sea level and (crosses) relative vorticity. Eigenvalues are normalized so that they sum to 100, and each represents the percentage of variance explained by the corresponding eigenvector.
Since we are interested in relating the variations in PDFs to skewness and kurtosis, it would be nice if the EOFs fell naturally into symmetric and antisymmetric categories. They do not, but the importance of symmetry is clear from the fact that very nearly symmetric and antisymmetric functions can be formed from the obvious pairs of EOFs. If we take the first two EOFs of sea level, we can construct from these by a rotation, two different orthonormal vectors $mathbf{C}$ and $mathbf{D}$ chosen to minimize the quantity $(mathbf{C} +mathbf{C}^r)^2 + (mathbf{D} -mathbf{D}^r)^2$, where the superscript $r$ represents the reverse of the vector (i.e. the components listed in reverse order). This minimizes the sum of the squares of the symmetrical component of $mathbf{C}$ and the antisymmetric component of $mathbf{D}$. In other words, $mathbf{C}$ represents a linear combination of the first two EOFs which is close to antisymmetric, and $mathbf{D}$ an orthogonal linear combination which is close to symmetric. The results of such a minimization applied to the pairs of EOFs identified from Fig. 2 are shown in Fig. 3. The solid lines are constructed from pairs of EOFs of the sea level PDFs, and dashed lines from relative vorticity. To show how closely these approximate the ideal symmetry, crosses represent the exactly antisymmetric or exactly symmetric components of the corresponding sea level EOF curves. Success in this minimization is not inevitable. For example, no combination of the first and third EOFs can produce anything like a symmetric and antisymmetric pair of functions. This success suggests that it is meaningful to combine the EOFs in this way.
Fig. 3: Rotated eigenvectors of the first 4 EOFs (solid) of the PDFs for sea level and the first 2 EOFs (dashed) for relative vorticity. Crosses are half of the corresponding sea level vector plus or minus its reverse, illustrating the corresponding perfectly symmetrical or antisymmetric curves.
The projection of the PDFs onto these rotated EOFs is shown in Figs. 4 and 5. The pattern of the first rotated EOF for sea level is clearly very similar to the skewness map presented by Thompson and Demirov (2006). Major eastward currents are delineated by the boundary between large positive and large negative values, and preferred paths of eddies, such as in the Alaskan Stream along the Aleutian island chain at the northern boundary of the PaciÞc (Ueno et al., 2009), and southwest of Australia (Morrow et al., 2004) also stand out. The tropical PaciÞc is also prominent. As Thompson and Demirov (2006) point out, this is the result of the dominance of the large 1997Ð1998 El Nino event in the region. This highlights a disadvantage of considering sea level: large scale sea level signals can dominate the time series at a given point, but there may be little or no associated current or other dynamical change at that point. Dynamically, sea level is a non-local variable on time scales of several days or longer. For this reason, the localization of physical processes is better determined using vorticity or potential vorticity. This is illustrated for relative vorticity in Fig. 5. The spatial pattern for the first rotated EOF is clearly related to that for sea level (with a sign change since a positive localized sea level anomaly represents an anticyclonic circulation), but the relative vorticity map shows finer scales and more localized structures (particularly in the Southern Ocean) than the corresponding map based on sea level. Using relative vorticity also avoids a dominant influence of the El Nino event, making it possible to pick out clear structures to the west of Hawaii and Central America.
Fig. 4: Projection of the sea level PDFs onto the first and second rotated eigenvectors from Fig. 3.
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-2
|
Fig. 3: Rotated eigenvectors of the first 4 EOFs (solid) of the PDFs for sea level and the first 2 EOFs (dashed) for relative vorticity. Crosses are half of the corresponding sea level vector plus or minus its reverse, illustrating the corresponding perfectly symmetrical or antisymmetric curves.
The projection of the PDFs onto these rotated EOFs is shown in Figs. 4 and 5. The pattern of the first rotated EOF for sea level is clearly very similar to the skewness map presented by Thompson and Demirov (2006). Major eastward currents are delineated by the boundary between large positive and large negative values, and preferred paths of eddies, such as in the Alaskan Stream along the Aleutian island chain at the northern boundary of the PaciÞc (Ueno et al., 2009), and southwest of Australia (Morrow et al., 2004) also stand out. The tropical PaciÞc is also prominent. As Thompson and Demirov (2006) point out, this is the result of the dominance of the large 1997Ð1998 El Nino event in the region. This highlights a disadvantage of considering sea level: large scale sea level signals can dominate the time series at a given point, but there may be little or no associated current or other dynamical change at that point. Dynamically, sea level is a non-local variable on time scales of several days or longer. For this reason, the localization of physical processes is better determined using vorticity or potential vorticity. This is illustrated for relative vorticity in Fig. 5. The spatial pattern for the first rotated EOF is clearly related to that for sea level (with a sign change since a positive localized sea level anomaly represents an anticyclonic circulation), but the relative vorticity map shows finer scales and more localized structures (particularly in the Southern Ocean) than the corresponding map based on sea level. Using relative vorticity also avoids a dominant influence of the El Nino event, making it possible to pick out clear structures to the west of Hawaii and Central America.
Fig. 4: Projection of the sea level PDFs onto the first and second rotated eigenvectors from Fig. 3.
Fig. 5: Projection of the relative vorticity PDFs onto the first and second rotated eigenvectors from Fig. 3.
The projections of sea level and relative vorticity PDFs onto the second rotated EOFs bear a similar relationship to each other (without the sign change, since the second rotated EOF is close to symmetrical). Strong currents now stand out as low values of the projection, and these features are more clearly deÞned in the relative vorticity plot.
From the forms of the EOFs, we expect the projections to be closely related to skewness and kurtosis respectively, and Fig. 6 shows that this is the case for relative vorticity (the equivalent maps for sea level skewness and kurtosis are not shown, but bear a similar relation to the sea level EOF projections). The EOF projections can be described as slightly “cleaner”: definition of some features is better, such as the Loop Current in the Gulf of Mexico, and features along the Falklands shelf. There are also some isolated spots of large skewness and kurtosis which are not visible in the EOF maps, which suggests that they may be due to rogue data points (a few time series which have been checked are consistent with this, consisting of a rather ßat curve with one sudden spike). A problem with the gridding in the region north of Iceland and Norway also shows up much more clearly in skewness and kurtosis than in the EOF maps. However, it can generally be said that maps of skewness and kurtosis are capturing the same spatial variability as the two EOF maps and, since only two EOFs are above the background noise for relative vorticity, that means that skewness and kurtosis capture all that can currently be captured about spatial variations in the PDF of relative vorticity. In the case of sea level, the spatial patterns associated with the third and fourth rotated EOFs (not shown) appear very noisy except in the vicinity of the very strongest currents, suggesting that they do contain physically meaningful information, but only in these select regions.
Fig. 6: Skewness and kurtosis of relative vorticity time series.
It is difficult to assess the statistical noise levels on these estimates, as the weekly sea level maps are not independent. A standard result estimates the standard error on skewness as $sqrt{6/n}$, and that on kurtosis as $sqrt{24/n}$, where $n$ is the number of independent samples, although kurtosis has a strongly asymmetric distribution, having a minimum value of 1, Gaussian value of 3 and inÞnite maximum possible value for a continuous PDF. As a guide, the 5 and 95 percentiles for skewness and kurtosis generated from a Gaussian distribution sampled at a Þnite number $n$ of independent times have been calculated by Monte Carlo simulation (using 100,000 random input time series) for $n = 690$ (the number of points in the time series), $n = 300$, and $n = 100$. The results are shown in Table 1. The strongest justification for the significance of these results, however, is the spatial coherence and physical plausibility of the resulting patterns.
Table 1: Values of skewness ($S$), kurtosis minus 3 $(K - 3)$ and projections of rotated EOF1 and rotated EOF2 generated by chance from Þnite samples of length $n$ taken from Gaussian distributions. The 5th and 95th percentiles are given.
$n$
%
$S$
$K - 3$
EOF1
EOF2
690
5
-0.14
-0.36
-0.10
-0.11
95
0.14
0.16
0.10
0.07
300
5
-0.21
-0.48
-0.15
-0.16
95
0.21
0.29
0.15
0.12
100
5
-0.36
-0.73
-0.26
-0.27
95
0.36
0.51
0.26
0.23
Interpretation of low kurtosis regions
As stated in the introduction, the lowest possible kurtosis is 1, and occurs when the variable ($zeta/f$ or $h$) is always at one of two values, and occupies those two values with equal probability. Consider a sharp jet, which may be approximated as a step in sea level. If that jet meanders, then sea level within the region over which it meanders will always be at one of two values (either to the left, or to the right of the jet). Along some line, the jet will spend equal amounts of time to the left and to the right of that line. On that line, the kurtosis of sea level would be 1.
Off the line, the fraction of time spent in each state varies, becoming more asymmetrical with distance from the centre line until beyond the limit of meanders where sea level becomes constant. If the fractions of time spent at each value are $A$ at the lower value, and $B = 1 - A$ at the higher value, then it is simple to calculate that $K = -3 + 1/P$, $S = (A -B)/sqrt{P}$, $S^2 = -4 + 1/P$, where $P = AB$ has a maximum possible value of 1/4. It will be noticed that this rather extreme situation gives the relationship $K = S^2 + 1$. This in fact represents the minimum possible $K$ for a given $S$ (Pearson, 1916). Idealized though this model is, it does capture the main features surrounding jets in Fig. 6: low kurtosis and zero skewness at the centre (mean position) of the jet, with kurtosis growing to large positive values on either side, as skewness grows to large positive values on one side and large negative values on the other side of the jet.
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-3
|
0.10
0.07
300
5
-0.21
-0.48
-0.15
-0.16
95
0.21
0.29
0.15
0.12
100
5
-0.36
-0.73
-0.26
-0.27
95
0.36
0.51
0.26
0.23
Interpretation of low kurtosis regions
As stated in the introduction, the lowest possible kurtosis is 1, and occurs when the variable ($zeta/f$ or $h$) is always at one of two values, and occupies those two values with equal probability. Consider a sharp jet, which may be approximated as a step in sea level. If that jet meanders, then sea level within the region over which it meanders will always be at one of two values (either to the left, or to the right of the jet). Along some line, the jet will spend equal amounts of time to the left and to the right of that line. On that line, the kurtosis of sea level would be 1.
Off the line, the fraction of time spent in each state varies, becoming more asymmetrical with distance from the centre line until beyond the limit of meanders where sea level becomes constant. If the fractions of time spent at each value are $A$ at the lower value, and $B = 1 - A$ at the higher value, then it is simple to calculate that $K = -3 + 1/P$, $S = (A -B)/sqrt{P}$, $S^2 = -4 + 1/P$, where $P = AB$ has a maximum possible value of 1/4. It will be noticed that this rather extreme situation gives the relationship $K = S^2 + 1$. This in fact represents the minimum possible $K$ for a given $S$ (Pearson, 1916). Idealized though this model is, it does capture the main features surrounding jets in Fig. 6: low kurtosis and zero skewness at the centre (mean position) of the jet, with kurtosis growing to large positive values on either side, as skewness grows to large positive values on one side and large negative values on the other side of the jet.
The observed values of $K$ are, inevitably, never as low as this extreme model would predict. This prompts a slightly more sophisticated model: instead of constant sea level to either side of the jet, add Gaussian noise to the sea level on either side. Thus, we consider the situation in which there is a sharp step in sea level across the jet, which meanders, but there is also random sea level variability producing a Gaussian PDF either side of the step (for simplicity, we choose the standard deviations of the Gaussians to be the same on each side of the step). The time series at any point is then a random variation about a certain mean at times when the point is to the north of the jet, and a random variation about a different mean at times when the point is to the south of the jet. The resulting PDF consists of the sum of two Gaussian PDFs, with centres separated by a distance $d$ (the size of the step). We measure $d$ in units of the Gaussian standard deviation, so that $d$ represents the ratio of step size to the size of the Gaussian noise. We now define $A$ as the integral of the Gaussian centered at the lower value (i.e. the probability of being on the low side of the step), and $B = 1 - A$ is the integral of the second Gaussian. Again, we will have $A = B = 0.5$ at the mean central position of the jet, with $A$ decreasing and $B$ increasing to one side of that point, and the converse on the other side.
At the jet centre, the sum of two Gaussians with small separation would produce a PDF with a flatter centre region than a single Gaussian alone (and hence kurtosis less than 3). For larger separation ($d > 2$) the PDF becomes bimodal, and kurtosis becomes even smaller, dropping towards 1 as the separation of the Gaussians becomes larger (when the noise to either side of the jet becomes a small fraction of the size of the step).
Fig. 7: Time series of relative vorticity (plotted as $zeta/f$) from two points with particularly low kurtosis, from (top) the Gulf Stream extension and (bottom) the Agulhas Return Current. Panels to the right show the corresponding PDF, calculated by kernel density estimation using a Gaussian kernel of standard deviation 0.2.
Fig. 7 shows the time series, and associated normalized PDF, for $zeta/f$ at two points of particularly low kurtosis in the Gulf Stream extension and the Agulhas Return Current. In both cases the vorticity clearly spends about half its time in the vicinity of one value, and half its time close to another value, with clusters about those two values overlapping to a degree, but clearly separate. This is reflected in the bimodal PDFs.
The model remains simplified, but this has the advantage that it can be solved analytically for skewness and kurtosis as a function of $A$ and $d$. The resulting relationships (derived in Appendix A) are
$$ K - 3 = frac{d^4P(1-6P)}{(1 + d^2P)^2} $$, (3)
$$ S = frac{d^3P(A-B)}{(1+d^2P)^{3/2}} $$, (4)
$$ S^2 = frac{d^6P^2(1-4P)}{(1+d^2P)^3} $$, (5)
remembering that $B = 1 - A$ and $P = AB$. At the mean position of the jet, $A = B = 1/2$ giving a skewness of zero, and reducing (3) to $K = 3 - 2/(1 + 4/d^2)^2$. A series of curves, each corresponding to changing $A$ at constant $d$ (i.e. representing how skewness and kurtosis would vary across a jet for a particular ratio of noise to step size) is shown as the thin black curves in Fig. 8. The different curves represent integer values of $d$ from 1 to 6 (innerÐouter), showing how the distance from the Gaussian values $S = 0$, $K = 3$ increases as the step size $d$ increases in comparison to the noise. To understand this plot, consider a jet with negative skewness to the south (for relative vorticity, an eastward jet in the southern hemisphere would show this pattern, for sea level it would be a northern hemisphere jet). As we move from south to north, we follow one of the curves in an anticlockwise direction. Far to the south, the noise dominates over the influence of the jet and the PDF is a single Gaussian ($P = 0$), producing $S = 0$, $K = 3$. As the influence of sea level from the other side of the jet becomes stronger ($P$ increases), skewness decreases and kurtosis increases, reaching a maximum at $P = 1/(d^2+12)$. Kurtosis then starts to decrease while skewness continues to decrease until it reaches a minimum at $P = 2/(d^2+12)$, where $K = 3 + 3S^2/2$. Kurtosis drops below 3 at $P = 1/6$, decreasing to its minimum at the centre of the jet where $P = 1/4$, $S = 0$. Then kurtosis starts to rise and the curve follows the positive skewness branch to the right and up, returning finally to $S = 0$, $K = 3$ far to the north.
Fig. 8: The relationship between skewness and kurtosis in the vicinity of a front. Thin curves represent the relationship resulting from the simple model described in the text. Each curve corresponds to a particular ratio d of step size to noise (values d .1Ð6 are plotted), with curves becoming larger as d increases (noise decreases). For relative vorticity, the curve is followed anticlockwise when passing from poleward to equatorward of an eastward jet. Crosses are values at points in the vicinity of the Agulhas Return Current. The thick line with diamonds is the trajectory described by statistics averaged at constant meridional distance from the centre of the current.
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-4
|
Fig. 8: The relationship between skewness and kurtosis in the vicinity of a front. Thin curves represent the relationship resulting from the simple model described in the text. Each curve corresponds to a particular ratio d of step size to noise (values d .1Ð6 are plotted), with curves becoming larger as d increases (noise decreases). For relative vorticity, the curve is followed anticlockwise when passing from poleward to equatorward of an eastward jet. Crosses are values at points in the vicinity of the Agulhas Return Current. The thick line with diamonds is the trajectory described by statistics averaged at constant meridional distance from the centre of the current.
For small $d$ (small step size compared to noise), the trajectories remain close to $S = 0$, $K = 3$, extending further from this point as $d$ increases. In fact, allowing all values of $d$ produces a family of curves which Þll the entire allowed space $K geq S^2 + 1$. Only for $d > 2$ does the PDF become bimodal at the jet centre, at which point we would then have $K < 2.5$, although for more general distributions, the PDF can only be guaranteed to be bimodal if $K < S^2 + 1.512$ (Klaassen et al., 2000).
There are many ways in which this model is oversimplified. Noise is the same (and Gaussian) on either side of the jet, and the jet is still modelled as a step function. A slightly more realistic model has also been investigated numerically, modelling the jet as $a(t)tanh{(chi - chi_0(t))} + b(t)$, with Gaussian random time series for $a$, $b$, and $chi_0$. Results from this are not shown as the curves produced are very similar (though not identical) to those given by the simpler model, and do not seem to provide much greater insight. Two main criteria determine whether the trajectory forms a wide loop about the point $S = 0$, $K = 3$: the jet must meander by more than its width, and the sea level noise either side of the jet must be smaller than the sea level step across the jet.
We have illustrated the actual skewness-kurtosis relationship for the Agulhas return current in Fig. 8. The centre of the jet at each longitude between 23.3˚E and 50˚E was defined as the point of minimum kurtosis in a narrow latitude range south of Africa. Kurtosis and skewness were then regridded, shifting each longitude to the north or south so that it was centered on the jet centre. Skewness and kurtosis at all points from 10 grid points south to 10 grid points north of the centre (a total range of about 4.8 degrees) are plotted in the figure as grey crosses. Then skewness and kurtosis were averaged at constant northward distance from the jet centre, and the resulting trajectory plotted as the thick line in Fig. 8.
Although the relationship does not lie along a particular constant $d$ curve, it is clear that the trajectory forms a fairly broad loop around $S = 0$, $K = 3$, often outside the $d = 2$ contour, and with minimum $K$ below 2.5 consistent with the observed bimodal distribution, and with the interpretation as a meandering jet. The asymmetry is interesting, suggesting that noise is more significant in the Antarctic Circumpolar Current (ACC) to the south of the jet, and that the meanders are the more dominant signal on the northern side, in the Indian Ocean. Thus, although kurtosis falls below 3 only in a small region around the mean jet position, the statistics remain consistent with interpretation as the effect of a meandering jet to a distance of several degrees either side of the jet.
It will not have escaped the readerÕs attention that the discussion has been in terms of sea level, whereas most of the illustrations are of relative vorticity. While it is clear that a jet must be associated with a drop in sea level, the associated vorticity pattern is not so clear, except to note that, as velocity is a maximum at the jet centre (assuming an eastward jet), relative vorticity must be cyclonic on the poleward side and anticyclonic on the equatorward side of the jet, and small far from the jet. It is not inevitable that the strongest gradient in relative vorticity lies at the jet centre.
In one sense, it does not matter. The arguments above apply if there is a sharp, meandering front in any quantity, and the low kurtosis region can then be taken to represent the mean position of that front. However, there is a more concrete model which is rather appealing, which is clearest if we consider things in terms of potential vorticity (PV). One model of a jet, recently reviewed by Dritschel and McIntyre (2008, D&M hereafter, see also references therein), is as the result of a step in PV. In this paradigm, jets represent a barrier to the mixing of PV, so PV tends to become mixed to two different, constant values either side of a jet, with a sharp gradient across the jet. In turn, inverting the PV distribution shows that such a PV staircase actually implies the existence of a jet at the position of the PV step, so a positive feedback exists tending to maintain this configuration. As PV is materially conserved, time series of PV in the vicinity of the jet will be close to the ideal of switching between two constant values which produces the lowest possible kurtosis values for a given skewness.
Our time series is, of necessity, relative vorticity rather than PV. However, if we assume we are in a dynamical regime in which variations of PV are dominated by vorticity rather than thickness variations (or if we assume a constant relationship between thickness and relative vorticity changes), then the time series of relative vorticity at a fixed point (so that $f$ is constant) will be equivalent to time series of PV. In this case, we can see that the low kurtosis regions are consistent with the existence of a PV step at the jet centre. This prompts the question of whether kurtosis bears a relationship to the presence of mixing barriers, which will be considered in the next section.
First, though, we turn our attention to the many sharply-deÞned low kurtosis features which are clear in Figs. 5 and 6. The Gulf Stream, Kuroshio, and Agulhas Return Current are clear, but there are many other features, particularly in the Southern Ocean, which could also plausibly represent jets or frontal features. From our model, the centres of jets which meander strongly should be characterized by regions where the zero contour of skewness coincides with a value of kurtosis less than 3. In Fig. 9 we plot these contours in black, using $zeta/f$ skewness and kurtosis, and insisting on a degree of spatial continuity by using a 5 by 5 grid point smoothed version of the fields. The contours are superimposed on a map (top) of mean surface geostrophic ßow speed based on the Rio05 mean dynamic topography (Rio and Hernandez, 2004). It is immediately clear that the technique correctly identifies not only the major eastward-ßowing jets, but a number of weaker, mid-ocean jets in all ocean basins. There are, however, significant disagreements with the Rio05 data, most notably in the Southern Ocean. Here, agreement is generally good in the northern parts of the ACC, but is less good further south, especially in the eastern PaciÞc sector where a number of apparent jets are identified which are absent from Rio05.
However, small-scale features in the Rio05 data rely for their detection primarily on the surface drifter data, and these southern regions of the ACC are precisely where the density of drifter data drops off. It may be that there are really jets in these regions, but they are not resolved by the measurements available to produce the Rio05 map. In order to test this possibility, we have turned to sea surface temperature (SST) gradients. These are not always indicative of surface currents, but the fact that the ACC is to first-order an equivalent barotropic ßow (Killworth, 1992; Killworth and Hughes, 2002) means that temperature at any depth does tend to be a good proxy for the dynamic topography in this region (Sun and Watts, 2001). In order to calculate a mean SST gradient, we have used merged infrared and microwave satellite data from the Mersea Odyssea project, downloaded from ftp://ftp.ifremer.fr/ ifremer/medspiration/data/l4hrsstfnd/eurdac/glob/odyssea. The data are provided as daily fields at 0.1 degree resolution. Over the period 1st October 2007 to 12th May 2009, 451 fields were available. These were differentiated to produce temperature gradients and each field inspected by eye to check for obvious artifacts. On this basis, 30 daily fields were eliminated. The remaining 421 fields of SST gradient were averaged, and regridded onto the AVISO altimetry grid.
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-5
|
However, small-scale features in the Rio05 data rely for their detection primarily on the surface drifter data, and these southern regions of the ACC are precisely where the density of drifter data drops off. It may be that there are really jets in these regions, but they are not resolved by the measurements available to produce the Rio05 map. In order to test this possibility, we have turned to sea surface temperature (SST) gradients. These are not always indicative of surface currents, but the fact that the ACC is to first-order an equivalent barotropic ßow (Killworth, 1992; Killworth and Hughes, 2002) means that temperature at any depth does tend to be a good proxy for the dynamic topography in this region (Sun and Watts, 2001). In order to calculate a mean SST gradient, we have used merged infrared and microwave satellite data from the Mersea Odyssea project, downloaded from ftp://ftp.ifremer.fr/ ifremer/medspiration/data/l4hrsstfnd/eurdac/glob/odyssea. The data are provided as daily fields at 0.1 degree resolution. Over the period 1st October 2007 to 12th May 2009, 451 fields were available. These were differentiated to produce temperature gradients and each field inspected by eye to check for obvious artifacts. On this basis, 30 daily fields were eliminated. The remaining 421 fields of SST gradient were averaged, and regridded onto the AVISO altimetry grid.
The resulting SST gradient plot is shown in the lower panel of Fig. 9, with our putative jet contours superimposed. It is clear that the Southern Ocean contours do indeed correspond with frontal features which were unresolved in the Rio05 data. In order to test how robust these comparisons are, we have repeated them with the Maximenko and Niiler (2005) dynamic topography, and with 7.25 years of SST data from the coarser-resolution AMSR-E microwave temperature measurements (Wentz and Meissner, 2004). The resulting pictures (not shown) are very similar, with a little smoothing of the SST gradient, and a little less smoothing of the geostrophic ßow speed (at the expense of more small-scale noise).
Fig. 9: Magnitude of the mean current (top) and mean sea surface temperature gradient (bottom), with black contours superimposed where the skewness/kurtosis relationship implies the mean centre of a jet or front to lie.
One final feature worth noting is that the identified path of the Kuroshio seems to be on the northern flank of the jet itself. The same is also true if sea level is used to identify this jet (not shown). This may be a result of the different averaging periods used for the mean current and the skewness and kurtosis; preliminary calculations using different subsets of the altimeter data produce more variation in results around the Kuroshio than elsewhere. Close inspection of the Gulf Stream also reveals some fine scale structure in the vorticity diagnostics which are not present in the sea level equivalents. It may be that, by combining the two analyses, more detailed information about the lateral structure of the jets can be extracted.
In summary, the pattern of a low kurtosis zone at the centre of a change in sign of skewness seems to be a reliable method of identifying meandering jets or frontal zones. When applied to time series of relative vorticity, this has allowed us to identify several jets previously unresolved by drifter data. In the next section, we will consider whether these low kurtosis zones also represent mixing barriers.
Does low kurtosis imply a mixing barrier?
As discussed above, the PV staircase model reviewed by D&M implies that jets occur at steps in PV, and that they act as mixing barriers. In fact D&M make the argument that mixing across a jet requires the presence of vortices with PV anomalies larger than the PV step which is associated with the jet. This sounds very similar to the criterion necessary for the formation of a low kurtosis region. If vortices are considered to be the ÔÔnoiseÓ on either side of the jet, then low kurtosis at the jet centre only occurs when the noise is smaller than the step, suggesting that low kurtosis should qualitatively be an indicator of a mixing barrier.
In order to test this suggestion, we turn to a set of idealized model experiments, initially run in order to investigate the effect of topography on jets and mixing in a zonal channel (Thompson, 2009). These are two-layer, quasigeostrophic simulations in a doubly-periodic channel, forced by an implicit zonal momentum flux which maintains a constant difference between the total zonal transports in the upper and lower layers. These model runs are not chosen because they are supposed to model particular parts of the real ocean, but because they explore a wide range of jet types and behaviors, including intermittent jets, meridionally-drifting jets, and topographically-steered jets, as well as steady, zonal jets. Another reason for the model choice is that the mixing diagnostics have already been performed, making it simple to compare mixing with kurtosis.
Four model experiments are considered. Experiment 1 is a ßat-bottomed channel, and produces four, steady, eastward jets, with weaker westward flow in-between. Experiment 32 has sinusoidal topography as a function of latitude only, and produces a sequence of jets which form in regions of strong background PV gradient, but drift north or south to regions of weak PV gradient, where they decay. Experiment 84 has topography which is sinusoidal in both latitude and longitude, producing a series of three strongly-steered eastward jets, with weaker westward ßow in between. Experiment 87 has similar topography, but only one strong eastward jet, which is more weakly steered and which intermittently breaks up in a bout of strong mixing. More details of these model runs are given in Thompson (2009). Mean and eddy kinetic energies vary by a factor of more than 40 between experiments, which clearly represent a wide range of conditions and kinds of jet.
Flow fields and PV kurtosis maps for the top layer are shown in Fig. 10 (in the case of experiment 32, this is a plot of zonally-aver aged ßow and kurtosis as a function of time and latitude, with kurtosis calculated using a moving window). It is clear that kurtosis is robustly low at the centre of the jets. For these experiments, the effective diffusivity $K_{eff}$ of upper layer PV was calculated as a function of time and equivalent latitude using the methodology of Shuckburgh and Haynes (2003). In order to compare across the range of experiments, it was found most effective to normalize the diffusivity by the square root of the domain-averaged EKE. The resulting normalized diffusivities would have dimensions of length, but the experiments were all non-dimensionalized using the Rossby radius $R_0$ as the length scale, and $R_0/U$ for time, where $U$ is the average imposed velocity difference between layer 1 and layer 2, so the normalized diffusivity should be multiplied by $R_0$ to give a dimensional value.
Fig. 10. Kurtosis of upper layer PV (shaded) and upper layer streamfunction (contours) for the four model experiments considered here. Plots are time averages, except for experiment 32, which is a zonal average as a function of time, the kurtosis being a running average over 20 time units.
The time-averaged values of $K_{eff}$, normalized by $sqrt{EKE}$, were compared with zonally-averaged values of PV kurtosis (in the case of experiments 84 and 87 the average was not zonal but along mean streamlines, because the mean flow is strongly-steered by topography). The resulting relationship between kurtosis and $K_{eff}/sqrt{EKE}$ is plotted for all experiments in Fig. 11. There is not just a qualitative relationship between the two, at low values of diffusivity there appears to be a strong, universal, linear relationship. As a guide (not any kind of formal Þt), the straight line $K_{eff}/sqrt{EKE} = (K - 1.3)/30$ has been drawn, which appears to fit the distribution fairly well.
Fig. 11: Scatter plot of surface layer normalized effective diffusivity against zonally-averaged kurtosis of PV (along stream-averaged for experiments 84 and 87) for the four numerical experiments. The solid line represents a suggested suitable linear relationship, but it is not a formal Þt. Values of the normalizing constant, non-dimensional domain-averaged $sqrt{EKE}$, are listed for each experiment.
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-6
|
Fig. 10. Kurtosis of upper layer PV (shaded) and upper layer streamfunction (contours) for the four model experiments considered here. Plots are time averages, except for experiment 32, which is a zonal average as a function of time, the kurtosis being a running average over 20 time units.
The time-averaged values of $K_{eff}$, normalized by $sqrt{EKE}$, were compared with zonally-averaged values of PV kurtosis (in the case of experiments 84 and 87 the average was not zonal but along mean streamlines, because the mean flow is strongly-steered by topography). The resulting relationship between kurtosis and $K_{eff}/sqrt{EKE}$ is plotted for all experiments in Fig. 11. There is not just a qualitative relationship between the two, at low values of diffusivity there appears to be a strong, universal, linear relationship. As a guide (not any kind of formal Þt), the straight line $K_{eff}/sqrt{EKE} = (K - 1.3)/30$ has been drawn, which appears to fit the distribution fairly well.
Fig. 11: Scatter plot of surface layer normalized effective diffusivity against zonally-averaged kurtosis of PV (along stream-averaged for experiments 84 and 87) for the four numerical experiments. The solid line represents a suggested suitable linear relationship, but it is not a formal Þt. Values of the normalizing constant, non-dimensional domain-averaged $sqrt{EKE}$, are listed for each experiment.
For kurtosis values significantly higher than 3, the relationship becomes looser. There is no reason to expect a relationship at these high $K$ values, so this is unsurprising. The relationship is also significantly worse for experiment 32, which again is not surprising as the value at each latitude is an average over times when there is low mixing and times when there is high mixing at that latitude. The surprise is that it works as well as it does, and falls on roughly the same range of values as the other experiments. Fig. 12: The same values of normalized effective diffusivity from Fig. 11, plotted as a function of effective latitudinal coordinate measured in Rossby radii. The dashed line is the value which would be predicted from kurtosis of PV, using the linear relationship suggested in Fig. 11.
Fig. 12 uses the linear scaling proposed in Fig. 11 to plot normalized $K_{eff}$ as a function of latitude for each experiment, together with the value which would be predicted from the kurtosis (dashed lines). This shows how well kurtosis captures the structure as well as values at the minima of diffusivity. There is a tendency to underestimate diffusivity where jets are drifting (experiment 32) or intermittent (experiment 87), in which case our simple model is no longer adequate, but even here there is a reasonable correspondence. Much better fits can be found for individual experiments by adding quadratic terms, but that is at the expense of universality, since the quadratic terms differ strongly between experiments.
Fig. 12: The same values of normalized effective diffusivity from Fig. 11, plotted as a function of effective latitudinal coordinate measured in Rossby radii. The dashed line is the value which would be predicted from kurtosis of PV, using the linear relationship suggested in Fig. 11.
Conclusions and discussion
Meandering jets in the ocean are associated with a characteristic pattern of skewness and kurtosis of sea level and, more clearly, relative vorticity. The mean position of the jet or front lies along the zero contour of skewness, which is also a region of low (less than 3) kurtosis. This can be explained using a model in which the jet or front represents a sharp step in sea level or relative vorticity, and meanders over a distance wider than the width of the step. We find little evidence that more useful data can be extracted from the spatial variation of PDFs beyond what is apparent from skewness and kurtosis. Using this relationship we have identified several Southern Ocean jets which were previously unresolved by drifter-based climatologies.
The fact that these features are seen more clearly in relative vorticity than in sea level suggests the use of a model of a jet as a step in PV, between two regions of well-mixed PV, as discussed recently by D&M. In this model, when the jump in PV across the step is larger than the eddy variations to either side, the step acts as a mixing barrier. These are precisely the conditions in which time series of PV would exhibit low kurtosis at the mean position of the jet centre. That led us to ask whether low kurtosis regions were indicative of the presence of a mixing barrier.
Across a wide variety of idealized model experiments, we find a strong, universal, linear relationship between PV kurtosis and effective diffusivity normalized by the square root of domain-averaged EKE. The relationship is particularly strong at low values of kurtosis, which represent the strongest mixing barriers. This suggests that the regions of low kurtosis from the relative vorticity time series may indeed represent mixing barriers in the ocean.
There are a couple of difficulties with linking the model experiments and our interpretation to the data. The data only tell us about relative vorticity, not PV. Variations in $f$ are not a problem, as the time series are at constant latitude, but if thickness variations are not either small or simply related to relative vorticity variations, then the time series we have may not be representative of PV variations. The second problem is that the relationship we find is between PV kurtosis and a diffusivity normalized by the square root of domain-averaged EKE. In the real ocean, what would be the appropriate region over which to average? Using local EKE in the model diagnostics results in significantly more scatter in the relationship, so some degree of spatial averaging is clearly needed, perhaps over an eddy Rhines scale? These difficulties mean that it would be premature to produce quantitative estimates of real ocean diffusivities using this method: a study is needed using more realistic ocean model geometry to determine how best to apply the relationship we find.
Kurtosis does, however, have two advantages over effective diffusivity: it is very simple to calculate, and it is a local quantity, meaning that maps are easily produced, unlike effective diffusivity which only varies in one spatial dimension (although it is less obvious how to produce time series of kurtosis than of diffusivity). This means that it may be useful for quick identifications of mixing barriers in a number of contexts. For example, it would be simple to extend the present analysis to subsurface regions in an ocean model, permitting the investigation of the three-dimensional geometry of mixing barriers. Similarly, the ideas should apply equally well to atmospheric data. As White (1980) showed, a similar pattern (a zero skewness contour between two regions of significant skewness of opposite signs, coinciding with a region of low kurtosis) occurs in maps derived from 500 mbar geopotential height, though not at 1000 mbar. As with sea level, it may be that this picture would be sharpened by considering relative vorticity or PV.
There is a good case to make skewness and kurtosis (whether it is of sea level, relative vorticity, or PV) standard diagnostics to be used to assess the realism of eddying ocean models, as well as to understand the dynamics of jets and mixing.
Appendix A. Derivation of statistics for a PDF which is the sum of two Gaussians
If we write the Gaussian distribution with standard deviation $sigma$ as
$$ G(chi, sigma) = frac{1}{sigmasqrt{2pi}}expleft({-chi^2/2sigma^2}right) $$, (6)
which has been normalized so that its integral is 1, then integration by parts shows that
$$ int_{-infty}^{infty}{chi^2 , G(chi, sigma) dchi} = sigma^2 $$, (7)
$$ int_{-infty}^{infty}{chi^4 , G(chi, sigma) dchi} = 3sigma^4 $$, (8)
and odd moments of $G$ are zero by symmetry.
The PDF which consists of two Gaussians separated by $d$ standard deviations is
$$ p = A G(chi + Bsigma d, sigma) + B G(chi - A sigma d, sigma) $$, (9)
where $B = 1 - A$, and the origin has been chosen so that the mean value of the PDF is zero (to construct this, note that the distances of the Gaussian centres from the origin must be inversely proportional to their integrals $A$ and $B$, and that the distance between the Gaussians is deÞned to be $sigma d$). The second moment of this distribution, which we will set to 1, is then given by
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
a4e559be412f-7
|
There is a good case to make skewness and kurtosis (whether it is of sea level, relative vorticity, or PV) standard diagnostics to be used to assess the realism of eddying ocean models, as well as to understand the dynamics of jets and mixing.
Appendix A. Derivation of statistics for a PDF which is the sum of two Gaussians
If we write the Gaussian distribution with standard deviation $sigma$ as
$$ G(chi, sigma) = frac{1}{sigmasqrt{2pi}}expleft({-chi^2/2sigma^2}right) $$, (6)
which has been normalized so that its integral is 1, then integration by parts shows that
$$ int_{-infty}^{infty}{chi^2 , G(chi, sigma) dchi} = sigma^2 $$, (7)
$$ int_{-infty}^{infty}{chi^4 , G(chi, sigma) dchi} = 3sigma^4 $$, (8)
and odd moments of $G$ are zero by symmetry.
The PDF which consists of two Gaussians separated by $d$ standard deviations is
$$ p = A G(chi + Bsigma d, sigma) + B G(chi - A sigma d, sigma) $$, (9)
where $B = 1 - A$, and the origin has been chosen so that the mean value of the PDF is zero (to construct this, note that the distances of the Gaussian centres from the origin must be inversely proportional to their integrals $A$ and $B$, and that the distance between the Gaussians is deÞned to be $sigma d$). The second moment of this distribution, which we will set to 1, is then given by
$$ int_{-infty}^{infty}{chi^2 , p dchi} = A int_{-infty}^{infty}{(chi - B sigma d)^2 G(chi, sigma)} dchi + B int_{-infty}^{infty}{(chi + A sigma d)^2 G(chi, sigma)} dchi $$. (10)
Expanding the squared terms, odd terms in $chi$ integrate to zero, and even terms were evaluated above, so this gives, after some gathering of terms,
$$ 1 = sigma^2(1 + d^2P) $$, (11)
where $P = AB$, or
$sigma = (1 + d^2P)^{-1/2}$. (12)
The same procedure can be applied to the third and fourth moments, leading to
$$ S = sigma^3 d^3 P(A - B) $$, (13)
and
$$ K = 3sigma^4 + d^2 sigma^4 P[6 + d^2(1 - 3P)] $$. (14)
Substituting for $sigma$ and simplifying then leads to (3) and (4).
|
https://sealeveldocs.readthedocs.io/en/latest/hughes10.html
|
1ea2eff08fb1-0
|
DeConto and Pollard (2016)
Title:
Contribution of Antarctica to past and future sea-level rise
Key Points:
Antarctic ice sheet (AIS) mass loss contributed significantly to past sea-level rise during warmer periods.
Model predicts over 1 m sea-level rise by 2100, 15 m by 2500 if emissions continue unabated.
Atmospheric warming might become the dominant driver of AIS while ocean warming will delay recovery of the AIS
Keywords:
Antarctic ice sheet, sea-level rise, climate change, greenhouse gas emissions, ice sheet modelling
Corresponding author:
Robert M. DeConto
Citation:
DeConto, R. M., & Pollard, D. (2016). Contribution of Antarctica to past and future sea-level rise. Nature, 531(7596), 591–597. doi:10.1038/nature17145
URL:
https://www.nature.com/articles/nature17145
Abstract
Polar temperatures over the last several million years have, at times, been slightly warmer than today, yet global mean sea level has been 6–9 metres higher as recently as the Last Interglacial (130,000 to 115,000 years ago) and possibly higher during the Pliocene epoch (about three million years ago). In both cases the Antarctic ice sheet has been implicated as the primary contributor, hinting at its future vulnerability. Here we use a model coupling ice sheet and climate dynamics—including previously underappreciated processes linking atmospheric warming with hydrofracturing of buttressing ice shelves and structural collapse of marine-terminating ice cliffs—that is calibrated against Pliocene and Last Interglacial sea-level estimates and applied to future greenhouse gas emission scenarios. Antarctica has the potential to contribute more than a metre of sea-level rise by 2100 and more than 15 metres by 2500, if emissions continue unabated. In this case atmospheric warming will soon become the dominant driver of ice loss, but prolonged ocean warming will delay its recovery for thousands of years.
Editorial Summary: A 500-year model of Antarctica’s contribution to future sea-level rise
Robert DeConto and David Pollard use a newly improved numerical ice-sheet model calibrated to Pliocene and Last Interglacial sea-level estimates to develop projections of Antarctica’s evolution over the next five centuries, driven by a range of greenhouse gas scenarios. The modelling shows that the Antarctic ice sheet has the potential to contribute between almost nothing, to contributing more than a metre of sea-level rise by 2100 and more than 15 metres by 2500. The startling high-end estimate arises from unabated emissions and previously underappreciated mechanisms: ice-fracturing by surface meltwater and collapse of large ice cliffs. The low end shows that a scenario of strong climate mitigation can radically reduce societal exposure to higher sea levels.
Introduction
Reconstructions of the global mean sea level (GMSL) during past warm climate intervals including the Pliocene (about three million years ago)1 and late Pleistocene interglacials2,3,4,5 imply that the Antarctic ice sheet has considerable sensitivity. Pliocene atmospheric CO2 concentrations were comparable to today’s (~400 parts per million by volume, p.p.m.v.)6, but some sea-level reconstructions are 10–30 m higher1,7. In addition to the loss of the Greenland Ice Sheet and the West Antarctic Ice Sheet (WAIS)2, these high sea levels require the partial retreat of the East Antarctic Ice Sheet (EAIS), which is further supported by sedimentary evidence from the Antarctic margin8. During the more recent Last Interglacial (LIG, 130,000 to 115,000 years ago), GMSL was 6–9.3 m higher than it is today2,3,4, at a time when atmospheric CO2 concentrations were below 280 p.p.m.v. (ref. 9) and global mean temperatures were only about 0–2 °C warmer10. This requires a substantial sea-level contribution from Antarctica of 3.6–7.4 m in addition to an estimated 1.5–2 m from Greenland11,12 and around 0.4 m from ocean steric effects10. For both the Pliocene and the LIG, it is difficult to obtain the inferred sea-level values from ice-sheet models used in future projections.
Marine ice sheet and ice cliff instabilities
Much of the WAIS sits on bedrock hundreds to thousands of metres below sea level (Fig. 1a)13. Today, extensive floating ice shelves in the Ross and Weddell Seas, and smaller ice shelves and ice tongues in the Amundsen and Bellingshausen seas (Fig. 1b) provide buttressing that impedes the seaward flow of ice and stabilizes marine grounding zones (Fig. 2a). Despite their thickness (typically about 1 km near the grounding line to a few hundred metres at the calving front), a warming ocean has the potential to quickly erode ice shelves from below, at rates exceeding 10 m yr−1 °C−1 (ref. 14). Ice-shelf thinning and reduced backstress enhance seaward ice flow, grounding-zone thinning, and retreat (Fig. 2b). Because the flux of ice across the grounding line increases strongly as a function of its thickness15, initial retreat onto a reverse-sloping bed (where the bed deepens and the ice thickens upstream) can trigger a runaway Marine Ice Sheet Instability (MISI; Fig. 2c)15,16,17. Many WAIS grounding zones sit precariously on the edge of such reverse-sloped beds, but the EAIS also contains deep subglacial basins with reverse-sloping, marine-terminating outlet troughs up to 1,500 m deep (Fig. 1). The ice above floatation in these East Antarctic basins is much thicker than in West Antarctica, with the potential to raise GMSL by around 20 m if the ice in those basins is lost13. Importantly, previous ice-sheet simulations accounting for migrating grounding lines and MISI dynamics have shown the potential for repeated WAIS retreats and readvances over the past few million years18, but could only account for GMSL rises of about 1 m during the LIG and 7 m in the warm Pliocene, which are substantially smaller than geological estimates.
Figure 1: Antarctic sub-glacial topography and ice sheet features. a, Bedrock elevations13 interpolated onto the 10-km polar stereographic ice-sheet model grid and used in Pliocene, LIG, and future ice-sheet simulations. b, Model surface ice speeds and grounding lines (black lines) show the location of major ice streams, outlet glaciers, and buttressing ice shelves (seaward of grounding lines) relative to the underlying topography in a. Features and place names mentioned in the text are also shown. AS, Amundsen Sea; BS, Bellingshausen Sea; WDIC, WAIS Divide Ice Core. The locations of the Pine Island, Thwaites, Ninnis, Mertz, Totten, and Recovery glaciers are shown. Model ice speeds (b) are shown after equilibration with a modern atmospheric and ocean climatology (see Methods).
Figure 2: Schematic representation of MISI and MICI and processes included in the ice model. Top-to-bottom sequences (a–c and d–f) show progressive ice retreat into a subglacial basin, triggered by oceanic and atmospheric warming. The pink arrow represents the advection of warm circumpolar deep water (CDW) into the shelf cavity. a, Stable, marine-terminating ice-sheet margin, with a buttressing ice shelf. Seaward ice flux is strongly dependent on grounding-line thickness h. Sub-ice melt rates increase with open-ocean warming and warm-water incursions into the ice-shelf cavity. b, Thinning shelves and reduced buttressing increase seaward ice flux, backing the grounding line onto reverse-sloping bedrock. c, Increasing h with landward grounding-line retreat leads to an ongoing increase in ice flow across the grounding line in a positive runaway feedback until the bed slope changes. d, In addition to MISI (a–c), the model physics used here account for surface-meltwater-enhanced calving via hydrofracturing of floating ice (e), providing an additional mechanism for ice-shelf loss and initial grounding-line retreat into deep basins. f, Where oceanic melt and enhanced calving eliminate shelves completely, subaerial cliff faces at the ice margin become structurally unstable where h exceeds 800 m, triggering rapid, unabated MICI retreat into deep basins.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-1
|
Figure 1: Antarctic sub-glacial topography and ice sheet features. a, Bedrock elevations13 interpolated onto the 10-km polar stereographic ice-sheet model grid and used in Pliocene, LIG, and future ice-sheet simulations. b, Model surface ice speeds and grounding lines (black lines) show the location of major ice streams, outlet glaciers, and buttressing ice shelves (seaward of grounding lines) relative to the underlying topography in a. Features and place names mentioned in the text are also shown. AS, Amundsen Sea; BS, Bellingshausen Sea; WDIC, WAIS Divide Ice Core. The locations of the Pine Island, Thwaites, Ninnis, Mertz, Totten, and Recovery glaciers are shown. Model ice speeds (b) are shown after equilibration with a modern atmospheric and ocean climatology (see Methods).
Figure 2: Schematic representation of MISI and MICI and processes included in the ice model. Top-to-bottom sequences (a–c and d–f) show progressive ice retreat into a subglacial basin, triggered by oceanic and atmospheric warming. The pink arrow represents the advection of warm circumpolar deep water (CDW) into the shelf cavity. a, Stable, marine-terminating ice-sheet margin, with a buttressing ice shelf. Seaward ice flux is strongly dependent on grounding-line thickness h. Sub-ice melt rates increase with open-ocean warming and warm-water incursions into the ice-shelf cavity. b, Thinning shelves and reduced buttressing increase seaward ice flux, backing the grounding line onto reverse-sloping bedrock. c, Increasing h with landward grounding-line retreat leads to an ongoing increase in ice flow across the grounding line in a positive runaway feedback until the bed slope changes. d, In addition to MISI (a–c), the model physics used here account for surface-meltwater-enhanced calving via hydrofracturing of floating ice (e), providing an additional mechanism for ice-shelf loss and initial grounding-line retreat into deep basins. f, Where oceanic melt and enhanced calving eliminate shelves completely, subaerial cliff faces at the ice margin become structurally unstable where h exceeds 800 m, triggering rapid, unabated MICI retreat into deep basins.
So far, the potential for MISI to cause ice-sheet retreat has focused on the role of ocean-driven melting of buttressing ice shelves from below16,18,19,20. However, it is often overlooked that the major ice shelves in the Ross and Weddell seas and the many smaller shelves and ice tongues buttressing outlet glaciers are also vulnerable to atmospheric warming. Today, summer temperatures approach or just exceed 0 °C on many shelves21, and their flat surfaces near sea level mean that little atmospheric warming would be needed to dramatically increase the areal extent of surface melting and summer rainfall.
Meltwater on ice-shelf surfaces causes thinning if it percolates through the shelf to the ocean. If refreezing occurs, the ice is warmed, reducing its viscosity and speeding its flow22. The presence of rain and meltwater can also influence crevassing and calving rates23 (hydrofracturing) as witnessed on the Antarctic Peninsula’s Larson B ice shelf during its sudden break-up in 200224. Similar dynamics could have affected the ice sheet during ancient warm intervals25, and given enough future warming, could eventually affect many ice shelves and ice tongues, including the major buttressing shelves in the Ross and Weddell seas.
Another physical mechanism previously underappreciated at the ice-sheet scale involves the mechanical collapse of ice cliffs in places where marine-terminating ice margins approach 1 km in thickness, with >90 m of vertical exposure above sea level26. Today, most Antarctic outlet glaciers with deep beds approaching a water depth of 1 km are protected by buttressing ice shelves, with gently sloping surfaces at the grounding line (Fig. 2d). However, given enough atmospheric warming above or ocean warming below (Fig. 2e), ice-shelf retreat can outpace its dynamically accelerated seaward flow as buttressing is lost and retreating grounding lines thicken15. In places where marine-terminating grounding lines are thicker than 800 m or so, this would produce >90 m subaerial cliff faces that would collapse (Fig. 2f) simply because longitudinal stresses at the cliff face would exceed the yield strength (about 1 MPa) of the ice26.
More heavily crevassed and damaged ice would reduce the maximum supported cliff heights. If a thick, marine-terminating grounding line began to undergo such mechanical failure, its retreat would continue unabated until temperatures cooled enough to reform a buttressing ice shelf, or the ice margin retreated onto bed elevations too shallow to support the tall, unstable cliffs25. If protective ice shelves were suddenly lost in the vast areas around the Antarctic margin where reverse-sloping bedrock is more than 1,000 m deep (Fig. 1a), exposed grounding-line ice cliffs would quickly succumb to structural failure, as is happening in the few places where such conditions exist today (the Helheim and Jakobsavn glaciers on Greenland and the Crane Glacier on the Antarctic Peninsula), hinting that a Marine Ice Cliff Instability (MICI) in addition to MISI could be an important contributor to past and future ice-sheet retreat.
Our three-dimensional ice sheet–ice shelf model25,27 (Methods) predicts the evolution of continental ice thickness and temperature as a function of ice flow (deformation and sliding) and changes in mass balance via precipitation, runoff, basal melt, oceanic melt under ice shelves and on vertical ice faces, calving, and tidewater ice-cliff failure. The model captures MISI (Fig. 2a–c) by accounting for migrating grounding lines and the buttressing effects of ice shelves with pinning points and side-shear. To capture the dynamics of MICI (Fig. 2d–f), new physical treatments of surface-melt and rainwater-enhanced calving (hydrofracturing) and grounding-line ice-cliff dynamics have been added25. Including these processes was found to increase the model’s contribution to Pliocene GMSL from +7 m (ref. 18) to +17 m (ref. 25). The model formulation used here is similar to that described in ref. 25, but with improvements in the treatment of calving, thermodynamics, and climate–ice–ocean coupling (Methods).
The Antarctic Ice Sheet in the Pliocene
The warm mid-Pliocene and LIG provide complementary targets for model performance, via the ability to produce ~5–20 m and ~3.5–7.5 m GMSL from Antarctica, respectively. These two time periods highlight model sensitivities to different processes, because Pliocene summer air temperatures were capable of producing substantial surface meltwater, especially during warm austral summer orbits28. Conversely, LIG temperatures were cooler29, with limited potential for surface meltwater production. Instead, ocean temperatures30 could have been the determining factor in LIG ice retreat31.
To simulate Pliocene and LIG ice sheets, we couple the ice model to a high-resolution, atmospheric regional climate model (RCM) adapted to Antarctica and nested within a global climate model (GCM; see Methods). The RCM captures the orographic details of ice shelves and adjacent ice-sheet margins, which is critical here because the new calving and grounding line processes are mechanistically linked to the atmosphere.
High-resolution ocean modelling beneath time-evolving ice shelves on palaeoclimate timescales exceeds existing capabilities. Instead, we use a modern ocean climatology32 interpolated to our ice-sheet grid, with uniformly imposed sub-surface ocean warming providing melt rates on sub-ice-shelf and calving-front surfaces exposed to sea water. The RCM climatologies and imposed ocean warming are applied to quasi-equilibrated initial ice-sheet states, with atmospheric temperatures and the precipitation lapse-rate corrected as the ice sheet evolves.
As in ref. 25, the Pliocene simulation uses a RCM climatology with 400 p.p.m.v. CO2, a warm austral summer orbit28, and 2 °C imposed ocean warming to represent maximum mid-Pliocene warmth (Extended Data Fig. 1). The model produces an 11.3-m contribution to GMSL rise, reflecting a reduction in its sensitivity of about 6 m relative to the formulation in ref. 25, but within the range of plausible sea-level estimates1,7. Pliocene retreat is triggered by meltwater-induced hydrofracturing of ice shelves, which relieves backstress and initiates both MISI and MICI retreat into the deepest sectors of WAIS and EAIS marine basins.
The Antarctic Ice Sheet during the LIG
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-2
|
The Antarctic Ice Sheet in the Pliocene
The warm mid-Pliocene and LIG provide complementary targets for model performance, via the ability to produce ~5–20 m and ~3.5–7.5 m GMSL from Antarctica, respectively. These two time periods highlight model sensitivities to different processes, because Pliocene summer air temperatures were capable of producing substantial surface meltwater, especially during warm austral summer orbits28. Conversely, LIG temperatures were cooler29, with limited potential for surface meltwater production. Instead, ocean temperatures30 could have been the determining factor in LIG ice retreat31.
To simulate Pliocene and LIG ice sheets, we couple the ice model to a high-resolution, atmospheric regional climate model (RCM) adapted to Antarctica and nested within a global climate model (GCM; see Methods). The RCM captures the orographic details of ice shelves and adjacent ice-sheet margins, which is critical here because the new calving and grounding line processes are mechanistically linked to the atmosphere.
High-resolution ocean modelling beneath time-evolving ice shelves on palaeoclimate timescales exceeds existing capabilities. Instead, we use a modern ocean climatology32 interpolated to our ice-sheet grid, with uniformly imposed sub-surface ocean warming providing melt rates on sub-ice-shelf and calving-front surfaces exposed to sea water. The RCM climatologies and imposed ocean warming are applied to quasi-equilibrated initial ice-sheet states, with atmospheric temperatures and the precipitation lapse-rate corrected as the ice sheet evolves.
As in ref. 25, the Pliocene simulation uses a RCM climatology with 400 p.p.m.v. CO2, a warm austral summer orbit28, and 2 °C imposed ocean warming to represent maximum mid-Pliocene warmth (Extended Data Fig. 1). The model produces an 11.3-m contribution to GMSL rise, reflecting a reduction in its sensitivity of about 6 m relative to the formulation in ref. 25, but within the range of plausible sea-level estimates1,7. Pliocene retreat is triggered by meltwater-induced hydrofracturing of ice shelves, which relieves backstress and initiates both MISI and MICI retreat into the deepest sectors of WAIS and EAIS marine basins.
The Antarctic Ice Sheet during the LIG
Summer air temperatures in the RCM are slightly warmer at 116 kyr ago than 128 kyr ago, but remain below freezing in both cases, with little to no surface melt (Extended Data Fig. 2). As a result, substantial oceanic warming >4 °C is required to initiate WAIS retreat at 128 kyr ago, which occurs once an ocean-melt threshold is reached in the stability of the Thwaites grounding line (Extended Data Fig. 3a and d). Allowing two-way coupling between the RCM and the ice-sheet model (Methods) captures dynamical atmospheric feedbacks as the ice margin retreats. This enhances retreat (Extended Data Fig. 3b, e), but still requires >4 °C of ocean warming to produce a >3.5 m increase in GMSL. We find that by accounting for the additional influence of circum-Antarctic ocean warming on the RCM atmosphere (Methods), the GMSL contribution increases to >6.5 m with just 3 °C sub-surface ocean warming (Extended Data Fig. 3c and f), despite the cooler orbit of the Earth 128 kyr ago. The ocean-driven continental warming at 128 kyr ago agrees with ice core records29 and supports a Southern Ocean control on the timing of ice-sheet retreat30,31, possibly through Northern Hemisphere influences on the ocean meridional overturning circulation33.
Alternative simulations (Fig. 3) use time-evolving atmospheric and oceanic climatologies (Methods) based on marine and ice-core proxy reconstructions29. These time-continuous simulations produce GMSL contributions of 6–7.5 m early in the interglacial, followed by a prolonged plateau and rapid recovery of the ice sheet beginning around 115 kyr ago. This result matches the magnitude, temporal pattern, and rate of LIG sea-level change in ref. 3. (Fig. 3a), and the simulated recovery of the WAIS satisfies the presence of ice >70 kyr ago at the bottom of the WAIS Divide Ice Core34.
Figure 3: Ice-sheet simulations and Antarctic contributions to GMSL through the LIG driven by a time-evolving, proxy-based atmosphere–ocean climatology. a, Change in GMSL in LIG simulations starting at 130 kyr ago and initialized with a modern ice sheet (blue) or a bigger LGM ice sheet representing glacial conditions at the onset of the LIG (red). A probabilistic reconstruction of Antarctica’s contribution to GMSL is shown in black3 with uncertainties (16th and 84th percentiles) as dashed lines. b, c, Ice-sheet thickness at the time of maximum retreat using modern initial conditions (b) and using glacial initial conditions (c). Ice-free land surfaces are brown. The bigger sea-level response when initialized with the ‘glacial’ ice sheet is caused by deeper bed elevations and the ~3,000-yr lagged bedrock response to ice retreat50, which enhances bathymetrically sensitive MISI dynamics. d, The same simulation as b without the new model physics accounting for meltwater-enhanced calving or ice-cliff failure27. GMSL contributions are shown at top left.
Combined with estimates of Greenland ice loss11,12,35 and ocean thermal effects10, the simulated, Antarctic contributions to Pliocene and LIG sea level are in much better agreement with geological estimates2,3,4 than previous versions of our model18,27, which lacked these new treatments of meltwater-enhanced calving and ice-margin dynamics, suggesting that the new model is better suited to simulations of future ice response.
Future simulations
Using the same model physics and parameter values as used in the Pliocene and LIG simulations, we apply the ice-sheet model to long-term future simulations (Methods). Here, atmospheric forcing is provided by high-resolution RCM simulations (Extended Data Fig. 4) following three extended Representative Carbon Pathway (RCP) scenarios (RCP2.6, RCP4.5 and RCP8.5)36. Future circum-Antarctic ocean temperatures used in our time-evolving sub-ice melt-rate calculations come from matching, high-resolution (1°) National Center for Atmospheric Research (NCAR) CCSM4 simulations (ref. 37, Extended Data Fig. 5). The simulations begin in 1950 to provide some hindcast spinup, and are run for 550 years to 2500.
The RCP scenarios (Fig. 4) produce a wide range of future Antarctic contributions to sea level, with RCP2.6 producing almost no net change by 2100, and only 20 cm by 2500. Conversely, RCP4.5 causes almost complete WAIS collapse within the next five hundred years, primarily owing to the retreat of Thwaites Glacier into the deep WAIS interior. The Siple Coast grounding zone remains stable until late in the simulation, thanks to the persistence of the buttressing Ross Ice Shelf (see Supplementary Video 2). In RCP4.5, GMSL rise is 32 cm by 2100, but subsequent retreat of the WAIS interior, followed by the fringes of the Wilkes Basin and the Totten Glacier/Law Dome sector of the Aurora Basin produces 5 m of GMSL rise by 2500.
Figure 4: Future ice-sheet simulations and Antarctic contributions to GMSL from 1950 to 2500 driven by a high-resolution atmospheric model and 1° NCAR CCSM4 ocean temperatures. a, Equivalent CO2 forcing applied to the simulations, following the RCP emission scenarios in ref. 36, except limited to 8 × PAL (preindustrial atmospheric level, where 1 PAL = 280 p.p.m.v.). b, Antarctic contribution to GMSL. c, Rate of sea-level rise and approximate timing of major retreat and thinning in the Antarctic Peninsula (AP), Amundsen Sea Embayment (ASE) outlet glaciers, AS–BS, Amundsen Sea–Bellingshausen Sea; the Totten (T), Siple Coast (SC) and Weddell Sea (WS) grounding zones, the deep Thwaites Glacier basin (TG), interior WAIS, the Recovery Glacier, and the deep EAIS basins (Wilkes and Aurora). d, Antarctic contribution to GMSL over the next 100 years for RCP8.5 with and without a +3 °C adjustment in ocean model temperatures in the Amundsen and Bellingshausen seas as shown in Extended Data Fig. 5d. e–g, Ice-sheet snapshots at 2500 in the RCP2.6 (e), RCP4.5 (f) and RCP8.5 (g) scenarios. Ice-free land surfaces are shown in brown. h, Close-ups of the Amundsen Sea sector of WAIS in RCP8.5 with bias-corrected ocean model temperatures.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-3
|
Figure 4: Future ice-sheet simulations and Antarctic contributions to GMSL from 1950 to 2500 driven by a high-resolution atmospheric model and 1° NCAR CCSM4 ocean temperatures. a, Equivalent CO2 forcing applied to the simulations, following the RCP emission scenarios in ref. 36, except limited to 8 × PAL (preindustrial atmospheric level, where 1 PAL = 280 p.p.m.v.). b, Antarctic contribution to GMSL. c, Rate of sea-level rise and approximate timing of major retreat and thinning in the Antarctic Peninsula (AP), Amundsen Sea Embayment (ASE) outlet glaciers, AS–BS, Amundsen Sea–Bellingshausen Sea; the Totten (T), Siple Coast (SC) and Weddell Sea (WS) grounding zones, the deep Thwaites Glacier basin (TG), interior WAIS, the Recovery Glacier, and the deep EAIS basins (Wilkes and Aurora). d, Antarctic contribution to GMSL over the next 100 years for RCP8.5 with and without a +3 °C adjustment in ocean model temperatures in the Amundsen and Bellingshausen seas as shown in Extended Data Fig. 5d. e–g, Ice-sheet snapshots at 2500 in the RCP2.6 (e), RCP4.5 (f) and RCP8.5 (g) scenarios. Ice-free land surfaces are shown in brown. h, Close-ups of the Amundsen Sea sector of WAIS in RCP8.5 with bias-corrected ocean model temperatures.
In RCP8.5, increased precipitation causes an initial, minor gain in total ice mass (Fig. 4d), but rapidly warming summer air temperatures trigger extensive surface meltwater production38 and hydrofracturing of ice shelves by the middle of this century (Extended Data Fig. 4). The Larsen C is one of the first shelves to be lost, about 2055. Around the same time, major thinning and retreat of outlet glaciers commences in the Amundsen Sea Embayment, beginning with Pine Island Glacier (Fig. 4h), and along the Bellingshausen margin. Massive meltwater production on shelf surfaces, and eventually on the flanks of the ice sheet, would quickly overcome the buffering capacity of firn39. In the model, the meltwater accelerates WAIS retreat via its thermomechanical influence on ice rheology (Methods) and the influence of hydrofacturing on crevassing and structural failure of the retreating margin. Antarctica contributes 77 cm of GMSL rise by 2100, and continued loss of the Ross and Weddell Sea ice shelves drives WAIS retreat from three sides simultaneously (the Amundsen, Ross, and Weddell seas), all with reverse-sloping beds into the deep ice-sheet interior. As a result, WAIS collapses within 250 years. At the same time, steady retreat into the Wilkes and Aurora basins, where the ice above floatation is >2,000 m thick, adds substantially to the rate of sea-level rise, exceeding 4 cm yr−1 (Fig. 4c) in the next century, which is comparable to maximum rates of sea-level rise during the last deglaciation40. At 2500, GMSL rise for the RCP8.5 scenario is 12.3 m. As in our LIG simulations, atmosphere–ice sheet coupling accounting for the warming feedback associated with the retreating ice sheet adds an additional 1.3 m of GMSL to the RCP8.5 scenario (Fig. 4b).
The CCSM4 simulations providing the model’s sub-ice-shelf melt rates (Extended Data Fig. 5) underestimate the penetration of warm Circum-Antarctic Deep Water into the Amundsen and Bellingshausen seas observed in recent decades41. As a result, the model fails to capture recent, 21st-century thinning and grounding-line retreat along the southern Antarctic Peninsula42 and the Amundsen Sea Embayment43. Correcting for the ocean-model cool bias along this sector of coastline improves the position of Pine Island and Thwaites grounding lines relative to observations42,43 (Fig. 4h) and increases GMSL rise by 9 cm at 2100 (mainly due to the accelerated retreat of Pine Island Glacier), but the correction has little effect on longer timescales (Extended Data Table 1). Ocean warming is important to the behaviour of individual outlet glaciers early in the simulations, but we find that most of the long-term sea-level rise in RCP4.5 and RCP8.5 scenarios is caused by atmospheric warming and the onset of extensive surface meltwater production, rather than ocean warming as implied by other recent studies44,45,46. Without atmospheric warming, the magnitude of RCP8.5 ocean warming in CCSM4 is insufficient to cause the major retreat of the WAIS or East Antarctic basins; and even with >3 °C additional warming in the Amundsen and Bellingshausen seas it takes several thousand years for WAIS to retreat via ocean-driven MISI dynamics alone (Extended Data Fig. 6). We note that despite the 10-km grid resolution, the model simulates major ice streams well (Fig. 1), including their internal variability18. However, during drastic subglacial-basin retreat the internal variability is quickly overtaken as grounding lines recede into deep interior catchments (see Supplementary Video 10).
Large Ensemble analysis
To better utilize Pliocene and LIG geological constraints on model performance, we perform a Large Ensemble analysis (Methods) to explore the uncertainty associated with the primary parameter values controlling (1) relationships between ocean temperature and sub-ice-shelf melt rates, (2) hydrofracturing (crevasse penetration in relation to surface liquid water supply), and (3) maximum rates of marine-terminating ice-cliff failure. The combination of Pliocene and LIG sea level targets is ideal, because Pliocene retreat is dominated by processes associated with (2) and (3), while the LIG is dominated by process (1).
Both Pliocene and LIG ensembles are run with combinations of widely ranging parameter values associated with the three processes, and the combinations are scored by their ability to simulate target ranges of Pliocene and LIG Antarctic sea-level contributions (Methods). The filtered subsets of parameter values capable of reproducing both targets are then used in ensembles of future RCP scenarios (Extended Data Table 2), providing both an envelope of possible outcomes and an estimate of the model’s parametric uncertainty (Fig. 5). Importantly, the ensemble analysis supports our choice of ‘default’ model parameters used in the nominal Pliocene, LIG, and future simulations (Fig. 4, Extended Data Table 2). The lack of substantial ice-sheet retreat in the optimistic RCP2.6 scenario remains unchanged, but the Large Ensemble analysis substantially increases our RCP4.5 and RCP8.5 2100 sea-level projections to 49 ± 20 cm and 105 ± 30 cm, if higher (>10 m instead of >5 m) Pliocene sea-level targets are used. Adding the ocean temperature correction in the Amundsen and Bellingshausen seas (Fig. 4d and h) further increases the 2100 projections in RCP2.6, RCP4.5 and RCP8.5 to 16 ± 16 cm, 58 ± 28 cm and 114 ± 36 cm, respectively (see Methods and Extended Data Tables 1 and 2).
Figure 5: Large Ensemble model analyses of future Antarctic contributions to GMSL. a, RCP ensembles to 2500. b, RCP ensembles to 2100. Changes in GMSL are shown relative to 2000, although the simulations begin in 1950. Ensemble members use combinations of model parameters (Methods) filtered according to their ability to satisfy two geologic criteria: a Pliocene target of 10–20 m GMSL and a LIG target of 3.6–7.4 m. c and d are the same as a and b, but use a lower Pliocene GMSL target of 5–15 m. Solid lines are ensemble means, and the shaded areas show the standard deviation (1σ) of the ensemble members. The 1σ ranges represent the model’s parametric uncertainty, while the alternate Pliocene targets (a and b versus c and d) illustrate the uncertainty related to poorly constrained Pliocene sea-level targets. Mean values and 1σ uncertainties at 2500 and 2100 are shown.
Long-term commitment to elevated sea level
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-4
|
Figure 5: Large Ensemble model analyses of future Antarctic contributions to GMSL. a, RCP ensembles to 2500. b, RCP ensembles to 2100. Changes in GMSL are shown relative to 2000, although the simulations begin in 1950. Ensemble members use combinations of model parameters (Methods) filtered according to their ability to satisfy two geologic criteria: a Pliocene target of 10–20 m GMSL and a LIG target of 3.6–7.4 m. c and d are the same as a and b, but use a lower Pliocene GMSL target of 5–15 m. Solid lines are ensemble means, and the shaded areas show the standard deviation (1σ) of the ensemble members. The 1σ ranges represent the model’s parametric uncertainty, while the alternate Pliocene targets (a and b versus c and d) illustrate the uncertainty related to poorly constrained Pliocene sea-level targets. Mean values and 1σ uncertainties at 2500 and 2100 are shown.
Long-term commitment to elevated sea level
Ocean warming alone may be limited in its potential to trigger massive, widespread ice loss, but the multi-millennial thermal response time of the ocean47 will have a profound influence on the ice sheet’s recovery. In simulations run 5,000 years into the future, we conservatively assume no ocean warming beyond 2300 and simply maintain those ocean temperatures while the atmosphere cools assuming different scenarios of CO2 drawdown beginning in 2500 (Methods). For RCP8.5 and natural CO2 drawdown, GMSL continues to rise until 3500 with a peak of about 20 m, after which the warm ocean inhibits the re-advance of grounding lines into deep marine basins for thousands of years (Extended Data Fig. 7). Even in the moderate RCP4.5 scenario with rapidly declining CO2 after 2500, WAIS is unable to recover until the global ocean cools, implying a multi-millennial commitment to several metres of sea-level rise despite human-engineered CO2 drawdown.
Given uncertainties in model initial conditions, simplified hybrid ice dynamics, parameterized sub-ice melt, calving, structural ice-margin failure, and the ancient sea-level estimates used in our Large Ensemble analysis, the rates of ice loss simulated here should not be viewed as actual predictions, but rather as possible envelopes of behaviour (Fig. 5) that include processes not previously considered at the continental scale. These are among the first continental-scale simulations with model physics constrained by ancient sea-level estimates, simultaneously accounting for high-resolution atmosphere–ice sheet coupling and ocean model temperatures.
However, several important processes are lacking and should be included in future work. In particular, the model lacks two-way coupling between the ice sheet and the ocean. This is especially relevant for RCP8.5, in which >1 Sv of freshwater and icebergs would be supplied to the Southern Ocean during peak retreat (Extended Data Fig. 8). Rapid calving and ice-margin collapse also implies ice mélange in restricted embayments that could provide buttressing and a negative feedback on retreat. The loss of ice mass would also have a strong effect on relative sea level at the margin owing to gravitational and solid-earth deformation effects48, which could affect MISI and MICI dynamics because of their strong dependency on bathymetry. Future simulations should include coupling with Earth models that account for these processes. Improved ancient sea-level estimates are also needed to further constrain model physics and to reduce uncertainties in future RCP scenarios (Fig. 5).
Despite these limitations, our new model physics are shown to be capable of simulating two very different ancient sea-level events: the LIG, driven primarily by ocean warming and MISI dynamics, and the warmer Pliocene, in which surface meltwater and MICI dynamics are also important. When applied to future scenarios with high greenhouse gas emissions, our palaeo-filtered model ensembles show the potential for Antarctica to contribute >1 m of GMSL rise by the end of this century, and >15 m metres of GMSL rise in the next 500 years. In RCP8.5, the projected onset of major ice-sheet retreat occurs sooner (about 2050), and is substantially faster (>4 cm yr−1 after 2100) and higher (Figs 4 and 5) than implied by other recent studies44,45,49. These differences are mainly due to our addition of model physics linking surface meltwater and ice dynamics via hydrofracturing of buttressing ice shelves and structural failure of marine-terminating ice cliffs. In addition, we use (1) freely evolving grounding-line dynamics that preclude the need for empirically calibrated retreat rates49, (2) highly resolved atmosphere and ocean model components rather than intermediate-complexity climate models45 or simplified climate forcing44, and (3) calibration based on major retreat during warm palaeoclimates rather than recent minor retreat driven by localized ocean forcing.
As in these prior studies, we also find that ocean-driven melt is an important driver of grounding-line retreat where warm water is in contact with ice shelves, but in scenarios with high greenhouse gas emissions we find that atmospheric warming soon overtakes the ocean as the dominant driver of Antarctic ice loss. Surface meltwater may lead to the ultimate demise of the major buttressing ice shelves (Supplementary Videos 8 and 9) and extensive grounding-line retreat, but it is the long thermal memory of the ocean that will inhibit the recovery of marine-based ice for thousands of years after greenhouse gas emissions are curtailed.
Methods
Ice sheet–ice shelf model
We use an established ice-sheet model, with hybrid ice dynamics following the formulation described in ref. 27, and an internal condition on ice velocity at the grounding line15 that captures MISI (Fig. 2a–c) by accounting for migrating grounding lines and the buttressing effects of ice shelves with pinning points and side shear. Bedrock deformation under changing ice loads is modelled as an elastic lithospheric plate above local isostatic relaxation. A grid resolution of 10 km is used for all simulations, the finest resolution computationally feasible for long-term continental simulations. The model includes newly added treatments of hydrofracturing and ice cliff failure (Fig. 2d–f) described in ref. 25 and extended here. Basal sliding coefficients are determined by an inverse method51, iteratively matching ice-surface elevations to observations until a quasi-equilibrium is reached. In this case, inverted sliding coefficients are derived from a modern (preindustrial) surface climatology, using the same RCM used in our Pliocene, LIG, and future simulations.
In addition to the Pliocene and LIG targets highlighted here, the ice sheet–ice shelf model has been shown capable of simulating: (1) the modern ice sheet, including grounding-line positions, ice thicknesses, velocities, ice streams, and ice shelves (Fig. 1b), (2) the Last Glacial Maximum (LGM) extent27, (3) the timing of post-LGM retreat18, and (4) the ability of the ice sheet to regrow to its modern extent following retreat25.
Calving and hydrofracturing
Calving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200 m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200 × max[0, min[1, (α − 40)/20]], where α is the ‘arc to open ocean’ (in degrees), crudely representing the effects of ice mélange in narrow seaways. The unconfined onset thickness of 200 m was increased from its value of 150 m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on α is imposed for oceanic sub-ice-shelf melt rates, as described below.
Surface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:
0 for R < 1.5 m yr^{-1}
4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}
R^2 for R > 3 m yr^{-1} (as before)
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-5
|
Calving and hydrofracturing
Calving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200 m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200 × max[0, min[1, (α − 40)/20]], where α is the ‘arc to open ocean’ (in degrees), crudely representing the effects of ice mélange in narrow seaways. The unconfined onset thickness of 200 m was increased from its value of 150 m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on α is imposed for oceanic sub-ice-shelf melt rates, as described below.
Surface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:
0 for R < 1.5 m yr^{-1}
4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}
R^2 for R > 3 m yr^{-1} (as before)
This supposes that minimal hydrofracturing occurs for relatively small R values. The linear segment between 1.5 m yr−1and 3 m yr−1 intersects the R2 parabola as a tangent at R = 3. This modification prevents small amounts of recession in some East Antarctic basins for modern conditions, where small amounts of summer melt and rainfall occur.
Structural failure of ice cliffs
To account for structural ice-cliff failure26,54 (MICI in Fig. 2), a wastage rate of ice W is applied locally to the grid cell adjacent to tidewater grounding lines with no floating ice, if the required stresses at the exposed cliff face exceed the yield strength of ice. This condition depends on the subaerial cliff height at the interpolated grounding line relative to the maximum ice thickness that can be supported, modified locally to account for any meltwater-enhanced crevasse penetration (hydrofracturing), and any reductions in crevassing caused by backstress. For dry crevassing at an ice margin with no hydrofracturing and no buttressing (backstress), the maximum exposed cliff height is 100 m, assuming an ice yield strength of 1 MPa25,26. The formulation of W results in a steep ramp in wastage rates of 0–3 km yr−1, where exposed ice cliffs ramp from 80 m to 100 m. The maximum wastage rate of 3 km yr−1 used as our default is conservatively chosen, based on recent observations of the Jakobshavn Isbrae Glacier (up to ~12 km yr−1) and the Crane Glacier (~5 km yr−1) following the loss of their ice-buttressing shelves55,56,57.
Other modifications to ice-sheet model physics
The model is modified from ref. 25 to include a more physically based parameterization of the vertical flow of surface mobile liquid water (runoff and rainfall) through moulins and other fracture systems towards the base22,58, which affects the vertical temperature profiles within the ice sheet. Vertical sub-grid-scale columns of liquid water are assumed to exist, through which the water freely drains while exchanging heat by conduction with the surrounding ambient ice that cools and can freeze some or all of the liquid water within the ice interior.
We use uniform parameter values everywhere: we set the fractional area of sub-grid columns to overall area to be 0.1, and the horizontal scale of drainage elements to be 10 m (R in ref. 22, used in the calculations of conductive heat exchange with ambient ice). The fractional area includes both large moulins and any downward movement of liquid water in crevasses or cracks of all scales, which would be prevalent in the future melting scenarios investigated here. Offline sensitivity tests show low sensitivity of our model behaviour to these values, but further investigation is warranted.
For reasonable numerical behaviour, the horizontal heat exchange needs to be part of the time-implicit vertical diffusive heat solution for ambient ice temperature in the main model. To avoid an iterative procedure in cases where all liquid water is frozen before reaching the bed, a time-explicit calculation of the water penetration is made first, and one of the following measures is applied in the time-implicit ice-temperature step: (1) the conductive heat exchange coefficient at all levels is reduced by a constant factor for the column, so that the liquid penetrates to the lowest layer but no further; and (2) the conductive coefficient is set to zero below the depth of furthest penetration. Both methods give very similar results in idealized single-column tests; method (1) was used for all runs here. In cases with greater surface liquid flux, there is no reduction of coefficients and some water reaches the base.
A minor bug fix is corrected in the calculation of vertical velocities within the ice (w′ in ref. 27), which previously did not account for the removal of ice at the base due to oceanic melting. This only affects advection of temperature in ice shelves, and has negligible effects on results.
Ice-sheet initial conditions
Ice-sheet initial conditions and basal sliding coefficients are provided by a 100-kyr inverse simulation following the methodology in ref. 51, using mass-balance forcing provided by a bias-corrected RCM climatology and modern observed ocean temperatures (described below). In the inverse procedure, basal sliding coefficients under modern grounded ice are adjusted iteratively to reduce the misfit with observed ice thickness, with grounding-line positions fixed to observed locations. The LIG simulation using ‘glacial’ initial conditions (Fig. 3) uses the same basal sliding coefficients (along with a relatively slippery value for modern ocean beds), but initialized from a previous simulation of the LGM with a prescribed, cold glacial climate representing conditions at ~20 kyr ago. The total ice volume in the modern and glacial ice sheets is 26.55 × 106 km3 and 32.30 × 106 km3, respectively, equivalent to bedrock-compensated GMSL values of 56.80 m and 62.28 m.
Atmospheric coupling
Atmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.
Anomaly methods are used to correct a small <2 °C Antarctic cold bias in the RCM:
T = T_{exp} + T_{obs} - T_{ctl}
P = P_{exp} * P_{obs} / P_{ctl}
where T is monthly surface air temperature and P is monthly precipitation. Subscripts ‘exp’, ‘obs’ and ‘ctl’ refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.
In the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by ΔT = γΔz, where γ = −0.008 °C m−1 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and Δz is the elevation difference. Now, precipitation P is multiplied by a Clausius–Clapeyron-like factor:
P * 2^{∆T/10}
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-6
|
Atmospheric coupling
Atmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.
Anomaly methods are used to correct a small <2 °C Antarctic cold bias in the RCM:
T = T_{exp} + T_{obs} - T_{ctl}
P = P_{exp} * P_{obs} / P_{ctl}
where T is monthly surface air temperature and P is monthly precipitation. Subscripts ‘exp’, ‘obs’ and ‘ctl’ refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.
In the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by ΔT = γΔz, where γ = −0.008 °C m−1 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and Δz is the elevation difference. Now, precipitation P is multiplied by a Clausius–Clapeyron-like factor:
P * 2^{∆T/10}
Rates of surface snowfall and rainfall are now consistently multiplied by a factor ρw/ρi ≈ 1.1, where ρw and ρi are the densities of liquid water and of ice respectively. This consistently converts between the units of most climate models and climatological databases (metres of liquid water equivalent per year) and the ice-model surface budget terms (metres of ice equivalent per year).
Oceanic sub-ice shelf and calving-face melt rates
Direct coupling of high-resolution ocean models and ice sheets remains challenging. For present-day simulations we use a parameterization of sub-ice shelf melt rates, similar to that used by other model groups64. The parameterization27 links oceanic melt rates to the nearest observed (or modelled) ocean temperatures:
OM = (KTρwCw/ρiLf) abs(To - Tf) (To - Tf)
where To is ocean temperature interpolated from the nearest point in an observational (or ocean model) gridded data set, Tf is the local freezing-point temperature at the depth of the ice base, and Cw is the specific heat of ocean water. The transfer factor KT = 15.77 m yr−1 °C−1 results in a combined coefficient (KTρwCw/ρiLf) of 0.224 m yr−1 °C−2. The depth dependence on Tf produces higher melt rates at the grounding line, as observed, and the dependence on T0 − Tf is quadratic65. Although spatially coarse observational data sets and standard GCM ocean models fail to capture detailed ocean current systems below ice-shelf cavities, this approach (Extended Data Fig. 6e and f) is preferable to the ad hoc prescription of single temperatures and transfer coefficients along individual sectors of the Antarctic margin as in ref. 27.
The effects of confined geography on ocean currents are represented by reducing basal melting depending on the total arc to open ocean α, representing the concavity of the coastline25. The melt rate computed from ocean temperatures as above is multiplied by the factor: max[0, min[1, alpha - 20) / 20]]
This effect, combined with the reduction of thin-ice calving with a similar dependence on α described above, allows ice to expand into interior basins during cool-climate recovery after major retreats of marine-based ice, as presumably occurred many times in West Antarctica over the last several million years66.
Melting of vertical ice surfaces in direct contact with ocean water is derived from the oceanic melt rate (OM) of surrounding grid cells, but is increased by a scaling factor of 10, producing more realistic calving front positions and in better agreement with hydrographic melt rate observations and detailed modelling67. Present-day sub-ice shelf and calving-face melt rates described here use the 1° resolution World Ocean Atlas32,68 temperatures at 400-m depth, interpolated to the time-evolving ice model grid and propagated under ice-shelf surfaces using contiguous neighbour iteration to provide To. The depth of 400 m represents typical observed levels of Circum-Antarctic Deep Water, a main source of warm-water incursions into the Amundsen Sea Embayment today69.
Pliocene simulation
Our default Pliocene simulation uses the same nested GCM–RCM climatology used in a prior study25, with 400 p.p.m.v. CO2 and a generic warm austral summer orbit28 (Extended Data Fig. 1). Ocean temperatures are increased uniformly by 2 °C everywhere in the Southern Ocean. The resulting Antarctic contribution of 11.3 m GMSL implies >15 m GMSL rise if an additional ~5 m contribution from Greenland70 and the steric effects of a warm Pliocene ocean are also considered. This result is ~6 m less than in ref. 25, reflecting a reduction in the sensitivity of the model with the changes described above.
LIG simulations
The LIG spans a ~20-kyr interval with greenhouse-gas atmospheric mixing ratios comparable to the pre-industrial Holocene9. Opportunities for Antarctic ice-sheet retreat within this interval include a peak in the duration of Antarctic summers coeval with a boreal summer insolation maximum at 128 kyr ago, and an Antarctic summer insolation maxima one half-precession cycle later at 116 kyr ago (Extended Data Fig. 2). We target these two orbital time slices because they contrast radiatively long and weak (128 kyr ago) versus short and intense Antarctic summers (116 kyr ago), both of which have been postulated to be important drivers of ice volume on glacial–interglacial timescales71.
LIG simulations that include climate–ice sheet feedback asynchronously couple the GCM–RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate–ice feedbacks improves model performance, relative to simple lapse-rate adjustments.
LIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM–RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1–5 °C applied uniformly over the Southern Ocean grid domain.
To allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM–RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2 °C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model–data fit. With this technique, only 3 °C of assumed sub-surface ocean warming is required to produce >6 m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-7
|
LIG simulations that include climate–ice sheet feedback asynchronously couple the GCM–RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate–ice feedbacks improves model performance, relative to simple lapse-rate adjustments.
LIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM–RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1–5 °C applied uniformly over the Southern Ocean grid domain.
To allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM–RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2 °C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model–data fit. With this technique, only 3 °C of assumed sub-surface ocean warming is required to produce >6 m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.
The two time-continuous LIG simulations using prescribed climatologies (Fig. 3) use bias-corrected, present-day RCM climatologies with a uniform, time-evolving perturbation derived from the average of Antarctic ice-core climatologies compiled in ref. 29. Southern Ocean temperatures are treated similarly, with World Ocean Atlas temperatures32 increased according to the average of circum-Antarctic LIG anomalies29. Only records from marine drill-cores poleward of 45° S are used in the averages, but we note that there is considerable uncertainty in the proxy sea surface temperature estimates (>2 °C)29. This approach also assumes that the proxy sea surface temperatures reflect changes at sub-surface depths (~400 m), which is uncertain. The resulting anomalies are applied to the ice sheet model at 130 kyr ago, 125 kyr ago, 120 kyr ago, and 115 kyr ago and the ice-sheet model is run continuously from 130 kyr ago to 115 kyr ago. The pairs of air and ocean temperature perturbations applied at each 5-kyr LIG timestep are 1.97° and 1.70°, 1.41° and 1.51°, 0.83° and 1.09°, −1.57° and 0.31°, respectively.
The time-continuous LIG simulations are initialized from either a present-day initial ice state (Fig. 1b), or from a prior Last Glacial Maximum simulation with 5.76 × 106 km3 more ice than today. The latter initial condition may better represent the ice sheet at the onset of the LIG and leads to a greater potential sea-level rise owing to the deeper bed conditions early in the deglaciation, which enhances the bathymetrically sensitive MISI dynamics.
The proxy-forced LIG simulation clearly supports a maximum Antarctic contribution to GMSL early in the interglacial period (Fig. 3). However, we note that owing to the demonstrated influence of Southern Ocean temperature on the timing of retreat and the uncertain magnitude and chronology of our imposed forcing29, these results cannot definitively rule out maximum Antarctic retreat at the end of the LIG, as has also been proposed4,74
Future simulations
Because of the new ice-model physics that directly involve the atmosphere via meltwater enhancement of crevassing and calving, highly resolved atmospheric climatologies are needed at spatial resolutions beyond those of most GCMs. However, multi-century RCM simulations are computationally infeasible. To accommodate the need for long but high-resolution climatologies, the nested GCM–RCM is run to equilibrium with 1 × PAL, 2 × PAL, 4 × PAL and 8 × PAL CO2. In the ice-sheet simulations, CO2 follows the extended RCP greenhouse gas emissions36 to the year 2500, and the climate at any time is the average of the two appropriate surrounding RCM solutions, weighted according to the logarithm of the concentration of CO2. The RCM climatologies follow total equivalent CO2, which accounts for all radiatively active trace gases in the RCP timeseries. In RCP8.5, equivalent CO2 forcing exceeds 8 × PAL after 2175, but it is conservatively limited here to a maximum of 8 × PAL (Fig. 4a). A 10-yr lag is imposed in the RCM climatologies to reflect the average offset between sea surface temperatures and surface air temperatures in the equilibrated RCM (with equilibrated sea surface temperatures from the parent GCM) and the transient response of the real ocean’s mixed layer.
Ocean temperatures in the RCP scenarios are provided by high-resolution (0.5° atmosphere and 1° ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3 °C to the CCSM4 ocean temperatures increases melt rates to 25–30 m yr−1 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).
Extended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-8
|
Ocean temperatures in the RCP scenarios are provided by high-resolution (0.5° atmosphere and 1° ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3 °C to the CCSM4 ocean temperatures increases melt rates to 25–30 m yr−1 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).
Extended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.
Future high-resolution ocean-model output is not available on multi-millennial timescales. In our long (5,000-year) future simulations (Extended Data Fig. 7), CCSM4 ocean temperatures at 400 m depth are assumed to remain at their 2300 values for thousands of years beyond 2300 (until 7000). This assumption is based on the thermal inertia of the deep ocean (thousands of years)47, its longwave radiative feedback on atmospheric temperatures77, and its relative isolation from surface variations. The response of the intermediate and deep ocean to atmospheric and surface-ocean warming before 2300 is heavily lagged in time, and consequently deep-ocean temperatures would continue to rise long after CO2 levels and surface temperatures began to decline after 250077. However, at some point several thousand years later, intermediate- and deep-ocean waters would start to cool if CO2 levels decay as in Extended Data Fig. 7. The trajectory of these temperatures would vary spatially and depend on details of the ocean circulation. To our knowledge, the state of the ocean as it recovers from a greenhouse gas perturbation over these timescales is largely unknown, as relevant coupled atmosphere–ocean global climate model simulations at the resolution and duration appropriate to our ice model have not been run. Consequently, our assumption of constant 400-m ocean temperatures after 2300, although likely to be conservative beyond 2500, may be questionable for the latter parts of the simulations assuming fast, engineered CO2 drawdown. However, assuming the slow, natural pace of CO2 recovery76, atmospheric concentrations would remain above twice the current level of carbon dioxide (2 × CO2) for thousands of years in the RCP8.5 scenario (Extended Data Fig. 7). Assuming a global temperature sensitivity of ~3 °C per doubling of CO2, our ocean temperatures applied to the long RCP8.5 scenario are probably conservative over the duration of the simulation.
Geologically constrained Large Ensemble analysis of future ice-sheet retreat
To quantify model uncertainty due to poorly known parameter values, ensembles of future RCP scenarios are performed with varying model parameters affecting sub-ice oceanic melt rates, meltwater-enhanced calving (hydrofracturing) and marine-terminating ice cliff failure. Ensemble members use the high-resolution atmospheric and ocean forcing described in the main text and above. Alternative ensembles are run both with and without the bias correction of CCSM4 ocean temperatures in the Amundsen and Bellingshausen Seas. The three parameters and four values used for each are as follows.
OCFAC is the coefficient in the parameterization of sub-ice-shelf oceanic melt, which is proportional to the square of the difference between nearby ocean water temperature at 400-m depth, and the pressure-melting point of ice. It corresponds to K in equation (17) of ref. 27. The relationship between proximal ocean conditions and melting at the base of floating ice shelves remains a challenging topic of ongoing research78, and a simple parameterization64 is used here. Ensemble values of OCFAC are 0.1, 1, 3 and 10 times the default value of 0.224 m yr−2 °C−2.
CREVLIQ is the coefficient in the parameterization of hydrofracturing due to surface liquid. It replaces the constant 100 in equation (B.6) of ref. 25, and is the additional crevasse depth due to surface melt plus rainfall rate, with a quadratic dependence. This crudely represents the complex relationship between surface water and crevasse propagation, and basic model sensitivity is shown in supplementary figure 7b of ref. 25. Values of CREVLIQ are 0 m, 50 m, 100 m and 150 m per (m yr−1)−2.
VCLIF is the maximum rate of horizontal wastage due to ice-cliff structural failure. It replaces the default value of 3,000 (3 km yr−1) in equation (A.4) of ref. 25. Its magnitude is based on observed retreat rates of modern large ice cliffs, and basic model sensitivity is shown in supplementary figure 7a of ref. 25. Values of VCLIF are 0 km yr−1, 1 km yr−1, 3 km yr−1 and 5 km yr−1.
Medium-range, default values of OCFAC, CREVLIQ, and VCLIF used in our nominal Pliocene (Extended Data Fig. 1), LIG (Fig. 3), and Future (Fig. 4) simulations are OCFAC = 1 (corresponding to 0.224 m yr−2 °C−2), CREVLIQ = 100 m per (m yr−1)−2, and VCLIF = 3 km yr−1, respectively.
Simulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6–7.4 m) and the Pliocene (10–20 m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5–15 m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1σ range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model’s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica’s GMSL contribution by ~9 cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10 m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1σ standard deviation to 16 ± 16 cm in 2100 and 62 ± 76 cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen–Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-9
|
Simulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6–7.4 m) and the Pliocene (10–20 m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5–15 m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1σ range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model’s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica’s GMSL contribution by ~9 cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10 m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1σ standard deviation to 16 ± 16 cm in 2100 and 62 ± 76 cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen–Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.
Extended data figures and tables
Extended Data Figure 1: Warm mid-Pliocene climate and ice-sheet simulation. a, January (warmest monthly mean) difference in 2-m (surface) air temperature simulated by the RCM relative to a preindustrial control simulation with 280 p.p.m.v. CO2 and present-day orbit. The temperature difference is lapse-rate-corrected to account for the change in ice-sheet geometry and surface elevations. The Pliocene simulation uses 400 p.p.m.v. CO2, a warm austral summer orbit, and assumes a retreated WAIS to represent maximum Pliocene warm conditions. b, The Pliocene ice-sheet is shown after 5,000 model years, driven by the RCM climate in a, and assuming 2 °C ocean warming relative to a modern ocean climatology32. In the model formulation used here, maximum Pliocene ice-sheet retreat with default model parameters is equivalent to 11.26 m GMSL, about 6 m less than in ref. 25.
Extended Data Figure 2: LIG greenhouse gases, orbital parameters, and RCM climates. a, Greenhouse gas concentrations9,72 converted to radiative forcing shows the LIG interval (light red bar) and the best opportunity for ice-sheet retreat. b, Summer insulation at 70° latitude in both hemispheres73 (red, south; blue, north) and summer duration at 70° S (black)79 shown over the last 150 kyr, and the two orbital time slices (vertical dashed black lines at 128 kyr ago and 116 kyr ago). c, Table showing the greenhouse gas atmospheric mixing ratios (CO2 in parts per million by volume; CH4 and N2O in parts per billion by volume) and orbital parameters (eccentricity, obliquity, precession) used in the GCM–RCM at the LIG time slices (dashed lines 1 and 2 in a and b), respectively. d–f, January (warmest monthly mean) differences in 2-m surface air temperature relative to a preindustrial control simulation at 128 kyr ago (d), 116 kyr ago (e), and the present-day (2015) (f). Simulated austral summer temperatures at 116 kyr ago (e) with relatively high-intensity summer insolation is warmer than the long-duration summer orbit at 128 kyr ago (d), but unlike the Pliocene (Extended Data Fig. 1a), neither LIG climatology is as warm as the present day, producing little to no rain or surface melt on ice-shelf surfaces.
Extended Data Figure 3: Effect of Southern Ocean warming on Antarctic surface air temperatures and the ice sheet at 128 kyr ago. a–c, January (warmest monthly mean) differences in 2-m surface air temperature at 128 kyr ago, relative to a preindustrial control simulation (top row). GHG, greenhouse gas; SST, sea surface temperature. d, e, Ice-sheet thickness (m) after 5,000 model years, driven by the corresponding climate in a–c. a and d, Without climate–ice sheet coupling (present-day ice extent and surface ocean temperatures in the RCM), and prescribed 5 °C sub-surface ocean warming felt only by the ice sheet. b and e, With asynchronous coupling between the RCM atmosphere and ice sheet, and prescribed 5 °C sub-surface ocean warming felt only by the ice sheet. c and f, With asynchronous coupling between the RCM atmosphere and ice sheet, prescribed 3 °C sub-surface ocean warming felt by the ice sheet, and ~2 °C surface ocean warming felt by the RCM atmosphere. c shows the locations of East Antarctic ice cores (EDC, EPICA Dome C; V, Vostock; DF, Dome F; EDML, EPICA Dronning Maud Land) indicating warming early in the interglacial29 and previously attributed to WAIS retreat80; this warming is similar to that simulated in c from a combination of ice-sheet retreat and warmer Southern Ocean temperatures, supporting the notion that the timing of LIG retreat was largely driven by far-field ocean influences, rather than local astronomical forcing.
Extended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a–d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2 × CO2 (b), 4 × CO2 (c), and 8 × CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e–h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals—e, 2050; f, 2100; g, 2150; and h, 2500—with superposed meltwater production rates.
Extended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950–1960 to 2290–2300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950–1960 to 2010–2020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3 °C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-10
|
Extended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a–d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2 × CO2 (b), 4 × CO2 (c), and 8 × CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e–h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals—e, 2050; f, 2100; g, 2150; and h, 2500—with superposed meltwater production rates.
Extended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950–1960 to 2290–2300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950–1960 to 2010–2020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3 °C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.
Extended Data Figure 6: Effect of future ocean warming only. a, Antarctic contribution to future GMSL rise in long, 5,000-yr ice-sheet simulations driven by sub-surface ocean warming simulated by CCSM4, following RCP8.5 (black line), with a +3 °C adjustment in the Amundsen and Bellingshausen seas (blue line; see Extended Data Fig. 5) and a warmer +5 °C adjustment (red line). Atmospheric temperatures and precipitation are maintained at their present values. b–d, Ice-sheet thickness at model-year 5,000, driven by sub-surface ocean forcing from CCSM4 (b) and from CCSM4 with a +3 °C (c) or +5 °C (d) adjustment in the Amundsen and Bellingshausen seas. Note the near-complete loss of ice shelves, but modest grounding-line retreat in b, the retreat of Pine Island Glacier in c, and the near-complete collapse of WAIS once a stability threshold in the Thwaites Glacier grounding line is reached in d.
Extended Data Figure 7: The long-term future of the ice sheet and GMSL over the next 5,000 years following RCP8.5 and RCP4.5. a, Equivalent CO2 forcing following RCP8.5 until the year 2500, and then assuming zero emissions after 2500 and allowing a natural relaxation of greenhouse gas levels (red) or assuming a fast, engineered drawdown (blue) with an e-folding timescale of 100 years. b. Antarctic contribution to GMSL over the next 5,000 years, following the greenhouse gas scenarios in a. c, The same as a, except showing long-term RCP4.5 greenhouse gas forcing. d, The same as b, except following the RCP4.5 scenarios in c. The insets in b and d show the ice sheet (and remaining sea-level rise) after 5,000 model years in RCP8.5 and RCP4.5, respectively, assuming fast CO2 drawdown (blue lines), highlighting the multi-millennial commitment to a loss of marine-based Antarctic ice, even in the moderate RCP4.5 scenario. Note the different y-axes in RCP8.5 versus RCP4.5.
Extended Data Figure 8: Freshwater input to the Southern Ocean. Total freshwater and iceberg flux from 1950 to 2500, following the future RCP scenarios shown in Fig. 4b. Freshwater input calculations include contributions from ice loss above and below sea level and exceed 1 Sv in RCP8.5.
Extended Data Table 1: Summary of Antarctic contributions to GMSL during the Pliocene, LIG, future centuries, and future millennia. Antarctic contributions to GMSL for the Pliocene and LIG simulations (rows 1–9) with +2 °C ocean warming in the Pliocene and incrementally imposed ocean warming in the LIG simulations. Values shown represent ice retreat at the end of quasi-equilibrated 5000-yr simulations. Time-continuous LIG simulations forced by proxy-based atmosphere and ocean climatologies (rows 10–12) list maximum GMSL contributions occurring early in the LIG (Fig. 3a). The remaining rows list Antarctic contributions to GMSL at specific times (years as shown) in time-dependent future simulations. Ensemble means and standard deviations (1σ) of the RCP ensemble members listed in Extended Data Table 2 are also shown. Future GMSL contributions are shown relative to 2000.
Extended Data Table 2: Ensemble simulations of Pliocene, LIG, and future Antarctic contributions to GMSL. Varying combinations of three model parameters (first column) correspond to OCFAC, CREVLIQ and VCLIF, respectively (see Methods). The resulting GMSL contributions of each ensemble member driven by Pliocene and LIG climatologies are shown in the second and third columns. Combinations of model parameters satisfying Pliocene and LIG sea-level targets are assigned a Large Ensemble number (LE#) in the fourth column. Default model parameter values (LE# 12) and resulting Pliocene and LIG GMSL rise are in bold type. Four future ensembles using alternative sets of the palaeo-filtered Large Ensemble members and following RCP2.5, RCP4.5 and RCP8.5 emissions scenarios are shown at right. The top two ensembles use 29 combinations of parameter values that satisfy LIG sea-level targets and a range of Pliocene sea-level targets between 5 m and 15 m. The bottom two ensembles use a more restricted set of 15 parameter combinations that satisfy a higher Pliocene target range >10 m. Future RCP ensembles at left correspond to the GMSL time series in Fig. 5. The two ensemble sets at far right include the ocean-temperature bias correction described in the text, Fig. 4 and Extended Data Fig. 5. Antarctic GMSL contributions for each ensemble member are shown at 2100 and 2500. Ensemble means and 1σ standard deviations are also shown. GMSL contributions in future ensembles are relative to 2000.
Supplementary information
RCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)
RCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-11
|
Supplementary information
RCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)
RCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)
RCP8.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 584 kb)
RCP2.6 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 593 kb)
RCP4.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 691 kb)
RCP8.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 808 kb)
RCP2.6 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 477 kb)
RCP4.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 594 kb)
RCP8.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 778 kb)
RCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)
Nature Podcast Discussion
Adam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.
After all, how do you work out what the future holds for the climate when you’ve only got one planet? You’re still learning how it works, and you can’t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.
But what if you only have limited data from the real world, and how do you cope with processes that haven’t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
1ea2eff08fb1-12
|
RCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)
Nature Podcast Discussion
Adam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.
After all, how do you work out what the future holds for the climate when you’ve only got one planet? You’re still learning how it works, and you can’t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.
But what if you only have limited data from the real world, and how do you cope with processes that haven’t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.
But understanding what’s going to happen to Antarctica’s ice is vital to understanding how global warming will impact the world.
Robert DeConto: There’s just so much potential sea level rise locked up in Antarctica there. There’s such a vast amount of ice.
Adam Levy: This is Rob DeConto from the University of Massachusetts who reporters in this week’s nature.
He’s been trying to peer into the future by modeling how Antarctica contributes to sea level rise.
Robert DeConto: So even a small fraction of Antarctica being mobilized and going into the ocean is going to have a global impact.
Adam Levy: Because it could have such a big influence. Lots of different groups have tried simulating Antarctica’s future and have come up with a broad range of results.
Here’s Tamsin Edwards of the Open University who published a study a few months ago on future ice loss in the Antarctic.
Tamsin Edwards: I would say it’s the the biggest unknown in future sea level rise.
Adam Levy: But why? What makes it so hard to pin down?
Tamsin Edwards: Pretty much everything about it. All of these different ways in which ice can flow, can crack, can be lost and gained, it makes quite a complicated picture.
Adam Levy: Both Tamsin Edwards and Rob DeConto have used models to try to get to grips with this problem, but they’re somewhat divided about what their models should be based on. Here’s Tamsin again.
Tamsin Edwards: So we kind of assumed that if the model is good at simulating the recent past, it’s more likely to be good at predicting the future.
Adam Levy: But Rob thinks there’s only so much that the last few decades can teach us.
Robert DeConto: In the very recent past, the climate and the oceans have been certainly not as warm as they’re predicted to become in the next century. So we compare the results that we get with geologic records.
Adam Levy: Geologic records that just means records of the climate from the distant past, deduced from things like the erosion of now inland cliffs.
Rob favors using data like these because there’ve been times in the Earth’s past where the climate has looked pretty similar to today’s situation.
Robert DeConto: 125,000 years ago, the world looks a lot like it does today. Similar climate, and yet sea level was between six and nine meters higher.
Adam Levy: So where Tamsin’s model uses direct observations of Antarctica from the last few decades, Rob’s uses our understanding of sea levels from thousands of years ago.
But whatever you are checking your model against, you can never be sure it’ll apply to the future. Says Tamsin
Tamsin Edwards: If you’re calibrating with past data, and that includes paleo climate data as well, because you never find a perfect analog of the future in paleo climate. There are always different things going on, so you have to bear that in mind when you’re thinking about your predictions and be a bit cautious.
Adam Levy: And the same goes for models based on today’s climate. It’s not a done deal that tomorrow will behave like today. And what if Antarctica loses ice in different ways tomorrow than it does today? Rob’s model includes certain processes that we haven’t observed in Antarctica. For example, the possibility that melt water on top of ice could make ice cliffs unstable.
This could cause ice to collapse into the sea much faster than we’re seeing today. Rob says his model is only accurate if he includes these kind of dramatic processes. But it’s not easy to build these processes into a model.
Robert DeConto: I would say that these are just really the first baby steps to try to incorporate processes like these in the models.
Adam Levy: But Tamsin is not convinced that including processes like this, that we’ve not really seen taking place yet, is the best bet.
Tamsin Edwards: We haven’t seen direct evidence of this. I would say that really says we have to put it in the models. Basically at the moment. It’s an exciting time. The jury’s out.
Adam Levy: So whereas Tamsin’s model is limited to the behavior we know to have happened in Antarctica, Rob’s includes processes that may or may not arise in the future.
They’re both trying to make the best use of limited information. And so to the results: According to these different models, how much is the Antarctic going to contribute to sea level rise by 2100? We’ll get to what these numbers mean in a minute, but first his Tamsin’s estimate.
Tamsin Edwards: We came up with the most likely of about 10 centimeters, quite low, and we came up with a prediction that there was only a 1-in-20 chance it would be more than 30 centimeters by the end of the century.
Adam Levy: How about Rob’s model?
Robert DeConto: We’re getting something between 64 centimeters and a little over a meter.
Adam Levy: It’s a huge difference. Yes, the two models used slightly different scenarios of greenhouse gas emissions, and yes, there are plenty of other uncertainties, but the difference is still striking. And Rob’s results could mean, for example, that low lying island nations could have to evacuate sooner than was previously anticipated.
Robert DeConto: You know, I hope we’re wrong.
Adam Levy: Understandable, when Rob’s model also predicts over 10 meters of sea level rise 500 years from now. And remember, Antarctica is just one piece of the sea level rise puzzle added to other sources of sea level rise, like the Greenland ice sheet. Even Tamsin’s estimate could lead to sea level rises of about a meter by the end of the century. A huge challenge for coastal cities around the world.
But such big uncertainties mean that it’s hard for the world to know what to prepare itself for. Rob is hopeful that techniques like his and Tamsin’s could be combined in the future to take advantage of both recent observations and geological records.
Tamsin, on the other hand, thinks that for the time being, it’s good that we have a range of models tackling the problem in different ways.
Tamsin Edwards: We may come up with some super ice sheet model that captures everything perfectly, but it’s a good idea to have different models with different approaches and that they’d be independent and you can compare their results.
Adam Levy: After all, if you can’t compare lots of different Earths, at least you can compare lots of different models.
Podcaster: The details of both those model studies are available at nature.com/nature. You heard from Tamsin Edwards, whose paper came out in Nature in December, and Rob DeConto, whose paper is out this week.
|
https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html
|
ad4932bbfb3a-0
|
Index
|
https://sealeveldocs.readthedocs.io/en/latest/genindex.html
|
3ca884893a78-0
|
Kuhlbrodt and Gregory (2012)
Title:
Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change
Key Points:
The spread of the OHU efficiency explains half of the spread in total OHU
Most models are biased towards a too weak stratification and a too strong OHU
The Southern Ocean and its stratification dominate global OHU in the models
Corresponding author:
Kuhlbrodt
Keywords:
CMIP5 models, climate change, ocean heat uptake, sea level rise
Citation:
Kuhlbrodt, T., and J. M. Gregory (2012), Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change, Geophys. Res. Lett., 39, L18608, doi:10.1029/2012GL052952
URL:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL052952
Abstract
Under increasing greenhouse gas concentrations, ocean heat uptake moderates the rate of climate change, and thermal expansion makes a substantial contribution to sea level rise. In this paper we quantify the differences in projections among atmosphere-ocean general circulation models of the Coupled Model Intercomparison Project in terms of transient climate response, ocean heat uptake efficiency and expansion efficiency of heat. The CMIP3 and CMIP5 ensembles have statistically indistinguishable distributions in these parameters. The ocean heat uptake efficiency varies by a factor of two across the models, explaining about 50% of the spread in ocean heat uptake in CMIP5 models with CO2 increasing at 1%/year. It correlates with the ocean global-mean vertical profiles both of temperature and of temperature change, and comparison with observations suggests the models may overestimate ocean heat uptake and underestimate surface warming, because their stratification is too weak. The models agree on the location of maxima of shallow ocean heat uptake (above 700 m) in the Southern Ocean and the North Atlantic, and on deep ocean heat uptake (below 2000 m) in areas of the Southern Ocean, in some places amounting to 40% of the top-to-bottom integral in the CMIP3 SRES A1B scenario. The Southern Ocean dominates global ocean heat uptake; consequently the eddy-induced thickness diffusivity parameter, which is particularly influential in the Southern Ocean, correlates with the ocean heat uptake efficiency. The thermal expansion produced by ocean heat uptake is 0.12 m YJ^{-1}, with an uncertainty of about 10% (1 YJ = 10^{24} J).
Introduction
Ocean heat uptake moderates the rate of time-dependent climate change. Thermal expansion of sea-water is a consequence of ocean heat uptake and one of the major contributors to global-mean sea level rise [Church et al., 2011]. Our general aim in this paper is to quantify the differences in predictions of the magnitude and distribution of ocean heat uptake, and its consequences for global-mean surface air temperature change and thermal expansion, among atmosphereÐocean general circulation models (which we henceforth refer to simply as “models”, for convenience) used for projections of anthropogenic climate change.
We analyse results from 22 models that participated in the Coupled Model Intercomparison Project Phase 3 (CMIP3), and from the 20 models in the CMIP5 project whose data were available at the time of writing this paper (Spring 2012). See Figure 1 and Table 1 in Text S1 in the auxiliary material, for a list.1 We mainly use the control experiments and experiments with atmospheric CO_2 concentration increasing at 1%/year (details in the auxiliary material).
Ocean Heat Uptake Efficiency and Transient Climate Response
Gregory and Forster [2008] showed that there is an approximately linear relationship between the global mean surface air temperature change ΔTa and the radiative forcing F (due to greenhouse gases etc.): ΔTa = F/ρ, with the climate resistance ρ in W m−2 K−1. This relationship holds well for observations and model simulations of recent decades, and for projections of climate change under a continuously increasing forcing, which is a characteristic of most scenarios considered for the 21st century. The basis of this relationship is that the difference between the radiative forcing and the radiative feedback yields the net heat flux N into the climate system: N = F − ΔTa, and N can be approximated by N ≃ κΔTa. The climate resistance ρ is thus the sum of α, the climate feedback parameter, and κ, which is identified as the ocean heat uptake efficiency because nearly all the added heat is stored in the ocean [e.g., Church et al., 2011].
Following Gregory and Forster [2008], the ocean heat uptake efficiency κ, the climate feedback parameter α and the climate resistance ρwere calculated for CMIP5 by ordinary least squares regression (OLS) of decadal-meanN, F-N and F respectively against ΔTa under the standard idealized scenario of CO2 increasing at 1% per year, giving a forcing F(t) = F2×t/70 which is linear with time t in years, where F2× is obtained from experiments in which CO2 is instantaneously increased and then held constant [Andrews et al., 2012] (Table 1 in Text S1). The transient climate response (TCR) was calculated, following its definition, as ΔTafor the time-mean of years 61–80 in this scenario (Figure 1 and Table 1 in Text S1). The coefficient of variation (ratio of ensemble standard deviation to ensemble mean) of TCR is about 20% in CMIP5.
Figure 1: The ocean heat uptake efficiency κ (blue bars), the climate feedback parameter α (red bars), the transient climate response (crosses) and the expansion efficiency of heat ϵ (circles) for the CMIP3 (numbers) and the CMIP5 (letters) models. The total bar length is the climate resistance ρ = α + κ. The models are arranged in order of κ. See Table 1 in Text S1 in the auxiliary material for an alphabetical list of the models. It can be seen from this diagram that TCR and κ are anticorrelated (the crosses are further left towards the bottom), but there is no relationship between κ and α or ϵ (the red bars and the circles do not show any tendency from top to bottom). For several technical reasons, not all parameters could be calculated for every model.
We see that α obtained by this method agrees closely with α obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2× is not correlated with α or κ. Whereas Gregory and Forster [2008] found α and κto be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which haveα and κ that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large α and large κ.
The definition of ρ implies that TCR = F2×/ρ = F2×/(α + κ). Thus, a larger κ gives a smaller TCR (correlation of κand TCR is −0.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so thatκ is uncorrelated with α, we can compute the fraction of the across-model variance of TCR explained byκ by comparing var(F2×/(α + κ)) with var(〈F2×〉/(〈α〉 + κ)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.
Boé et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Boé et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.
|
https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html
|
3ca884893a78-1
|
We see that α obtained by this method agrees closely with α obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2× is not correlated with α or κ. Whereas Gregory and Forster [2008] found α and κto be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which haveα and κ that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large α and large κ.
The definition of ρ implies that TCR = F2×/ρ = F2×/(α + κ). Thus, a larger κ gives a smaller TCR (correlation of κand TCR is −0.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so thatκ is uncorrelated with α, we can compute the fraction of the across-model variance of TCR explained byκ by comparing var(F2×/(α + κ)) with var(〈F2×〉/(〈α〉 + κ)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.
Boé et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Boé et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.
The time-integrated heat uptake in the 1%/year CO2 scenario up to year 70 is H2× = ∫070N(t) dt ≃ 35F2×κ/(κ + α) (in W year m−2). Across the CMIP5 1%/year CO2 scenarios, it has a coefficient of variation of about 10%. Using the same CMIP5 models and method as for TCR (see also the auxiliary material), we find that H2× has a correlation of 0.92 with F2×κ/(κ + α), and the fraction of variance of H2× explained by κ is ∼50%. Thus κ influences heat uptake more than it influences surface warming because of its appearance in the numerator of H2×. (In the auxiliary material, we derive a formula for var(H2×) in terms of var(κ) and var(TCR).)
The distributions of κ, α, ρ and TCR are not significantly different for the CMIP3 and CMIP5 ensembles according to Kolmogorov–Smirnov tests. In both ensembles, κ varies by about a factor of 2. Investigating the reasons for this substantial spread motivates the next section.
Vertical Distribution of Temperature and Temperature Change
Ocean heat uptake efficiency depends on how fast the heat can be transported downwards. We put forward the hypothesis that a model with a weak vertical temperature gradient in the control state has a larger capacity for downward heat transport (e.g. because a large diapycnal mixing coefficient erodes the stratification) and therefore should have a larger κ.The hypothesis applies to net global-mean vertical heat transport, comprising diapycnal mixing and other processes.
Figure 2a shows the global-mean vertical temperature profile from the control runs of the CMIP3 and CMIP5 models (the average over the first 20 years that are parallel to the 1%/year CO2 runs) and from observations (WOA05 [Locarnini et al., 2006]), each profile being expressed as a difference from its surface temperature. This confirms that in the top 2000 m most models are less stratified than the real ocean. To elucidate the relationship between κ and the global temperature profiles, we use a simple measure of the vertical temperature gradient, namely the vertical temperature difference Tz between two layers, 0–100 m and 1500–2000 m (similar to Boé et al. [2009]). The relationship of κ to Tz is shown in Figure 3a and is negative, as expected (r = −0.35 with p= 0.07 [one-sided]). HadGEM2-ES (model J) has a very smallκ and is strongly stratified in the uppermost layers, being closer to the observed profile than most other models, particularly in the top 500 m. The κ-Tz relationship therefore suggests that κ tends to be too large in AOGCMs.
Figure 2: (a) Globally averaged temperature profiles for the control runs of the CMIP3 and CMIP5 models shown as difference from surface temperature, with observations for comparison (dash-dotted; WOA05 [Locarnini et al., 2006]). NorESM1-M is an outlier in that it is unusually weakly stratified in the top 200 m, giving a largeκ, but very strongly stratified in the 500 m or so below, giving a large Tz. Another outlier is giss_e_r with an extremely weak stratification. (b) Change of the temperature profiles in the 1%/year CO2 runs, divided by the vertical integral between 0 m and 2000 m. Units are dimensionless (“DL”). (c) Change of the temperature profiles in the CMIP3 models during the observational record [Levitus et al., 2012] (“Lev12”), scaled as in Figure 2b. Shown is the difference of a 20-year average (2000 to 2019) from the SRES A1B runs minus a 20-year average from 20C3M (1945–1964). Two models (red, orange) overestimate surface warming because of their too small total heat uptake. To some extent, a few models capture the surface intensification (“SFI” [light green]: bccr_bcm2_0, gfdl_cm2_0, gfdl_cm2_1, miub_echo_g, mri_cgcm2_3_2a) seen in the observations (dash-dotted). Also note the shallow subsurface maximum warming in observations, but not in models, for which we have no explanation.
Figure 3: The ocean heat uptake efficiency κ [W m−2 K−1] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change ΔTz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameterκGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of ΔTz from Levitus et al. [2012].
The change of the global vertical temperature profile averaged over the years 61–80 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of κ across models is strongly related to ΔTz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = −0.66) is significant at the 99% level (p < 0.01). If ΔTz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small κ. Conversely, models that distribute the additional heat further down have a smaller ΔTz and a larger κ.
The κ-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.
Geographical Distribution of Ocean Heat Uptake
|
https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html
|
3ca884893a78-2
|
Figure 3: The ocean heat uptake efficiency κ [W m−2 K−1] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change ΔTz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameterκGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of ΔTz from Levitus et al. [2012].
The change of the global vertical temperature profile averaged over the years 61–80 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of κ across models is strongly related to ΔTz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = −0.66) is significant at the 99% level (p < 0.01). If ΔTz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small κ. Conversely, models that distribute the additional heat further down have a smaller ΔTz and a larger κ.
The κ-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.
Geographical Distribution of Ocean Heat Uptake
The projected ocean heat uptake (OHU, i.e., the increase in ocean heat content) in model simulations with an increasing CO2 content has a distinct regional structure. We analyse this for the CMIP3 SRES A1B scenario, for which we have the largest number of models available. For comparison, the same analysis for the 1% CO2 runs of CMIP3 and CMIP5 can be found in the auxiliary material. They show generally less heat uptake because ∫F dt is smaller, but the geographical features are similar.
The ensemble-mean top-to-bottom integrated OHU is shown inFigure 4a. It was calculated as the difference between the 20-year averages 2080–2099 and 1980–1999. It is largest in the Southern Ocean, in a band around 40°S, with maxima in the Argentine Basin and south of Africa. This leads to a clear signal in steric sea level rise [cf.Pardaens et al., 2011, Figure 2], which is predominantly thermosteric in the Southern Ocean. The models agree on these features (R > 1, thin black contours), and they are also visible in the top 700 m alone (Figure 4b), which accounts for up to 50% of the heat uptake in the full depth.
Figure 4: Vertically integrated ocean heat uptake (colour shading; in GJ m−2) in the ensemble average of the SRES A1B scenario of 17 CMIP3 models for (a) the total water column, (b) the upper 700 m and (c) below 2000 m. Thick black line: zonal total in 1015 J m−1 (scale in the upper left corner), with ±1 standard deviation (dotted). Note the different scales in Figure 4c. Black contours show the ratio R of ensemble mean and ensemble standard deviation (solid: R > 1, thick solid: R = 1, dashed: R < 1). For Figures 4a and 4b, R> 1 in most areas indicating agreement across models. An exception are the deep-water formation regions in the Southern Ocean and the North Atlantic. In Figure 4c the models mainly show OHU in the Southern Ocean.
OHU below 2000 m is substantial in several large areas of the Southern Ocean (Figure 4c), including the Argentine basin and the area west of the Drake Passage, where there are maxima of top-to-bottom OHU. The pattern bears resemblance to observations [Purkey and Johnson, 2010]. In these areas, the deep OHU can amount to up to 40% of the total. In the deep-water formation areas in the Southern Ocean and in the North Atlantic the ensemble mean OHU displays minima above 700 m. The models show a large spread in these areas (R < 1).
The zonal total heat uptake (thick black line in the left hand side of the panel, dotted: one standard deviation) confirms that the global maximum of OHU per degree latitude is in the mid-latitude Southern Ocean [Stouffer et al., 2006]. Therefore, the stratification in that region could have a particularly large influence on κ.In the large majority of the models, the Southern Ocean stratification is strongly influenced by the parameterization of the eddy-induced tracer transports. Consistent with this, we find that the quasi-Stokes diffusivity parameterκGM(often called the eddy-induced thickness diffusivity) has a significant influence onκ (Figure 3c). When κGM is small, the isopycnal layers are steep, leading to a strong horizontal density gradient [Kuhlbrodt et al., 2012, Figure 1c] but a weak stratification and thus a large κ.
Expansion Efficiency of Heat
The expansion efficiency of heat [Russell et al., 2000], as a property of a model in m YJ^{−1} (1 YJ ≡ 1024 J), is defined as ϵ = hx/H, where hx is the global mean sea level rise due to thermal expansion and Hthe global-integral OHU. We calculateϵ by OLS regression of hx against H, using results from 1%/year CO2 and all available 21st-century scenarios.
In all models, there is an excellent scenario-independent linear relationship, butϵ varies across models (Figure 1 and Table 1 in Text S1) because the thermal expansivity of sea water (1/ρ) ∂ρ/∂T increases with pressure and temperature. Therefore, the magnitude of thermal expansion depends on the latitudes and depths at which the heat is actually stored; this pattern depends on the model, but not on the scenario for a given model.
The ranges of ϵ in the CMIP3 and CMIP5 ensembles are similar: 0.12 ± 0.01 m YJ−1 in CMIP3 and 0.11 ± 0.01 m YJ−1 in CMIP5. This is consistent with the observational estimates for 0 m to 2000 m, 1955–2010 [Levitus et al., 2012], from which we infer ϵ = 0.12 ± 0.01 m YJ−1. The observational estimates by Church et al. [2011] for 1972–2008 for the full ocean depth indicate ϵ = 0.15 ± 0.03 m YJ−1, which is slightly higher but not significantly different. We did not find any correlation of ϵ with κ, Tz or ΔTz, although such relationships would be plausible. It might well be that the stratification in the individual regions which are particularly important to OHU (section 4) influences ϵmore than global-mean properties do.
Concluding Remarks
Our analysis of CMIP3 and CMIP5 model results indicates that model spread in ocean vertical heat transport processes is responsible for a substantial part of the spread in predictions of global-mean ocean heat uptake (about 50% in the CMIP5 1%CO2/year experiments), and for some of the spread in predictions of surface warming. Since most AOGCMs have weaker global-mean stratification than observed, it is possible that they generally overestimate ocean heat uptake and underestimate surface warming [Forest et al., 2008]. The ocean heat uptake in CMIP5 1%CO2/year experiments has a spread of about 10%, and there is also a spread of about 10% in the expansion efficiency of heat ϵ, due to the different spatial distribution of the warming in the models. These factors contribute roughly equally to the spread of thermal expansion projection in response to CO2. Comparison, analysis and evaluation of model processes of ocean interior heat transport is essential to make progress in reducing uncertainties in projections of the magnitude and distribution of ocean heat uptake and the consequent sea-level rise.
|
https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html
|
d4e5a3445e08-0
|
Chen et al. (2017)
Title:
The increasing rate of global mean sea-level rise during 1993–2014
Key Points:
The global mean sea level (GMSL) rose from 2.2 ± 0.3 mm yr−1 in 1993 to 3.3 ± 0.3 mm yr−1 in 2014, indicating an acceleration in sea-level rise during this period.
The mass loss from the Greenland Ice Sheet significantly increased during this period, accounting for less than 5% of the GMSL rate in 1993 but more than 25% in 201
The mass contributions to GMSL, which include glacier mass loss, Greenland and Antarctic ice sheets, and anthropogenic terrestrial water storage, increased from about 50% in 1993 to 70% in 2014, indicating their growing role in sea-level rise.
Keywords:
Global mean sea-level rise, acceleration, Greenland Ice Sheet, Mass contributions, Satellite altimetry
Corresponding author:
Xianyao Chen
Citation:
Chen, X., Zhang, X., Church, J. A., Watson, C. S., King, M. A., Monselesan, D., et al. (2017). The increasing rate of global mean sea-level rise during 1993–2014. Nature Climate Change, 7(7), 492–495. doi:10.1038/nclimate3325
URL:
https://www.nature.com/articles/nclimate3325
Abstract
Global mean sea level (GMSL) has been rising at a faster rate during the satellite altimetry period (1993–2014) than previous decades, and is expected to accelerate further over the coming century1. However, the accelerations observed over century and longer periods2 have not been clearly detected in altimeter data spanning the past two decades3,4,5. Here we show that the rise, from the sum of all observed contributions to GMSL, increases from 2.2 ± 0.3 mm yr−1 in 1993 to 3.3 ± 0.3 mm yr−1 in 2014. This is in approximate agreement with observed increase in GMSL rise, 2.4 ± 0.2 mm yr−1 (1993) to 2.9 ± 0.3 mm yr−1 (2014), from satellite observations that have been adjusted for small systematic drift, particularly affecting the first decade of satellite observations6. The mass contributions to GMSL increase from about 50% in 1993 to 70% in 2014 with the largest, and statistically significant, increase coming from the contribution from the Greenland ice sheet, which is less than 5% of the GMSL rate during 1993 but more than 25% during 2014. The suggested acceleration and improved closure of the sea-level budget highlights the importance and urgency of mitigating climate change and formulating coastal adaption plans to mitigate the impacts of ongoing sea-level rise.
Main
Projections of future sea levels must be based on a sound understanding of historical changes in GMSL and its underlying processes, as well as recent changes in the rate of rise1. In a previous study, the apparent decrease in the rate of GMSL rise from 3.2 mm yr−1 in the first decade of satellite altimetry to 2.8 mm yr−1 in the second was suggested to be primarily a result of natural interannual variability, related to water exchange between ocean and land during El Niño/Southern Oscillation (ENSO) cycles3. After removing this variability, the underlying rate of GMSL rise was 3.3 ± 0.4 mm yr−1 for both decades, with neither deceleration nor acceleration of GMSL inferred over 1993 to 2014. This lack of observed acceleration of GMSL contrasts with a simultaneously increased contribution from the Greenland ice sheet (GIS) and a less certain increase from the Antarctica ice sheet (AIS) overall7, and is inconsistent with the positive acceleration presented in century-long tide gauge data8 and global mean sea-level reconstructions2.
By comparing tide gauge and satellite altimeter sea-level observations, a recent study6 identified a possible systematic drift within the altimeter record, particularly affecting the first six years (1993–1999). This systematic error erroneously elevates the GMSL trend during 1993–1998 by between 0.9 ± 0.5 and 1.5 ± 0.5 mm yr−1, depending on whether a glacial isostatic adjustment (GIA) or Global Positioning System (GPS) data set was used to correct for the effects of land motion at tide gauges used in the bias estimation process. After removing these biases, the estimated rate of GMSL rise from 1993 to mid-2014 was between 2.6 ± 0.4 and 2.9 ± 0.4 mm yr−1, with a positive but not statistically significant acceleration of 0.041 ± 0.058 mm yr−2, compared with a not statistically significant deceleration of −0.057 ± 0.058 mm yr−2 for unadjusted data.
GMSL rise results from the ocean thermal expansion, loss of mass from glaciers9, the GIS and the AIS7, and changes in land water storage from climate variability and anthropogenic effects10,11. To study how the rate of the GMSL rise varies during the satellite period, we investigate the time-varying intrinsic trend in GMSL and these contributing components by separating them from their interannual variability using an adaptive data analysis approach.
An intrinsic trend is defined as ‘an intrinsically fitted monotonic function or a function in which there can be at most one extremum within a given data span’12. Unlike the commonly used linear polynomial trend that requires a priori assumptions regarding stationarity and linearity of time series, the intrinsic trend is not defined by a predetermined functional form of the trend and, hence, is more adaptive to the underlying physical properties of observations. The method we apply to derive the intrinsic trend in GMSL and its components is ensemble empirical mode decomposition (EEMD)13, which is based on the empirical mode decomposition (EMD) method designed for adaptive analysis of nonlinear and non-stationary time series14 (see Methods and Supplementary Information) and has only recently been applied to sea-level trend estimation8. The main benefit of using EMD is that it can separate non-stationary oscillations (such as natural variations on different timescales) from the long-term trend, and the trend is found empirically without any assumptions about its shape.
Figure 1a presents the unadjusted GMSL from four different processing groups, and the adjusted CSIRO GMSL derived using vertical land motion (VLM) estimates at tide gauges based on GIA and GPS6. We note there is not yet a homogeneously reprocessed altimeter data set that addresses the likely systematic bias estimated by ref. 6. In the absence of such a data set, an assessment of all available records (including the adjusted record from ref. 6) is entirely appropriate. The intrinsic trend and interannual variability of each time series are shown in Fig. 1a, b, respectively. The significance of the intrinsic trend is tested against a null hypothesis of red background noise with the same lag-1 autocorrelation as the raw time series (Supplementary Fig. 1), and it is shown that the increase in the intrinsic trend of the GPS-based adjusted GMSL record is statistically significant during the recent decade (Supplementary Fig. 2).
Figure 1: Global mean sea level (GMSL). Curves show the GPS-based and GIA-based adjusted GMSL, and unadjusted GMSL from four different groups. a, GMSL and the time-varying secular trend from EEMD analysis. b, The interannual variability of GMSL. c, The instantaneous rate of GMSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades.
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
d4e5a3445e08-1
|
Figure 1a presents the unadjusted GMSL from four different processing groups, and the adjusted CSIRO GMSL derived using vertical land motion (VLM) estimates at tide gauges based on GIA and GPS6. We note there is not yet a homogeneously reprocessed altimeter data set that addresses the likely systematic bias estimated by ref. 6. In the absence of such a data set, an assessment of all available records (including the adjusted record from ref. 6) is entirely appropriate. The intrinsic trend and interannual variability of each time series are shown in Fig. 1a, b, respectively. The significance of the intrinsic trend is tested against a null hypothesis of red background noise with the same lag-1 autocorrelation as the raw time series (Supplementary Fig. 1), and it is shown that the increase in the intrinsic trend of the GPS-based adjusted GMSL record is statistically significant during the recent decade (Supplementary Fig. 2).
Figure 1: Global mean sea level (GMSL). Curves show the GPS-based and GIA-based adjusted GMSL, and unadjusted GMSL from four different groups. a, GMSL and the time-varying secular trend from EEMD analysis. b, The interannual variability of GMSL. c, The instantaneous rate of GMSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades.
We derive the rate of the time-varying intrinsic trend by calculating its first-order temporal derivative (Fig. 1c). Consistent with previous studies3, the unadjusted GMSL exhibits a slightly decreasing rate of rise from about 3.5 mm yr−1 during the first decade to 3.0–3.3 mm yr−1 during the second. In contrast, the rate of the GPS-based adjusted GMSL rise increases by 0.5 mm yr−1 from about 2.4 ± 0.2 (1σ) mm yr−1 in 1993 to around 2.9 ± 0.3 mm yr−1 in 2014 (2.8 ± 0.2 to 3.2 ± 0.3 mm yr−1 for the GIA-based adjusted GMSL). That is, the time-varying trend of the adjusted altimeter data suggests an acceleration in GMSL in agreement with ref. 6, with the dominant increase in the rate of rise occurring in the recent decade.
Figure 1b shows the interannual variability of all GMSL records derived by EEMD. It includes a significant drop of water level related to the transfer of water from the ocean to the land during the strong La Niña event in 2011 and the subsequent rapid recovery in the following two years15. This interannual variability agrees well with the interannual variability of the land water storage based on the global hydrological model16 and the interannual variability of the thermosteric sea level17, and is significantly correlated (0.42 for the unadjusted CSIRO-based time series, and up to 0.56 for the others) with the ENSO index18. By definition of the EMD method, this interannual variability does not contribute to the intrinsic trend over the whole period.
We determined global mean steric sea-level (GMSSL) anomalies using a range of subsurface measurements of temperature and salinity data sets19. The GMSSLs from these data sets exhibit wide discrepancies owing to the inhomogeneous observations in the ocean, different data quality control procedures, XBT (expendable bathythermograph) bias corrections, mapping methods and model structures20. These discrepancies are especially pronounced until 2005 when sufficient spatial data coverage was obtained from Argo floats. We select ocean temperature–salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trend of GMSSL during the Argo period (2005–2014) remains within the 2σ range of that derived from three Argo gridded data sets (Supplementary Table 1). Figure 2 shows monthly GMSSL anomalies, interannual variability and the intrinsic trends from seven data sets based on the above selection criteria.
Figure 2: Global mean steric sea level (GMSSL). Coloured curves show the global mean steric sea level from seven data sets. a, The GMSSL and its time-varying secular trend. b, The interannual variability of GMSSL. c, The instantaneous rate of GMSSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades. In c, the dots denote the median of all GMSSL records at each year, with the uncertainty estimated using the median statistical method. Note that the different length of the GMSSL time series affects the median rates over the last few years, and consequently affects the budget over the last few years as shown in Fig. 4.
Even with these relatively strict criteria, the GMSSLs of the selected ocean temperature–salinity data sets still exhibit remarkable differences over the whole period. The instantaneous rate of the GMSSL of some models indicates acceleration, whereas others not. To reduce the impact of the skewness, we estimate the instantaneous rate of GMSSL rise as the median of that derived from seven data sets at each year. The derived mean thermal expansion contribution is about 0.94 ± 0.16 mm yr−1 during 1993–2014, which is equivalent to about 0.48 ± 0.08 W m−2 net surface heat flux into the ocean, and consistent with the observed top-of-atmosphere heat imbalance21. The ensemble estimate of the GMSSL rise suggests little acceleration during the satellite altimetry period.
The main contributions to the global ocean mass changes are from the GIS, the AIS and glaciers. The GIS and AIS mass changes are investigated using the estimates based on altimetry, gravimetry and mass flux data for 1993–20127, and the GRACE observations during 2003–2014 by adjusting its trend to match the published data over 2003–200922 (Supplementary Fig. 5). The glacier data are estimated from a glacier mass balance model driven by gridded climate observations9.
Figure 3 shows that all three sources of mass loss exhibit an increasing contribution to GMSL. The rate of glacier mass loss increased over 1993 to 2005, from 0.60 ± 0.15 to 0.87 ± 0.21 mm yr−1 GMSL equivalent, but is then nearly unchanged up to 2013 (Fig. 3c). The GIS mass loss increased from around 0.11 ± 0.03 mm yr−1 in 1993 to around 0.85 ± 0.03 mm yr−1 in 2014, approaching an average acceleration of 0.03 mm yr−2. The rate of the AIS mass loss is around 0.22 ± 0.02 mm yr−1 in 1993, and only slightly increases to 0.31 ± 0.02 mm yr−1 in 2014. These trends agree quantitatively with previous linear estimates7,9 over the whole satellite period, and contribute to the acceleration of GMSL.
Figure 3: Global mean ocean mass change. Curves show the land-glacier, AIS and GIS and anthropogenic TWS contributions to GMSL. a–c, Each mass component and its secular trend (a), the interannual variability (b), and the instantaneous rate (c) of the ocean mass change. In c, the black dots and their error bars show the rate of thermal expansion, GMSSL, from Fig. 2 for comparison with the mass change rate. The uncertainties of the derived interannual variability, intrinsic secular trend, and their instantaneous rates are shown in coloured shades.
Another contribution to changes in the global ocean mass is from terrestrial water storage (TWS), including that associated with anthropogenic activities (groundwater extraction, irrigation, impoundment in reservoirs, wetland drainage, and deforestation) and natural climate variability. Here, the anthropogenic TWS changes are based on the estimates of ref. 11, with their groundwater depletion being replaced with the estimates of ref. 10, which are 20% smaller. This smaller estimate is consistent with 80% of the extracted ground water making its way to the ocean23. The intrinsic trend and its instantaneous rate of the anthropogenic TWS show a slightly increased contribution to GMSL from around 0.11 ± 0.04 mm yr−1 during the first decade to about 0.24 ± 0.06 mm yr−1 during the second (Fig. 3c).
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
d4e5a3445e08-2
|
Figure 3: Global mean ocean mass change. Curves show the land-glacier, AIS and GIS and anthropogenic TWS contributions to GMSL. a–c, Each mass component and its secular trend (a), the interannual variability (b), and the instantaneous rate (c) of the ocean mass change. In c, the black dots and their error bars show the rate of thermal expansion, GMSSL, from Fig. 2 for comparison with the mass change rate. The uncertainties of the derived interannual variability, intrinsic secular trend, and their instantaneous rates are shown in coloured shades.
Another contribution to changes in the global ocean mass is from terrestrial water storage (TWS), including that associated with anthropogenic activities (groundwater extraction, irrigation, impoundment in reservoirs, wetland drainage, and deforestation) and natural climate variability. Here, the anthropogenic TWS changes are based on the estimates of ref. 11, with their groundwater depletion being replaced with the estimates of ref. 10, which are 20% smaller. This smaller estimate is consistent with 80% of the extracted ground water making its way to the ocean23. The intrinsic trend and its instantaneous rate of the anthropogenic TWS show a slightly increased contribution to GMSL from around 0.11 ± 0.04 mm yr−1 during the first decade to about 0.24 ± 0.06 mm yr−1 during the second (Fig. 3c).
Regarding the natural variability of TWS, global values are not reliable before the GRACE mission in 2002. Interannual fluctuations of TWS based on the continental water balance model are estimated as about 0.25 mm yr−1 (GMSL equivalent) during 1993–199824, whereas the GRACE observations during 2002–2012 suggested a natural TWS contribution to GMSL of around −0.71 ± 0.20 mm yr−1 (ref. 25). This rate is approximately consistent with the 5.5 mm fall in GMSL over 2002–2012 in the interannual variability (Fig. 1b), which is highly correlated with the La Niña-like variability in the Pacific15, when precipitation decreases over the ocean and increases over the land. Because of the strong ENSO-related interannual variability, there can be significant trends in TWS over periods of a decade or shorter. Therefore, short-period linear trend estimates do not adequately represent the time series over the whole satellite altimeter period, and it is likely that the total trend is small (but poorly quantified).
Using time series of GMSL, GMSSL and all components of global ocean mass change, Fig. 4 shows the instantaneous budget of GMSL over the satellite period. The thermal expansion component is about 50% of the total contributions in 1993. Although the rate of this contribution did not change much throughout the record, by the end of the record it is reduced to about 30% of the sum of the contributions because of the acceleration in the global ocean mass component, consistent with a previous estimate of the changing relative roles of ocean thermal expansion and ocean mass26. The ocean mass change is initially dominated by the contribution of glacier mass loss, with smaller contributions from the GIS and AIS mass loss and anthropogenic TWS changes. But in the recent decade, the acceleration of the mass loss from the GIS was the largest, and its contribution to the GMSL became almost equal to that from thermal expansion and glaciers by 2014. The year-by-year contribution from the AIS mass loss is nearly constant while the glacier contribution increases slowly.
Figure 4: Instantaneous closure of the global mean sea-level budget. Yearly instantaneous rate of change of the GPS-based adjusted (black dots) and mean unadjusted GMSL (grey stars) and that of the GMSSL, and ocean mass contributions from the GIS, the AIS, the anthropogenic TWS and glaciers, and ocean thermal expansion (each shown in coloured shades, ordered from top to bottom). The blue dots denote the sum of the instantaneous rates of change of each component with its uncertainty estimated as the square root of the sum of the squares of the uncertainty in each instantaneous rate, as shown in previous figures. The time series of the loss of mass from the glaciers and the anthropogenic TWS stops in 2012, and 2009, respectively. Their rates in the years up to 2014 are assumed unchanged and shown in a lighter colour.
In all future projection scenarios of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change27, the largest contribution to changes in GMSL is the ocean thermal expansion, accounting for 30–55% of the projection, whereas the glaciers are the second largest, accounting for 15–35%. Our analysis of recent observations shows that the acceleration of ocean thermal expansion during 1993–2014 is not significant. Climate model simulations indicate the fall in ocean heat content following the 1991 volcanic eruption of Mount Pinatubo and the subsequent recovery has probably resulted in a rate of thermal expansion about 0.5 mm yr−1 higher than would be expected from greenhouse gas forcing alone28. The recovery in ocean thermal expansion following major volcanic eruption takes more than 15 years28,29. Thus, the underlying acceleration of thermal expansion in response to the anthropogenic forcing may emerge over the next decade or so, resulting in a further acceleration in the rate from that reported here and recent estimates30. In contrast to the lack of observed acceleration in the ocean thermal expansion, there has been a significant acceleration in the mass contributions, dominated by the increased GIS mass loss. This results in an approximate closure of the sea level budget throughout the study period from 1993 to 2014 and, importantly, both the sum of contributions and the GPS (and GIA)-based adjusted altimeter rates indicate an acceleration in sea level over the satellite altimeter period.
This approximate but improved closure of the sea-level budget throughout 1993–2014 is progress with respect to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, and increases confidence in our observations and understanding of recent changes in sea level. The study period is still short and ongoing observations are required to understand the longer-term significance of this finding, and to identify the contributions of decadal and multi-decadal variations that are unresolved in the 20-year-long records. The estimated increase in the rate of rise has important implications for projections of sea-level rise and for society.
Methods
Data
Satellite altimetry
We use six different altimetry-based monthly sea-level data from four processing groups: Archiving Validation and Interpretation Satellite Oceanographic Center (AVISO; https://podaac.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V4); Colorado University (CU, Release 4; http://sealevel.colorado.edu/files/2015_rel4/sl_ns_global.txt); Goddard Space Flight Center (GSFC; https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html); Commonwealth Scientific and Industrial Research Organization (CSIRO) and University of Tasmania (ftp://ftp.marine.csiro.au/pub/legresy/gmsl_files/CSIRO_Alt_refined.csv); adjusted CSIRO data set using a model of glacial isostatic adjustment to estimate vertical land motion at tide gauges; and adjusted CSIRO data set using GPS data to estimate vertical land motion at tide gauges. All six data sets are based on TOPEX, Jason-1 and OSTM/Jason-2 data. The global average is computed over 66° S–66° N for AVISO, CU and GSFC, but over 65° S–65° N for CSIRO. Detailed descriptions of each data set are available in the corresponding websites.
Steric sea-level data sets
We use seven products describing the global ocean monthly temperature–salinity to compute the global mean steric sea level. Two of these are objective analyses based on optimal interpolation without constraints from ocean model dynamics, and five are reanalyses based on data assimilation with models. From 20 global ocean temperature–salinity data sets [19], we select a subset of seven ocean temperature–salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trends of GMSSL during the Argo period (2005–2014) remain within the 2σ range of that derived from three Argo gridded data sets. Supplementary Table 1 provides the basic information of these data sets.
Land glaciers
The global yearly glacier mass data set used in this paper is produced with a glacier model driven by gridded climate observations [9].
Greenland and Antarctic ice sheets
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
d4e5a3445e08-3
|
Data
Satellite altimetry
We use six different altimetry-based monthly sea-level data from four processing groups: Archiving Validation and Interpretation Satellite Oceanographic Center (AVISO; https://podaac.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V4); Colorado University (CU, Release 4; http://sealevel.colorado.edu/files/2015_rel4/sl_ns_global.txt); Goddard Space Flight Center (GSFC; https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html); Commonwealth Scientific and Industrial Research Organization (CSIRO) and University of Tasmania (ftp://ftp.marine.csiro.au/pub/legresy/gmsl_files/CSIRO_Alt_refined.csv); adjusted CSIRO data set using a model of glacial isostatic adjustment to estimate vertical land motion at tide gauges; and adjusted CSIRO data set using GPS data to estimate vertical land motion at tide gauges. All six data sets are based on TOPEX, Jason-1 and OSTM/Jason-2 data. The global average is computed over 66° S–66° N for AVISO, CU and GSFC, but over 65° S–65° N for CSIRO. Detailed descriptions of each data set are available in the corresponding websites.
Steric sea-level data sets
We use seven products describing the global ocean monthly temperature–salinity to compute the global mean steric sea level. Two of these are objective analyses based on optimal interpolation without constraints from ocean model dynamics, and five are reanalyses based on data assimilation with models. From 20 global ocean temperature–salinity data sets [19], we select a subset of seven ocean temperature–salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trends of GMSSL during the Argo period (2005–2014) remain within the 2σ range of that derived from three Argo gridded data sets. Supplementary Table 1 provides the basic information of these data sets.
Land glaciers
The global yearly glacier mass data set used in this paper is produced with a glacier model driven by gridded climate observations [9].
Greenland and Antarctic ice sheets
Greenland and Antarctic ice sheet records during 1993–2012 available at http://imbie.org/data-downloads [7] are used in this study. To extend the records to the end of 2014, observations based on the GRACE satellite are used. Noting the potential GIA error in GRACE, especially for Antarctica31, we adjusted the trend of the GRACE records so that they agreed with the published trends over 2003–2009. Then two records are connected in 2003. After 2003, the GRACE record is used. The derived monthly time series are shown in Supplementary Fig. 5.
Anthropogenic terrestrial water storage
The yearly data of anthropogenic terrestrial water storage are extracted from the century-long time series [11], after their groundwater depletion is replaced with the most recent estimates [10].
Ensemble empirical mode decomposition method
The main method used in this study is ensemble empirical mode decomposition (EEMD) [13], which was developed on the basis of the empirical mode decomposition (EMD)14 method. The EMD and EEMD methods have been applied to oceanic and climatic time series analysis32, and are also used to study regional [8,33,34] and global sea-level variability35. Here we briefly introduce the general decomposition procedure and mainly introduce the tests used to assess statistical significance and the estimation of the uncertainty of the intrinsic secular trend derived by the EMD/EEMD method.
Decomposition and intrinsic secular trend
In EMD, a time series x(t) is decomposed into a set of amplitude–frequency-modulated oscillatory functions (so-called intrinsic mode functions, IMFs) Cj(t), j = 1,2, … n and a residual R(t): x(t) = ∑ j=1nCj(t) + R(t) through a sifting process. The following is undertaken: (1) locate all maxima and minima and connect all maxima (minima) with a cubic spline as an upper (lower) envelope of the time series; (2) compute the difference between the time series and the mean of the upper and lower envelopes to yield a new time series h(t); (3) for the time series h(t), repeat steps 1 and 2 until upper and lower envelopes are symmetric with respect to zero mean under the stopping criteria13,14, then an IMF, Cj(t), is derived as the time series h(t); and (4) subtract Cj(t) from original time series to yield a residual R(t) and treat R(t) as the original time series and repeat steps 1–3 until the residual R(t) becomes a monotonic function or a function with only one extremum; then, the whole sifting process is completed and all IMFs and the residual function, namely, the intrinsic trend of x(t), are obtained.
The EEMD approach is based on EMD13. In EEMD, multiple noise realizations are added to the time series x(t), from which an ensemble average of the corresponding IMFs is extracted to yield scale-consistent signals. The main steps in the EEMD are as follows: (1) add a white noise series to the targeted data; (2) decompose the data with the added white noise into IMFs; (3) repeat step 1 and 2 again and again, but with different white noise series each time; and (4) obtain (ensemble) means of the respective IMFs of the decompositions as the final result. The advantage of the EEMD is that by using an ensemble mean, non-physical oscillations due to random data errors are reduced and thus low-frequency modes are more accurate.
It is proved that the added white noise with the variance σ will have at most impact on the resulting IMFs13, where N is the number of ensemble members. When N increases, this impact is negligibly small. In this paper, we always use the white noise with variance σ = 0.2 relative to the variance of the original time series, and N = 1,000 ensemble members.
As demonstrated in previous applications of the EEMD method involving trend analysis of global mean surface temperature36, global land surface air temperature37, and the sea-level observations along the eastern US coast8,33, the residual function R(t) is derived by removing any, but not a predetermined, variability on shorter timescales than the length of time series, as represented by the IMFs Cj(t). Consequently, R(t) can take any unspecified shape and will preserve the potential variability on longer timescales than the length of time series. For the observations used here (22 year duration for the altimetry), the relatively high-frequency variability on the interannual timescales will be shown by summing all of the IMFs, that is, ∑ j=1nCj(t) and the residual R(t) will be regarded as the intrinsic trend.
It should be noted that the intrinsic trend R(t) is in the same unit as the raw time series (in this case for the global mean sea level used here, the unit is millimetres). Taking the first-order time derivative of the time-varying intrinsic trend yields the instantaneous rate of the trend, in units of millimetres per year for global mean sea-level rise, which provides more time-varying information on how the intrinsic trend has evolved within the given time region, compared with a typical fitted polynomial and the time-varying estimations based on the sliding window approach38,39.
The validity of the intrinsic trend is strongly based on the specified data duration. The properties of the trend beyond the data length require further investigation with more observations. In this study, the potential decadal variability of GMSL on the timescale longer than the length of satellite altimetry cannot be separated from the secular trend, which implies that the accelerated GMSL may partially reflect the internal decadal variability, as well as the effects of the anthropogenic forcing.
Significant test of the intrinsic secular trend
To test the statistical significance of the intrinsic secular trend, one needs to reject a null hypothesis that it arises by chance for stochastic processes with zero means at given confidence levels. In climate sciences, two widely used null hypotheses are that the underlying processes are noise characterized as white (that is, no temporal correlation) or red (with lag temporal correlation). There are many methods to test the statistical significance of a linear, curve-fitted, or time-varying trend against a white or red noise null hypothesis33,40,41,42. Here we applied one approach developed for testing the time-varying trend derived by the EMD/EEMD method37. Although the detail of the statistical significance test is given in their Supplementary Section 2, the general procedures of this approach are introduced as follows, in order for the integrity of this work.
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
d4e5a3445e08-4
|
It should be noted that the intrinsic trend R(t) is in the same unit as the raw time series (in this case for the global mean sea level used here, the unit is millimetres). Taking the first-order time derivative of the time-varying intrinsic trend yields the instantaneous rate of the trend, in units of millimetres per year for global mean sea-level rise, which provides more time-varying information on how the intrinsic trend has evolved within the given time region, compared with a typical fitted polynomial and the time-varying estimations based on the sliding window approach38,39.
The validity of the intrinsic trend is strongly based on the specified data duration. The properties of the trend beyond the data length require further investigation with more observations. In this study, the potential decadal variability of GMSL on the timescale longer than the length of satellite altimetry cannot be separated from the secular trend, which implies that the accelerated GMSL may partially reflect the internal decadal variability, as well as the effects of the anthropogenic forcing.
Significant test of the intrinsic secular trend
To test the statistical significance of the intrinsic secular trend, one needs to reject a null hypothesis that it arises by chance for stochastic processes with zero means at given confidence levels. In climate sciences, two widely used null hypotheses are that the underlying processes are noise characterized as white (that is, no temporal correlation) or red (with lag temporal correlation). There are many methods to test the statistical significance of a linear, curve-fitted, or time-varying trend against a white or red noise null hypothesis33,40,41,42. Here we applied one approach developed for testing the time-varying trend derived by the EMD/EEMD method37. Although the detail of the statistical significance test is given in their Supplementary Section 2, the general procedures of this approach are introduced as follows, in order for the integrity of this work.
For any time series x(t) with time-varying secular trend R(t) derived by the EEMD method, the statistical significance test includes: (1) computing the lag-1 autocorrelation α of the time series x(t). If α = 0 then the null hypothesis that the white background noise is applied; if α > 0, then the null hypothesis that the red background noise is applied; (2) generating 5,000 samples of red noise time series with the same temporal data length of x(t) and the lag-1 autocorrelation α; (3) deriving the intrinsic trend of each generated red noise time series by using the EEMD method. This yields an empirical probability density function of the intrinsic trends, which is approximately normally distributed, at any temporal locations; (4) comparing the intrinsic trend of the studied time series with the two-standard-deviation spread value of the trends of the red noise time series (around 95% of confidence) at any temporal locations. If the former is larger, the intrinsic trend of the studied time series is considered statistically significant and the null hypothesis that the intrinsic trend of the time series is from noise could be rejected; (5) taking the first-order time derivative of the intrinsic trend yields its instantaneous rate. If the intrinsic trend is statistically significant, we will consider its instantaneous rate is significant.
In this approach, the noise time series are generated on the basis of the AR(1) process x(t) = αx(t − Δt) + w(t), where the coefficient α is the autoregressive parameter (that is, lag-1 correlation coefficient), Δt is the sampling rate and w(t) is the white noise with the unit standard deviation. A more general case is to generate the red noise on the basis of the ARMA(p, q) process43,44. Empirically, the selection of the red noise model may change the probability density function shape of the EEMD trends of each red noise time series, but it will not change the general patterns of the statistical significance test if we go through all possibilities of the lag-1 autocorrelation from 0 to 0.99. In this study, we adopt the AR(1) model.
Taking the GPS-based adjusted GMSL time series as an example, Supplementary Figs 2–4 present the analysis of its intrinsic trend, and the test of its statistical significance. Supplementary Fig. 2 shows that the lag-1 autocorrelation coefficient of the GPS-based adjusted GMSL is α = 0.84. With this lag-1 autocorrelation coefficient, 5,000 AR(1) time series are generated and then decomposed by the EEMD method to derive their intrinsic trend (Supplementary Fig. 2a). Both thick black lines in Supplementary Fig. 2a are two-standard-deviation spread lines of the trend of AR(1) time series. Note that these intrinsic trends of the background noise are dimensionless. To test the statistical significance of the intrinsic trend of GPS-based adjusted GMSL time series, which is in the same unit of millimetres, we divide it by the standard deviation of the linearly detrended GMSL time series (red line in Supplementary Fig. 2a) and compare it with two standard deviations of the intrinsic trend of the red background noise at each temporal location. If the former is larger, the trend of GMSL is considered statistically significant. Supplementary Fig. 2b, c presents the comparison at two randomly selected years 1999 and 2009, respectively, in which the trend of GMSL time series is not statistically different from the trend of AR(1) red noise with 0.84 lag-1 autocorrelation in 1999, but significantly different in 2009. In Supplementary Fig. 2a, comparing the temporal variability of the intrinsic secular trend of the GPS-based adjusted GMSL time series with the two-standard-deviation line (around 95% confidence) of the intrinsic trend of the 5,000 AR(1) processes with 0.84 lag-1 autocorrelation shows that the intrinsic trend of GPS-based adjusted GMSL becomes statistically significant since 2005.
As for the definition of the intrinsic trend12, this statistical significance test is also valid only during the studied period, because the properties of the intrinsic trend beyond the data length may change a lot, and so their statistical significance.
To test the time series with different lag-1 autocorrelation, Supplementary Fig. 3 shows the two-standard-deviation line (around 95% confidence) of the intrinsic secular trend of the 5,000 AR(1) processes with the lag-1 autocorrelation ranging from 0 to 0.99. The trend spread depends on the value of lag-1 autocorrelation. When the noise is getting redder (larger lag-1 autocorrelation), the corresponding spreads become wider37.
Based on the 95% confidence levels of different AR(1) time series with lag-1 autocorrelation ranging from 0 to 0.99, the statistical significance of the intrinsic secular trend of the GMSL, the GMSSL, and the global ocean mass change can be tested, as shown in Supplementary Fig. 4a–c, respectively.
Estimation of the uncertainty of the intrinsic trend
To estimate the uncertainties in the intrinsic trend, the down sampling approach36 is applied. This method is also used to study the increasing flooding hazard in Miami Beach, Florida [34].
For the monthly time series of global mean sea level, global mean steric sea level, or the Greenland and Antarctic ice sheet mass loss, we randomly pick a value of the time series for each calendar year to represent the entire annual average. This step can theoretically yield 12 (ref. 22) different time series for 22 years of monthly data. We randomly choose 1,000 series and re-compute their intrinsic secular trend, and then obtain the mean of the trend, and the spread of the trends provides the confidence interval. For the yearly time series of glacier and anthropogenic terrestrial water storage time series, we randomly pick up a value of the time series within two standard deviations of the time series to represent the spread of the time series, and choose 1,000 different series and re-compute their intrinsic secular trend. The rate of the intrinsic trend is obtained by computing the mean of the time derivative of each intrinsic trend and its uncertainty. This approach can also be applied to estimate the uncertainty of the other IMFs of the time series if the timescale of the function is longer than a month.
Since the higher-frequency variability of the time series is gradually separated using EEMD, the uncertainty of the intrinsic trend is generally less than the uncertainty estimation of the linear trend of original whole time series. The uncertainty of the intrinsic trend at the start and end of the data range is relatively large given the edge effects. This is unavoidable for any temporally local analysis method, such as the Gibbs effect of the Fourier transform and the ‘cone of influence’ of wavelet analysis45. Compared with these methods, the temporal locality of EEMD is smaller, and so are the uncertainties at the two ends, as discussed in the study of uncertainty of the global sea surface temperature [36].
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
d4e5a3445e08-5
|
Based on the 95% confidence levels of different AR(1) time series with lag-1 autocorrelation ranging from 0 to 0.99, the statistical significance of the intrinsic secular trend of the GMSL, the GMSSL, and the global ocean mass change can be tested, as shown in Supplementary Fig. 4a–c, respectively.
Estimation of the uncertainty of the intrinsic trend
To estimate the uncertainties in the intrinsic trend, the down sampling approach36 is applied. This method is also used to study the increasing flooding hazard in Miami Beach, Florida [34].
For the monthly time series of global mean sea level, global mean steric sea level, or the Greenland and Antarctic ice sheet mass loss, we randomly pick a value of the time series for each calendar year to represent the entire annual average. This step can theoretically yield 12 (ref. 22) different time series for 22 years of monthly data. We randomly choose 1,000 series and re-compute their intrinsic secular trend, and then obtain the mean of the trend, and the spread of the trends provides the confidence interval. For the yearly time series of glacier and anthropogenic terrestrial water storage time series, we randomly pick up a value of the time series within two standard deviations of the time series to represent the spread of the time series, and choose 1,000 different series and re-compute their intrinsic secular trend. The rate of the intrinsic trend is obtained by computing the mean of the time derivative of each intrinsic trend and its uncertainty. This approach can also be applied to estimate the uncertainty of the other IMFs of the time series if the timescale of the function is longer than a month.
Since the higher-frequency variability of the time series is gradually separated using EEMD, the uncertainty of the intrinsic trend is generally less than the uncertainty estimation of the linear trend of original whole time series. The uncertainty of the intrinsic trend at the start and end of the data range is relatively large given the edge effects. This is unavoidable for any temporally local analysis method, such as the Gibbs effect of the Fourier transform and the ‘cone of influence’ of wavelet analysis45. Compared with these methods, the temporal locality of EEMD is smaller, and so are the uncertainties at the two ends, as discussed in the study of uncertainty of the global sea surface temperature [36].
The above uncertainty estimation of the intrinsic trend does not take into account systematic (non-averaging) error terms present in the time series. For the case of the adjusted GMSL time series, uncertainty associated with the bias drift estimation for each mission needs to be considered. The above uncertainty estimation method can be applied to each realization of the time series, with each realization generated sampling the bias drifts and intra/inter-mission bias and associated uncertainties. Applying the EEMD analysis to each time series and estimating the uncertainty of the derived intrinsic trend gives a joint uncertainty estimation of the instantaneous rate of the GPS-based adjusted GMSL rise (not shown). The slightly higher uncertainty of the instantaneous rate of the GMSL change (from ±0.6 mm yr−1 during 1993 to ±0.4 mm yr−1 during 2014) reflects the different mission lengths and the split between TOPEX side A and side B in the early part of the record.
|
https://sealeveldocs.readthedocs.io/en/latest/chen17.html
|
bdedab7bad2b-0
|
Sadai et al. (2020)
Title:
Future climate response to Antarctic Ice Sheet melt caused by anthropogenic warming
Corresponding author:
Shaina Sadai
Citation:
Sadai, S., Condron, A., DeConto, R., & Pollard, D. (2020). Future climate response to Antarctic Ice Sheet melt caused by anthropogenic warming. Science Advances, 6(39), eaaz1169. doi:10.1126/sciadv.aaz1169
URL:
https://www.science.org/doi/10.1126/sciadv.aaz1169
Abstract
Meltwater and ice discharge from a retreating Antarctic Ice Sheet could have important impacts on future global climate. Here, we report on multi-century (present-2250) climate simulations performed using a coupled numerical model integrated under future greenhouse-gas emission scenarios IPCC RCP4.5 and RCP8.5, with meltwater and ice discharge provided by a dynamic-thermodynamic ice sheet model. Accounting for Antarctic discharge raises subsurface ocean temperatures by >1˚C at the ice margin relative to simulations ignoring discharge. In contrast, expanded sea ice and 2˚C to 10˚C cooler surface air and surface ocean temperatures in the Southern Ocean delay the increase of projected global mean anthropogenic warming through 2250. In addition, the projected loss of Arctic winter sea ice and weakening of the Atlantic Meridional Overturning Circulation are delayed by several decades. Our results demonstrate a need to accurately account for meltwater input from ice sheets in order to make confident climate predictions.
Introduction
Observational evidence indicates that the West Antarctic Ice Sheet (WAIS) is losing mass at an accelerating rate (1, 2). Recent advances in ice sheet modeling have improved our understanding of Antarctic Ice Sheet (AIS) evolution in response to anthropogenic greenhouse gas forcing and show that the AIS could contribute substantially to sea level rise by the end of this century (3-6). A more accurate understanding of the impacts that this evolution might have on atmospheric and oceanic dynamics is needed to constrain possible future changes in the climate system. However, ice sheet physics are not adequately represented in the current generation of global climate models (GCM) used in future projections (7, 8). The AIS is considered a tipping element within the climate system (9) with the potential to contribute several tens of centimeters of global mean sea level rise in the next two centuries, but the climate system response to such large-scale ice loss is not well constrained, especially beyond 2100.
Today, freshwater input to the ocean is increasing in response to climatic warming, largely from a combination of net precipitation and increasing riverine input resulting from an invigorated hydrologic cycle, and the loss of sea and land ice (10). Previous modeling work investigating the relative impacts of freshwater forcing in the North Atlantic versus the Southern Ocean (11, 12) has demonstrated that the location and magnitude of the additional freshwater are central to the modeled climate response. Methodology for modeling the climatic impact of freshwater perturbations has also varied widely in terms of strength, duration, and location of meltwater input: Historically, so-called “hosing” approaches added water uniformly within given latitude bands (11-14), while more recent work has applied freshwater forcing at specific locations around global coastlines or spread according to iceberg movements (6, 15-19). Despite differences in model resolution and representation of Earth system processes, several elements of the climate response to freshwater perturbations in the Southern Ocean have been broadly consistent, such as a decrease in surface air temperatures (SATs) over the Southern Ocean, a decrease in the strength of the Atlantic Meridional Overturning Circulation (AMOC), and the expansion of Southern Ocean sea ice.
Here, we present results from a series of climate model simulations performed using a high-resolution, fully coupled, ocean-atmosphere-cryosphere-land model, Community Earth System Model (CESM) 1.2.2 with Community Atmospheric Model 5 (CAM5) atmospheric physics (20), under Representative Concentration Pathway (RCP) 4.5 and RCP8.5 (10) spanning 2005-2250 (see Materials and Methods). In our freshwater forcing simulations, referred to throughout the paper as RCP4.5FW and RCP8.5FW, time-evolving freshwater (liquid melt-water and solid ice) input from Antarctica is provided from a continental ice sheet/ice shelf model (3) responding to the same atmospheric forcing scenarios. The control runs (RCP4.5CTRL and RCP8.5CTRL) have no additional freshwater forcing beyond what is already simulated by the CESM model. To account for spatial and temporal variations in runoff and to improve on classic hosing experiments, we released time-variant AIS meltwater and ice discharge into the ocean at the nearest surface-level coastal grid cell to where ice calving and/or ocean melt is occurring in the ice sheet model (Fig. 1A; see Materials and Methods) such that considerable volumes of meltwater and ice enter the ocean from the Amundsen Coast of West Antarctica, including Pine Island and Thwaites glaciers. In our experiments, liquid melt-water and solid ice discharge from the AIS are input separately to account for the latent heat of melting the solid component. In both RCP scenarios, the solid ice component dominates the discharge, with 62 to 87% of the total discharge being ice in RCP8.5FW and 71 to 86% in RCP4.5 (fig. S1). This is due to ice model advances that include hydrofracturing and ice-cliff calving. Here, we use the term “AIS discharge” to refer to the total freshwater forcing from the ice sheet model from both the solid ice and liquid meltwater components.
In RCP4.5FW, total discharge increases throughout the 21st century and remains between 0.4 and 0.8 sverdrup (sverdrup = 10^6 m^3/s) from 2050 to 2250; in contrast, the meltwater input in RCP4.5CTRL never exceeds 0.1 sverdrup (Fig. 1D). In RCP8.5FW, AIS discharge is dominated by the retreat of the WAIS in the ice sheet model during the 21st century, peaking at >2 sverdrup around ~2125 when the Ross Ice Shelf has collapsed and the inland ice behind it drains into the Ross Sea. Discharge then remains above 1 sverdrup through 2200 due to increasing contributions from the East Antarctic Ice Sheet (EAIS). This is in sharp contrast to RCP8.5CTRL in which discharge increases steadily throughout the run but never exceeds 0.2 sverdrup (Fig. 1D). As such, our methodology allows a direct comparison of the climate response to changing atmospheric greenhouse gas concentrations with and without a major Antarctic meltwater contribution that accounts for both the liquid meltwater and solid ice components of AIS discharge (see Materials and Methods). While projected changes in meltwater and ice discharge from Greenland are not included in our simulations, their potential impacts on climate are discussed in Materials and Methods.
Figure 1: Freshwater forcing quantities and salinity response. (A) Spatially distributed, time-varying freshwater forcing from AIS discharge, which includes both the liquid meltwater and solid ice components, was input at the surface level around the continental margin. Forcing in September 2121 CE is shown here. (B) Combined liquid and solid forcing components are shown in relation to the global mean surface temperature in RCP8.5. Solid components are the dominant portion of the forcing, as seen in fig. S1. (C) Decadal (2121-2130) sea surface salinity anomaly based on the difference between RCP8.5FW and RCP8.5CTRL, reflecting the freshwater input during peak ice sheet retreat. (D) Same as in (B) except for RCP4.5.
Results
|
https://sealeveldocs.readthedocs.io/en/latest/sadai20.html
|
bdedab7bad2b-1
|
In RCP4.5FW, total discharge increases throughout the 21st century and remains between 0.4 and 0.8 sverdrup (sverdrup = 10^6 m^3/s) from 2050 to 2250; in contrast, the meltwater input in RCP4.5CTRL never exceeds 0.1 sverdrup (Fig. 1D). In RCP8.5FW, AIS discharge is dominated by the retreat of the WAIS in the ice sheet model during the 21st century, peaking at >2 sverdrup around ~2125 when the Ross Ice Shelf has collapsed and the inland ice behind it drains into the Ross Sea. Discharge then remains above 1 sverdrup through 2200 due to increasing contributions from the East Antarctic Ice Sheet (EAIS). This is in sharp contrast to RCP8.5CTRL in which discharge increases steadily throughout the run but never exceeds 0.2 sverdrup (Fig. 1D). As such, our methodology allows a direct comparison of the climate response to changing atmospheric greenhouse gas concentrations with and without a major Antarctic meltwater contribution that accounts for both the liquid meltwater and solid ice components of AIS discharge (see Materials and Methods). While projected changes in meltwater and ice discharge from Greenland are not included in our simulations, their potential impacts on climate are discussed in Materials and Methods.
Figure 1: Freshwater forcing quantities and salinity response. (A) Spatially distributed, time-varying freshwater forcing from AIS discharge, which includes both the liquid meltwater and solid ice components, was input at the surface level around the continental margin. Forcing in September 2121 CE is shown here. (B) Combined liquid and solid forcing components are shown in relation to the global mean surface temperature in RCP8.5. Solid components are the dominant portion of the forcing, as seen in fig. S1. (C) Decadal (2121-2130) sea surface salinity anomaly based on the difference between RCP8.5FW and RCP8.5CTRL, reflecting the freshwater input during peak ice sheet retreat. (D) Same as in (B) except for RCP4.5.
Results
The impact of applying spatially varying freshwater forcing is immediately apparent in the salinity field (Fig. 1 and fig. S2). By the end of the 21st century, the sea surface salinity (SSS) in the RCP8.5FW experiment is reduced by up to −5 practical salinity unit (psu) (compared to RCP8.5CTRL) over most of the Southern Ocean and begins spreading northward (Fig. 1 and fig. S2). By the time of peak WAIS retreat, around year 2120, the negative SSS anomaly exceeds −15 psu around the Antarctic margin, especially in the Amundsen and Bellingshausen seas and portions of the Ross and Weddell seas (Fig. 1C). By the middle of the 22nd century, the anomaly has spread pervasively throughout all the ocean basins, to depths of ~4000 m (fig. S2). In RCP4.5FW, the ice sheet collapse does not peak and decline in the same way as RCP8.5FW but rather is maintained throughout most of the run, resulting in a persistent and steady freshwater forcing (Fig. 1, B and D). The associated salinity anomaly patterns are spatially similar to the RCP8.5FW simulation but lower in magnitude (−1 to −2 psu) and remain confined to the Southern Ocean (fig. S2).
Prescribing AIS discharge from the ice sheet model has a profound impact on sea ice. Accurately capturing this response is important because seasonal freeze and melt cycles in the Southern Ocean act as a deepwater pump (21); thus, changes in sea ice are linked to changes in Southern Ocean overturning. The balance between brine rejection from sea ice formation, freshwater forcing, and associated changes in ocean convection also lead to alterations in air-sea heat exchange that can trap warm waters at depths and increase melt rates under neighboring ice shelves (22). Substantial changes in sea ice extent affect the radiative balance through sea ice albedo feedbacks and can markedly affect ecosystems. For example, shifts in sea ice formation have already begun to affect penguin colonies (23) and will likely have wide-reaching effects on microfauna communities, krill abundance, and larger ocean predators (24).
In our simulations, sea ice expands in both RCP4.5FW and RCP8.5FW, despite the strongly elevated radiative forcing (Fig. 2). The large AIS discharge in both simulations reduces salinity, raises the freezing temperature, and stratifies the water column around the coast. This, in turn, reduces convection, suppresses Southern Ocean overturning, and leads to a substantial buildup in perennial sea ice extent and thickness. Spatially, the greatest sea ice growth in the perturbation experiments is within the South Pacific sector, where the freshwater input is largest. Sea ice accumulates within the first few decades in both the RCP4.5 and RCP8.5 AIS discharge experiments, compared to the control simulations. In RCP8.5FW, Southern Ocean sea ice extent reaches a maximum in the 2120’s during peak AIS discharge, with sea ice thickness exceeding 10 m in the Amundsen, Bellingshausen, and Ross seas and parts of the EAIS margin (Fig. 2). As the freshwater forcing from AIS discharge declines following WAIS collapse, sea ice extent and thickness also begin to decline, although >10-m-thick sea ice still persists in several regions in year 2200 (fig. S3, A and C). After peak AIS discharge has occurred in RCP8.5FW in the 2120’s, sea ice extent and thickness markedly decline in this scenario. This is in contrast to RCP4.5FW, where >5-m-thick perennial sea ice persists into the 22nd century, despite the substantial anthropogenic greenhouse gas forcing (fig. S3, B and D). In contrast to the large quantities of sea ice produced in the perturbation experiments, sea ice never expands in RCP4.5CTRL and RCP8.5CTRL and declines over the course of those runs, with minimal sea ice in the Southern Ocean by 2100, and no austral winter sea ice by 2200 (Fig. 2A and fig. S3).
Figure 2: Sea ice response to freshwater forcing. (A) Time series of Southern Ocean sea ice area in February showing the extent of perennial sea ice in austral summer. Lower anthropogenic radiative forcing allows for a much greater sea ice area in the 22nd century in RCP4.5FW, despite a similar magnitude of freshwater forcing to that of RCP8.5FW. (B to E) February sea ice thickness decadally averaged for 2121–2130 for (B) RCP8.5FW, (C) RCP4.5FW, (D) RCP8.5CTRL, and (E) RCP4.5CTRL. Note the difference in scale for (D) and (E).
Projected changes in sea ice resulting from accelerated AIS discharge produces a strong albedo feedback that delays atmospheric warming in both perturbation experiments (Fig. 1, B and D). Spatially, the cooler temperatures relative to the control simulations are maximized directly over the Antarctic continental margin where the AIS discharge perturbation is applied (Fig. 3, A and B). The effect of the freshwater forcing from AIS discharge on global mean surface temperature (GMST) reaches a maximum at the time of peak ice sheet retreat in RCP8.5FW, with GMST values 2.5°C lower than the control run (Fig. 1B and fig. S4). This finding demonstrates that AIS mass loss could provide a negative feedback on anthropogenic warming, despite catastrophic impacts to the climate system as a whole, and substantial contributions to sea level rise. It is important to note, although, that while the rate of anthropogenic warming is mitigated somewhat until Antarctica is largely exhausted of ice, global temperatures still rise substantially above present-day values in both RCP4.5FW and RCP8.5FW (Fig. 1, B and D, and table S1).
|
https://sealeveldocs.readthedocs.io/en/latest/sadai20.html
|
bdedab7bad2b-2
|
Figure 2: Sea ice response to freshwater forcing. (A) Time series of Southern Ocean sea ice area in February showing the extent of perennial sea ice in austral summer. Lower anthropogenic radiative forcing allows for a much greater sea ice area in the 22nd century in RCP4.5FW, despite a similar magnitude of freshwater forcing to that of RCP8.5FW. (B to E) February sea ice thickness decadally averaged for 2121–2130 for (B) RCP8.5FW, (C) RCP4.5FW, (D) RCP8.5CTRL, and (E) RCP4.5CTRL. Note the difference in scale for (D) and (E).
Projected changes in sea ice resulting from accelerated AIS discharge produces a strong albedo feedback that delays atmospheric warming in both perturbation experiments (Fig. 1, B and D). Spatially, the cooler temperatures relative to the control simulations are maximized directly over the Antarctic continental margin where the AIS discharge perturbation is applied (Fig. 3, A and B). The effect of the freshwater forcing from AIS discharge on global mean surface temperature (GMST) reaches a maximum at the time of peak ice sheet retreat in RCP8.5FW, with GMST values 2.5°C lower than the control run (Fig. 1B and fig. S4). This finding demonstrates that AIS mass loss could provide a negative feedback on anthropogenic warming, despite catastrophic impacts to the climate system as a whole, and substantial contributions to sea level rise. It is important to note, although, that while the rate of anthropogenic warming is mitigated somewhat until Antarctica is largely exhausted of ice, global temperatures still rise substantially above present-day values in both RCP4.5FW and RCP8.5FW (Fig. 1, B and D, and table S1).
Figure 3: Air and ocean temperatures. (A) SAT difference (RCP8.5FW minus RCP8.5CTRL), decadally averaged for 2121–2130, shows strong cooling throughout the Southern Ocean. (B) Same as in (A), but for RCP4.5FW minus RCP4.5CTRL. Note that the cooling is limited to the Southern Hemisphere. (C) Decadally averaged sea surface temperature (SST) difference (RCP8.5FW minus RCP8.5CTRL) for 2121–2130 showing Southern Ocean cooling spreading to the equator and parts of the Northern Hemisphere. (D) Same as in (C), except for RCP4.5FW minus RCP4.5CTRL. (E) Subsurface ocean temperature difference (RCP8.5FW minus RCP8.5CTRL) at 400-m water depth, representative of continental shelf depths at the mouth of ice shelf cavities. Warming is concentrated in the Ross Sea. (F) Same as in (E), but for RCP4.5FW minus RCP4.5CTRL, showing warming concentrated in the Weddell Sea.
Freshwater forcing from AIS discharge strongly modifies the trajectory of polar climate in both hemispheres. During peak WAIS collapse, when the SAT in the Arctic (north of 60°N) is up to 2.5°C cooler in RCP8.5FW compared to RCP85CTRL, the decline in Arctic winter sea ice is slowed such that complete loss of Arctic sea ice is delayed by ~30 years (fig. S5). In the Southern Ocean, expanded sea ice growth suppresses surface warming, particularly in the Amundsen Sea region of Antarctica where sea ice formation is maximized. The resultant sea ice cooling feedback is so strong that SATs in portions of the Southern Ocean are colder after 2100 than at the beginning of the simulation in the early 21st century (fig. S6). This effect is seen in both RCP4.5FW and RCP8.5FW. The cooling effect persists until the end of the run under RCP4.5FW, as steady ice loss continues throughout the simulation. In contrast, the cooling effect disappears in RCP8.5FW after the peak in AIS discharge—when the West and East Antarctic basins become exhausted of ice and temperatures over the Southern Ocean begin to rise rapidly, ending >10°C warmer than the start of the run (fig. S6).
Global sea surface temperatures (SSTs) increase because of anthropogenic emissions in all simulations. Under RCP8.5FW, the Southern Ocean is an exception as SSTs cool by as much as 2°C during the 21st century and through the period of peak AIS discharge, as compared to the start of the run (fig. S7). Compared to RCP8.5CTRL, we find that SSTs in RCP8.5FW are significantly lower, with a 2° to 10°C cooling in the Southern Hemisphere at the time of peak AIS discharge during the 2120s, while a slight warming of ~2°C is observed in the North Atlantic and subtropical Pacific (Fig. 3C). The spatial patterns of temperature anomalies in RCP4.5FW are similar to those in RCP8.5FW, but of smaller magnitude. For example, SSTs in the Southern Hemisphere are 1° to 3°C cooler, while in the North Atlantic and subtropical Pacific, the warming is, at most, ~0.5° to 1°C (Fig. 3D).
The cooling response of Southern Ocean surface waters contrasts with subsurface warming at depths (~400 m) broadly representative of sills at the entrances of ice shelf cavities around the ice sheet margin. This juxtaposition is caused by the expanded sea ice cover, increased surface stratification in the upper water column, and reduced vertical mixing as seen in other studies (18). The subsurface warming in RCP8.5FW is more intense in our simulation relative to other recent studies (6, 18), because our integrations are run forward long enough to capture peak in AIS discharge associated with maximum WAIS retreat in the early 22nd century. The strongest subsurface ocean warming in RCP8.5FW is in the Ross Sea, where temperatures at 400-m water depth are ~2° to 4°C warmer than in RCP8.5CTRL in the 2120s (Fig. 3E). The strongest warming in RCP4.5FW is observed in the Weddell Sea at this time (Fig. 3F), although as noted previously, the WAIS does not undergo the same rapid collapse in this scenario. By 2250, temperatures are up to 3°C warmer in RCP4.5FW and up to 6°C warmer in RCP8.5FW, as compared to the start of run averages (fig. S8). The subsurface warming effect remains confined to the Southern Ocean, south of the Antarctic Circumpolar Current, as large parts of the deep ocean display the same cooling anomaly seen in the SSTs (fig. S9).
The contrasting surface cooling and subsurface warming have clear implications for the future stability of the AIS. A previous ice sheet modeling study (6) using an intermediate-complexity climate model to capture ice-climate feedbacks found that the subsurface ocean warming feedback dominates over changes in SATs, but the ice sheet model did not account for processes like ice shelf hydrofracturing (3), which is sensitive to SATs and surface melt, so the relative importance of these competing feedbacks (subsurface ocean warming versus atmospheric cooling) has yet to be fully tested. Here, we find rapid increases in subsurface temperatures in the Ross and Weddell seas during the 21st century in RCP8.5FW (fig. S8). The warming subsequently slows into the start of the 22nd century as the temperatures over the Southern Ocean briefly decrease because of sea ice growth. In the later part of the 22nd century through the end of the simulations, atmospheric warming increases much more rapidly than ocean temperatures, which may point to SAT becoming the dominant control on ice loss. Determining the relative impacts of these two competing feedbacks will require dynamic coupling of ice sheet/ice shelf models with global climate models.
Past changes in the AMOC strength are associated with rapid shifts in past climate (25). In addition, observational records show that the AMOC has slowed since the 1950s (26). In previous Southern Ocean freshwater forcing experiments (11, 14), a low-salinity anomaly was found to spread northward into the North Atlantic, suppressing deepwater formation. However, those experiments applied the freshwater forcing uniformly over a large region of the Southern Ocean rather than at the location of ice and meltwater discharge at the ocean surface around the Antarctic margin. In our experiments, the low-salinity anomaly spreads throughout the Southern Ocean, but it does not reach the North Atlantic at sufficient strength to inhibit overturning. This difference could be a result of the salinity perturbation in these earlier studies being applied across the Southern Ocean, rather than specific locations adjacent to the ice sheet as in this study (27).
|
https://sealeveldocs.readthedocs.io/en/latest/sadai20.html
|
bdedab7bad2b-3
|
The contrasting surface cooling and subsurface warming have clear implications for the future stability of the AIS. A previous ice sheet modeling study (6) using an intermediate-complexity climate model to capture ice-climate feedbacks found that the subsurface ocean warming feedback dominates over changes in SATs, but the ice sheet model did not account for processes like ice shelf hydrofracturing (3), which is sensitive to SATs and surface melt, so the relative importance of these competing feedbacks (subsurface ocean warming versus atmospheric cooling) has yet to be fully tested. Here, we find rapid increases in subsurface temperatures in the Ross and Weddell seas during the 21st century in RCP8.5FW (fig. S8). The warming subsequently slows into the start of the 22nd century as the temperatures over the Southern Ocean briefly decrease because of sea ice growth. In the later part of the 22nd century through the end of the simulations, atmospheric warming increases much more rapidly than ocean temperatures, which may point to SAT becoming the dominant control on ice loss. Determining the relative impacts of these two competing feedbacks will require dynamic coupling of ice sheet/ice shelf models with global climate models.
Past changes in the AMOC strength are associated with rapid shifts in past climate (25). In addition, observational records show that the AMOC has slowed since the 1950s (26). In previous Southern Ocean freshwater forcing experiments (11, 14), a low-salinity anomaly was found to spread northward into the North Atlantic, suppressing deepwater formation. However, those experiments applied the freshwater forcing uniformly over a large region of the Southern Ocean rather than at the location of ice and meltwater discharge at the ocean surface around the Antarctic margin. In our experiments, the low-salinity anomaly spreads throughout the Southern Ocean, but it does not reach the North Atlantic at sufficient strength to inhibit overturning. This difference could be a result of the salinity perturbation in these earlier studies being applied across the Southern Ocean, rather than specific locations adjacent to the ice sheet as in this study (27).
To assess the impact of Antarctic discharge on future AMOC strength, we calculated the maximum overturning values throughout the full depth range of the water column in the Atlantic Ocean from 20° to 50°N. In both RCP8.5 simulations, an almost complete collapse of the overturning circulation is seen, with the strength of the AMOC decreasing from 24 sverdrup in 2005 to 8 sverdrup by 2250 (Fig. 4A). In RCP8.5FW, the collapse of the overturning circulation (based on the timing when overturning strength drops below 10 sverdrup for 5 consecutive years) is delayed by 35 years, relative to RCP8.5CTRL (Fig. 4A). The largest difference in AMOC in these simulations corresponds to the timing of peak discharge around 2120. The stronger AMOC in RCP8.5FW may be a contributing factor to the higher SST and SAT temperatures in the North Atlantic at this time as compared to RCP8.5CTRL. In RCP4.5FW, the strength of the overturning declines in the beginning of the run and settles into a lower equilibrium of 19 sverdrup, but it does not fully collapse. After 2200, AMOC begins to recover in RCP4.5CTRL but remains suppressed in RCP4.5FW (Fig. 4A).
Figure 4: North Atlantic Ocean heat transport, AMOC, and global precipitation. (A) Time series of the AMOC strength in sverdrup (Sv). (B) Decadally averaged precipitation difference for 2121–2130 (RCP8.5FW minus RCP8.5CTRL). (C) Northward heat transport difference for 2121–2130 (RCP8.5FW minus RCP8.5CTRL). (D) Same as in (B), except for RCP4.5FW minus RCP4.5CTRL.
In our model simulations, the AIS discharge–forced changes in the AMOC act to increase northward heat transport in the Atlantic Ocean (Fig. 4C). In our RCP8.5FW experiment, we find that during the period of maximum AIS discharge, the largest change in northward heat transport (compared to RCP8.5CTRL) is between 20° and 40°N, with an increase of ~0.16 PW (1 PW = 1015 W). A similar pattern emerges in the RCP4.5 simulations, but to a lesser extent. Last, the delayed warming in the Southern Hemisphere and enhanced warming in the North Hemisphere associated with a stronger AMOC in our perturbation simulations result in a northward shift in the intertropical convergence zone under both RCP4.5FW and RCP8.5FW scenarios. The patterns of precipitation change in the RCP8.5FW and RCP4.5FW simulations relative to the control simulations are broadly similar in both experiments, although the magnitude of the changes is smaller in the RCP4.5FW scenario (Fig. 4, B and D).
Discussion
In summary, our climate model simulations show that future changes in meltwater and ice discharge from the AIS will have major implications for both regional and global climates. The multi-century simulations shown here (i) span the interval of peak AIS discharge in the 22nd century (under RCP8.5), (ii) account for spatially distributed (surface) and temporally varying freshwater forcing, and (iii) partition the fresh water into liquid meltwater and solid ice discharge simulated by an ice sheet model (3). The simulations highlight the potential importance of AIS discharge on the trajectory of future global climate. Our results point to a more complicated picture of WAIS stability based on standalone ice-sheet simulations that do not account for ice-ocean-atmosphere interactions. By including the freshwater forcing from AIS discharge in future greenhouse gas forcing scenarios, we find that the increased stratification of the Southern Ocean and the large-scale expansion of sea ice cause subsurface warming that could accelerate sub-ice melt rates and ice shelf thinning. At the same time, sea ice–driven surface cooling provides a strong negative feedback that could mitigate surface melt and hydrofracturing of ice shelves. Last, we find a delay in the future decline in AMOC strength that enhances northward heat transport. The results shown here clearly demonstrate the need for interactive, or fully synchronous, simulations of ice sheets with fully coupled global climate models to more accurately assess the future stability of the AIS and the broader global climate impacts of substantial ice loss from Antarctica (6).
Material and Methods
Model configuration
Three model simulations were conducted using CESM 1.2.2 with CAM5 physics (20). Model integrations were conducted using a 1° grid resolution for the ocean and sea ice components, with a displaced pole over Greenland, and a finite-volume 0.9° × 1.25° grid for the atmosphere and land components. The ocean model contains 60 vertical layers, and there are 30 vertical layers representing the atmosphere. Integrations were initialized from 20th century restart files and run under IPCC RCP4.5 and RCP8.5 greenhouse gas forcing scenarios from 2005 to 2250.
AIS discharge forcing
For the RCP4.5 and RCP8.5 perturbation simulations (RCP4.5FW and RCP8.5FW), the AIS discharge data were obtained from previous offline ice sheet model simulations, driven by the same RCP4.5 and RCP8.5 emission scenarios (3). In our CESM simulations, discharge from the AIS is spatially and temporally distributed and differentiates between liquid and solid components (fig. S1). Partitioning of liquid and solid components within CESM has the advantage of taking into account the latent heat of melting for the solid component. Accounting for latent heat has been found to be an important component in ocean response (19). Liquid components from the ice sheet model include sub-ice ocean melt, cliff face melt, and parameterized vertical flow, while solid components represent ice calving and basal refreezing (3). Using the ice sheet model component quantities allows for a larger magnitude of input as opposed to using ice sheet volume change as done in previous studies (18). The freshwater flux from the polar stereographic ice sheet model grid is spatially interpolated and applied as a perturbation at the nearest surface level coastal grid cells following each longitude band in the CESM gx1v6 grid. This provides input at 320 grid cell locations around the continental margin. For the RCP8.5 control run (RCP8.5CTRL), freshwater runoff is calculated by the standard CESM with no additional forcing from the ice sheet model. Because of computational limitations, no control run was done for RCP4.5, and instead, the data from the CCSM4 b.e11.BRCP45C5CN.f09_g16.001 run were obtained from Earth System Grid and used as a control (referred to as RCP4.5CTRL).
|
https://sealeveldocs.readthedocs.io/en/latest/sadai20.html
|
bdedab7bad2b-4
|
AIS discharge forcing
For the RCP4.5 and RCP8.5 perturbation simulations (RCP4.5FW and RCP8.5FW), the AIS discharge data were obtained from previous offline ice sheet model simulations, driven by the same RCP4.5 and RCP8.5 emission scenarios (3). In our CESM simulations, discharge from the AIS is spatially and temporally distributed and differentiates between liquid and solid components (fig. S1). Partitioning of liquid and solid components within CESM has the advantage of taking into account the latent heat of melting for the solid component. Accounting for latent heat has been found to be an important component in ocean response (19). Liquid components from the ice sheet model include sub-ice ocean melt, cliff face melt, and parameterized vertical flow, while solid components represent ice calving and basal refreezing (3). Using the ice sheet model component quantities allows for a larger magnitude of input as opposed to using ice sheet volume change as done in previous studies (18). The freshwater flux from the polar stereographic ice sheet model grid is spatially interpolated and applied as a perturbation at the nearest surface level coastal grid cells following each longitude band in the CESM gx1v6 grid. This provides input at 320 grid cell locations around the continental margin. For the RCP8.5 control run (RCP8.5CTRL), freshwater runoff is calculated by the standard CESM with no additional forcing from the ice sheet model. Because of computational limitations, no control run was done for RCP4.5, and instead, the data from the CCSM4 b.e11.BRCP45C5CN.f09_g16.001 run were obtained from Earth System Grid and used as a control (referred to as RCP4.5CTRL).
Recent observations show a northward expansion of sea ice in some sectors of the Southern Ocean and a cooling of the ocean surface (28). However, models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) predict a sea ice decline over the modern period continuing into the future (8). Since freshwater forcing from the ice sheets is lacking in the current suite of climate models, inaccurate freshwater runoff has been suggested as the cause of discrepancies between models and observations (8). Previous climate simulations using CESM1 (CAM5) for 1980–2013 (17) found that after an initial adjustment period, sea ice area showed no increase in response to freshwater forcing, suggesting that other methods could be at play in driving recently observed sea ice trends. Modeling studies of future climate response to freshwater forcing in the Southern Ocean show expansion of sea ice extent in response to freshwater perturbations (18, 29). There may be a threshold beyond which AIS discharge becomes a dominant control on sea ice formation. The forcing applied in (17) was much less than applied in our long-term future simulations. That study (17) found that sea ice response was insensitive to the perturbation depth where the fresh water was added to the ocean. Our study uses a forcing scheme similar to that recently used in (18), with fresh water applied at the surface only. Other groups have shown distinct regional differences in sea ice sensitivity, suggesting that regional differences in freshwater perturbations will be important for assessing future ice response (22).
Future changes in Greenland Ice Sheet discharge
In all our experiments, freshwater input from the Greenland Ice Sheet uses the default CESM freshwater forcing scheme. While a consideration of Greenland Ice Sheet freshwater forcing is outside of the scope of this paper, inclusion of both ice sheets via dynamic coupling with global climate models will be an important step for future research and for accurately projecting future climate states. In particular, increased meltwater discharge from Greenland has been shown to slow the AMOC (6), which could offset (to some degree) the stronger overturning circulation projected in our simulations as a response to increased AIS discharge. We hypothesize that a weakened AMOC might reduce the increased northward transport of heat simulated by our model simulations and cool the North Atlantic sector.
|
https://sealeveldocs.readthedocs.io/en/latest/sadai20.html
|
494096f52fd1-0
|
Please activate JavaScript to enable the search functionality.
|
https://sealeveldocs.readthedocs.io/en/latest/search.html
|
f4751a4b49b7-0
|
Yin et al. (2020)
Title:
Response of Storm-Related Extreme Sea Level along the U.S. Atlantic Coast to Combined Weather and Climate Forcing
Keywords:
Meridional overturning circulation, Extreme events, Sea level, Storm surges, Climate change, Climate models
Corresponding author:
Jianjun Yin
Citation:
Yin, J., Griffies, S. M., Winton, M., Zhao, M., & Zanna, L. (2020). Response of Storm-Related Extreme Sea Level along the U.S. Atlantic Coast to Combined Weather and Climate Forcing. Journal of Climate, 33(9), 3745–3769. doi: 10.1175/jcli-d-19-0551.1
URL:
https://journals.ametsoc.org/view/journals/clim/33/9/jcli-d-19-0551.1.xml
Abstract
Storm surge and coastal flooding caused by tropical cyclones (hurricanes) and extratropical cyclones (nor’easters) pose a threat to communities along the Atlantic coast of the United States. Climate change and sea level rise are altering the statistics of these extreme events in a rather complex fashion. Here we use a fully coupled global weather/climate modeling system (GFDL CM4) to study characteristics of extreme daily sea level (ESL) along the U.S. Atlantic coast and their response to global warming. We find that under natural weather processes, the Gulf of Mexico coast is most vulnerable to storm surge and related ESL. New Orleans is a striking hotspot with the highest surge efficiency in response to storm winds. Under a 1% per year atmospheric CO2 increase on centennial time scales, the anthropogenic signal in ESL is robust along the U.S. East Coast. It can emerge from the background variability as soon as in 20 years, or even before global sea level rise is taken into account. The regional dynamic sea level rise induced by the weakening of the Atlantic meridional overturning circulation facilitates this early emergence, especially during wintertime coastal flooding associated with nor’easters. Along the Gulf Coast, ESL is sensitive to the modification of hurricane characteristics under the CO2 forcing.
Introduction
The U.S. Atlantic coast (including both the East Coast and the Gulf of Mexico coast) is an active region for tropical and extratropical storms. Geographically, this densely populated coastal region is surrounded by a broad (100–300 km) and shallow (<100 m) continental shelf (Fig. 1a), making it particularly vulnerable to severe storm surge and associated socioeconomic damages and life loss. Notable examples include Hurricane Katrina in 2005 (Fritz et al. 2007) and Superstorm Sandy in 2012 (Sobel 2014), as well as more recent wintertime coastal flooding caused by “bombogenesis” (Buell 2018).
Figure 1: Geometry and bathymetry along the U.S. Atlantic coast. (a) The U.S. Atlantic coastline in nature is highlighted by the red color. Large coastal cities are marked from north to south and west: Halifax, Boston, New York, Baltimore, Charleston, Miami, Tampa, New Orleans, and Houston/Galveston. (b) Representation of coastal geometry and bathymetry (km) in CM4. Coastal ocean grid boxes in red, green, and purple indicate the NE (north of Cape Hatteras), SE (Cape Hatteras to the south tip of Florida), and GOM regions. The color scale uses 100-m intervals for 0–500-m depth and 500-m intervals below 500 m.
The twenty-first-century outlook of storm surge often invokes the “noise + trend” model, namely, global sea level rise (SLR) will lead to elevated storm surge (USGCRP 2017). However, the real world situation is more complex. Storm surge critically depends on such storm characteristics as intensity, frequency, size, path, translational speed, and landfall angle (Simpson 1974; Weisberg and Zheng 2006; Irish et al. 2008; Rego and Li 2009; Hall and Sobel 2013). In addition to chaotic/stochastic “noise” processes, the generation, development, and propagation of tropical cyclones (TCs) and extratropical cyclones (ECs) over the North Atlantic and North America are influenced by El Niño–Southern Oscillation (ENSO) (Hirsch et al. 2001; Donnelly and Woodruff 2007), the North Atlantic Oscillation (Elsner et al. 2000; Ezer and Atkinson 2014), the Atlantic multidecadal variability (Zhang and Delworth 2006), anthropogenic greenhouse gas and aerosol forcing (Mann and Emanuel 2006; Lin et al. 2012; Little et al. 2015; Garner et al. 2017; Rahmstorf 2017; Marsooli et al. 2019), and other factors. These factors mutually interact and modify sea surface temperature (SST), ocean heat distribution, vertical wind shear, meridional temperature gradient, large-scale oceanic and atmospheric circulation, and regional and global sea level. Given their distinct spatiotemporal scales and possible opposing effects on storms and storm surge, it remains scientifically challenging to study sea level extremes and their impact along the U.S. Atlantic coast in the face of natural and anthropogenic climate variability and change.
Here we address this challenge using a fully coupled global climate model (CM4) recently developed at the Geophysical Fluid Dynamics Laboratory (GFDL) of NOAA. Under the protocol of phase 6 of the Coupled Model Intercomparison Project (CMIP6) (Eyring et al. 2016), a series of climate change experiments have been performed with CM4. With these simulations, we focus on weather–climate interactions and their combined effect on storm-related extreme daily sea level (ESL) along the U.S. Atlantic coast. The paper is organized as follows. Section 2 describes the model and daily sea level analysis methods. Section 3 evaluates the model performance in sea level simulations. Section 4 presents characteristics and statistics of ESL under natural weather processes. Their response to CO2 forcing is described in section 5, followed by the conclusions and discussion of model limitations toward the end.
Model, data, and methods
The GFDL CM4 climate model
CM4 is the latest generation of the climate models developed and used at GFDL (Held et al. 2019). The atmospheric model (AM4.0) (Zhao et al. 2018a,b) adopts finite-volume cubed-sphere dynamical core with 96 (~1.0° grid spacing) or 192 (~0.5° grid spacing) grid boxes per cube face. It has 33 vertical levels and the model top is located at 1 hPa. The model incorporates updated physics such as a double-plume scheme for shallow and deep convection and single-moment cloud microphysics. Due to improvements in model resolution, physics, and dynamics, CM4 can better simulate strong TCs and ECs over the North Atlantic and North America with hurricane-force winds, reasonable storm tracks, seasonal cycle, and interannual variability (Zhao et al. 2018a), although the strongest (e.g., category 4 and 5) hurricanes are not simulated (Fig. 2).
Figure 2: Simulations of TC and EC in the long-term piControl of CM4. (a) Global map of TC tracks. (b) TCs over the North Atlantic. Black contours (hPa) indicate the mean subtropical high during June–October. (c) Global map of EC tracks. (d) ECs over the North Atlantic and North America. Black contours (°C) indicate the near-surface temperature and its gradient during December–February. The color scale denotes daily winds (m s−1) associated with storms.
We use a Lagrangian approach and the 6-h data for detecting and tracking TCs and ECs in the CM4 simulations (Fig. 2) (Zhao et al. 2009). Among multiple criteria, TCs should have a maximum surface wind speed of at least 14 m s−1 and their trajectories must last at least 3 days. In addition, TCs should have a warm core of at least 1°C above the surrounding temperatures between 300 and 500 hPa, thus allowing TCs to be distinguished from ECs and other storms. The relative vorticity at 850 hPa in TCs should be greater than 1.6 × 10^{−4} s^{−1}. We use the sea level pressure field to identify ECs that should have a maximum wind speed of 25 m s−1 and last for at least 3 days. Detailed algorithms and codes for detecting and tracking storms can be found at https://www.gfdl.noaa.gov/tstorms/.
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-1
|
Figure 2: Simulations of TC and EC in the long-term piControl of CM4. (a) Global map of TC tracks. (b) TCs over the North Atlantic. Black contours (hPa) indicate the mean subtropical high during June–October. (c) Global map of EC tracks. (d) ECs over the North Atlantic and North America. Black contours (°C) indicate the near-surface temperature and its gradient during December–February. The color scale denotes daily winds (m s−1) associated with storms.
We use a Lagrangian approach and the 6-h data for detecting and tracking TCs and ECs in the CM4 simulations (Fig. 2) (Zhao et al. 2009). Among multiple criteria, TCs should have a maximum surface wind speed of at least 14 m s−1 and their trajectories must last at least 3 days. In addition, TCs should have a warm core of at least 1°C above the surrounding temperatures between 300 and 500 hPa, thus allowing TCs to be distinguished from ECs and other storms. The relative vorticity at 850 hPa in TCs should be greater than 1.6 × 10^{−4} s^{−1}. We use the sea level pressure field to identify ECs that should have a maximum wind speed of 25 m s−1 and last for at least 3 days. Detailed algorithms and codes for detecting and tracking storms can be found at https://www.gfdl.noaa.gov/tstorms/.
The oceanic model of CM4 is based on the Modular Ocean Model version 6 (MOM6). It uses the arbitrary Lagrangian–Eulerian algorithm in the vertical to allow for the combination of different vertical coordinates including geopotential, isopycnal, and terrain following. The model adopts the C-grid stencil in the horizontal and is configured on a tripolar grid. It has a 0.25° eddy-permitting horizontal grid spacing (~20 km at midlatitudes) and 75 hybrid vertical layers down to the 6500-m maximum bottom depth. On the shelf, the vertical grid spacing can be as fine as 2 m. The ocean model configuration used here as part of CM4 is documented by Adcroft et al. (2019).
MOM6 roughly resolves important bays and estuaries embedded along the U.S. Atlantic coastline and their connections to the open ocean, such as Massachusetts Bay, Long Island Sound, Delaware Bay, and Chesapeake Bay (Fig. 1b). However, the model resolution is not fine enough to resolve smaller bays and harbors such as Tampa Bay, Galveston Bay, and New York Harbor, as well as the chains of barrier islands east of North Carolina and south of Florida to Texas. MOM6 realistically represents the broad and gently sloping continental shelf and the sharp ocean deepening across the shelf break. Previous research showed that accurate representation of coastal geometry and bathymetry is important in capturing the fine structures of storm surge (Resio and Westerink 2008; Rego and Li 2010; Mori et al. 2014).
In terms of SLR and storm surge, CM4 simulates ocean steric and dynamic effects. Like many other CMIP6 models, CM4 does not incorporate an ice sheet component, and therefore cannot simulate land ice melt and its increasing contribution to global SLR in a warming climate (Chen et al. 2017). In addition, CM4 does not simulate tides which can interact with storm surge constructively and nonlinearly and lead to the so-called tide surge (Rego and Li 2010; Muis et al. 2019). Incorporating these processes would further heighten ESL during severe storms. Other model limitations will be discussed in the discussion and conclusions section (section 6).
CMIP6 experiments with CM4 and CM4HR
As summarized in Table 1, the standard version of CM4 (1.0° atmosphere and 0.25° ocean) has been used to carry out the CMIP6 experiments including the Diagnostic, Evaluation and Characterization of Klima (DECK) and the Scenario Model Intercomparison Project (ScenarioMIP) (Eyring et al. 2016; O’Neill et al. 2016). A 250-yr model spinup was carried out prior to the DECK runs. Meanwhile, a higher-resolution version of CM4 (CM4HR) has also been configured (0.5° atmosphere and 0.25° ocean). CM4HR has been used for the High Resolution Model Intercomparison Project (HighResMIP) of CMIP6 (Haarsma et al. 2016). Daily and even hourly data critical for conducting storm and storm surge analysis have been saved. In this study, we focus on the simulations with the standard CM4 and present available results from CM4HR, thus showing the impact of atmospheric model resolution.
Table 1: CMIP6 Experiments with GFDL CM4 and CM4HR used in this study.
Daily sea level analysis
In the preindustrial control simulation (piControl) of CM4, we calculate daily mean sea level anomalies (SLA; Δhc) for a particular day and location according to
Δhc = Δηc + Δbc, (1)
where Δbc = −Δpc/ρ0g, (2)
Δηc(x,y,t)=ηc(x,y,t)−˜ηc(x,y,t1), and (3)
Δpc(x,y,t)=pc(x,y,t)−˜pc(x,y,t1),t1=1,2,…,365. (4)
The subscript c denotes piControl. The terms ηc, ˜ηc, and Δηc are daily dynamic sea level (relative to a time invariant geoid), its climatology and anomaly, respectively. By definition, all of these terms have a zero global mean. Along the coast, daily fluctuations of ηc mainly reflect ocean rise and fall associated with transient weather processes and corresponding coastal waves. On interannual and longer time scales, ηc is also influenced by large-scale ocean circulation, climate modes, and external forcing. CM4 incorporates the effects on ηc of ocean temperature, salinity, and mass redistribution, as well as rainfall, evaporation, and river runoff (Griffies et al. 2014).
Because CM4 does not explicitly simulate the inverse barometer effect on sea level, we diagnose its contribution (Δbc) using sea level pressure anomalies and an equilibrium relationship [Eqs. (2) and (4)] (Ponte 2006). The terms pc,˜pc, and Δpc are daily sea level pressure and its climatology and anomaly, respectively. In this study, ˜ηc and ˜bc are removed when calculating SLA values [Eqs. (1), (3), and (4)]. But it should be noted that the absolute surge is generally higher during warm seasons than cold seasons due to the seasonal cycles (see below).
Under anthropogenic CO2 forcing, the ocean absorbs most of the excess heat due to radiative imbalance at the top of the atmosphere, and thus causing global mean thermosteric SLR (ΔGe). The term ΔGe in CM4 can be diagnosed as ΔGe(t)=−1/A∫_A ∫_{-H}^{ηe} 1/ρ0 Δρ dz dA, (5)
where Δρ is the anomaly of in situ density of seawater, ρ0 is the reference seawater density, A is the global ocean surface area, H is the ocean depth, and ηe is the dynamic sea level in the CO2 experiments. The subscript e denotes CO2 experiments. In these experiments, SLA (Δhe) without global thermosteric SLR is calculated as Δhe = Δηe + Δbe, (6)
where Δηe and Δbe are computed relative to ˜ηc and ˜bc in piControl:
Δηe(x,y,t) = ηe(x,y,t)−˜ηc(x,y,t1), (7)
Δpe(x,y,t) = pe(x,y,t)−˜pc(x,y,t1) + ϵ, t1 = 1,2,…,365. (8)
In addition to daily weather processes, regional trends of ηe and pe and the change of their seasonal cycles under the CO2 forcing also contribute to Δηe and Δbe. Note that ε is a small correction term due to the redistribution of air mass loading between the land and ocean in the CO2 experiments. SLA with global thermosteric SLR is calculated as Δhe(x, y, t) + ΔGe(t).
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-2
|
Under anthropogenic CO2 forcing, the ocean absorbs most of the excess heat due to radiative imbalance at the top of the atmosphere, and thus causing global mean thermosteric SLR (ΔGe). The term ΔGe in CM4 can be diagnosed as ΔGe(t)=−1/A∫_A ∫_{-H}^{ηe} 1/ρ0 Δρ dz dA, (5)
where Δρ is the anomaly of in situ density of seawater, ρ0 is the reference seawater density, A is the global ocean surface area, H is the ocean depth, and ηe is the dynamic sea level in the CO2 experiments. The subscript e denotes CO2 experiments. In these experiments, SLA (Δhe) without global thermosteric SLR is calculated as Δhe = Δηe + Δbe, (6)
where Δηe and Δbe are computed relative to ˜ηc and ˜bc in piControl:
Δηe(x,y,t) = ηe(x,y,t)−˜ηc(x,y,t1), (7)
Δpe(x,y,t) = pe(x,y,t)−˜pc(x,y,t1) + ϵ, t1 = 1,2,…,365. (8)
In addition to daily weather processes, regional trends of ηe and pe and the change of their seasonal cycles under the CO2 forcing also contribute to Δηe and Δbe. Note that ε is a small correction term due to the redistribution of air mass loading between the land and ocean in the CO2 experiments. SLA with global thermosteric SLR is calculated as Δhe(x, y, t) + ΔGe(t).
In summary of the analysis methods, we distinguish SLA in piControl (Δhc) and CO2 experiments (Δhe + ΔGe) to emphasize that the latter also includes global thermosteric SLR and regional dynamic SLR in addition to storm surge and other factors. Storm surge refers to the change in sea surface height relative to the predicted tide during a storm (Gregory et al. 2019). Strictly, it should not include any factors that would affect sea level in the absence of a storm. Thus, we choose to use the term “ESL” in the following to discuss high-end (extreme) daily sea levels, which incorporate all the above effects represented in CM4.
Observational and reanalysis data
In terms of data–model comparison for evaluation purposes, we use the daily tide gauge data provided by the University of Hawaii Sea Level Center (Caldwell et al. 2015) (https://uhslc.soest.hawaii.edu/). We choose long-term high-quality stations mostly along the U.S. Atlantic coast (Table 2). The data are detrended and deseasonalized. It should be noted that this comparison is not ideal since tide gauges, often located inside bays or harbors, are point measurements, while the model results represent averaged values over the coastal ocean grid cells. For the altimetry data of dynamic sea level, we use the multisatellite merged gridded dataset from the Copernicus Marine Environment Service (http://marine.copernicus.eu/). The daily anomaly data with a 0.25° spatial resolution span 1993–2017 (Pujol et al. 2016). The long-term mean dynamic sea level is based on the period of 1993–2012. For sea level pressure, we use the NCEP/NCAR reanalysis for the 1948–2018 period (Kalnay et al. 1996). The daily data have a 2.5° spatial resolution (https://www.esrl.noaa.gov).
Table 2: Daily tide gauge data used in the present study. (Note that the linear trends are not directly comparable due to different data length at different stations.)
Evaluating sea level simulations in piControl of CM4
CM4 captures the pronounced features of the long-term mean dynamic sea level observed by satellites (Figs. 3a,b). These features include the peak-to-peak range, the asymmetry associated with the gyre circulation, the sharp gradients across the Gulf Stream, Kuroshio, and the Antarctic Circumpolar Current, and the contrast between subpolar and subtropical regions and between the Pacific and Atlantic basins.
Figure 3: Dynamic sea level η in the altimetry data and piControl simulations of CM4. (a),(b) Long-term mean (m). (c),(d) Seasonal cycle as quantified by the difference between September and March (m). (e),(f) Daily variability as quantified by the standard deviation of the detrended and deseasonalized daily dynamic sea level (m). (left) Altimetry data and (right) CM4 simulations.
CM4 simulates a seasonal cycle of the dynamic sea level ˜ηc similar to the observations (Figs. 3c,d). In the Northern Hemisphere, the dynamic sea level is higher by up to 0.2 m during early autumn than during early spring, especially along the Gulf Stream and Kuroshio and nearby regions. This is mainly due to seasonal heating and cooling of the ocean, as well as seasonal changes of prevailing winds and ocean circulation. In CM4, ˜ηc along the U.S. Atlantic coast resembles that in the ocean interior, and shows increasing amplitudes from the north toward the south (Fig. 4a). In nature, annual and semiannual long tides also contribute to higher coastal sea levels during late summer and early autumn (Sweet et al. 2018). In the tropical Pacific, the belt-like feature reflects the north–south shift of the ITCZ and associated trade winds. Compared with ocean interior, ˜ηc reduces in some shelf regions such as in the Okhotsk Sea, South of Alaska, along the west coast, and on the northeast shelf of North America. The shallow ocean column on shelf limits the magnitude of seasonal thermal expansion and contraction.
Figure 4: Daily climatology and seasonal cycle of dynamic sea level ˜η and the inverse barometer effect ˜b at large coastal cities in the 150-yr piControl of CM4. (a) Dynamic sea level climatology. (b) Inverse barometer effect climatology. The long-term mean at each city is removed for better comparison. Notice the different y-axis scales in (a) and (b).
The jet-like Gulf Stream and deep western boundary current are better simulated in CM4 compared with previous model generations (Adcroft et al. 2019; Held et al. 2019). CM4 somewhat underestimates mesoscale eddy activities along the Gulf Stream, Loop Current, and Kuroshio, as well as the associated daily variability of dynamic sea level (Figs. 3e,f). This is partly due to the eddy-permitting (rather than eddy “resolving”) resolution of the ocean model. While most of the mesoscale eddies do not directly impact coastal sea levels, the warm-core rings could cause sudden TC intensification due to their anomalously high heat content (Goni et al. 2009). A notable example is Hurricane Katrina, which rapidly intensified to a category 5 hurricane after passing over a warm-core ring prior to its landfall near New Orleans (Jaimes and Shay 2009). Recent studies also suggest that in addition to direct impacts through winds and pressure, coastal storms could disrupt the Gulf Stream flow, thereby indirectly influencing sea level along the U.S. East Coast (Ezer et al. 2017; Ezer 2018, 2019).
As for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of ˜bc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).
Figure 5: Sea level pressure (hPa) and its variability in the NCEP–NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November–March). (c),(d) Mean sea level pressure and its daily variability during summer (June–October). (left) NCEP–NCAR reanalysis and (right) CM4 simulations.
Characterizing storm-related ESL in piControl
Statistics of SLA along the U.S. Atlantic coast
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-3
|
As for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of ˜bc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).
Figure 5: Sea level pressure (hPa) and its variability in the NCEP–NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November–March). (c),(d) Mean sea level pressure and its daily variability during summer (June–October). (left) NCEP–NCAR reanalysis and (right) CM4 simulations.
Characterizing storm-related ESL in piControl
Statistics of SLA along the U.S. Atlantic coast
According to the correlation of SLA Δhc, we divide the U.S. Atlantic coast into three regions: northeast (NE), southeast (SE), and the Gulf of Mexico (GOM) (Fig. 1b). In piControl of CM4, the standard deviation σ of SLA shows a clear separation of coastal and interior ocean dynamics, roughly along the 100-m isobaths with lower σ values (Fig. 6a). Vigorous mesoscale eddies dominate in ocean interior, while wind surge and coastal waves dominate variability near the coast (Hughes et al. 2019). The bowl-shaped coastline can enhance coastal SLA variability, such as from Cape Cod to Cape Hatteras, east of Georgia, along the Florida Panhandle, and south of Louisiana and Texas. The coastal SLA variability in CM4 is consistent with the estimate from the tide gauge data, with slightly underestimated magnitudes at some sites (Fig. 6a).
Figure 6: Characteristics and statistics of SLA (Δhc) variability along the U.S. Atlantic coast in the 150-yr piControl of CM4. (a) The standard deviation (m), (b) skewness, and (c) kurtosis. Colored circles indicate the tide gauge observations (Table 2). The black line shows the 100-m isobath.
Skewness and kurtosis describe the shape of the probability distribution of SLA at different locations (see appendix A). Figure 6b shows a positive skewness of SLA along the U.S. Atlantic coast. A positive skewness indicates a longer tail at the positive end than the negative end, which occurs when ocean surge dominates in magnitude over ocean fall due to the passing of storms. TCs and ECs tend to propagate northeastward just offshore of the NE and SE coast (Fig. 2). This preferred storm track is related to the dynamics of the subtropical (Bermuda–Azores) high during summer (Elsner et al. 2000) and the midlatitude baroclinicity during winter (Lunkeit et al. 1998; Brayshaw et al. 2011). The northeasterly wind on the west and northwest side of these cyclones can cause large positive SLA values through shoreward Ekman transport. For the GOM, the northward movement (i.e., translational speed) of landfalling TCs perpendicular to the coastline causes stronger landward winds and ocean surge on the east side than the seaward winds and ocean fall on the west side. Land friction also slows down seaward winds and therefore reduces the magnitude of negative storm surge.
Kurtosis measures the “tailedness” of the SLA distribution and is a useful indicator of large storm surge and coastal vulnerability to ESL. Its value is sensitive to rare and extreme events that can lead to catastrophe. In piControl of CM4, the geographical map of kurtosis shows a striking hotspot around New Orleans with values greater than 10 (Fig. 6c). Enhanced values are also found along the west coast of Florida and the south coast of Texas. The kurtosis pattern along the coast is consistent with extreme surge height.
In addition to the moments of SLA, we also evaluate return levels of ESL by fitting the generalized Pareto distribution to the ESL values with the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) (see appendix B for details). Along the NE coast, the 1-, 10- and 100-yr return levels are generally underestimated in CM4 compared with the tide gauge data, particularly at New York (Fig. 7). The tide gauge at the Battery is inside of New York Harbor. Local large storm surge at lower Manhattan is influenced and amplified by the dynamics of the harbor and Hudson River, which are not resolved in CM4 (Blumberg et al. 2015). The ESL return levels along the SE and GOM coast are better simulated in CM4, despite the lack of the most catastrophic event like the >2-m daily surge at Galveston induced by Hurricane Carla in September 1961 (Fig. 7).
Figure 7: Comparison of SLA variability and ESL events between (left) the tide gauge data and the control simulations of (middle) CM4 and (right) CM4HR. The daily data have been detrended and deseasonalized. Six cities in the NE, SE, and GOM regions with high-quality tide gauge data are chosen: Halifax, Boston, New York (at the Battery), Charleston, Miami (at Virginia Key), and Galveston. The gray dashed lines upward show the 1-, 10- and 100-yr return levels, respectively. The shape k, scale σ, and location θ parameters (with the standard error) of the GPD fit are shown at the upper-right corner; see appendix B for details. The ESLs induced by Hurricanes Sandy and Carla are marked at New York and Galveston, respectively. Notice that the tide gauge data are point measurements at coast, while the model data are the area averaged values over the coastal ocean grid cells.
Along the GOM coast, large spikes in the simulated SLA time series are caused by landfalling TCs/hurricanes during summer and early autumn with August as the peak month (Fig. 8a), also evidenced by the long positive tail of the SLA histogram. The GOM coast is relatively quiet during winter and spring. On the NE coast, the SLA time series show a periodic wave-packet-like pattern: its variability is largely suppressed in summer but amplified in winter (Fig. 8c). Thus, most ESL events in this region occur during cold seasons associated with ECs/nor’easters (Colle et al. 2010, 2015). Nonetheless, some of the North Atlantic TCs/hurricanes can occasionally strike this northerly region during late summer and early autumn. In fact, the record high daily surge of 1.2 m at New York in the tide gauge data was induced by Sandy in October 2012 (Fig. 7), which was a large tropical–extratropical system at landfall with an unusual path perpendicular to the New Jersey shoreline (Hall and Sobel 2013). It exceeds the simulated extreme surge height at New York by CM4 and contributes to the higher 100-yr return level of ESL in the tide gauge data (Fig. 7).
Figure 8: Time series of SLA (Δhc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge Δηc and pressure surge Δbc to large positive surge events (Δhc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.
Wind–surge relationship
The piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%–90% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-4
|
Figure 8: Time series of SLA (Δhc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge Δηc and pressure surge Δbc to large positive surge events (Δhc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.
Wind–surge relationship
The piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%–90% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.
Figure 9: Large daily surge event induced by a strong and large TC in piControl of CM4. During this event, a surge of up to 1.8 m (Δhc) occurs along the GOM coast on 24 Aug, year 138. (a) Daily dynamic sea level anomalies Δηc (m) associated with this event. (b) SLA due to the inverse barometer effect Δbc (m). (c) Daily surface wind vector and speed (m s−1). (d) Daily precipitation (cm day−1). (e) Surface current vector and speed (m s−1). (f) SST anomalies (°C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s−1) during its propagation.
Wind stress at the ocean surface can be calculated based on the following empirical bulk aerodynamic formula:
τ = Cd ρair U10 U10, (9)
where τ is the wind stress vector, Cd a drag coefficient, ρair surface air density, and U10 and U10 the wind speed and vector at 10 m above the sea, respectively, computed relative to the ocean surface currents. According to Eq. (9), the wind stress magnitude is a quadratic function of 10-m wind speed. The value of Cd can increase with the increase of wind speed (Large and Pond 1981; Weisberg and Zheng 2008). At the high end of the wind spectrum associated with hurricanes and strong ECs, however, Cd reduces with the increase of wind speed (Powell et al. 2003; Oey et al. 2007).
At the coast, storm surge creates a sea surface slope and an adverse pressure gradient in the offshore (x) direction. This pressure gradient tends to balance wind stress at the ocean surface:
∂η/∂x ≈ τ/(ρ0 g H). (10)
Here η is dynamic sea level, ρ0 the reference seawater density, g the gravitational acceleration, and H the ocean depth. At the coastal regions where H reduces, the sea surface slope becomes steeper and storm surge becomes higher (Pugh 1987).
The warm, semi-enclosed, and oval-shaped GOM has a basin size, geometry, and bathymetry favorable for wind setup from rotating synoptic systems (Fig. 1). When a counterclockwise rotating hurricane enters the gulf from the Caribbean Sea, water piles up at the coast due to the longshore winds and resultant shoreward Ekman transport (Hope et al. 2013). At landfall, the strongest wind is typically at its eastern and northeastern sector (Fig. 10a). So a storm track slightly west of New Orleans could realize the worst-case scenario of storm surge for the city. The intense southeasterly storm wind blows almost perpendicular into the funneling land geometry east of the Mississippi river delta, and is therefore highly efficient at raising coastal water levels (As-Salek 1998). In piControl of CM4, the wind surge height at New Orleans scales up well (r = 0.75) with the local/nearby wind speed following a quadratic relationship (Figs. 10c,d). This wind–surge relationship, as classified by the Saffir–Simpson scale (Simpson 1974; Needham and Keim 2014), highlights the nonlinear increase in coastal vulnerability as a storm intensifies.
Figure 10: Simulated wind–surge relationship in piControl of CM4. (a) Typical wind pattern for large surges at New Orleans. (b) Typical wind pattern for large surges at New York. Shading shows the correlation of large daily surge at New Orleans and New York with daily wind speed. Contours and vectors are linear regressions of sea level pressure (hPa m−1) and uυ winds (m s−1 m−1) on the large surge values. (c) Scatterplot of large daily wind surge at New Orleans and New York as a function of local wind speed. The nonlinear fit is based on a quadratic wind–surge relationship. (d) The quadratic wind–surge relationship at nine cities along the Atlantic coast. Values in the legend indicate the fit correlation.
During the landfall of a GOM hurricane, the maximum sustained wind, intense storm precipitation, and coastal surge center almost coincide (Figs. 9a,c,d). The downpour, while capable of causing inland flooding, can further increase the coastal surge height by dumping a large amount of water at the ocean surface in a short time (Wong and Toumi 2016). Over the shallow continental shelf waters, it can take a few days for the water bulge to spread and disperse through surface gravity and coastal waves. This enhancement of surge height by heavy rainfall does not work as efficiently along the NE and SE coast in part due to the narrower continental shelf. CM4 simulates the TC intensification in the GOM after passing over warm core rings north of the Loop Current (Figs. 9c,e). Due to the storm-induced ocean vertical mixing and divergent Ekman transport away from the TC center, a cool wake is evident behind the TC propagation in the CM4 simulations (Fig. 9f).
For New York, a large wind surge typically occurs when the low pressure system is located to the south and the alongshore winds induce shoreward Ekman transport (Figs. 10b,c,d). The surge at Baltimore and Miami shows weak or even no correlation with local/nearby winds. Baltimore is located in the Chesapeake Bay, where the surge is limited by the bay geometry. In nature, large storm surges in the Chesapeake Bay do exist provided that coastal storms push large amounts of waters into the bay (Ezer 2018, 2019). The narrow passage connecting the bay and open ocean is represented by one grid cell in CM4 (Fig. 1b), which may not be sufficient for simulating large inflow events. Although Miami is next to the open ocean and at the forefront of hurricane paths, the continental shelf offshore is exceptionally narrow (Fig. 1). In addition, Miami is at the southern tip of the Florida peninsula with a convex-shaped coastline. These features make storm surge less efficient at concentrating its energy. The observed tide gauge data confirm that the daily surge around Miami has not exceeded 0.4 m since the 1990s (Fig. 7). Strong winds, heavy rainfall, and big ocean waves during hurricanes are of more serious concern at Miami.
Characterizing response of ESL to CO2 forcing
Our assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather–climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) scenarios (O’Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather–climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.
Simulated changes in weather, climate, and sea level in 1pctCO2
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-5
|
Characterizing response of ESL to CO2 forcing
Our assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather–climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) scenarios (O’Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather–climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.
Simulated changes in weather, climate, and sea level in 1pctCO2
In 1pctCO2 of CM4, both global mean surface temperature and global thermosteric SLR display upward trends during the 150-yr model simulation (Fig. 11a). Global thermosteric SLR (ΔGe) initially lags the surface temperature response, due to the gradual downward heat penetration and enormous thermal inertia of the ocean, and shows a faster acceleration after year 50. Note that ΔGe is 0.09 m at year 70 (time of CO2 doubling) and 0.34 m at year 140 (time of CO2 quadrupling); ΔGe in 1pctCO2 is corrected by removing a slow drift of the deep ocean in piControl. As a consequence of excess heat uptake mainly by the upper layers, the ocean becomes more stratified in 1pctCO2.
Figure 11: Simulated climate change and SLR in 1pctCO2 of CM4. (a) Time series of global mean surface air temperature anomalies, SST anomalies, and global thermosteric SLR. (b) Time series of dynamic SLR at large cities along the East and Gulf Coast.
In the North Atlantic and along the U.S. East Coast, ocean dynamics plays an important role in regionally modifying SLR (Levermann et al. 2005; Yin et al. 2009; Ezer 2015). In response to 1pctCO2, the Atlantic meridional overturning circulation (AMOC) weakens, which results in a 0.1-m dynamic SLR along NE at year 70 and 0.2-m dynamic SLR at year 140 in 1pctCO2 (Figs. 11b and 12a). CM4 simulates a vigorous AMOC in piControl with interannual to multidecadal variability (Figs. 13a,b). The regional enhancement of SLR along NE (on the top of global mean SLR) due to AMOC weakening is a robust feature in the previous CMIP3 (Yin et al. 2009) and CMIP5 (Yin 2012) simulations and projections, although the exact magnitude can vary across models. Compared with the previous results (Yin et al. 2009; Yin 2012; Yin and Goddard 2013), the dynamic SLR signal in CM4 extends farther southward to north of Miami (Fig. 12a). This extension may in part be due to the refined oceanic model resolution and associated representation of the continental shelf geometry and western boundary current in CM4 compared with previous model generations. Detailed mechanisms are worthy of further investigation in the future. The reduced current shear, cross-current dynamic sea level gradient, and baroclinicity tend to reduce the ocean mesoscale eddy activities (Fig. 12b).
Figure 12: Simulated ocean changes during years 131–150 in 1pctCO2 of CM4 relative to piControl. (a) Dynamic sea level anomalies (m) with a zero global mean. Contours are the long-term mean dynamic sea level (m) in piControl. (b) Response of the ocean mesoscale eddies. Shading shows the anomalies of the standard deviation of daily dynamic sea level (m). Contours are the standard deviation in piControl. To calculate the eddy-related changes in dynamic sea level, the background and large-scale SLR in 1pctCO2 is removed. (c) Pattern of SST anomalies (°C) with the global mean value removed. The green box indicates the main development region of TCs. (d) Pattern of ocean heat content anomalies (109 J m−2) with the global mean value removed.
Figure 13: Upper bound of AMOC-induced dynamic SLR under CO2 forcing. (a) Atlantic meridional overturning streamfunction (Sv) as a function of latitude and depth (m) in the long-term piControl. (b) Time series of the AMOC index defined as the maximum Atlantic overturning streamfunction values north of 30°N in piControl and the CO2 experiments. (c) Global map of dynamic sea level changes (m) during years 131–150 of abrupt 4xCO2 relative to piControl. (d) Time series of dynamic SLR in abrupt 4xCO2 at large coastal cities. The smooth curves are the exponential fit to the dynamic SLR at New York (NE), Charleston (SE), and New Orleans (GOM).
Given the importance of this dynamic SLR, it is of interest to quantify its upper bound in the stronger abrupt 4xCO2 experiment. In response to the instantaneous CO2 quadrupling, the AMOC quickly spins down and the dynamic SLR equilibrates at about 0.40 m along NE after 80 years, 0.27 m along SE, and 0.10 m along GOM (Figs. 13c,d). The e-folding time of the response is 27, 11, and 8 years, respectively. The longer response time scale at NE is likely due to the slower baroclinic processes in the higher latitudes associated with the modification of ocean density properties under CO2 forcing.
As for weather processes in a warming climate, CM4 simulates an increase in the strength (i.e., based on the maximum sustained wind and central pressure) of strong TCs/hurricanes over the North Atlantic, and a decrease in the annual count of all TCs after 100 years in 1pctCO2 (Figs. 14a,c) (Knutson et al. 2013, 2019). Despite warmer SSTs in the TC main development region (10°–25°N, 80°–20°W) (Fig. 12c), a greater warming in the tropical upper troposphere leads to a decrease in the lapse rate and an increase in static stability, which tend to inhibit atmospheric convection and TC formation in 1pctCO2 (Vecchi and Soden 2007; Knutson et al. 2008; Sobel et al. 2016). Previous studies show that the hurricane intensity may have increased during the past decades (Emanuel 2005), with stronger intensity for longer period of time (Ezer 2018). The track density map reveals that the reduction in TC frequency in CM4 mainly occurs east of the Caribbean Sea so that the number of landfalling TCs/hurricanes along the U.S. Atlantic coast remains almost unchanged (Fig. 14a). Meanwhile, extreme storm precipitation increases along the U.S. Atlantic coast in the CO2 experiments (Fig. 15), although the annual precipitation does not.
Figure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2° × 2° boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).
Figure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-6
|
Figure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2° × 2° boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).
Figure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.
The total number of ECs/nor’easters offshore of the U.S. East Coast shows a more significant reduction after 100 years in 1pctCO2 of CM4 (Fig. 14b). On global scales, polar amplification of global warming can lead to a reduced meridional temperature gradient near the surface at midlatitudes, especially during wintertime (Holland and Bitz 2003; Colle et al. 2015; Shaw et al. 2016). Regionally, SST anomalies in 1pctCO2 show a “warm–cool–warm” tripolar pattern (relative to the global mean) among the regions north of the Gulf Stream, east of the subpolar gyre, and in the Nordic seas (Fig. 12c) (Rahmstorf et al. 2015). In particular, the larger ocean warming on the northeast U.S. continental shelf extends from the surface to the bottom of the shelf ocean, and is mainly caused by the weakening of the AMOC (Saba et al. 2015; Caesar et al. 2018). Recently, this region has been identified as one of the hotspots for marine heat waves (Frölicher et al. 2018; IPCC 2019) that could impact marine ecosystems (Pershing et al. 2015). This faster ocean warming, along with the faster land surface warming, reduces the temperature contrast across the Gulf Stream as well as across the land–sea boundary, thereby weakening the near-surface baroclinicity and storm track intensity of ECs/nor’easters during winter.
Compared with the SST anomalies, the maximum increase in heat content of the entire ocean column occurs at the offshore side of the shelf break (Fig. 12d). The dynamic SLR along the U.S. East Coast, the tripolar SST anomaly pattern, and the faster ocean heat accumulation along the shelf break are consistent manifestations and consequences of the AMOC weakening in CM4.
Response of ESL to CO2 forcing
Figure 16 compares the SLA distribution in the historical, SSP projection, 1pctCO2, and abrupt 4xCO2 runs with (Δhe + ΔGe) and without (Δhe) global thermosteric SLR. It is evident that the increase in CO2 forcing progressively shifts the probability density function (PDF) curve to the right and toward higher values. In the historical run, the shift is relatively small due to the anthropogenic aerosol forcing largely counteracting greenhouse gas forcing until about 1990, which leaves insufficient time for sea level response (Held et al. 2019). The shift is more significant in the historical run without anthropogenic aerosol and land use forcing, in the SSP projections, and in 1pctCO2, and is strongest in the abrupt 4xCO2 run.
Figure 16: Progressive responses of ESL to different strength of external forcing. The histograms indicate the distributions of SLA values in piControl, 1pctCO2, abrupt 4xCO2, the historical runs (with and without anthropogenic aerosol and land use forcing), and SSP projection runs of CM4. (a) SLA in piControl (Δhc) and climate change experiments without global thermosteric SLR (Δhe). (b) SLA with global thermosteric SLR (Δhe + ΔGe). The y axis indicates the total number of surge days summed over all coastal ocean grid points in the NE, SE, and GOM regions. All values have been normalized to a 150-yr period for comparison. (left) The piControl with idealized 1pctCO2 and abrupt 4xCO2 simulations and (right) piControl with the historical and SSP projection runs, for (top) NE, (middle) SE, and (bottom) GOM.
Without global thermosteric SLR, the nearly uniform shift of the PDF curve in 1pctCO2 and the elevated daily surge height along the NE and SE coast is mainly attributable to the AMOC-induced dynamic SLR (Fig. 16a). The Kolmogorov–Smirnov statistical test indicates that the shift of the PDF curve is statistically significant. Along the GOM coast, the overall shift of the PDF curve to the right is relatively small, except having a disproportionately longer tail (Fig. 16a). This heightening of ESL is consistent with the increase in TC intensity under the CO2 forcing (Fig. 15). Adding global thermosteric SLR substantially widens the SLA distribution, and reduces its skewness and kurtosis (Fig. 16b).
In piControl of CM4, the return levels for 1-, 10- and 100-yr ESL events differ dramatically among three major coastal cities (Fig. 17) (see appendix B). The tightly packed return levels at Miami are lowest, in sharp contrast with the highest and widely separated return levels at New Orleans, especially for the 1-in-100-year events (0.26 m at Miami vs 1.83 m at New Orleans) (Tebaldi et al. 2012). SLA at Miami shows small variability and a lack of tail at both ends of its histogram (Fig. 17b). The opposite occurs at New Orleans with large surge spikes and a long histogram tail (Fig. 17c), while the surge at New York is in the middle (Fig. 17a).
Figure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (Δhc) and 1pctCO2 (Δhe + ΔGe), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.
In climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (Δhe + ΔGe), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-7
|
Figure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (Δhc) and 1pctCO2 (Δhe + ΔGe), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.
In climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (Δhe + ΔGe), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.
The early TOE in ESL at New York is facilitated by the AMOC-induced dynamic SLR in this region (Figs. 11b and 12a). The anthropogenic signal first shows up in wintertime ESL events and coastal flooding associated with nor’easters. The early TOE at Miami is primarily due to the weak background SLA variability especially the low surge height in piControl. More significantly in 1pctCO2, the 1-, 10- and 100-yr return levels of ESL are permanently exceeded at Miami by the rising mean sea level at year 71, 92, and 102, respectively (Fig. 17b). By contrast, New Orleans shows no permanent exceedance. We find that along the U.S. East Coast, the anthropogenic emergence occurs even before global thermosteric SLR is taken into account.
Impact of the atmospheric model resolution
The refined atmospheric model resolution (0.5°) in CM4HR leads to more intense TCs/hurricanes with stronger winds and smaller size in the control simulation (Fig. 18). These magnify SLA extremes at both ends, but with a greater influence on the positive side along the SE and GOM coast (Fig. 19). For example, the highest daily surge at the GOM coast increases from 1.8 m in CM4 to 2.3 m in CM4HR. The simulations of ECs in CM4 and CM4HR are similar due to their large size relative to TCs. Compared with CM4, the return levels of the 1-, 10- and 100-yr ESL are higher in CM4HR, closer to those for the tide gauge data (Fig. 7). We find that in abrupt 4xCO2, the responses of storm-related ESL and the impact factors are qualitatively similar between CM4 and CM4HR, including storm characteristics, surge statistics, and oceanic and atmospheric circulation, as well as global and regional sea level (Fig. 19).
Figure 18: Large daily surge event induced by a strong TC in the control run of CM4HR. During this event, a surge of up to 2.3 m (Δhc) occurs along the GOM coast on 1 Sep, year 80. (a) Daily dynamic sea level anomalies ηc (m) associated with this event. (b) SLA due to the inverse barometer effect Δbc (m). (c) Daily surface wind vector and speed (m s−1). (d) Daily precipitation (cm day−1). (e) Surface current vector and speed (m s−1). (f) SST anomalies (°C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s−1) during its propagation. Note that Fig. 9 shows similar plots but for CM4.
Figure 19: Histograms of SLA in the 150-yr control and abrupt 4xCO2 runs of CM4 and CM4HR. (left) SLA in the control run (Δhc) and in the CO2 run without global thermosteric SLR (Δhe) and (right) SLA in the control run (Δhc) and in the CO2 run with global thermosteric SLR (Δhe + ΔGe), for (top) NE, (middle) SE, and (bottom) GOM.
Conclusions and model limitations
In the present study, we use a seamless and self-consistent global modeling framework (GFDL CM4) to study weather–climate interactions and their combined effect on extreme sea level along the U.S. Atlantic coast. Thanks to recent progress in model development and improvement, some outstanding questions of significant societal concerns can be answered now for the first time. We compare the characteristics of storm-related ESL among the NE, SE, and GOM regions and their responses to CO2 forcing. We find that under internal weather processes, the low-lying Gulf Coast is most vulnerable to hurricanes and related storm surge. New Orleans is a striking hotspot with the highest surge efficiency in response to storm winds. In response to a 1% per year atmospheric CO2 increase, the elevated surge height along the U.S. East Coast is mainly caused by the background SLR, while that along the Gulf Coast is sensitive to the modification of hurricane characteristics by the external forcing.
Our results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor’easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.
Nonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge–tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
f4751a4b49b7-8
|
Our results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor’easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.
Nonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge–tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.
Without an ice sheet model, CM4 cannot simulate the impacts of Greenland melt on sea level, AMOC and geoid changes along the U.S. East Coast (Kopp et al. 2010; Bakker et al. 2016). Finally, CM4 does not simulate climate-unrelated factors. Most of the U.S. Atlantic coast is influenced by land subsidence, particularly at New Orleans and along the Texas coast (Nienhuis et al. 2017), which can increase relative SLR and exacerbate the impact of storm surge and coastal flooding (Table 2). By contrast, land uplift in some of the New England coastal regions can offset and mitigate the dynamic SLR (Karegar et al. 2016).
Ideally, projections of SLR and storm-related ESL along the U.S. Atlantic coast should take all these factors into account. We trust that future model development will continue to address these and other limitations and further improve the model’s ability and capacity, thereby providing more accurate information for effective planning and preparedness along the U.S. Atlantic coast.
Appendix
Appendix A: Calculation of Skewness and Kurtosis of SLA
Skewness and kurtosis describe the shape of the probability distribution of SLA (Hughes et al. 2010). In piControl, the skewness of SLA values is the third standardized moment
skew = E [ ( Δhc − μ / σ )^3 ], (A1)
with μ and σ being the long-term mean and standard deviation of Δhc, and E the expectation operator. The kurtosis is the fourth standardized moment and is computed by
kurt = E [ ( Δhc − μ / σ)^4 ]. (A2)
The kurtosis of a normal (Gaussian) distribution is 3. Sometimes it is useful to compare the kurtosis of a distribution to this value (the so-called excess kurtosis). In this study, we use the original calculation of kurtosis based on Eq. (A2). Large kurtosis values indicate more extreme outliners in the distribution.
Appendix B: Return Level and Period of ESL in piControl
We use the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) to calculate return levels of storm-related ESL corresponding to particular return periods in the 150-yr piControl. We set the 99th percentile of SLA (Δhc) as the threshold to extract the subset of extreme values. We fit the empirical distribution of the subset with the generalized Pareto distribution (GPD).
y = p(x|k,σ,θ)= (1/σ) (1 + k (x − θ)/ σ)^{−1−1/k} , k ≠ 0
= (1/σ) e^{−(x−θ)/σ}, k = 0, (B1)
for x ≥ θ when k > 0, and θ ≤ x ≤ θ − σ/k when k < 0. Here y is the PDF of GPD; k, σ, and θ are the shape, scale, and location parameters, respectively. For k = 0, GPD becomes the exponential distribution. Given a particular return period T (1, 10, or 100 years) of ESL events, the corresponding return level zT is
zT = θ + σ/k { [ (1 − F(θ)) / p ]^k − 1 }, k ≠ 0= θ + σlog [ (1 − F(θ)) / p ], k = 0 (B2)
where p and F(θ) are the probability of the event and cumulative density function, respectively.
Appendix C: Time of Emergence of ESL in 1pctCO2
For the 1-in-1-year ESL events, we use a 20-yr moving window and the 99.73 percentile of SLA (empirical 1-yr event return level) as the threshold to extract the event samples (Si, i = year 20, 21, …, 150). For example, S20 and S21 denote the subset exceeding the 99.73 percentile of SLA during years 1–20 and 2–21, respectively. We then identify the median value of Si in piControl (m^i_c) and 1pctCO2 (m^i_e). The subscripts c and e denote piControl and CO2 experiments, respectively. The mean Mc and standard deviation σc of m^i_c are
Mc = 1/131 ∑^150_{i=20} m^i_c,
σc = [∑^150_{i=20} (m^i_c - Mc)^2 / 131 ]^{1/2}.
(C1)
In 1pctCO2, TOE in ESL height of the 1-yr events is defined as the year i beyond which m^i_e permanently exceeds (Mc + 2σc). If the anthropogenic signal emerges within the first 20 years, TOE is marked as year 20. For the 10-yr events, we follow the same detection procedure except using a 50-yr moving window instead to increase the sample size and the 99.97 percentile as the threshold. We do not evaluate TOE in ESL height for the 100-yr event due to its extreme rareness in the 150-yr simulations of CM4.
To quantify TOE in ESL frequency, we count the occurrence time above the 1- and 10-yr return level in piControl using a 20- and 50-yr moving window, respectively. TOE in ESL frequency is defined as the year beyond which the occurrence time in 1pctCO2 permanently exceeds the mean plus two standard deviation of the occurrence time in piControl (similar to the method above for ESL height). For the 100-yr event, TOE is the year beyond which its occurrence time in 1pctCO2 within a 50-yr moving window permanently exceeds 1 (i.e., ≥2).
|
https://sealeveldocs.readthedocs.io/en/latest/yin2020.html
|
0bbafafddd15-0
|
Bamber et al. (2022)
Title:
Ice Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach
Key Points:
Greenland surface melt is a dominant uncertainty in 21st century contributions from the ice sheets
Ice shelf buttressing is the dominant uncertainty in Antarctic ice dynamics in the 21st century
East Antarctic ice dynamics only play a significant role in the 22nd century for a high temperature scenario
Keywords:
ice sheets, sea level rise, expert judgement, uncertainty
Corresponding author:
Bamber
Citation:
Bamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2022). Ice Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach. Earth’s Future, 10(10). https://doi.org/10.1029/2022ef002772
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF002772
Abstract
The ice sheets covering Antarctica and Greenland present the greatest uncertainty in, and largest potential contribution to, future sea level rise. The uncertainty arises from a paucity of suitable observations covering the full range of ice sheet behaviors, incomplete understanding of the influences of diverse processes, and limitations in defining key boundary conditions for the numerical models. To investigate the impact of these uncertainties on ice sheet projections we undertook a structured expert judgement study. Here, we interrogate the findings of that study to identify the dominant drivers of uncertainty in projections and their relative importance as a function of ice sheet and time. We find that for the 21st century, Greenland surface melting, in particular the role of surface albedo effects, and West Antarctic ice dynamics, specifically the role of ice shelf buttressing, dominate the uncertainty. The importance of these effects holds under both a high-end 5°C global warming scenario and another that limits global warming to 2°C. During the 22nd century the dominant drivers of uncertainty shift. Under the 5°C scenario, East Antarctic ice dynamics dominate the uncertainty in projections, driven by the possible role of ice flow instabilities. These dynamic effects only become dominant, however, for a temperature scenario above the Paris Agreement 2°C target and beyond 2100. Our findings identify key processes and factors that need to be addressed in future modeling and observational studies in order to reduce uncertainties in ice sheet projections.
Plain Language Summary
The ice sheets covering Antarctica and Greenland are the largest source of future sea level rise but projections of their behavior are extremely uncertain. This is partly because of processes that are poorly understood in terms of their importance and potential contribution in the future. To investigate these issues and the relative importance of different processes in driving uncertainties in projections we solicited expert judgements from a group of scientists actively working on the topic. This exercise revealed that the dominant factors controlling the uncertainties depends on how far into the future one looks and the warming scenario assumed. For the 21st century, surface melting on the Greenland ice sheet is a dominant source of uncertainty alongside possible ice flow instabilities in West Antarctica. The East Antarctic Ice Sheet, the largest ice mass by an order of magnitude, does not play a significant role until the 22nd century and only for relatively high levels of future warming, based on the expert judgements. These findings quantify the relative role of different processes in driving uncertainty and indicate key areas for future focus to improve ice sheet projections and reduce the uncertainty in future sea level rise estimates.
Introduction
Substantial sea level rise (SLR) is considered to be one of the most serious consequences of climate warming (Bamber et al., 2019). The largest contributors and uncertainty in projecting future SLR are the ice sheets that cover Antarctica and Greenland (Bamber et al., 2019; Fox-Kemper et al., 2021). These ice sheets respond over timescales ranging from diurnal, for example, tides (Gudmundsson, 2006) to multi-millennial, for example, changes in climate at the end of the last glacial, 12,000 years BP (Huybrechts, 2002).
Observations of the ice sheets at high temporal resolution, however, are limited to just the last few decades and may not be adequate to assess or constrain projections of deterministic numerical models (Fox-Kemper et al., 2021). Conditions at the base of an ice sheet are important for determining its sensitivity to external forcing (Ritz et al., 2015) but are unlikely ever to be definitively observable, due to inaccessibility. During the 1990s, satellite observations indicated relatively rapid and large amplitude changes in ice dynamics in the Amundsen Sea Embayment of West Antarctica and in Greenland that were not reproduced by the numerical models available at that time (Vaughan & Arthern, 2007). This required a re-evaluation of the sensitivity of the numerical models to external forcing. More recently, a process called the Marine Ice Cliff Instability (MICI) has been hypothesized to have contributed to SLR high-stands in the last interglacial and further back in time (DeConto & Pollard, 2016). Including MICI in numerical models can result in a dramatic increase in ice sheet sensitivity to external forcing (DeConto & Pollard, 2016; DeConto et al., 2021) but its importance to past ice sheet behavior and its relevance to the contemporary Antarctic Ice Sheet is unclear, and disputed (Bassis et al., 2021; Edwards et al., 2019).
These two examples of our limited understanding of ice sheet processes illustrate the problem of determining epistemic uncertainties associated with major natural systems that are under-sampled or sparsely observed (Attenberg et al., 2015). Other factors, such as poorly constrained model input data and boundary conditions, present significant challenges for deterministic modeling approaches. The limitations of ice sheet model projections are highlighted in a recent study comparing contemporary observations with an ensemble of state-of-the-art models and the spread in their hindcasts and projections (Aschwanden et al., 2021). Few models are able to reproduce the observations, and for the AIS, estimates are uncertain even on the sign of the contribution both in the recent past and near future.
Additionally, all three present-day ice sheets possess hypothesized instabilities (including the MICI), the details of which are outlined in Note S1 in Supporting Information S1. Note that we partition the Antarctic Ice Sheet into the West (WAIS) and East (EAIS) Antarctic Ice Sheets due to the different factors that influence their behavior (see Note S1 in Supporting Information S1 and other studies, e.g., Seroussi et al., 2020). Paleo-proxy records suggest that instabilities drove abrupt ice loss in the past (Liu et al., 2016; Wise et al., 2017). In all three cases, however, the instability thresholds are likely to be state- and rate-dependent and difficult, therefore, to constrain reliably. These factors create a further profound challenge for future SLR projections based on deterministic numerical modeling.
Nonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called “worst-case” and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question “what is the most extreme physically-plausible dynamic response of the ice sheets” (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was “implausible” but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-1
|
Nonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called “worst-case” and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question “what is the most extreme physically-plausible dynamic response of the ice sheets” (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was “implausible” but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).
Structured expert judgement (SEJ) using calibrated expert responses provides a formal, rigorous, reproducible and well-established framework for tackling this type of problem (Aspinall, 2010; Bamber & Aspinall, 2013; Oppenheimer et al., 2016). SEJ can capture epistemic uncertainties that are challenging for deterministic modeling approaches to identify (Attenberg et al., 2015). There is, for example, evidence available to the expert about past ice sheet behavior that is difficult to incorporate into a deterministic numerical model. An example of this is paleo sea level records that indicate a rapid SLR of 2–4 cm/yr for multiple centuries at around 14.6–14.3 Kyr BP, known as Meltwater Pulse 1A (Liu et al., 2016). This entailed an 8–15 m SLR which must have been associated with one or more ice sheet instabilities, but the precise source, dynamics and forcing mechanism(s) are unclear (Liu et al., 2016). The longer-term sea level record, covering glacial-interglacial cycles clearly shows a pattern of slow ice sheet growth and rapid decay, providing further evidence of instabilities in ice sheet behavior during or entering a warming inter-glacial period, such as the one we are in today. Further evidence from the paleo-sea level record comes from the last interglacial period when the sea level high stand was about 5–10 m above present-day (Gulev et al., 2021) and when global mean temperatures peaked at about 0.9°C and averaged 0.2°C above the pre-industrial value for global sea surface temperatures (Turney et al., 2020). These data provide the expert with evidence that ice sheets can generate high rates of SLR (circa 4 m/century) over centennial timescales and that they can be sensitive to relatively small temperature perturbations.
Previously, we reported the key findings from an SEJ elicitation undertaken in 2018 via two workshops, one held in the USA and the other in the UK, involving 22 experts in total (hereafter B19) (Bamber et al., 2019). The primary findings presented in B19 were the respective contributions to SLR from each ice sheet, for each time period and temperature change scenario considered. For the high temperature scenario (5°C by 2100; roughly equivalent to the high end emissions scenario RCP8.5), the 95th percentile ice sheet contribution to SLR was 178 cm at 2100CE. When combined with the contribution from glaciers and thermal expansion of the oceans this implied about a 10% chance of exceeding a SLR of 2 m by 2100CE (Bamber et al., 2019) (Figure 1), comparable with the plausibility experiment discussed earlier (Pfeffer et al., 2008) and the high-end scenario for SLR in the Sixth Assessment Report of the IPCC (Fox-Kemper et al., 2021). We present, in Figure 1, these findings expressed in terms of SLR as a function of time for different probabilities from 5 to 95%. This is useful for practitioners who will have different level of risk tolerance depending on the asset and hazard or who may be concerned about the probability of exceeding a specific value of SLR by a certain date (M. Oppenheimer et al., 2019). For example, the blue dashed lines indicate the probability of exceeding 1 m of SLR by 2100 (50%) or 2150 (∼90%) for the high temperature scenario. For 2 m of SLR it is 10% and 30%, respectively. The full table of values for 1%–99.9% are given in the Table S1 in Supporting Information S1.
Figure 1: Projected substantial sea level rise (SLR) as a function of time for different probabilities between the 5th and 95th percentile for the High temperature scenario (5°C by 2100). The dashed blue lines indicate the probability of equaling or exceeding a given SLR at a specific date in the future: in this case 1 m by 2100 and 2150 (green) or 2 m (red) by those dates.
What was not considered in B19 was which ice sheet processes are responsible for the projected upper SLR values, and which of these processes dominate the uncertainty in future projections as a function of temperature scenario and ice sheet. This requires further and deeper interrogation of the expert judgements at the process level. This is what is presented here. To our knowledge, this is the first quantitative analysis of the relative importance of the processes that influence the uncertainty in ice sheet projections using SEJ as opposed to deterministic modeling, which has various limitations as mentioned above.
Materials and Methods
The overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively) and for two schematic temperature change scenarios. The first temperature trajectory (denoted L for low) stabilizes in 2100CE at +2°C above pre-industrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H for High) stabilizes in 2100 at +5°C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.
The experts were weighted according to an impartial and rigorous approach that assesses each expert’s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000–2010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-2
|
Materials and Methods
The overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively) and for two schematic temperature change scenarios. The first temperature trajectory (denoted L for low) stabilizes in 2100CE at +2°C above pre-industrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H for High) stabilizes in 2100 at +5°C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.
The experts were weighted according to an impartial and rigorous approach that assesses each expert’s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000–2010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.
In addition, we also investigate the role of various drivers of changes in D, A and R. To achieve this, we draw on additional qualitative information acquired during the 2018 SEJ (Note S3 in Supporting Information S1) supported, where available, with relevant literature related to developments in ice sheet process understanding and observations of past and recent ice sheet behavior. Specifically, we examine probability distributions for the SLR contributions of each ice sheet individually, considering the physical mechanisms that drive the response of those ice sheets via atmospheric, oceanic, or internal and surface forcings. In so doing, we quantify the rank-order of factors or processes that are influencing projection uncertainties in relation to each ice sheet independently, and where future research effort could reap the greatest benefits by addressing those sources of uncertainty. Some of the processes display non-Gaussian distributions with long upper tails, which can only be explored and characterized using a probabilistic approach (e.g., Figure 2).
Figure 2: Indicative probability distribution plots for substantial sea level rise (SLR) contributions by 2100CE from the three ice sheets and for three physical processes, identified on the x-axis (runoff from East Antarctic Ice Sheet (EAIS) is omitted as this is presumed zero under either temperature rise scenario). Results are derived from expert elicitation for the 2100L (low +2°C) global temperature trajectory (left hand curves) and for the 2100H (high +5°C) global temperature trajectory (right hand curves); probability density curves are approximate and extend from values corresponding to a 99% chance of SLR being exceeded to a 1% chance of SLR being exceeded. The 5th, 95th and 50th percentile values of the distributions are shown by red and black rectangles, respectively.
Ice-Sheet Processes and Drivers
Accumulation, A, and surface runoff, R, relate to what is termed the surface mass balance (SMB) of the ice sheet and are modulated, primarily, by atmospheric processes such as moisture content (affecting snowfall), air mass circulation, cloud cover, surface albedo, air temperature and wind speed (Paterson, 1994). Discharge, D, relates to the speed of the ice at the point that it reaches the ocean, known as the grounding line, where the ice first comes into contact with the ocean (Van der Veen, 1999). It is influenced by forces acting on the ice column including the buttressing effect of floating ice downstream of the grounding line (Van der Veen, 1999). Variations in ocean heat content, due to either changes in water temperature or circulation, can affect the strength of the buttressing force. Thus, discharge is primarily forced by the physical state of the ocean and SMB primarily by atmospheric conditions. In general, changes in discharge are related to ice dynamics, which have a longer time-constant compared to SMB and tend to vary smoothly in time. Surface melting can, however, affect calving rates and ice shelf collapse by hydrofracture and sub-shelf melting so that each process is not necessarily entirely independent (Lai et al., 2020). These correlations may be important when assessing the integrated response of the ice sheet to external forcing (Bamber et al., 2019) but here we consider each process independently as a function of the forcing.
Some processes that affect A, R, and D are comparatively well understood, such as the relationship between ice thickness and strain rate in the ice, while others are either poorly understood or poorly constrained. In particular, all three ice sheets may possess thresholds in their behavior beyond which an irreversible response in part of the ice sheet is initiated. However, the precise location of the threshold in parameter space is highly uncertain (Bassis et al., 2021; DeConto & Pollard, 2016; Edwards et al., 2019; Gregory et al., 2004, 2020; Joughin et al., 2014; Seroussi et al., 2020). The relative importance of various factors influencing A, R, and D were elicited as part of the SEJ workshops (Note S3 in Supporting Information S1 and (Bamber et al., 2019)).
Results and Discussion
In the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.
Figure 3: As for Figure 2 but for 2200.
For 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [−5, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th–95th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980–2012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003–2018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-3
|
Results and Discussion
In the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.
Figure 3: As for Figure 2 but for 2200.
For 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [−5, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th–95th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980–2012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003–2018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.
Table 1: 5th, 50th, and 95th Percentile Elicited Estimates for SLR Contributions by Each Ice Sheet and Each Process (G Denotes GrIS, W WAIS, E EAIS; A Denotes Accumulation, R Runoff, D Discharge). Note: GrIS, Greenland ice sheet; EAIS, East Antarctic Ice Sheet; SLR, sea level rise; WAIS, West Antarctic Ice Sheet. The orange shaded cells denote values that are greater than 25% of the total combined SLR contribution from the ice sheets in the final column. The totals are not the sum of the components because of dependencies between processes and ice sheets (see Note S3 in Supporting Information S1). NB all numbers in the table exclude the 2000–2010 baseline of 0.7 mm/yr because this was added post-hoc to the values elicited from the experts (Bamber et al., 2019).
For each of the three primary processes elicited (D, A, R), there are several potential atmospheric, oceanic or ice-sheet variables that could act as drivers of change. To identify which factors were considered important, during the SEJ workshops we asked the experts to rank climate drivers in relation to the primary ice sheet processes. Here, qualitative information about the rank order of the drivers was obtained rather than the quantiles elicited for the three processes: D, A, and R (see Note S3 and Figures S4–S6 in Supporting Information S1). Not all experts answered all sections of the rationale questionnaire and our findings are based, therefore, on the qualitative responses that were obtained. As such, these should be regarded as indicative of the relative importance of different drivers.
As part of the elicitation, factors influencing A and R were grouped into SMB processes that could be modified by changes in atmospheric moisture or circulation, albedo changes and changes in summer sea ice extent; the influences of these factors were elicited separately for floating and for grounded ice (Figure 4 and Figure S4 in Supporting Information S1).
Figure 4: Expert judgements on the relative role to the overall uncertainty for six drivers of changes in ice dynamics: buttressing by ice shelves, basal traction, transverse stresses, hydrofracturing, ice cliff instability, and dissipation after iceberg formation at exit gates; and two drivers for changes in surface mass balance (SMB): atmospheric moisture and circulation, and albedo. Note that buttressing is directly related to the initiation and evolution of MISI and also hydrofracture and ice cliff instability. Descriptive definitions for these factors are provided in the Note S3 in Supporting Information S1. SMB processes were considered separately for grounded and floating ice and shown here are the results for the former only. This figure is for the three ice sheets at 2100, 2200, and 2300 for the High temperature scenario only. SMB and D are scaled according to their relative contribution to the integrated ice sheet substantial sea level rise. The equivalent plot for the Low temperature scenario including floating ice is shown in Figure S4 in Supporting Information S1 and for the High scenario including ice shelves in Figure S5 in Supporting Information S1.
From these expert judgements, changes in albedo are determined to be the dominant control on the SMB response of the GrIS (Figure 4). This is not surprising as surface albedo is the single most important variable in modulating the surface energy balance of the GrIS and, as a consequence, melt rates (Fitzgerald et al., 2012). Nonetheless, that GrIS runoff has a comparable uncertainty range to WAIS discharge for both temperature scenarios for 2100 was an unexpected result and we examine, therefore, both the modeling and observational evidence that supports this finding.
Albedo is sensitive to several variables that are poorly constrained in climate models, including changes in cloud cover characteristics and extent (Hofer et al., 2019), impurity and algal content of the surface (Tedstone et al., 2020), and the seasonality of changes in precipitation and air temperature. For example, most General Circulation Models (GCMs) project the largest temperature increase in the Arctic to occur in winter (Koenigk et al., 2013) as reflected by the observational record (Hanna et al., 2021), resulting in increased winter precipitation. This can act to reduce runoff by depositing a high-albedo insulating snow layer in winter (Day et al., 2013). Conversely, increased summertime precipitation can have the opposite effect as it results in greater rainfall, which acts to accelerate melting and reduce the surface albedo (Fausto et al., 2016). Indeed, non-radiative energy fluxes such as rain are generally poorly captured in GCMs, and hence also regional climate models, but will become increasingly important as temperatures rise above the freezing point of water (Fausto et al., 2016). Hence, seasonal atmospheric changes play a critical role in modulating R, but are, in general, not well constrained by GCMs.
Changes in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th–95th range of ±5.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9–10°C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010–2019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th–84th (equivalent to one sigma) percentile range of 14–33 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-4
|
Changes in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th–95th range of ±5.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9–10°C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010–2019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th–84th (equivalent to one sigma) percentile range of 14–33 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.
In Table 1, the dominant processes driving the median and 95th percentile SLR are highlighted in orange. For both temperature scenarios and all epochs GrIS runoff and WAIS dynamics are the two processes dominating the uncertainty. EAIS dynamics becomes important mainly for the High temperature scenario except for 2300L where the 95th percentile value is about 26% of the total SLR. This suggests that improvements in modeling these two processes would reduce SLR projection uncertainty. This is, however, not limited to improvements in ice sheet modeling but also in reducing uncertainties in the driving climate forcing that influences GrIS runoff on the one hand and WAIS dynamics on the other. The former relates to atmospheric processes while the latter is primarily oceanic.
Some drivers shown in Figure 4 are not independent of others (see also Note S3 in Supporting Information S1). Ice shelf buttressing, for example, will be affected by hydrofracture, ice cliff instability and dissipation of icebergs, which are also the three processes that control the MICI. The results are shown for each ice sheet and for three time periods, 2100, 2200, and 2300. For the GrIS, basal traction is considered the dominant process in influencing discharge for all time periods. This is not unexpected, as floating tongues and ice shelves are limited in extent in Greenland. The second most important process is buttressing but this decreases with time as the ice sheet shrinks in size, its marine margins recede and floating tongues disappear. For 2100L and H, GrIS dynamics provides the third largest uncertainty, after GrIS runoff and WAIS discharge (Figure 2). By 2200, however, it has been overtaken by WAIS accumulation (2200L and 2200H) and EAIS dynamics for 2200H (Figure 4), most likely because of a retreating marine margin over time.
For 2100H, WAIS discharge [0.1, 15, 91] cm and GrIS runoff [0.2, 11, 74] cm again account for close to half the median total ice sheet contribution of 51 cm [−1, 43, 170] and dominate the uncertainty with 5th–95th percentile credible ranges of 91 and 74 cm, respectively. However, for this high-end warming scenario, which after accounting for polar amplification, implies a temperature increase over the Antarctic Ice Sheet of about +7°C to +10°C, EAIS dynamics is responsible for the third largest uncertainty with a 5th–95th percentile range of 54 cm (Table 1). For 2100H relative to 2100L, the 5th–95th percentile credible range has roughly doubled for WAIS discharge and GrIS runoff, but approximately trebled for EAIS dynamics. This indicates that the experts consider that instabilities in the latter could be triggered by 2100 under +5°C warming, while for both temperature scenarios the experts infer it is plausible that the marine ice sheet instability (MISI) would be invoked for the WAIS with the amplitude of the response sensitive to temperature. This is in contrast with the latest ice sheet model intercomparison project for Antarctica, where the sign and sensitivity of the WAIS response to warming scenario, for example, varies between models (Seroussi et al., 2020).
For the WAIS, buttressing is the dominant ice sheet process for all the time periods considered (Figure 4), reflecting the view that this is the primary control on the MISI and grounding line migration rates (Schoof, 2007). However, its relative importance declines from 2100 to 2300, with ice cliff instability increasing in significance, presumably as ice shelves recede or collapse, leaving exposed ice cliffs—close to the grounding line—that may be susceptible to ice cliff failure (Seroussi et al., 2020). The MISI is driven by changes in the amount of buttressing afforded by floating ice shelves that “protect” the inland, grounded ice. This, in turn, is sensitive to sub-shelf melting which is affected by changes in ocean temperature and/or circulation. The experts considered two drivers for changes in ocean circulation in the elicitation process. These were alterations to: (a) circumpolar deep water intrusion onto the continental shelf (CDW) and (b) the meridional overturning circulation (AMOC). Of these, experts considered the first to be by far the most important for influencing Antarctic sub-shelf melt rates over all the time periods and both temperature scenarios. For the GrIS, changes in the AMOC were considered most important as the former two are primarily related to Southern Ocean circulation (Figure S6 in Supporting Information S1).
Gravitational, rotational and solid Earth deformation (collectively GRD) effects have been hypothesized to influence the stability of grounding lines on retrograde slopes (Whitehouse et al., 2019) and were considered as part of the rationale analysis but have been demonstrated to be of second order importance (Larour et al., 2019) (Note S4 and Figure S7 in Supporting Information S1). Over millennial timescales they may, however, be of first-order significance (Pan et al., 2021).
For the EAIS, the experts concluded that buttressing is the dominant and primary factor for all time periods (Figure 4). It is interesting to note that for 2200H the 95th percentile estimate for EAIS discharge is larger than any other ice sheet process and hydro-fracture is considered to be increasingly important (Table S2 in Supporting Information S1) and also, but to a lesser extent, for 2100H (Figure 4). This is consistent with recent evidence that suggests that as much as 60% of Antarctic ice shelf area is vulnerable to hydrofracture from surface meltwater, including almost all of the Filchner Ronne, Ross and Amery ice shelves that buttress large drainage basins in East Antarctica (Lai et al., 2020).
Conversely, because runoff is limited over both the WAIS and EAIS at present, it is considered to play a limited role in direct mass loss (as opposed to an indirect role in accelerating ice shelf collapse) under the high temperature scenario up to 2100 (Figure 2 and Table 1) and even up to 2200 (Figure 2, Table 1). Hence, albedo changes are considered to be of limited importance over grounded ice for both Antarctic ice sheets. In this case, it is changes in moisture content and circulation that are identified as the dominant control on SMB. Thus, for example, increased accumulation of the WAIS has a 5% probability of mitigating the ice sheet contribution to SLR by at least 65 cm for 2200H. This is also reflected in ice sheet model simulations using climate model output, particularly for the EAIS (Seroussi et al., 2020). The experts conclude that changes in summer sea ice extent will have some impact on ice shelf SMB for all three ice sheets up to 2200 (Figures S4 and S5 in Supporting Information S1), with the largest contribution over the GrIS.
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-5
|
For the EAIS, the experts concluded that buttressing is the dominant and primary factor for all time periods (Figure 4). It is interesting to note that for 2200H the 95th percentile estimate for EAIS discharge is larger than any other ice sheet process and hydro-fracture is considered to be increasingly important (Table S2 in Supporting Information S1) and also, but to a lesser extent, for 2100H (Figure 4). This is consistent with recent evidence that suggests that as much as 60% of Antarctic ice shelf area is vulnerable to hydrofracture from surface meltwater, including almost all of the Filchner Ronne, Ross and Amery ice shelves that buttress large drainage basins in East Antarctica (Lai et al., 2020).
Conversely, because runoff is limited over both the WAIS and EAIS at present, it is considered to play a limited role in direct mass loss (as opposed to an indirect role in accelerating ice shelf collapse) under the high temperature scenario up to 2100 (Figure 2 and Table 1) and even up to 2200 (Figure 2, Table 1). Hence, albedo changes are considered to be of limited importance over grounded ice for both Antarctic ice sheets. In this case, it is changes in moisture content and circulation that are identified as the dominant control on SMB. Thus, for example, increased accumulation of the WAIS has a 5% probability of mitigating the ice sheet contribution to SLR by at least 65 cm for 2200H. This is also reflected in ice sheet model simulations using climate model output, particularly for the EAIS (Seroussi et al., 2020). The experts conclude that changes in summer sea ice extent will have some impact on ice shelf SMB for all three ice sheets up to 2200 (Figures S4 and S5 in Supporting Information S1), with the largest contribution over the GrIS.
Finally, we asked the experts whether they considered the recent (decadal) trends in mass balance for the GrIS and WAIS, as observed from satellite data, were due predominantly to internal variability (IV) or external forcing (EF) (Figure 5). This is an important question for four reasons. First, these same observations are used to initialize numerical ice sheet models (DeConto et al., 2021; Seroussi et al., 2020). To do this, it is necessary to assign the recent trends to either IV or to EF, or some combination of the two. That is because, as for GCMs, ice sheet models are not aimed at reproducing the conditions of one particular day, a season or a year, but to model climatically forced trends. Second, this is a central question for process understanding and also for probabilistic approaches that are conditioned on the observations, as are semi empirical models (Little et al., 2013). Third, recent observations have been used to calibrate tuneable parameters in an ice sheet model (DeConto et al., 2021). This requires assigning the trend in the observations to IV or EF. Note that model calibration and initialization are not, in general, the same process. Fourth, observations are an important tool for verifying the performance of a numerical model but only if the signal(s) in the observations can be assigned to some combination of IV and EF (Randall et al., 2007). The experts concluded that the trends in Greenland are predominantly driven by EF, whereas for the WAIS there was no consensus and no certainty (Figure 5) as was also the case in a previous SEJ exercise (Bamber & Aspinall, 2013).
Figure 5: Expert judgements for whether internal variability (IV) or external forcing (EF) is the dominant driver of recent (last two decade) observational trends in mass balance for the Greenland Antarctic ice sheets (GrIS) and West Antarctic Ice Sheet (WAIS).
Conclusions
The findings just described, which are drawn from the SEJ exercise presented in B19, are generally consonant with recently reported observational evidence but are in sharp contrast to the latest ice sheet model intercomparison analyses in terms of both the dominant drivers of uncertainty and their magnitudes (Goelzer et al., 2020; Seroussi et al., 2020). An important contribution we have been able to provide through our analysis is to express these influences—on sea level projections and associated uncertainties—in probabilistic terms. We can, thus, quantify the relative role of different processes not just for their median response but also for the tails of the distributions, which are lower probability but higher impact. Where the distributions display high kurtosis (e.g., WAIS dynamics and GrIS runoff) the median and standard deviation do not capture the full uncertainty and risk associated with that process. In IPCC assessment reports prior to the AR6 (Fox-Kemper et al., 2021) this has been a major limitation in their sea level rise projections, which were limited to the likely range, equivalent to ± one standard deviation (Bamber et al., 2019).
We found that for all time periods out to 2300 CE, quantified uncertainties are dominated by WAIS dynamics and GrIS runoff. The former is influenced by the marine ice sheet instability, MISI, which in turn, is influenced by changes in ocean circulation and heat content in ways that are not well understood or, as yet, adequately modeled (Seroussi et al., 2020). Subglacial topography has an important controlling influence on the initiation of the MISI and how rapidly it evolves but is imperfectly known for many key sectors of the WAIS (Cornford et al., 2020; Rosier et al., 2021). GrIS runoff is relatively well understood as a process, but is sensitive to climate drivers that are poorly captured in GCMs and, therefore, imperfectly represented in future projections. For example, changes in cloud properties, such as optical depth, altitude and seasonality, can have a dramatic impact on melt rates but are inconsistent between GCMs and are known to be poorly modeled in general (Hofer et al., 2019). Runoff is also sensitive to albedo. Relatively small concentrations of both inorganic and organic material on the ice sheet surface can have a significant impact on albedo and, therefore, melting, but this is a factor that is yet to be included in ice sheet models (Williamson et al., 2020). The seasonality of both temperature and precipitation changes over Greenland has a strong influence on SMB trends but is also not consistently projected by GCMs. Reducing future uncertainties in ice sheet projections will require, therefore, improvements in ice sheet process understanding and modeling of those processes as well as more robust projections of the climate forcing for a given greenhouse gas emissions pathway.
An important challenge, building on this analysis, is to extend and refine our expert judgement elicitation so that we can better quantify critical parameters, variables and processes related to model projections of ice sheet contributions to sea level rise. For instance, while the uncertainties in our experts’ assessments likely include some elements that relate to processes that are not formally identified in the present exercise, an elicitation could be designed that would enable us to disaggregate these complexities, and their associated uncertainties, in more detail. This would allow us to quantify the role of additional factors in limiting process certainty. As is usual with structured elicitations of this type, such additional findings—based on informed expert judgements—will almost certainly highlight specific topics meriting further research and analysis. As discussed above, this is not limited to ice sheet processes but also to the climate projections used to force them.
Supporting Information
Ice Sheet Instabilities
For the Greenland Ice Sheet (GrIS), a potential key threshold relates to a concept termed the ‘small ice cap instability’ (Maqueda et al., 1998). This instability originates from a positive feedback between changes in surface elevation and increased runoff, i.e. it is linked to surface mass balance (SMB). As the ice sheet loses mass, the surface elevation lowers, resulting in warmer surface temperature and increased melting. When the amount of surface melting exceeds the total accumulation, via snowfall, the ice sheet is no longer sustainable in the long-term. The increase in global temperature required to pass this threshold has been estimated to lie between +0.8 to +3.2 ̊C above pre-industrial with a best estimate of +1.6 ̊C (Robinson et al., 2012). Recent evidence from satellite observations suggests that the GrIS had reached a state of persistent ice loss by about 2005 (King et al., 2020) and that it experienced its largest recorded mass loss, equivalent to 1.5 mm sea level equivalent, in 2018. About 60% of the mass loss over the last three decades is attributable to SMB and the rest to discharge (King et al., 2020; Sasgen et al., 2020). Whether the GrIS would completely disintegrate or reach a new, smaller metastable state is a topic of current debate (Gregory et al., 2020; Robinson et al., 2012).
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-6
|
An important challenge, building on this analysis, is to extend and refine our expert judgement elicitation so that we can better quantify critical parameters, variables and processes related to model projections of ice sheet contributions to sea level rise. For instance, while the uncertainties in our experts’ assessments likely include some elements that relate to processes that are not formally identified in the present exercise, an elicitation could be designed that would enable us to disaggregate these complexities, and their associated uncertainties, in more detail. This would allow us to quantify the role of additional factors in limiting process certainty. As is usual with structured elicitations of this type, such additional findings—based on informed expert judgements—will almost certainly highlight specific topics meriting further research and analysis. As discussed above, this is not limited to ice sheet processes but also to the climate projections used to force them.
Supporting Information
Ice Sheet Instabilities
For the Greenland Ice Sheet (GrIS), a potential key threshold relates to a concept termed the ‘small ice cap instability’ (Maqueda et al., 1998). This instability originates from a positive feedback between changes in surface elevation and increased runoff, i.e. it is linked to surface mass balance (SMB). As the ice sheet loses mass, the surface elevation lowers, resulting in warmer surface temperature and increased melting. When the amount of surface melting exceeds the total accumulation, via snowfall, the ice sheet is no longer sustainable in the long-term. The increase in global temperature required to pass this threshold has been estimated to lie between +0.8 to +3.2 ̊C above pre-industrial with a best estimate of +1.6 ̊C (Robinson et al., 2012). Recent evidence from satellite observations suggests that the GrIS had reached a state of persistent ice loss by about 2005 (King et al., 2020) and that it experienced its largest recorded mass loss, equivalent to 1.5 mm sea level equivalent, in 2018. About 60% of the mass loss over the last three decades is attributable to SMB and the rest to discharge (King et al., 2020; Sasgen et al., 2020). Whether the GrIS would completely disintegrate or reach a new, smaller metastable state is a topic of current debate (Gregory et al., 2020; Robinson et al., 2012).
The West Antarctic Ice Sheet (WAIS) is termed a marine ice sheet because most of the bedrock it rests on lies below sea level, in some places by as much as 2,500 m (Bamber et al., 2009). In addition, the ice sheet also rests, predominantly, on a retrograde bed slope: one that deepens inland. These two conditions are hypothesised to be necessary (but not sufficient) to invoke the Marine Ice Sheet Instability (MISI) whereby the grounding line is inherently unstable and can rapidly migrate inland (Schoof, 2007; Seroussi et al., 2020). Recent evidence indicates that part of the WAIS may already be experiencing irreversible grounding line retreat as a result of MISI (Joughin et al., 2014). Unlike the GrIS instability mechanism, the WAIS MISI is a dynamic response driven predominantly by ocean forcing.
The East Antarctic Ice Sheet (EAIS) has several marine basins, which could be vulnerable to oceanic erosion but are currently protected by regions of ice grounded above sea level or on prograde bed slopes (Bamber et al., 2009). For the two major marine basins, Aurora and Wilkes, this “safety band” is just tens of kilometers wide (Fig S1 and S2 of (Bamber et al., 2009). In addition, the two largest ice shelves in Antarctica, the Filchner Ronne and Ross, buttress large catchments in both the WAIS and EAIS. Inclusion of enhanced calving via hydrofracture and ice cliff failure (both components that contribute to marine ice cliff instability, MICI) in numerical models can lead to a significant loss of ice from the EAIS by 2100CE under RCP8.5 conditions (DeConto and Pollard, 2016). More recently, the rate of mass loss has been revised downward using updated climate forcing and calibration data (DeConto et al., 2021). Nonetheless, significant mass loss was predicted from the EAIS over the present century for RCP8.5 and a recent study suggests that as many as 60% of Antarctic ice shelves - which buttress inland ice - are vulnerable to hydrofracture if inundated by meltwater (Lai et al., 2020).
Explaining variation between ice sheets
In a given year, under a given temperature scenario, sea level rise (SLR) from the ice sheets is simply the sum of contributions from EAIS, WAIS and GrIS:
SLR(ice sheets) = EAIS + WAIS + GrIS
A natural question is how much the uncertainty of each ice sheet contribution influences the uncertainty in enumerating SLR(ice sheets). Suppose we could observe EAIS=x. Given this information our expectation for SLR is represented as E(SLR | EAIS = x). As we let x vary over its range, E(SLR | EAIS = x) will also vary. The question is, by how much? If EAIS had no effect on SLR, then the expected SLR value would not depend on x at all and would always be equal to the unconditional expectation E(SLR). On the other hand, if E(SLR | EAIS = x) varied substantially, that would mean that the value of EAIS has a big role in determining the value of SLR. We can capture that effect by comparing the variance of E(SLR | EAIS = x) as x varies, to the unconditional variance of SLR. This ratio is called (inappropriately) the ‘correlation ratio’ (CR), though is better thought of as the fraction of variance of SLR explained by variations in EAIS:
CR (SLR, EAIS) = Var(E(SLR | EAIS = x)) / Var(SLR).
When the variation of EAIS explains all the variation in SLR, then the above ratio is one.
For contributions from the three ice sheets, EAIS, WAIS and GrIS, if their variations are independent then:
Var(SLR) = Var(EAIS) + Var(WAIS) + Var(GrIS)
and the correlation ratios sum to one.
However, if the variations in individual ice sheet contributions are positively correlated then the sum of the correlation ratios is greater than one. In this case knowing, say, that EAIS = 2m tells us something about contributions from WAIS and GrIS. The following table gives the correlation ratios calculated from the expert judgements for High and Low temperature stabilization scenarios (H, L), for 2300CE and 2100CE.
Fraction of variance of SLR explained by each ice sheet
2300H
2300L
2100H
2100L
EAIS
0.75
0.41
0.49
0.30
GrIS
0.19
0.32
0.34
0.39
WAIS
0.61
0.63
0.67
0.57
sum
1.55
1.36
1.49
1.26
We observe that in all cases the correlation ratios sum to more than one, and that exceedances are greater for High temperature stabilization scenarios. This suggests the experts jointly consider ice sheet responses could be more strongly correlated under higher temperature trajectories, and possibly become even more so further ahead into the future. For instance, there is the implication that, under the High temperature scenario, variations in EAIS contributions could be the major influence on total SLR uncertainty by 2300CE (CR 0.49 → 0.75), while the related effect of GrIS variations will be much reduced (CR 0.34 → 0.19)
We do not extend this type of analysis down to the physical ice mass processes operating at the individual ice sheets: those processes are inter-dependent, sometimes with tail correlations, and each expert assessed such dependences for themself when making judgements on ice sheet contributions. While it might be possible to decompose, expert by expert, the variance of SLR into components – expressing numerically the way these processes appear to act at each individual ice sheet – more insight is gained by examining their joint appraisal of importance rankings for these drivers (Bamber et al, 2019).
Definitions of driving processes included in the rationale questionnaire
Six ice dynamic drivers and three SMB drivers were included in the expert rationale questionnaire, designed to provide an indication of the rationales for the uncertainties for each of the three ice sheet process elicited: accumulation, A, and runoff, R, (contributing to SMB) and discharge, D, across the grounding line. In the case of the rationale questionnaire, quantile values were not elicited but instead the relative rank order of each factor in driving the change in A, R or D (Bamber et al, 2019). Here, we provide brief descriptors for these drivers
Buttressing, B:
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
0bbafafddd15-7
|
Fraction of variance of SLR explained by each ice sheet
2300H
2300L
2100H
2100L
EAIS
0.75
0.41
0.49
0.30
GrIS
0.19
0.32
0.34
0.39
WAIS
0.61
0.63
0.67
0.57
sum
1.55
1.36
1.49
1.26
We observe that in all cases the correlation ratios sum to more than one, and that exceedances are greater for High temperature stabilization scenarios. This suggests the experts jointly consider ice sheet responses could be more strongly correlated under higher temperature trajectories, and possibly become even more so further ahead into the future. For instance, there is the implication that, under the High temperature scenario, variations in EAIS contributions could be the major influence on total SLR uncertainty by 2300CE (CR 0.49 → 0.75), while the related effect of GrIS variations will be much reduced (CR 0.34 → 0.19)
We do not extend this type of analysis down to the physical ice mass processes operating at the individual ice sheets: those processes are inter-dependent, sometimes with tail correlations, and each expert assessed such dependences for themself when making judgements on ice sheet contributions. While it might be possible to decompose, expert by expert, the variance of SLR into components – expressing numerically the way these processes appear to act at each individual ice sheet – more insight is gained by examining their joint appraisal of importance rankings for these drivers (Bamber et al, 2019).
Definitions of driving processes included in the rationale questionnaire
Six ice dynamic drivers and three SMB drivers were included in the expert rationale questionnaire, designed to provide an indication of the rationales for the uncertainties for each of the three ice sheet process elicited: accumulation, A, and runoff, R, (contributing to SMB) and discharge, D, across the grounding line. In the case of the rationale questionnaire, quantile values were not elicited but instead the relative rank order of each factor in driving the change in A, R or D (Bamber et al, 2019). Here, we provide brief descriptors for these drivers
Buttressing, B:
This is the influence of back stresses on the grounded ice from floating ice shelves. Discharge is determined by the force balance acting at the grounding line. This force balance is comprised of several terms. On one side is the gravitational driving stress that results in ice flow. Opposing this are transverse stresses (TS) such as at the margins of the glacier or ice stream, basal traction (BT) and the backstress at the grounding line due to the buttressing effect of floating ice.
Basal traction, BT:
See Buttressing. BT is the resistive force between the glacier bed and the ice in contact with it. For a frozen bed, this term is not relevant but fast-moving ice at the margins of the ice sheets the bed is not frozen, water is present, and basal sliding occurs. For ice streams, as much as 90% of the ice motion can be due to basal sliding, which is controlled by BT.
Transverse stresses, TS:
See Buttressing. TS are largely determined by the large difference in ice speed between the slow-flow margins of a glacier and the fast-moving central trunk. TS act as a resistive force to ice motion and are influenced by damage characteristics of the ice, which in turn is a function of strain history and ice rheology.
Hydrofracture, HF:
HF is a process that enhances crevasse propagation on both ice shelves and grounded ice. It weakens the ice by accelerating crevasse growth via water filled crevasses. HF is a key process in the MICI as it leads to rapid ice shelf collapse, with sufficient surface melting.
Ice cliff instability, IC:
IC is linked to HF and MICI. After rapid ice shelf collapse, an ice cliff forms at the grounding line (ice above sea level). Above a critical height, this ice cliff is unstable, resulting in brittle failure (the shear stress exceeds the yield stress of ice).
Dissipation of icebergs, DI:
This is related to IC and MICI. During IC, icebergs are formed, which, depending on the geometry of the ice shelf and bathymetry beneath can accumulate in an embayment or become rafter on a sill or alternatively can be advected away from the ice edge by ocean currents.
Atmospheric moisture and circulation, AM:
In a changing climate, the predominant patterns of atmospheric circulation and strength of multi-annual oscillations such as the Pacific Decadal Oscillation or Arctic Oscillation may change affecting both the source and magnitude of precipitation regionally. Circulation changes can also influence surface ocean heat transport, which in turn can affect buttressing but here we were only concerned with its influence on SMB.
Albedo, AL:
Changes in surface AL have a large impact on the radiative energy balance of the snow or ice surface, which affects melt rates. Several factors that are currently not included in SMB models are known to influence albedo such as organic and inorganic impurities deposited or growing on the surface.
Sea ice, SI:
SI acts as a barrier to moisture and heat exchange between the atmosphere and ocean and changes in sea ice extent or concentration can, therefore, influence both of these factors locally, affecting rates of precipitation and air temperatures.
Importance of gravitational, rotational and deformation effects
Recent observations and developments in numerical modeling have suggested that gravitational, rotational and solid Earth deformation (GRD) effects on regional sea level and isostatic bedrock elevation caused by changes in ice mass loading could have a stabilising effect on, in particular, grounding line migration associated with MISI. Fig S7 shows the results of the experts’ judgement on the importance of GRD for the stability of the three ice sheets where D implies decreasing stability, I is increasing stability and N is no impact. The GrIS has limited sectors that satisfy the MISI criteria: a retrograde bed slope that is below sea level close to, or at, the present- day grounding line. Consequently, GRD effects are considered of negligible significance here. The WAIS is the ice sheet that is most susceptible to the MISI and is thus the ice sheet where GRD may act as a negative, stabilising feedback. However, only 50% of the experts consider this to be the case and recent modeling suggest the effect is, however, small (Larour et al., 2019). For the EAIS, about a third of the experts consider GRD to be of relevance and, as for the WAIS, any reduction in grounding line migration due to GRD effects is likely to be small (Larour et al., 2019). Consequently, we do not discuss GRD effects further and consider them to be of second- order importance.
Supporting Figures
Figure S1: The two temperature scenarios prescribed: L (+2° C) and H (+5° C)
Figure S2: Indicative probability distribution plots for SLR contributions by 2050CE from the three ice sheets and for three physical processes, identified on the x-axis (runoff from EAIS is omitted as this is presumed zero under either temperature rise scenario). Results are derived from expert elicitation for the 2050L (low +2°C) global temperature trajectory (left hand curves) and for the 2050H (high +5°C) global temperature trajectory (right hand curves); probability density curves are approximate and extend from values corresponding to a 99% chance of SLR being exceeded to a 1% chance of SLR being exceeded. Median values are shown by the black rectangle and the total SLR contribution from the ice sheets is shown in orange.
Figure S3: As for figure S2 but for 2300.
Figure S4: Expert judgements on the relative role of the three drivers for changes in SMB: atmospheric moisture and circulation (AM), albedo (AL) and sea ice extent (SI) for both grounded and floating ice for the Low temperature scenario.
Figure S5: Expert judgements on the relative role of the three drivers for changes in SMB: atmospheric moisture and circulation (AM), albedo (AL) and sea ice extent (SI) for both grounded and floating ice for the Low temperature scenario.
Figure S6: Expert judgements on the relative role of the two ocean processes: circumpolar deep water (CDW) and the Atlantic Meridional Overturning Circulation (AMOC) for the High temperature scenario.
Figure S7: Relative importance of GRD effects for decreasing ice stability (D), increasing it (I) or having no effect (N).
Supporting Tables
Table S1: SLR for different probabilities from 1-99.9% and at ten year increments from 2010- 2300. All values are relative to the year 2000 baseline for the High temperature scenario. Values are in cms.
Table S2: Change in process significance between Low and High temperature scenarios for ice dynamic processes.
Table S3: As for Table S1 but for SMB processes.
|
https://sealeveldocs.readthedocs.io/en/latest/bamber22.html
|
9597ccc3a71c-0
|
van de Wal et al. (2022)
Title:
A High-End Estimate of Sea Level Rise for Practitioners
Key Points:
A high-end estimate of sea level rise in 2100 and 2300
Decisionmaker/practitioner perspective on high-end
Timing of collapse of ice shelves critical
Corresponding author:
Roderik S. W. van de Wal
Citation:
van de Wal, R. S. W., Nicholls, R. J., Behar, D., McInnes, K., Stammer, D., Lowe, J. A., et al. (2022). A High‐End Estimate of Sea Level Rise for Practitioners. Earth’s Future, 10(11), e2022EF002751. doi:10.1029/2022ef002751
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF002751
Abstract
Sea level rise (SLR) is a long-lasting consequence of climate change because global anthropogenic warming takes centuries to millennia to equilibrate for the deep ocean and ice sheets. SLR projections based on climate models support policy analysis, risk assessment and adaptation planning today, despite their large uncertainties. The central range of the SLR distribution is estimated by process-based models. However, risk-averse practitioners often require information about plausible future conditions that lie in the tails of the SLR distribution, which are poorly defined by existing models. Here, a community effort combining scientists and practitioners builds on a framework of discussing physical evidence to quantify high-end global SLR for practitioners. The approach is complementary to the IPCC AR6 report and provides further physically plausible high-end scenarios. High-end estimates for the different SLR components are developed for two climate scenarios at two timescales. For global warming of +2°C in 2100 (RCP2.6/SSP1-2.6) relative to pre-industrial values our high-end global SLR estimates are up to 0.9 m in 2100 and 2.5 m in 2300. Similarly, for a (RCP8.5/SSP5-8.5), we estimate up to 1.6 m in 2100 and up to 10.4 m in 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest 2°C warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica. This is highly uncertain due to low understanding of the driving processes. Hence both process understanding and emission scenario control high-end SLR.
Plain Language Summary
Taking a co-production approach between scientists and practioners, we provide high-end sea level rise (SLR) estimates for practitioner application based on an expert evaluation of physical evidence and approaches currently used in policy environments to understand high end risk. We do this for two global warming scenarios, a modest and a strong one, for two time slices 2100 and 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica as well as how practitioners use high end projections to frame risk. We stress that both emission scenario and limited physical understanding control the outcome.
Introduction
Sea level rise (SLR) is a key aspect of climate change, with important consequences for coastal societies and low-lying areas, especially small islands, deltas, and coastal cities (Oppenheimer et al., 2019). Human interference in the climate system leads to a continuing gradual warming and expansion of ocean water (i.e., the steric effect), mass loss from glaciers and polar ice sheets. Most of these effects continue long after emissions have slowed or stopped. Climate models simulating physical processes are used to reconstruct historical sea level change (excluding the ice sheet contribution), and consequently provide a method to project SLR given specific future anthropogenic CO2 emissions and associated warming of the Earth system. Such a process-based approach provides robust estimates of changes in the central part of the SLR distribution for projections and published studies using this method are in general agreement. However, estimating the tails of the distribution, which includes the ice sheet contribution remains contentious as not all the relevant processes are sufficiently understood or represented in the models, leading to variations between projections and multiple views of how the upper tail of the SLR distribution will evolve in future.
High-end SLR projections provide information about the upper tail of the probability distribution of SLR, and are especially important for decisionmakers and practitioners (collectively referred to as practitioners) assessing long-term risks and adaptation responses. High-end projections, though by definition unlikely to occur, can provide information for adaptation planning, that is, defining a plausible “worst case” SLR to consider in an adaptation plan (Hinkel et al., 2015; Nicholls, Hanson, et al., 2021; Vogel et al., 2016). In addition, high-end estimates provide insight on potential adaptation limits, tipping points and thresholds, and the level of climate mitigation required to keep SLR adaptation manageable in the future. In this context, it is also important to consider the long-term commitment of SLR, requiring high-end projections for time horizons well beyond 2100.
We emphasize that high-end SLR information does not replace the quantification of the more likely central parts of the SLR distribution, but rather supplements these estimates. For example, a default adaptation plan may follow the median projection, with high-end estimates used to inform the development of contingency options that can be applied in the case that high-end SLR manifests. Such a planning approach is known as “adaptive planning” or “dynamic adaptive planning” in the literature (Haasnoot et al., 2013; Ranger et al., 2013). This is particularly the case when there are long lead times for action (i.e., the time to plan, design, finance, obtain support and implement the work) and long operational lives, such as for storm surge barriers or nuclear power stations, or where there is significant path-dependency for decisions (e.g., when decisions have a long legacy that may preclude future options such as choosing between protection and retreat). Therefore, a “likely” range as used by Oppenheimer et al. (2019) as the central 66% of the probability distribution is not always sufficient (Hinkel et al., 2015).
Obtaining estimates of high-end SLR can be approached in a statistical sense with probabilistic projections, as provided by Kopp et al. (2017, 2019) and Le Bars et al. (2017), but this approach may not capture possible contributions from processes not yet understood or included in climate models. To overcome this some studies define every percentile of conditional probability distributions based on an underlying assumption, such as including the Antarctic contribution from a single study (e.g., Goodwin et al., 2017). This suggests a higher confidence in the outcomes than is warranted by current physical understanding and is potentially misleading to practitioners since it does not reflect or communicate limits in our physical understanding of these processes. An alternative approach that provides estimates to address these difficulties are structured expert elicitation studies which have also been applied to provide estimates of high-end SLR (Bamber et al., 2019). They attempt to capture the uncertainty due to the lack of knowledge (Lempert et al., 2003; Oppenheimer et al., 2019) that exists in model projections without relying on models, and which is impossible to constrain using a deterministic modeling approach. This approach combines the ad hoc judgment of a group of experts. However, the considerations regarding which processes are included, and which are not, is not made explicit and the interpretation of these estimates by experts is not necessarily the same as those of uninformed practitioners because they do not know the considerations of the experts. For this reason, in this paper, we prefer to use expert judgment based on physical reasoning to arrive at estimates which cannot be constrained by deterministic modeling. This is outlined in the Greenland and Antarctic sections and provides a transparent attribution of cause and effect.
|
https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html
|
9597ccc3a71c-1
|
Obtaining estimates of high-end SLR can be approached in a statistical sense with probabilistic projections, as provided by Kopp et al. (2017, 2019) and Le Bars et al. (2017), but this approach may not capture possible contributions from processes not yet understood or included in climate models. To overcome this some studies define every percentile of conditional probability distributions based on an underlying assumption, such as including the Antarctic contribution from a single study (e.g., Goodwin et al., 2017). This suggests a higher confidence in the outcomes than is warranted by current physical understanding and is potentially misleading to practitioners since it does not reflect or communicate limits in our physical understanding of these processes. An alternative approach that provides estimates to address these difficulties are structured expert elicitation studies which have also been applied to provide estimates of high-end SLR (Bamber et al., 2019). They attempt to capture the uncertainty due to the lack of knowledge (Lempert et al., 2003; Oppenheimer et al., 2019) that exists in model projections without relying on models, and which is impossible to constrain using a deterministic modeling approach. This approach combines the ad hoc judgment of a group of experts. However, the considerations regarding which processes are included, and which are not, is not made explicit and the interpretation of these estimates by experts is not necessarily the same as those of uninformed practitioners because they do not know the considerations of the experts. For this reason, in this paper, we prefer to use expert judgment based on physical reasoning to arrive at estimates which cannot be constrained by deterministic modeling. This is outlined in the Greenland and Antarctic sections and provides a transparent attribution of cause and effect.
The approach builds on Stammer et al. (2019), where they quantify high-end SLR by synthesizing all the available physical evidence across observations, model sensitivity studies and modeled SLR scenario studies, and then assess and synthesize this information. Importantly, this approach aims to meet practitioner needs, which depend less on precise estimates of likelihood and more on evidence that is sufficiently credible, salient, and legitimate to support adaptation planning, including financing (Cash et al., 2003, 2002). “Salient” is used here in the context of relevance to practical needs. Within this framework, projections supported by multiple lines of evidence and eliciting broader confidence from the scientific community are of greater value as compared to projections further along the tail that feature fewer lines of evidence, and hence have lower confidence. This is an expansion of the approach based on building blocks (Stammer et al., 2019), in which the building blocks represent the amount of SLR beyond the likely range that practitioners will consider according to their risk-averseness, emission scenarios, and how these evolve over time. It is key that the main processes are considered explicitly. The work is based on a WCRP grand challenge workshop on this topic where a wide variety of people were invited (∼25 scientists and ∼10 practitioners) including experts on all relevant sea level components and experts on the application of SLR information. The estimates for the specific components are made by a subset of authors as outlined in the acknowledgment statement.
Because the level of understanding of each sea level component differs, we employ different methods to assess each of them separately. For example, the understanding of the thermal expansion of the ocean and the glacier-melt component is sufficient to use distributions derived from climate models directly. For those components, we assume that all necessary knowledge of the high-end is captured in the distribution. However, for the Greenland and Antarctic ice sheet components the uncertainty is much larger, as understanding of physical processes is more limited, and hence a robust and reliable probability density function does not exist. We, therefore, choose to apply a process-based expert judgment to the available lines of evidence to estimate a high-end ice sheet contribution. By following this approach we deviate from (Fox-Kemper et al., 2021), which provides a high-end scenario with and without a specific Antarctic instability mechanism and includes structured expert elicitation. Hence, we take a complementary approach where we explicitly and transparently assess the physical processes leading to a high-end estimate for Greenland and Antarctica.
The aim of this paper is to develop high-end projections that are most strongly supported by physical evidence and yet are also salient for the decision and practitioner environment. We derive new high-end estimates based on present physical understanding and demonstrate a methodological approach that may be regularly updated as the science evolves and improves, especially knowledge on ice sheets. Table S1 lists the author’s contribution by section. Throughout this paper, we follow the definition of technical terms as defined in the glossary of the IPCC AR6 report (Matthews et al., 2021).
Practitioner Perspectives on High-End Sea Level Projections
This paper explicitly considers practitioner perspectives in addition to SLR science to promote developing salient projections (e.g., Hinkel et al., 2019). Risk-averse practitioners need to consider low likelihood, high consequence SLR futures that poses challenges to adaptation, in addition to median outcomes (Fox-Kemper et al., 2021; Garner et al., 2018; Haasnoot et al., 2020; Hall et al., 2019; Hinkel et al., 2015; Nicholls, Hanson, et al., 2021). While median SLR projections have been relatively stable over time, several high-end projections have emerged, especially in recent years (e.g., DeConto & Pollard, 2016). However, these high-end projections have not been reviewed systematically from a user perspective, and most adaptation practitioners find them challenging to use, if they use them at all. Those practitioners that have applied them have had to develop their own understanding and guidance, including expertise on sea level science. This constitutes a high overhead to application when adaptation is often poorly funded.
An influential approach linking scientific exploration and decision requirements advises that scientific influence on decisions depends on the “salience, credibility, and legitimacy” of the information presented from the decision perspective (Cash et al., 2003, 2002). Of particular importance for high-end SLR projections is salience, defined as “the relevance of information for an actor’s decision choices, or for the choices that affect a given stakeholder.” In our view, salience for high-end SLR projections derives from two factors.
First, scientific information used for decision-making must consider all the major uncertainties and ambiguities across experts and models (Gold, 1993; Jones et al., 2014; Simpson et al., 2016). This requirement may be at odds with the physics-based design of SLR projections. For example, the SLR scenarios provided by IPCC AR4 did not assign values outside the central likely range as information was absent (Meehl et al., 2007). In AR5, the possibility of several tenths of a meter above the likely range was considered as a high-end possibility, reflecting rapid melting of the Antarctica and Greenland ice sheets: these processes, however were poorly understood and not captured directly in the physics-based design (Church et al., 2013). While this exclusion is explicitly stated and makes sense from a physical science perspective, practitioners may misuse the results, as they will expect/assume that IPCC SLR scenarios cover all major uncertainties. AR6 moved to an emulator approach and covered a wider range of probabilities than earlier assessments reflecting the increased understanding of key physical processes that was unavailable for earlier assessments: the central range of estimates to 2100 is similar to earlier estimates, but also addresses high-impact/low-probability outcomes (Section 5), and provides a range of values from the literature. This evolution of the IPCC reports reflect increased understanding and provides improved treatment of the risk management context for adaptation planning, but alternative interpretations as presented here are possible, thereby increasing the understanding of high-end estimates.
Second, salience requires a differentiation between scientific endeavors in general and what is sometimes called “actionable science,” which in the climate field is intended to support risk assessment and adaptation planning/investment (Bamzai et al., 2021; Beier et al., 2017; Moss et al., 2013; Vogel et al., 2016). New studies that challenge prior lines of evidence should be carefully reviewed, assessed, and debated before any application or incorporation into guidance (Nicholls, Hanson, et al., 2021). This avoids the “whiplash effect” wherein planners and all their efforts are undermined each time a new study questions their adopted projections. In this respect, we advocate this work to be used alongside (Fox-Kemper et al., 2021) rather than replacing it.
|
https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html
|
9597ccc3a71c-2
|
First, scientific information used for decision-making must consider all the major uncertainties and ambiguities across experts and models (Gold, 1993; Jones et al., 2014; Simpson et al., 2016). This requirement may be at odds with the physics-based design of SLR projections. For example, the SLR scenarios provided by IPCC AR4 did not assign values outside the central likely range as information was absent (Meehl et al., 2007). In AR5, the possibility of several tenths of a meter above the likely range was considered as a high-end possibility, reflecting rapid melting of the Antarctica and Greenland ice sheets: these processes, however were poorly understood and not captured directly in the physics-based design (Church et al., 2013). While this exclusion is explicitly stated and makes sense from a physical science perspective, practitioners may misuse the results, as they will expect/assume that IPCC SLR scenarios cover all major uncertainties. AR6 moved to an emulator approach and covered a wider range of probabilities than earlier assessments reflecting the increased understanding of key physical processes that was unavailable for earlier assessments: the central range of estimates to 2100 is similar to earlier estimates, but also addresses high-impact/low-probability outcomes (Section 5), and provides a range of values from the literature. This evolution of the IPCC reports reflect increased understanding and provides improved treatment of the risk management context for adaptation planning, but alternative interpretations as presented here are possible, thereby increasing the understanding of high-end estimates.
Second, salience requires a differentiation between scientific endeavors in general and what is sometimes called “actionable science,” which in the climate field is intended to support risk assessment and adaptation planning/investment (Bamzai et al., 2021; Beier et al., 2017; Moss et al., 2013; Vogel et al., 2016). New studies that challenge prior lines of evidence should be carefully reviewed, assessed, and debated before any application or incorporation into guidance (Nicholls, Hanson, et al., 2021). This avoids the “whiplash effect” wherein planners and all their efforts are undermined each time a new study questions their adopted projections. In this respect, we advocate this work to be used alongside (Fox-Kemper et al., 2021) rather than replacing it.
Relevant examples of high-end scenarios in planning exist in other fields. These support sound risk management, while adhering to a reasonable standard of practice to ensure appropriate resource allocation to the level of risk aversion. Accordingly, planners have found it advisable to frame high-end risk with a standard that balances risk management objectives with finite resources, avoiding large opportunity costs where possible. For example, the UK National Risk Register defines a “reasonable worst-case scenario” (RWCS) for use in planning. This is defined as “the worst plausible manifestation of that particular risk (once highly unlikely variations have been discounted) to enable relevant bodies to undertake proportionate planning” (HM Government, 2020). The RWCS “is designed to exclude theoretically possible scenarios which have so little probability of occurring that planning for them would be likely to lead to disproportionate use of resources” (Memorandum Submitted by the Government Office for Science and the Cabinet Office, 2011). The US Army Corps of Engineers selected a “maximum probable flood” for design purposes after the Great Mississippi River Flood of 1927. This is the “greatest flood having a reasonable probability of occurrence” and was preferred over a larger “maximum possible flood”, reflecting a meteorological sequence that, though reflective of historic events, was deemed highly implausible (Jadwin, 1928). This reasonableness standard has stood the test of time, including periodic review, and may be modified in the future to reflect changes to climate, land use, or other factors as appropriate.
For SLR, an example of a salient approach is The Thames Estuary Plan (TE2100), which addresses management of future coastal flood risk for London, UK. It was one of the first long-term adaptation plans to address deep uncertainty (sometimes popularized as the unknown unknowns) with consideration of both more likely and high-end SLR (Ranger et al., 2013). The term “H++” was created by TE2100 to describe a highly unlikely but possible high-end range of SLR. While most attention is focused on the definite upper bound, the high-end represents a range of values. H++ was designed to support a “dynamic robustness” planning approach that allows for consideration of a wide range of adaptation options as SLR observations and science develop over time (Ranger et al., 2013). This approach examines which extreme adaptation options should be kept open, whilst actively planning for smaller more likely SLR estimates and regularly reviewing the observed rates of SLR and the robustness of SLR projections. In TE2100, an upper-end SLR exceeding 4.2 m in 2100 was initially adopted for planning. This includes a strom surge component which is not expected to change greatly in future. In 2009, after consideration of emerging science and observations, especially Greenland and West Antarctica, the 2100 upper-end SLR projection was revised downwards to 2.7 m, of which 2 m is the time-mean SLR (Lowe et al., 2009). This revised value is still used in practice today (Environmental Agency Guidance, 2021; Palmer et al., 2018). Hence, TE2100 demonstrates an adaptive process of science evaluation and revision of a salient high-end scenario for adaptation planning. This inspires the estimates in this paper.
How We Develop a High-End Estimate
To avoid overreliance on single studies, for example, as illustrated in the (Griggs, 2017) approach, we consider SLR-related processes that are ideally supported by multiple lines of independent evidence. Our approach to construct high-end SLR estimates uses information on SLR components that meet the following three requirements: (a) there is sufficient physical understanding of the relevant processes involved; (b) this understanding can be linked to a quantitative estimate of the associated SLR; (c) there is evidence to explain why the estimates we produce are expected to be in the upper tail of the range of responses. For SLR components where robust distributions are available, two times the standard deviation is warranted in view of the need to sample in the tail. For some components there is sufficient quantitative understanding to use the tail of a probability density function derived from physical models, but not for all components. In particular, the mean and variance of the ice sheet components are poorly constrained, and they cannot be derived directly from climate models. This continues to complicate development of a high-end estimate.
Additionally, the covariance between sea level components is largely unknown because only the ocean component of SLR is directly derived from a large ensemble of climate models in which the relevant processes are coupled. The other sea level components are calculated off-line from climate and land-ice models, and hence require ad-hoc assumptions about the co-variance between components (Lambert et al., 2021), similar to what has been done in Fox-Kemper et al. (2021) or via a covariance controlled by temperature changes (Palmer et al., 2020). To address this problem, we provide a range of high-end values based on the assumption that the different components (glaciers, Greenland, Antarctica, steric expansion, land water storage change [LWSC]) are fully dependent (covariances all equal to 1, maximizing the uncertainty, and hence the upper end of the range) or fully independent (covariance all equal to 0, minimizing the uncertainty, providing a lower end of the range). At present, this is the only fully transparent way to consider the co-variance between for instance the Greenland and Antarctic component. Additionally, it spans the full range of possible outcomes. However, it is unlikely that the complexity of processes involved, and the climate change patterns themselves are fully correlated or fully independent. To illustrate this one can think of the importance of atmospheric circulation changes and basal melt to high end. The first process is important in Greenland and the second in Antarctica. To what end both will change in a similar way is not known, hence full dependency is unlikely. At the same time global warming plays a role in both processes, hence fully independency is also unlikely.
For this reason, practitioners can decide whether to treat the uncertainties as fully independent, fully dependent, or in between depending on their level of risk-averseness. For the independent case (all co-variances zero), we take the median values of AR6 for the different components and define the high-end to be characterized by two standard deviations above the median value. For the dependent case we can simply add the estimates of the different components.
The problem of estimating high-end values for SLR is therefore not only about constraining the uncertainty in the component with the largest uncertainty, but also about understanding how the uncertainty in the SLR components are correlated with each other. The first problem is due to insufficient process understanding of the dynamics of the Antarctic ice sheet. The second problem is due to the surface mass balance (SMB) of the Greenland ice sheet, which requires Earth system models with fully coupled interactive ice sheets models to solve.
|
https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.