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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.
Here, we restrict ourselves to two time slices (2100 and 2300) and two climate scenarios (RCP2.6/SSP1-2.6 and RCP8.5/SSP5-8.5) which we call for simplicity the low and high scenario. The detailed physical reasoning behind the estimates of the individual cryospheric components is discussed in detail in Section 4 (Glaciers), Section 5 (Greenland), and Section 6 (Antarctica). Section 7 combines the storylines for the different SLR components in an estimate of the high-end global mean SLR for the four scenarios being 2100 and 2300 low and high-temperature change. We focus on the year 2100 because there is significantly more information available for this time horizon than for any other date in time. Moreover, the physical understanding decreases significantly after this time horizon. We focus on 2300 to highlight the long time-scales involved for SLR, the necessity for adaptation and the benefits of mitigation. The scenarios rely strongly on the well-known representative concentration pathways of RCP2.6/SSP1-2.6, which has a median response at 2100 of just under 2°C, and RCP8.5/SSP5-8.5 which has a median around 5°C in 2100 and 8°C–10°C in 2300. These correspond loosely to the core goal of the Paris Agreement and unmitigated emissions, respectively, and provide a significant range in future conditions. We limit our analyses to these scenarios because current understanding of the Antarctic response is not precise enough to distinguish intermediate scenarios between RCP2.6/SSP1-2.6 and RCP8.5/SSP5-8.5, as discussed in Section 7 in more detail. For each of the four scenarios, we provide a range in the high-end estimate of SLR constraint by the dependent or independent addition of the different components.
The method provides estimates of the high-end of projected global sea level change, and does not include the wide range of processes that contribute to regional sea level variations, nor does it consider regional and local vertical land motion, needed to determine the relative sea level changes at a particular coastal location, and that lead to changes in the frequency and magnitude of extreme sea level events at all time scales. Additionally, practitioners need to consider for example, bathymetric effects, possible changes in tides or surges and other near coastal processes. All these local effects and the possible changes therein need to be assessed separately, in particular human-induced subsidence (Nicholls, Lincke, et al., 2021). We in effect assume that the global terms contribute significantly to the uncertainty in local SLR at most locations, but the local terms in the uncertainty budget vary in importance with location. Hence we focus on what is common to all locations. A simple additional step that practitioners could take is to realize that a large Antarctic contribution will influence regional sea level with higher values far from Antarctica due to gravitational effects. Operational tools to include this effect and all the other local to regional processes already exist and are applicable to any global scenario.
Glaciers
In this section, we detail the physical reasoning behind the estimates of the individual cryospheric components starting with glaciers (Section 4, Greenland Section 5 and Antarctica Section 6), as they do not immediately follow from the IPCC model ensemble results. Sections 4–6, 4–6, 4–6 have a similar structure starting with the processes which are relevant and ending with an evaluation of the high-end contribution of the specific component. They each have a figure illustrating how the relevant processes contribute to high-end SLR. The critical processes are eventually per cryospheric component summarized in Table 1 for each scenario.
Table 1: Overview of Ciritical Processes for High-End Estimate of the Cryospheric Components of Sea Level Rise Per Time Scale and Scenario
2100-low
2100-high
2300-low
2300-high
Glaciers
Temperature increase
Temperature increase
Temperature increase, glacier
mass equilibrium
Temperature increase, amount of glacier ice
Greenland
Temperature increase,
outlet glacier
acceleration
Temperature increase,
albedo feedbacks,
atmospheric
circulation changes
Temperature increase
Temperature increase, albedo feedbacks,
atmospheric circulation changes, tipping points
Antarctica
SMB, BMB, switch in
flow below shelves
SMB, shelf collapse,
BMB, calving,
hydrofracturing
SMB, shelf collapse, BMB,
calving, hydrofracturing
MISI, MICI, basal sliding
The Glacier Model Intercomparison Project Phase 2 (GlacierMIP2; Marzeion et al., 2020), is a community effort based on CMIP5 model runs estimating the mass loss of global glaciers. It includes 11 different glacier models, of which seven include all the glaciers outside of Greenland and Antarctica, and four are regional. The glacier models are forced by up to 10 General Circulation Models (GCMs) per RCP scenario, such that a total of 288 ensemble members form the basis of this most recent estimate of glacier mass change projections for the 21st century. Compared to this, projections that include the 23rd century are sparse and based on individual models (e.g., Goelzer et al., 2012; Marzeion et al., 2012). Some information about long-term glacier mass change can be obtained from equilibrium experiments (e.g., Levermann et al., 2013; Marzeion et al., 2018).
Processes for Glaciers Relevant for High-End SLR Scenarios
Temperature changes are critical to calculate glacier volume changes. Through the spatial distribution of glaciers on the land surface and a strong bias to Arctic latitudes, glaciers experience roughly twice the temperature anomalies of the global mean (Marzeion et al., 2020). Biases of projected spatial patterns of temperature increase, particularly concerning Arctic Amplification (stronger temperature change at high latitude), thus have the potential to impact projected glacier mass loss. However, we assume that the GCM ensemble size of GlacierMIP2 is large enough to adequately represent this uncertainty.
Other processes which may play a role are related to debris cover and ice-ocean interaction. Only one of the glacier models taking part in GlacierMIP2 includes a parameterization of frontal ablation/calving (Huss & Hock, 2015), such that there is potential for underestimation of mass loss in the GlacierMIP2 ensemble as important ice-ocean interaction processes are not represented. However, frontal ablation and calving will most strongly affect mass loss of ice currently below mean sea level (Farinotti et al., 2019), and hence they will contribute relatively little to SLR since that constitutes only 15% of the total glacier mass. Additionally, the mass loss projected in GlacierMIP2 for 2100 under RCP2.6/SSP1-2.6 indicates that the number of tidewater glaciers will be greatly reduced even under low emissions and will retreat from contact with the ocean. Thus, ice-ocean interaction may have strong effects on the timing of mass loss within the 21st century, but this is unlikely to play a large role at the end of the 21st century or later, and for greater temperature increases.
None of the global models and only one of the regional models in GlacierMIP2 (Kraaijenbrink et al., 2017) includes effects of debris cover on glacier mass balance. Strong surface mass loss has the potential to cause the surface accumulation of debris layers (e.g., Kirkbride & Deline, 2013) thick enough to insulate the ice below it, thus reducing melt rates (e.g., Nicholson & Benn, 2006). At the same time, a thin debris cover layer could enhance melt rates. The lack of representation of debris cover in GlacierMIP2 is estimated to be unlikely to have a significant impact on the considered high-end range of projections.
Evaluation of the High-End Contribution for Glaciers
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Other processes which may play a role are related to debris cover and ice-ocean interaction. Only one of the glacier models taking part in GlacierMIP2 includes a parameterization of frontal ablation/calving (Huss & Hock, 2015), such that there is potential for underestimation of mass loss in the GlacierMIP2 ensemble as important ice-ocean interaction processes are not represented. However, frontal ablation and calving will most strongly affect mass loss of ice currently below mean sea level (Farinotti et al., 2019), and hence they will contribute relatively little to SLR since that constitutes only 15% of the total glacier mass. Additionally, the mass loss projected in GlacierMIP2 for 2100 under RCP2.6/SSP1-2.6 indicates that the number of tidewater glaciers will be greatly reduced even under low emissions and will retreat from contact with the ocean. Thus, ice-ocean interaction may have strong effects on the timing of mass loss within the 21st century, but this is unlikely to play a large role at the end of the 21st century or later, and for greater temperature increases.
None of the global models and only one of the regional models in GlacierMIP2 (Kraaijenbrink et al., 2017) includes effects of debris cover on glacier mass balance. Strong surface mass loss has the potential to cause the surface accumulation of debris layers (e.g., Kirkbride & Deline, 2013) thick enough to insulate the ice below it, thus reducing melt rates (e.g., Nicholson & Benn, 2006). At the same time, a thin debris cover layer could enhance melt rates. The lack of representation of debris cover in GlacierMIP2 is estimated to be unlikely to have a significant impact on the considered high-end range of projections.
Evaluation of the High-End Contribution for Glaciers
Glaciers store less than 1% of the global ice mass (Farinotti et al., 2019), and contributed 0.7 mm/yr over the period 2010–2018 (Hugonnet et al., 2021). Their potential to contribute to SLR is thus limited by their total mass, and which is estimated to be 0.32 ± 0.08 m SLE (Farinotti et al., 2019). However, this limit does not affect their contribution within the 21st century: even under RCP8.5/SSP5-8.5, GlacierMIP2 projects that 64% ± 20% of the glacier mass will remain by 2100. At the same time, the GlacierMIP2 projections show that the glacier contribution strongly depends on the temperature increase itself and less on precipitation changes, both affecting the SMB (Figure 1). This temperature increase is reasonably constrained by the large set of CMIP model ensemble and shows a Gaussian distribution.
Figure 1: Causal relation between processes leading to a high-end contribution of Glaciers to sea level rise (SLR). Climate forcing leads to patterns of temperature (ΔT) and precipitation (ΔP) change over the globe (colored stripes global mean change). These local climate variables control the surface mass balance (SMB) and thereby the volume change of glaciers which determines the SLR by the glacier component. Ice dynamics are usually highly simplified in glacier models and therefore omitted here.
Hence, both climate and appropriate physical processes are captured in the GlacierMIP2 projections and therefore a high-end estimate for glaciers is based on the mean and twice the standard deviation of the GlacierMIP2 experiment as outlined in our definition of a high-end estimate in Section 3. Table 1 and Figure 1 illustrate the critical processes required for a high-end estimate of the glacier contribution. Similar tables and figures are presented in the later ice Sections to demonstrate and contrast the different processes for the different cryospheric components. Table 3 provides the references to the papers from which we derived the actual values to estimate the high-end range. Our final high-end values for the glaciers are based on the GlacierMIP2 result: 0.079 ± 0.056 m of ice volume change under RCP2.6/SSP1-2.6 and 0.159 ± 0.086 m under RCP8.5/SSP5-8.5 in 2100. We convert these to sea level equivalents by correcting for the fact that approximately 15% of the glacier volume is below sea level and arrive at a high-end estimate of 0.15 m sea level equivalents under RCP2.6/SSP1-2.6 and 0.27 m under RCP8.5/SSP5-8.5 (being the mean plus twice the standard deviation). By 2300, glaciers might approach stabilization under RCP2.6/SSP1-2.6 after having contributed 0.28 m to SLR (Cazenave et al., 2018). Their contribution would be limited by their current ice mass above flotation of 0.32 ± 0.08 m (Farinotti et al., 2019), for higher emission scenarios, which is then by definition the highest contribution possible.
Table 3: summarizes all the references used for the different high-end estimates of all the components and provides a comparison to the results of Fox-Kemper et al. (2021).
Greenland
Currently, substantial ice mass loss is observed in Greenland (Bamber et al., 2018; Cazenave et al., 2018; A. Shepherd et al., 2020) with a rate over the period 2010–2019 equivalent to 0.7 mm/yr Global Mean Sea Level Rise (GMSLR; Fox-Kemper et al., 2021). This is to a large extent driven by a change in the SMB, but also by increased dynamic loss of ice via marine-terminating outlet glaciers (Csatho et al., 2014; Enderlin et al., 2014; King et al., 2020; Van Den Broeke, 2016).
Processes
For the 21st century outlet glaciers remain important (Choi et al., 2021; Wood et al., 2021), but for longer time scales changes in SMB are expected to dominate mass loss from the Greenland ice sheet, in particular for high-emission forcing, as some marine-terminating outlet glaciers begin to retreat onto land (e.g., Fürst et al., 2015). Since the IPCC AR5 report, several new studies with projections for Greenland up to 2100 have been published that were broadly consistent with the AR5 (e.g., Calov et al., 2018; Fürst et al., 2015; Golledge et al., 2019; Vizcaino et al., 2015). More recent studies, as also reported by Fox-Kemper et al. (2021), however, have obtained significantly larger mass loss rates with values of up to 33 cm by 2100 (Aschwanden et al., 2019; Hofer et al., 2020; Payne et al., 2021). This can be explained by a larger sensitivity used for converting air temperature to melt, and averaging of the forcing over a large domain and applying a spatially constant scalar anomaly, an approach that has been disputed (Fürst et al., 2015; Gregory & Huybrechts, 2006; Van De Wal, 2001).
The Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) ensemble mean results indicated a contribution of 0.096 ± 0.052 m for RCP8.5/SSP5-8.5 in 2100 for a representative range of CMIP5 GCMs (Goelzer et al., 2020), where an unaccounted contribution for committed sea level of 6 ± 2 mm is additionally added (Goelzer et al., 2020; Price et al., 2011). However, recent results with CMIP6 forcing show a larger range with one model suggesting a contribution of 256 mm (Hofer et al., 2020; Payne et al., 2021). These results were obtained with a limited number of CMIP6 models, some of which are known to exhibit a large climate sensitivity and therefore may be biased high. The ISMIP6 results based on CMIP5 therefore provide a reasonable estimate of the uncertainty caused by GCMs, but they do not include an estimate of the uncertainty due to the more detailed and accurate Regional Climate Models (RCMs), which are forced by GCMs to arrive at detailed mass balance changes. ISMIP6 results are based on only one RCM used for downscaling the GCM results to SMB changes.
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The Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) ensemble mean results indicated a contribution of 0.096 ± 0.052 m for RCP8.5/SSP5-8.5 in 2100 for a representative range of CMIP5 GCMs (Goelzer et al., 2020), where an unaccounted contribution for committed sea level of 6 ± 2 mm is additionally added (Goelzer et al., 2020; Price et al., 2011). However, recent results with CMIP6 forcing show a larger range with one model suggesting a contribution of 256 mm (Hofer et al., 2020; Payne et al., 2021). These results were obtained with a limited number of CMIP6 models, some of which are known to exhibit a large climate sensitivity and therefore may be biased high. The ISMIP6 results based on CMIP5 therefore provide a reasonable estimate of the uncertainty caused by GCMs, but they do not include an estimate of the uncertainty due to the more detailed and accurate Regional Climate Models (RCMs), which are forced by GCMs to arrive at detailed mass balance changes. ISMIP6 results are based on only one RCM used for downscaling the GCM results to SMB changes.
Uncertainties in modeling SMB have been further addressed using a common historical forcing (1980–2012) and comparing the output of 13 different SMB models for the Greenland ice sheet (Fettweis et al., 2020). They found that the ensemble mean produced the best estimate of SMB compared to observations, but the difference in surface melting between models was as much as a factor 3 (from 134 to 508 Gt/yr) and the trend in runoff also differed by a similar amount (from 4.0 to 13.4 Gt/yr/yr) for the common period 1980–2012. Combining the uncertainties in modeling SMB with those for the projected climate forcing indicates that the SMB component is poorly constrained and has large uncertainties, despite having dominated recent mass loss trends in Greenland (Van Den Broeke, 2016).
Further uncertainties in projections for the Greenland ice sheet related to specific processes include: (a) the importance of firn saturation which buffers meltwater prior to run off, (b) albedo lowering by darkening of the surface caused by dust or algal growth, (c) the strength of melt-albedo and height-SMB feedback mechanisms, both leading to additional mass loss, and (d) calving, all being processes that are poorly constrained and often not included in SMB models. Considering these processes has the potential to increase the contribution of Greenland and widen the uncertainty distribution. Furthermore, it is known that the current generation of GCMs do not capture recently observed atmospheric circulation changes (Delhasse et al., 2018, 2020; Fettweis et al., 2017; Hanna et al., 2018), and it is not yet clear whether these changes are forced by climate change or natural variability. Delhasse et al. (2018) estimated that Greenland atmospheric blocking, leading to persistence of enhanced warm air advection from the South and changes in cloudiness (Hofer et al., 2019), may lead to a doubling of mass loss due to SMB changes over the 21st century. This is an estimate for 2040–2050 which does not capture the positive albedo feedback arising from an expanding ablation zone, so we consider the doubling of the mass loss due to SMB changed caused on circulation changes as a lower bound of this effect. In all these studies, projections are made based by stand-alone climate models, lacking many of the feedbacks discussed above (Fyke et al., 2018).
In contrast to the Antarctic ice sheet (discussed in the next Section), only a limited contribution of the dynamics of the outlet glaciers is to be expected (Fürst et al., 2015; Goelzer et al., 2020; Nick et al., 2013), This is because they occupy only a small fraction of the ice sheet perimeter, whereas in Antarctica the majority of the perimeter is in direct contact with the ocean.
Paleo-simulations may be important for constraining near-future mass loss from the Antarctic ice sheet, but provide few constraints for the Greenland ice sheet for the future transient nature of high-end ice mass loss estimates on century time scales. They merely offer insight about sea level high stands during characteristic warm periods in the past.
Evaluation of the High-End Contribution for Greenland
Critically important for generating a high-end estimate for the Greenland ice sheet is the SMB as expressed in Figure 2. SMB and ocean changes are the driver for changes in outlet glaciers and ice sheet dynamics. While SMB and outlet glacier changes have contributed to observed SLR changes, SMB changes are expected to become more important on longer time scales and with stronger forcing. Changes in ice sheet dynamics are expected to be limited. For a high-end estimate of the Greenland ice sheet there is most likely a strong divergence between the low warming and the high warming scenario, particularly beyond 2100. A recent study (Noël et al., 2021), based on a regional climate model forced with a GCM, indicates that the SMB over the ice sheet is negative for a global warming above 2.7 K for a constant topography, ignoring elevation-change-related feedbacks. If so, no processes adding mass to the ice sheet will exist and this has been argued to be a “tipping-point” for the ice sheet. On the other hand, this is challenged by studies including dynamical changes of the topography (Gregory et al., 2020; Le clec’h et al., 2019) because the ice sheet may evolve to a smaller equilibrium state. The importance of the existence of a tipping-point is merely on the millennial time scales, but a negative SMB at least suggests a strong nonlinear response to a large climate forcing. Table 1 illustrates the critical processes to consider when estimating a high-end contribution for the Greenland ice sheet. For the 21st century, we estimate the high-end estimate for the +5°C scenario to be around 0.30 m, being twice the ISMIP6 results (Goelzer et al., 2020) where the factor two arises from the possible atmospheric circulation changes (Church et al., 2013; Delhasse et al., 2018, 2020) that are not captured in the models. This factor of two should be interpreted as the deep uncertainty around the SMB changes in a changing climate caused by a poor understanding of modeling circulation changes and surface processes affecting the albedo. At this point, our approach deviates from Fox-Kemper et al. (2021) who use expert judgment as part of their lines of evidence.
Figure 2: Causal relation between processes leading to a high-end contribution of Greenland to sea level rise (SLR). Critical processes are albedo, ocean forcing and atmospheric circulation changes. These three processes impact the surface mass balance (SMB). Outlet glaciers change by changes in SMB and ocean forcing and SMB also influences the dynamics of the main ice sheet, where the ocean affects the outlet glaciers, together controlling the SLR.
For a +2°C scenario there seem to be few processes that can be large, hence we use the upper end of the very likely range assessed by AR6 being 0.10 m as the high-end estimate (Fox-Kemper et al., 2021). The omission of feedbacks and circulation changes are judged to only be important for large perturbations, justifying excluding them for a high-end estimate. Consequently, high-end projections in 2300 for a +2°C scenario are still constrained and estimated to be 0.3 m, as the SMB is the main driving process. The few studies, based on intermediate complexity climate models (Table 13.8, Church et al., 2013) suggest a high-end contribution of 1.2 m in 2300 from the Greenland ice sheet under a high scenario. A more recent but similar result is obtained using an intermediate complexity model coupled to an ice sheet model (Van Breedam et al., 2020). Here, we suggest, following the projections in 2100, to include a factor 2 based on the possible atmospheric circulation changes above, as the deep uncertainty in the SMB, thereby arriving at a high-end estimate of 2.5 m for Greenland under a +8°C–10°C scenario in 2300. This is close to the structured expert judgment by Bamber et al. (2019), but higher than the experiment by Aschwanden where the degree-day factors are constrained by the observational period 2000–2015 (Fox-Kemper et al., 2021).
Antarctica
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Figure 2: Causal relation between processes leading to a high-end contribution of Greenland to sea level rise (SLR). Critical processes are albedo, ocean forcing and atmospheric circulation changes. These three processes impact the surface mass balance (SMB). Outlet glaciers change by changes in SMB and ocean forcing and SMB also influences the dynamics of the main ice sheet, where the ocean affects the outlet glaciers, together controlling the SLR.
For a +2°C scenario there seem to be few processes that can be large, hence we use the upper end of the very likely range assessed by AR6 being 0.10 m as the high-end estimate (Fox-Kemper et al., 2021). The omission of feedbacks and circulation changes are judged to only be important for large perturbations, justifying excluding them for a high-end estimate. Consequently, high-end projections in 2300 for a +2°C scenario are still constrained and estimated to be 0.3 m, as the SMB is the main driving process. The few studies, based on intermediate complexity climate models (Table 13.8, Church et al., 2013) suggest a high-end contribution of 1.2 m in 2300 from the Greenland ice sheet under a high scenario. A more recent but similar result is obtained using an intermediate complexity model coupled to an ice sheet model (Van Breedam et al., 2020). Here, we suggest, following the projections in 2100, to include a factor 2 based on the possible atmospheric circulation changes above, as the deep uncertainty in the SMB, thereby arriving at a high-end estimate of 2.5 m for Greenland under a +8°C–10°C scenario in 2300. This is close to the structured expert judgment by Bamber et al. (2019), but higher than the experiment by Aschwanden where the degree-day factors are constrained by the observational period 2000–2015 (Fox-Kemper et al., 2021).
Antarctica
Currently significant ice mass loss is observed in West-Antarctica (Bamber et al., 2018; Cazenave et al., 2018; Rignot et al., 2019; A. Shepherd et al., 2018): over the period 2010–2019 Antarctica contributed 0.4 mm/yr to GMSL rise (Fox-Kemper et al., 2021). Most studies indicate that ice loss in West Antarctica follows from increased rates of sub-ice shelf melting caused by ocean circulation changes, in particular in the Amundsen Sea sector (Adusumilli et al., 2018; Paolo et al., 2015), but it is questioned whether this is the result of anthropogenic climate change or natural variability in the ocean as suggested by Jenkins et al. (2018) or by a combination of both processes (Holland et al., 2019). Against this background, it is important to consider which processes may lead to substantial continued or accelerated mass loss from Antarctica, and therefore its contribution to high-end sea level scenarios. In addition, it needs to be considered whether there are instabilities in the system which influence high-end estimates. We explore this in more detail than for the previous two components because of the large uncertainty and the large potential contribution to SLR from Antarctica.
Processes in Antarctica Relevant for High-End Sea Level Scenarios
A major uncertainty in future Antarctic mass losses resulting in high-end SLR is connected to the possibility of rapid and/or irreversible ice losses through instabilities in marine-based parts of the ice sheet, as hypothesized for the Marine Ice Sheet Instability (MISI) and the Marine Ice Cliff Instability (MICI), see Pattyn et al. (2018) for further explanation. MISI is a self-reinforcing mechanism within marine ice sheets that lie on a bed that slopes down towards the interior of the ice sheet. If these instabilities are activated it might be that they overshadow climate forcing scenarios. At present, floating ice shelves exert back stress on the inland ice, limiting the flow of ice off the continent and resulting in a stable ice sheet configuration. In the absence of ice-shelf buttressing caused by loss of the shelf or substantial thinning, ice sheets on a bed sloping towards the interior are, under certain circumstances, inherently unstable (Schoof, 2007; Sergienko & Wingham, 2019, 2021), and stable grounding line positions can only be reached when the bed slopes in the opposite direction (sloping bed upwards to the interior; Pattyn et al., 2012). If ice shelf buttressing remains, however, stable grounding line positions can also be reached on downward sloping beds for specific geometric configurations (Cornford et al., 2020; Gudmundsson et al., 2012; Haseloff & Sergienko, 2018; Sergienko & Wingham, 2019). Weak buttressing may not prevent grounding-line retreat, but may slow it.
Antarctic ice shelves modulate the grounded ice flow, and their thinning and weakening is crucial in the timing and magnitude of major ice mass loss or the onset of MISI. This onset of rapid MISI is controlled by the timing of ice shelf breakup or collapse, and the resulting loss of buttressing that otherwise would prevent MISI from occurring. Ice sheet models demonstrate that the permanent removal of all Antarctic ice shelves leads to MISI, West Antarctic ice sheet collapse, and 2–5 m SLR over several centuries (Sun et al., 2020).
The MICI hypothesis of rapid, unmitigated calving of thick ice margins triggered by ice shelf collapse has been included in an ice sheet model by DeConto and Pollard (2016); DeConto et al. (2021) and Pollard et al. (2015). Including the MICI processes was partly motivated by inconsistencies with reconstructed paleo sea level proxies (Bertram et al., 2018; DeConto & Pollard, 2016), but also has a sound physical process based support (Bassis et al., 2021; Crawford et al., 2021). Like MISI, the onset of MICI is triggered by the loss of buttressing ice shelves facilitating the creation of ice cliffs which subsequently destabilize. Its onset also depends on the magnitude of ocean and atmospheric warming. A major difference is the more rapid calving of the ice cliffs at the front of the ice sheet inducing a faster retreat.
Importantly, without the disintegration of buttressing ice shelves, neither MISI nor MICI can operate and the dynamic mass loss contribution from Antarctica to SLR is limited. The current atmospheric state is too cold for a large contribution from surface melt. Further, a few degrees of Antarctic warming leads to more snow accumulation, partly offsetting the increases in oceanic melt and the resulting loss of ice by changes in the ice flow (Seroussi et al., 2020). However, the possibility of larger changes induced by ocean processes cannot be excluded. It has been argued that, in particular, the waters below the Filchner-Ronne ice-shelf could warm by more than 2°C as a result of changes in ocean circulation (Hellmer et al., 2012). Both observations (Darelius et al., 2016; Ryan et al., 2020) and models (Hazel & Stewart, 2020; Naughten et al., 2017) support this as a possibility, although a recent study (Naughten et al., 2021) suggests that such a change in circulation may be unlikely under the climate scenarios considered here for the 21st century. The LARMIP experiments (Levermann et al., 2020) provide an indication that the impact of such a change could be on the order of 0.2 m global mean SLR by 2100.
Observations of basal melt are hampered by the inaccessibility of the sub-ice-shelf cavities, and modeling of basal melt is challenging both because of the lack of observational validation and the limited resolution of the cavities that is possible in models covering continental scales. To date, most ocean model components within coupled climate models do not include the regions beneath the ice shelves. Simplified parameterizations of sub-shelf cavity circulation have been developed, such as the PICO-model (Reese et al., 2018), or the cross-sectional plume model (Lazeroms et al., 2018, 2019; Pelle et al., 2019). Alternatively (Jourdain et al., 2020), propose a parameterization of sub-shelf melt based on the use of low-resolution CMIP5 ocean models, calibrated to observed melt rates (see also Favier et al., 2019). Rather than attempting to explicitly resolve the sub-shelf circulation (Levermann et al., 2020), estimated the Antarctic contribution based on low-resolution ocean temperature change with a linear response function capturing all the uncertainties. This approach ignores dampening or self-amplifying processes and concentrates on the forced response but includes a dynamical response of the ice sheet itself.
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Observations of basal melt are hampered by the inaccessibility of the sub-ice-shelf cavities, and modeling of basal melt is challenging both because of the lack of observational validation and the limited resolution of the cavities that is possible in models covering continental scales. To date, most ocean model components within coupled climate models do not include the regions beneath the ice shelves. Simplified parameterizations of sub-shelf cavity circulation have been developed, such as the PICO-model (Reese et al., 2018), or the cross-sectional plume model (Lazeroms et al., 2018, 2019; Pelle et al., 2019). Alternatively (Jourdain et al., 2020), propose a parameterization of sub-shelf melt based on the use of low-resolution CMIP5 ocean models, calibrated to observed melt rates (see also Favier et al., 2019). Rather than attempting to explicitly resolve the sub-shelf circulation (Levermann et al., 2020), estimated the Antarctic contribution based on low-resolution ocean temperature change with a linear response function capturing all the uncertainties. This approach ignores dampening or self-amplifying processes and concentrates on the forced response but includes a dynamical response of the ice sheet itself.
Ideally, sub-shelf circulation and ocean melt should be represented in three dimensions, at the high spatial resolution, and interactively coupled with the ice sheet and the ocean models (Comeau et al., 2022; Smith et al., 2021). This represents a significant ongoing modeling challenge (e.g., Van Westen & Dijkstra, 2021), together with uncertainties in the bathymetry, limiting confidence in future projections of ice shelf loss.
It is also critical to consider other processes than basal melt or circulation changes that can lead to disintegration of the major ice shelves. In particular, one needs to consider calving and surface melt that can enhance ice shelf surface crevassing and hydrofracturing. While hydrofracturing is an important process to reduce or eliminate buttressing and facilitate ice sheet instability, fracturing without surface melt also weakens the ice shelves, particularly along their margins. This is observed in the Amundsen Sea region (Lhermitte et al., 2020), but is not yet fully implemented and validated in large-scale ice sheet models, hindering an estimate of the timing of ice shelf collapse.
As the pace of future atmospheric warming and the capacity of firn to absorb melt water remain uncertain, predictions of ice shelf surface melting by 2100 and subsequent ice shelf disintegration under RCP8.5/SSP5-8.5 vary widely. Based on a regional climate model (Trusel et al., 2015), compiled melt rates under warming scenarios. Under RCP8.5/SSP5-8.5, several small ice shelves will be exposed by 2100 to melt rates exceeding the values observed at the time that the Larsen-B ice-shelf broke up in 2002. However, the major ice shelves (e.g., Filchner-Ronne, Ross Amery) remain stable over this century, but likely not over longer time scales. These melt rates contrast with the results of independent simulations using simpler climate models and a different scheme to calculate surface melt (DeConto & Pollard, 2016) that suggest a much faster disintegration of the ice shelves. An updated assessment (DeConto et al., 2021) confirms the ice shelf stability for this century, but also shows a rapid disintegration soon after under RCP8.5/SSP5-8.5. An intercomparison study showed that the increased melt is partly compensated by increased accumulation (Seroussi et al., 2020), regardless of the emissions scenario followed. It shows disintegration of some small ice shelves, but not the big shelves which constrain high-end contributions to 2100. Soon after 2100, this is likely not the case any longer under RCP8.5/SSP5-8.5. So this facilitates the construction of high-end estimates for 2100 and 2300. For 2100, we can assume that the consequence in terms of SLR is not yet visible, but for 2300 we can be sure that the ice sheet has had sufficient time to start reacting to the break-up of ice shelves under strong forcing scenarios.
What If the Major Ice Shelves Break Up?
Both MISI and MICI might be important for SLR if and when ice shelves collapse. Ice-shelf collapse, therefore, can be considered the key prerequisite for these instabilities to commence. By “instability” we imply that, once initiated, the process of retreat continues irrespective of the applied climate forcing. MISI is a dynamic response of the ice sheet to a change in the buttressing conditions, whereas MICI might lead to direct mass loss via tall collapsing cliffs, which also may be a self-sustaining process. Research on MICI has focused on the critical height at which vertical ice cliffs become unstable (Bassis & Walker, 2012; Clerc et al., 2019; Parizek et al., 2019) and plausible rates of calving and retreat (Schlemm & Levermann, 2019). Estimates of ice-cliff calving have also used observations of calving ice-fronts in Greenland as a constraint (e.g., DeConto & Pollard, 2016), although Greenland glaciers might not be representative of the behavior of wider and thicker outlet glaciers in Antarctica that have lost their ice shelves. The importance of the ice cliff calving mechanism, while likely relevant to high-end sea level scenarios if ice shelves are lost, is currently disputed in the literature (Fox-Kemper et al., 2021).
A second major uncertainty in the response of ice margins once shelves are lost is the uncertainty about the physics of the basal friction conditions near the grounding line, which could further enhance seaward ice flow (Pattyn et al., 2018; Tsai et al., 2015). As a result, the few existing ice model projections for 2300 vary considerably (Bulthuis et al., 2019; Golledge et al., 2015; Levermann et al., 2020), but should all be considered physically plausible and thereby provide independent lines of evidence for a high-end SLR (see, Table 3 for values).
The Antarctic Buttressing Model Intercomparison project (ABUMIP; Sun et al., 2020) shows that instantaneous and sustained loss of all Antarctic ice shelves leads to multi-meter SLR over several centuries (1–12 m in 500 yr from present). The participating models did not include MICI, and the variation in magnitude of ice loss was found to be related to subglacial processes, where plastic friction laws generally lead to enhanced ice loss. This experiment should be considered as an upper bound as artificially regrowth of ice shelves was prevented, and other dampening effects were ignored.
Paleo evidence of past ice loss might provide some constraints on the uncertainty in ice sheet models, but available data are mostly restricted to total ice loss and remain limited in their ability to constrain rates of ice loss (Dutton et al., 2015).
Regardless of the processes driving ice loss on the ice shelves, the retreat of ice also leads to an instantaneous and time-delayed response of the underlying bedrock and an immediate reduction in gravitational attraction between the ice sheet and the nearby ocean. The resulting reduction of relative sea level at the grounding line may stabilize its retreat, providing a negative feedback (Barletta et al., 2018; DeConto et al., 2021; Gomez et al., 2010, 2015; Larour et al., 2019; Pollard et al., 2017) showed that these effects do little to slow the pace of retreat until after the mid-twenty-third century in the Amundsen Sea region. Coulon et al. (2021) also find that the West-Antarctic ice sheet destabilizes for high-forcing regardless of the mantle viscosity. At the same time, Kachuck et al. (2020) and Pan et al. (2022) indicate that the weak viscosity in West-Antarctica might significantly reduce the West-Antarctic contribution over the next 150 yr, because the rapid bedrock uplift compensates the grounding line retreat. Altogether, this suggests that for the shorter time scales over the next centuries, it cannot be excluded that this negative feedback plays a role, but improved 3D viscosity models are needed to quantify this effect.
Evaluation of the High-End Contribution for Antarctica
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The Antarctic Buttressing Model Intercomparison project (ABUMIP; Sun et al., 2020) shows that instantaneous and sustained loss of all Antarctic ice shelves leads to multi-meter SLR over several centuries (1–12 m in 500 yr from present). The participating models did not include MICI, and the variation in magnitude of ice loss was found to be related to subglacial processes, where plastic friction laws generally lead to enhanced ice loss. This experiment should be considered as an upper bound as artificially regrowth of ice shelves was prevented, and other dampening effects were ignored.
Paleo evidence of past ice loss might provide some constraints on the uncertainty in ice sheet models, but available data are mostly restricted to total ice loss and remain limited in their ability to constrain rates of ice loss (Dutton et al., 2015).
Regardless of the processes driving ice loss on the ice shelves, the retreat of ice also leads to an instantaneous and time-delayed response of the underlying bedrock and an immediate reduction in gravitational attraction between the ice sheet and the nearby ocean. The resulting reduction of relative sea level at the grounding line may stabilize its retreat, providing a negative feedback (Barletta et al., 2018; DeConto et al., 2021; Gomez et al., 2010, 2015; Larour et al., 2019; Pollard et al., 2017) showed that these effects do little to slow the pace of retreat until after the mid-twenty-third century in the Amundsen Sea region. Coulon et al. (2021) also find that the West-Antarctic ice sheet destabilizes for high-forcing regardless of the mantle viscosity. At the same time, Kachuck et al. (2020) and Pan et al. (2022) indicate that the weak viscosity in West-Antarctica might significantly reduce the West-Antarctic contribution over the next 150 yr, because the rapid bedrock uplift compensates the grounding line retreat. Altogether, this suggests that for the shorter time scales over the next centuries, it cannot be excluded that this negative feedback plays a role, but improved 3D viscosity models are needed to quantify this effect.
Evaluation of the High-End Contribution for Antarctica
A chain of processes illustrated in Figure 3 control the contribution from Antarctica to SLR. The stability of the ice shelves is central, and this is controlled by surface melt, bottom melt, calving and hydrofracturing. The relative importance of these factors changes because of regional climate change as estimated by global climate models. The uncertainty in the regional climate in the southern hemisphere is generally larger than in the northern hemisphere, increasing uncertainties in the Antarctic component (Heuzé et al., 2013; Russell et al., 2018). Once the ice shelves are broken up, the dynamics of the ice sheet, including the MISI and MICI mechanisms, control how much ice is lost. All studies for a 5°C warming at the end of the century indicate a multi-meter contribution to GMSL from Antarctica on longer than a century time scale. Major ice shelves will disintegrate eventually under that magnitude of warming. The timing of the disintegration is uncertain, but unlikely to have a large effect on high-end SLR already during the 21st century. For this reason, we consider the upper range of Bulthuis et al. (2019), Golledge et al. (2019, 2015), and Levermann et al. (2020), to estimate the high-end contribution of the Antarctic Ice Sheet in 2100 to be 0.39 m for a +2°C scenario (Levermann et al., 2020) and 0.59 m for a +5°C scenario, which is close to the results by Edwards et al. (2021). We do this as no formal probability distributions are available for the likelihood of ice shelf collapse and cliff instability. The study by DeConto and Pollard (2016) is not included for our estimates for 2100, because of a potential overestimation of surface melt rates which initiates shelf disintegration too early. For 2300, only a limited number of ice dynamical studies exist, but they all agree that several meters of SLR from Antarctica is possible because of ice shelf collapse, and limited constraints on instability mechanisms and ice dynamics. Based on Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015), we estimate a high-end contribution to be 1.35 m for a +2°C scenario and 6 m for a +8°C–10°C scenario in 2300. A more recent study by DeConto et al. (2021) including improved estimates for surface melt rates is included for the 2300 estimates. So, despite the different physics of all those studies, we believe that we can combine those studies for a high-end estimate because they agree on the onset of shelf disintegration around 2100 and far ahead of 2300. For the +8°C–10°C scenario, we take the average of the three dynamical studies, while realizing that constraints on the rates of mass loss are highly uncertain and vary strongly among the models.
Figure 3: Causal relation between processes leading to a high-end contribution of Antarctica to sea level rise (SLR). The Antarctic climate response affects Surface Melt and Bottom Melt, which together with Calving and Hydrofracturing determine the stability of the ice shelves. If the ice shelves break up, the dynamics encompassing instability mechanisms like Marine Ice Sheet Instability (MISI) and Marine Ice Cliff Instability (MICI) and basal sliding control the final contribution of the Antarctic ice sheet to high-end SLR.
Table 1 illustrates the critical processes for a high-end estimate for the Antarctic contribution.
In summary, it is not only the poor understanding of the dynamics of ice flow, but also the limited understanding of the processes controlling the break-up of the major ice shelves that determines the uncertainty in the timing and magnitude of the Antarctic contribution to sea level. When combined, this leads to the Antarctic component having the largest uncertainties in the sea level projections.
Lines of Evidence for High-End Scenarios
In Sections 4–6, 4–6, 4–6, we discussed the contribution of cryospheric components to SLR, which largely follow from CMIP climate model outputs applied as offline-forcing for ice sheet model simulations. The critical processes for the different components are summarized in Table 1.
In this section, we integrate these components into a total high-end SLR estimate focusing on the time slices 2100 and 2300 and the two temperature scenarios because there is a reasonable sample of studies available. The multiple lines of evidence enable us to go beyond single studies or even single multimodel experiments and provide a more complete synthesis of the plausible physical response, thereby creating estimates that are more salient to practitioners. Such an approach has been used for other seemingly intractable problems such as narrowing the range of Equilibrium Climate Sensitivity (Sherwood et al., 2020) as used in AR6.
For Greenland and Antarctica, the lines of evidence include an assessment of the physical processes. While we cannot define a precise percentile for the total high-end SLR, our interpretation of the multiple lines of evidence as outlined in the Greenland and Antarctic Sections above, is that it lies in the tail and comprises an unlikely outcome. Circulation changes may be important for high-end estimates but only under high forcing for Greenland, instability mechanisms and basal processes and uncertainty in timing of ice shelf collapse result in the high-estimate for Antarctica under a high forcing. For low forcing the SMB changes control the high-estimate for Greenland and the basal melt rate changes control the high-estimate for Antarctica.
Since for longer time scales and higher temperature scenarios, the Antarctic ice sheet contribution dominates the uncertainty in SLR, we can essentially obtain an estimate of high-end SLR by combining the cryospheric components and adding known contributions from thermal expansion and land water changes. Here, the thermal expansion component of SLR and its contribution to the high-end follows directly from the thermal expansion of sea water assessed by Fox-Kemper et al. (2021) as the resulting mean plus twice the standard deviation. The LWSC results mainly from groundwater changes and is partly induced by socio-economic changes and partly due to climate change. In a review by Bierkens and Wada (2019), the upper end of the socio-economic contribution is estimated to be 0.9 mm/yr, and the climate driven component is estimated to be 40 mm in 2100, independent of the scenario (Karabil et al., 2021). This is partly offset by the projections for more dams being built in the early 22nd century (Hawley et al., 2020; Zarfl et al., 2015). Recent papers argue for possible changes in precipitation (Wada et al., 2012), endorheic basin storage changes (Reager et al., 2016; Wang et al., 2018) and increased droughts (Pokhrel et al., 2021), all affecting SLR in a positive or a negative sense. As the LWSC components remains small in all cases and it is not critical for a high-end estimate, here we simply follow (Fox-Kemper et al., 2021).
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For Greenland and Antarctica, the lines of evidence include an assessment of the physical processes. While we cannot define a precise percentile for the total high-end SLR, our interpretation of the multiple lines of evidence as outlined in the Greenland and Antarctic Sections above, is that it lies in the tail and comprises an unlikely outcome. Circulation changes may be important for high-end estimates but only under high forcing for Greenland, instability mechanisms and basal processes and uncertainty in timing of ice shelf collapse result in the high-estimate for Antarctica under a high forcing. For low forcing the SMB changes control the high-estimate for Greenland and the basal melt rate changes control the high-estimate for Antarctica.
Since for longer time scales and higher temperature scenarios, the Antarctic ice sheet contribution dominates the uncertainty in SLR, we can essentially obtain an estimate of high-end SLR by combining the cryospheric components and adding known contributions from thermal expansion and land water changes. Here, the thermal expansion component of SLR and its contribution to the high-end follows directly from the thermal expansion of sea water assessed by Fox-Kemper et al. (2021) as the resulting mean plus twice the standard deviation. The LWSC results mainly from groundwater changes and is partly induced by socio-economic changes and partly due to climate change. In a review by Bierkens and Wada (2019), the upper end of the socio-economic contribution is estimated to be 0.9 mm/yr, and the climate driven component is estimated to be 40 mm in 2100, independent of the scenario (Karabil et al., 2021). This is partly offset by the projections for more dams being built in the early 22nd century (Hawley et al., 2020; Zarfl et al., 2015). Recent papers argue for possible changes in precipitation (Wada et al., 2012), endorheic basin storage changes (Reager et al., 2016; Wang et al., 2018) and increased droughts (Pokhrel et al., 2021), all affecting SLR in a positive or a negative sense. As the LWSC components remains small in all cases and it is not critical for a high-end estimate, here we simply follow (Fox-Kemper et al., 2021).
A summary overview of the different components to SLR is shown in Table 2. Assuming perfect correlation between all contributions, the total global high-end SLR estimate in 2100 amounts to 0.86 and 1.55 m for +2°C and +5°C, respectively. Focusing on 2300, these numbers increase considerably to 2.5 and 10.4 m, for +2°C and +8°C–10°C, respectively. Alternatively, assuming total independence of contributions, the high-end rise is 0.72 and 1.27 m for 2100 and 2.2 and 8.6 m in 2300, for +2°C and +8°C–10°C, respectively. Hence, the assumption of independence significantly lowers the estimates; for a high scenario, the difference is around 0.3 m in 2100 and nearly 2 m in 2300.
Table 2: The High-End Estimates for the Different Sea Level Components, and Their Sum
2100 2100 2300 2300
+2°C +5°C +2°C +8°C–10°C
Glaciers 0.15a 0.27 0.28 0.32
Greenland 0.10 0.29 0.39 2.5
Antarctica 0.39 0.59 1.35 6
Thermal expansion 0.18 0.36 0.35 1.51
LWSC 0.04 0.04 0.10 0.10
Total high-end estimateb Upper end of the range 0.9 1.6 2.5 10
Lower end of the range 0.7 1.3 2.2 9
^a Values are presented relative to 1995–2014 in meters. To compare to a baseline of 1986–2005 as used in AR5 and SROCC add 0.03 m for total sea level and 0.01 m for individual components.
^b The high-end of the range follows from the assumption of perfect correlation (all covariances between the components equal to one), the low-end of the range follows from the assumption of fully uncorrelated (all covariances between the components equal to zero).
Simply summing all high-end components implies a perfect dependency between all the components which is unlikely, as explained above. It would for instance imply that enhanced basal melting in Antarctica is perfectly correlated to specific atmospheric conditions surrounding the Greenland ice sheet. Alternatively, less risk-averse users could assume that all components are independent of each other, which is also not very likely. The high-end estimates should be considered in the context of the mean and likely ranges reported by the IPCC assessments. This also implies that users who are less risk-averse, or have the ability, to iteratively build resilience, can decide to consider the mean values for all components from an IPCC assessment and add the high-end contribution from Antarctica and Greenland to develop a tailored, but still transparent high-end estimate. In this way, the high-end components and how best to sum them encourage discussion between sea level scientists and practitioners and co-production of the most appropriate SLR scenarios for the respective needs, including the development of storylines (T. G. Shepherd & Lloyd, 2021). For a more easily accessible approach, and because both perfect correlation and full independence of all components seem unlikely based on today’s understanding, practitioners might simply average the high end estimate projections in this paper between the two to derive a single, high end projection for use in planning, if that is more useful than a range.
Table 2 also indicates that the high-end estimate for GMSL in 2100 for a significant warming of +5°C does differ from the conclusions drawn by Fox-Kemper et al. (2021) and Oppenheimer et al. (2019), who argue that a GMSL of 2 m cannot be excluded, as supported by results from an expert elicitation process (Bamber et al., 2019). Table 3 shows the detailed differences between this study and (Fox-Kemper et al., 2021) for Greenland and Antarctica showing lower values in this study for Greenland in 2100 for both scenarios and for Greenland and Antarctic for the 2°C scenario in 2300. A reason might be that the expert elicitation used by Fox-Kemper et al. (2021) was influenced by DeConto and Pollard (2016) which is not used here. However, the closed nature of the expert elicitation method does not allow a firm conclusion.
Table 3: A Comparison Between This Paper and the IPCC AR6 Values
References^a Approach/processes This paper AR6 (Table 9.8 and Table 9.11) Remarks
2100 +2°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 0.18b 0.18
Glaciers Marzeion et al. (2020) Temperature change, ensemble 10 climate models, 10 glacier models 0.15 0.11
Greenland Fox-Kemper et al. (2021) AR6 assessment, medium confidence 0.10 0.30 <<cAR6
Antarctica Levermann et al. (2020) Basal melt for 16 ice sheet models 0.39 0.25 >>AR6
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.04 0.04
Total Range depending on correlation (Section 3) 0.72–0.86 0.79
2100 +5°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 0.36 0.36
Glaciers Marzeion et al. (2020) Temperature change, ensemble 10 climate models, 10 glacier models 0.27 0.20
Greenland Delhasse et al. (2018, 2020) and Goelzer et al. (2020) ISMIP6 assessment including circulation changes and missing feedbacks leading to deep uncertainty 0.29 0.59 <<AR6
Antarctica Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015) Mixture basal melt and ice dynamical studies 0.59 0.56
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.04 0.04
Total Range depending on correlation (Section 3) 1.27–1.55 1.60
2300 +2°C
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References^a Approach/processes This paper AR6 (Table 9.8 and Table 9.11) Remarks
2100 +2°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 0.18b 0.18
Glaciers Marzeion et al. (2020) Temperature change, ensemble 10 climate models, 10 glacier models 0.15 0.11
Greenland Fox-Kemper et al. (2021) AR6 assessment, medium confidence 0.10 0.30 <<cAR6
Antarctica Levermann et al. (2020) Basal melt for 16 ice sheet models 0.39 0.25 >>AR6
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.04 0.04
Total Range depending on correlation (Section 3) 0.72–0.86 0.79
2100 +5°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 0.36 0.36
Glaciers Marzeion et al. (2020) Temperature change, ensemble 10 climate models, 10 glacier models 0.27 0.20
Greenland Delhasse et al. (2018, 2020) and Goelzer et al. (2020) ISMIP6 assessment including circulation changes and missing feedbacks leading to deep uncertainty 0.29 0.59 <<AR6
Antarctica Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015) Mixture basal melt and ice dynamical studies 0.59 0.56
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.04 0.04
Total Range depending on correlation (Section 3) 1.27–1.55 1.60
2300 +2°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 0.35 0.35
Glaciers Goelzer et al. (2012) and Marzeion et al. (2012) Temperature change, single parameterized glacier models 0.28 0.29
Greenland Fox-Kemper et al. (2021) AR6 assessment 0.39 1.28 <<AR6
Antarctica Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015) Four ice dynamical studies with a range of physical processes simulated 1.35 1.56
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.1 0.1
Total Range depending on correlation (Section 3) 2.19–2.47 3.1
2300 +8°C–10°C
Thermal expansion Fox-Kemper et al. (2021) AR6 assessment 1.51 1.51
Glaciers Farinotti et al. (2019) Temperature change, all glaciers melted 0.32 0.32
Greenland Church et al. (2013), Delhasse et al. (2018, 2020) SMB changes including deep uncertainty 2.5 2.23
Antarctica Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015) Four ice dynamical studies with a range of physical processes simulated 6 13.54 <<AR6
Land water storage change Fox-Kemper et al. (2021) AR6 assessment 0.10 0.10
Total Range depending on correlation (Section 3) 8.59–10.43 16.2
^a Reference used to compile the values in this study.
^b Values are in meters relative to a baseline period of 1995–2014.
^c >>/<< indicates more than 20% difference between this study and AR6. We used from AR6 the highest 83rd percentile projections across all probability distributions considered, including low confidence processes.
In 2300, the contribution of the Antarctic ice sheet is poorly constrained, so the high-end estimate is considerably higher than most previous estimates (Church et al., 2013; Oppenheimer et al., 2019), but not as high as (Fox-Kemper et al., 2021). This points to the large uncertainties in projecting sea levels over multiple centuries which arises from: (a) the poorly constrained timing of the collapse of major ice shelves around Antarctica, and (b) the limited understanding of ice-dynamical and subglacial processes. For 2100, the difference for Greenland seems to arise from the difference in structured expert judgment and our physical assessment of the literature.
All the high-end scenarios imply a major adaptation challenge due to SLR, especially beyond 2100 (Haasnoot et al., 2020). What we present builds on a combination of model results and an assessment of different studies leading to lines of evidence per component, thereby providing practical and flexible guidance to practitioners. Further discussions between sea level scientists and practitioners facilitate the application of this knowledge most effectively. We recommend that these storylines should be updated at regular intervals (consistent to the IPCC process), reflecting the evolution of the body of knowledge. This provides a more robust update process than a whiplash response due to single new papers, which may contain high-profile results but lack community consensus or understanding.
Table 2 indicates that the projected temperature has a large effect on the projected high-end SLR during the 21st century and beyond. It also shows that the long timescales associated with slow processes in the ocean and ice sheets provide a strong incentive for mitigation. An SLR of 10 m by 2300 would be extremely challenging and costly, suggesting the need for a near-universal retreat from the present coastline including the most developed and valuable areas, or alternatively, protection/advance on a scale that is hard to envisage, even where artificial protection is the norm today. For a 2°C temperature rise, a high-end 2.5 m rise by 2300 would still present significant challenges, but with rates of SLR that are much slower, offering a wider range of adaptation options and choices. Current experience of rapidly subsiding cities (Nicholls & Tol, 2006) demonstrates that protection for such a magnitude of SLR is feasible if desired and it can be financed. Hence, both from an adaptation and mitigation perspective, smaller temperature increases are preferred.
Considering 2050, there is little difference between low and high-temperature scenarios, as the tails of the distribution are more constrained on decadal time scales. This reflects that the major source of uncertainty—the break-up of major ice shelves in Antarctica—is not foreseen over these time scales.
Addressing 2150 as a time horizon is desirable as many decisions extend over a century (i.e., beyond 2100), but difficult scientifically because of the uncertainty in the timing of a possible break-up of the major Antarctica ice shelves. A first attempt is offered by Fox-Kemper et al. (2021). We argue that there is no evidence for an early break-up of major ice shelves combined with a major loss of grounded Antarctic ice mass influencing the high-end estimate during the 21st century. At the same time, DeConto et al. (2021) indicate a break up of major ice shelves around 2100 or soon after for the high-forcing scenario. The rate of mass loss which might then occur either by enhanced basal sliding or marine ice cliff and shelf instability is poorly constrained, making it extremely difficult to provide a high-end SLR for 2150. It illustrates the high uncertainty in the acceleration of Antarctic ice mass loss. This uncertainty affects the high-end estimate for 2300 much less than for 2150 under the high forcing scenario, as by then the major ice shelves are assumed to have broken up, and sufficient time has passed to allow for accelerated Antarctic ice mass loss. Hence, the precise timing is for this reason less critical at this time scale. For low +2°C forcing scenarios, the prevailing view (DeConto et al., 2021) is that ice shelf break up will occur in fewer regions and therefore the high-end contribution of Antarctica will be considerably lower irrespective of the time scale.
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Considering 2050, there is little difference between low and high-temperature scenarios, as the tails of the distribution are more constrained on decadal time scales. This reflects that the major source of uncertainty—the break-up of major ice shelves in Antarctica—is not foreseen over these time scales.
Addressing 2150 as a time horizon is desirable as many decisions extend over a century (i.e., beyond 2100), but difficult scientifically because of the uncertainty in the timing of a possible break-up of the major Antarctica ice shelves. A first attempt is offered by Fox-Kemper et al. (2021). We argue that there is no evidence for an early break-up of major ice shelves combined with a major loss of grounded Antarctic ice mass influencing the high-end estimate during the 21st century. At the same time, DeConto et al. (2021) indicate a break up of major ice shelves around 2100 or soon after for the high-forcing scenario. The rate of mass loss which might then occur either by enhanced basal sliding or marine ice cliff and shelf instability is poorly constrained, making it extremely difficult to provide a high-end SLR for 2150. It illustrates the high uncertainty in the acceleration of Antarctic ice mass loss. This uncertainty affects the high-end estimate for 2300 much less than for 2150 under the high forcing scenario, as by then the major ice shelves are assumed to have broken up, and sufficient time has passed to allow for accelerated Antarctic ice mass loss. Hence, the precise timing is for this reason less critical at this time scale. For low +2°C forcing scenarios, the prevailing view (DeConto et al., 2021) is that ice shelf break up will occur in fewer regions and therefore the high-end contribution of Antarctica will be considerably lower irrespective of the time scale.
These new high-end estimates provide practitioners with a range of plausible, transparent, and salient high-end sea level estimates that reflect our current physical understanding and reflect the author’s views that it is not possible with the current level of understanding to match these to precise likelihoods. Further, it encourages practitioners to consider their vulnerability and adaptation options without misleading them about the level of understanding. In this way sea level scientists and practitioners can learn together about the application and co-develop appropriate bespoke solutions. How practioners decide to use these numbers, including the low/high ranges should in our view depend on their risk-averseness, among other factors, which they have to evaluate themselves.
We also purposely choose to define high-end estimates for low/+2°C and high/+5°C in 2100 and +8°C–10°C in 2300 temperature increase, with respect to the pre-industrial levels. We cannot provide a likelihood for either of these emissions-driven warming scenarios, and moreover it is also not possible at present to define a high-end for an intermediate emissions or temperature rise scenario (e.g., RCP4.5). While it is obvious that this will be intermediate to the values in Table 2, more detailed specification is not possible due to limited understanding of the time scales and strengths of the feedbacks of the ice components for an intermediate scenario. Essentially, we are convinced that the ice shelves will break-up under high scenarios, but whether they will largely remain intact under lower scenarios is highly uncertain thereby making a distinction between RCP4.5 and RCP2.6/SSP1-2.6 impossible with present levels of knowledge. In addition, there are fewer studies available for a robust high-end estimate for RCP4.5. Irrespective of the scenario (Fox-Kemper et al., 2021) estimate the sea level commitment associated with historical estimates to be 0.7–1.1 m up to 2300, which could probably be considered as the lower end of SLR to consider for practitioners.
Discussion
In this paper, we have attempted to provide physically based high-end estimates of global SLR to 2100 and 2300 by providing specific high-end numbers for SLR under the assumption of a +2°C and +5°C global mean temperature increase (in 2100). In particular, we aimed to provide practitioners with salient well-supported information on low likelihood, high-consequence cases that complement those provided by Fox-Kemper et al. (2021). These high-end estimates can be debated and tailored to individual risk-averse decisions in adaptation planning and implementation, supporting more sound risk management, while adhering to a reasonable standard of practice to ensure appropriate resource allocation. In this way, planners have information available allowing them to frame high-end risk using a standard that balances risk management objectives with finite resources, while avoiding large opportunity costs where possible.
This approach is different than that taken by Fox-Kemper et al. (2021), in particular for projected sea level contributions from Greenland and Antarctica, and we highlight that our approach does not replace that of Fox-Kemper et al. (2021), but instead complements it. Details of the difference are given in Table 3.
We present a range for the high-end estimates, which is defined by the assumptions of how the different components are correlated. The choice of where in this range a user chooses to focus will depend on aspects such as their level of risk aversion and ideally will arise for any particular application through a detailed dialogue between the practitioners and sea level experts.
Hence, as an expert sea level community group we have attempted to quantify the processes controlling the sea level contribution from the different components based largely on the same evidence as used by Fox-Kemper et al. (2021). The independent assessment of the literature presented here results in a different outcome. A key difference in the methods is that here we emphasize that the Antarctic contribution is likely to be controlled by the timing of the loss of major ice shelves around Antarctica. We attempted to follow lines of physical evidence which represent a snapshot of the current knowledge, and this will evolve as knowledge improves. As new physical insights emerge, so individual components of the analysis could be repeated by sub-groups of experts (e.g., for Antarctica), resulting in an update of Table 3. In this way, the approach is modular and comparatively easy to update.
In this respect, the improved use of climate models including a dynamical ice sheet component will fill knowledge gaps with respect to the quantification of feedbacks which are not yet included in the modeling frameworks, and an improved understanding of correlations between different components of the climate system that contribute to global SLR. In addition, growing observational time series will also constrain the physics of the slow processes controlling ice shelf and ice sheet evolution. A strong focus on the timing of thinning and breakup of the Antarctic ice shelves is a critical aspect. At the same time, we also acknowledge that most studies fail to convincingly address the paleo sea level record and this requires further investigation, which may affect future high-end sea level estimates.
This work was originally inspired by questions focusing on “what is a credible high-end SLR for different timeframes?”, to aid climate risk assessment and adaptation planning. In addition, it demonstrates the large benefits of greenhouse gas mitigation for SLR over many centuries, which have only been explored in DeConto et al. (2021). Practitioners can use the high-end estimates to “stress-test” decisions for high-end SLR and develop robust adaptive plans that acknowledge uncertainties about SLR and identify short-term actions and long-term options to adapt as necessary. While our results suggest a plausible high-end, there are still aspects of sea level that are not well understood or which we cannot yet quantify and which might impact a future estimate of high-end SLR, especially on timescales beyond 2100. These include processes associated with the Antarctic ice sheet that are not well understood but which have the potential to cause rapid SLR: better understanding might impact future estimates of the high-end. Qualitatively this is consistent with the rapid expansion of high-end SLR uncertainty identified by Fox-Kemper et al. (2021) from 2100 to 2150, which is over a timescale of high interest to risk-adverse practitioners. Future research on high-end estimates in 2150 would be especially valuable, including under intermediate forcing scenarios (e.g., SSP3).
First, among these uncertainties is the rate of ice loss caused by MICI in Antarctica. The only continental-scale model attempting to quantify the contribution of MICI to future SLR, uses constraints based on observations of calving at the termini of large marine-terminating glaciers in Greenland. However, the geometry of some Antarctic outlet glaciers is very different to the relatively narrow, mélange-filled fjordal settings in Greenland. For example, Thwaites Glacier in West Antarctica is about 10 times wider than Jakobshavn and drains a deep basin in the heart of West Antarctica >2 km deep in places. While MICI has not commenced at Thwaites, the ongoing loss of shelf ice and the retreat of the grounding line onto deeper bedrock could eventually produce a much taller and wider calving front than anything observed on Earth today. Hence models that include MICI in Antarctica, but limit calving rates to those observed on Greenland could be too conservative (e.g., DeConto et al., 2021) and should not be considered an upper bound on the possible SLR contribution from Antarctica. Similar uncertainties also exist for basal processes controlling the rate of mass loss once buttressing ice shelves are lost, with a large simulated range in SLR from Antarctica in response to strong imposed forcing (Sun et al., 2020).
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First, among these uncertainties is the rate of ice loss caused by MICI in Antarctica. The only continental-scale model attempting to quantify the contribution of MICI to future SLR, uses constraints based on observations of calving at the termini of large marine-terminating glaciers in Greenland. However, the geometry of some Antarctic outlet glaciers is very different to the relatively narrow, mélange-filled fjordal settings in Greenland. For example, Thwaites Glacier in West Antarctica is about 10 times wider than Jakobshavn and drains a deep basin in the heart of West Antarctica >2 km deep in places. While MICI has not commenced at Thwaites, the ongoing loss of shelf ice and the retreat of the grounding line onto deeper bedrock could eventually produce a much taller and wider calving front than anything observed on Earth today. Hence models that include MICI in Antarctica, but limit calving rates to those observed on Greenland could be too conservative (e.g., DeConto et al., 2021) and should not be considered an upper bound on the possible SLR contribution from Antarctica. Similar uncertainties also exist for basal processes controlling the rate of mass loss once buttressing ice shelves are lost, with a large simulated range in SLR from Antarctica in response to strong imposed forcing (Sun et al., 2020).
Second, the timing when Antarctic ice shelves might be lost remains a key unknown. Shelf collapse may be caused by hydrofracturing, but this process is poorly understood. Some models assume hydrofracturing occurs if surface melt exceeds a threshold, but due to limited observations, the threshold is poorly constrained, as is the role of interannual variability in the melt, accumulation, and the detailed physics of the firn layer. For the break-up of the Larsen B Ice Shelf in 2002, this variability was probably important, but there is insufficient data for a robust calibration. In addition, break-up of ice shelves has been observed in response to processes triggered by ocean warming, processes which are not yet well quantified and that are omitted from all major existing models.
Third, most models are unable to capture the magnitude of SLR in previous warm periods in Earth history, suggesting that there are either processes missing or that the importance of the processes that are included are underestimated. Antarctica lost ice during these warm periods, but we do not know understand why, even not, if we use the lower estimates of Last Interglacial highstands as recently published (Dyer et al., 2021).
Because of these “Unknown Unknowns”, a flexible approach to risk and adaptation assessment is advisable recognizing the uncertainties of future SLR and realizing that major mitigation will prevent locking in a catastrophic commitment to SLR over multiple centuries. The fact that multiple lines of evidence are needed to build a salient and credible high-end estimate also implies that the publication of a single new study should not change the approach—overreaction and a whiplash approach needs to be prevented. However, it also implies that the evidence leading to the high-end values need to be periodically revisited at regular timescales to IPCC assessments.
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Slangen et al. (2022)
Title:
The evolution of 21st century sea-level projections from IPCC AR5 to AR6 and beyond
Keywords:
Sea-level changes, Numerical modelling, Climate change, Coastal change
Corresponding author:
Aimée B.A. Slangen
Citation:
Slangen, A. B. A., Palmer, M. D., Camargo, C. M. L., Church, J. A., Edwards, T. L., Hermans, T. H. J., et al. (2022). The evolution of 21st century sea-level projections from IPCC AR5 to AR6 and beyond. Cambridge Prisms: Coastal Futures, 1. https://doi.org/10.1017/cft.2022.8
URL:
https://www.cambridge.org/core/journals/cambridge-prisms-coastal-futures/article/evolution-of-21st-century-sealevel-projections-from-ipcc-ar5-to-ar6-and-beyond/BECA28410452901A67B01B68F9B358E0
Abstract
Sea-level science has seen many recent developments in observations and modelling of the different contributions and the total mean sea-level change. In this overview, we discuss (1) the evolution of the Intergovernmental Panel on Climate Change (IPCC) projections, (2) how the projections compare to observations and (3) the outlook for further improving projections. We start by discussing how the model projections of 21st century sea-level change have changed from the IPCC AR5 report (2013) to SROCC (2019) and AR6 (2021), highlighting similarities and differences in the methodologies and comparing the global mean and regional projections. This shows that there is good agreement in the median values, but also highlights some differences. In addition, we discuss how the different reports included high-end projections. We then show how the AR5 projections (from 2007 onwards) compare against the observations and find that they are highly consistent with each other. Finally, we discuss how to further improve sea-level projections using high-resolution ocean modelling and recent vertical land motion estimates.
Impact statement
Sea-level rise is an important aspect of climate change, with potentially large consequences for coastal communities around the world. Sea-level change is therefore an active area of research that has seen many developments in the past decades. Based on the available research, the Intergovernmental Panel on Climate Change (IPCC) provides regular updates on sea-level projections which are used by policymakers and for adaptation planning. In this review, we compare the sea-level projections from different IPCC reports in the past 10 years and explain what has changed in the methods used and in the numbers presented. We also compare observed changes from the 2021 IPCC report to projected changes from the 2013 IPCC report, for the overlapping period 2007–2018, and find that they are highly consistent. Finally, we share some potential future research directions on improving sea-level projections.
Introduction
Present-day sea-level change (SLC) is primarily a consequence of human-induced climate change, which will impact people and communities all over the world. From a decision-making perspective, knowing how much the sea level will rise, and when, can help to decide which protective measures need to be taken at which point in time. Therefore, sea-level projections are among the most anticipated outcomes of the Intergovernmental Panel on Climate Change (IPCC) assessment reports (ARs). While sea-level extremes are also an important consideration for future coastal hazards, in this review we focus our attention on projections of mean sea level.
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Impact statement
Sea-level rise is an important aspect of climate change, with potentially large consequences for coastal communities around the world. Sea-level change is therefore an active area of research that has seen many developments in the past decades. Based on the available research, the Intergovernmental Panel on Climate Change (IPCC) provides regular updates on sea-level projections which are used by policymakers and for adaptation planning. In this review, we compare the sea-level projections from different IPCC reports in the past 10 years and explain what has changed in the methods used and in the numbers presented. We also compare observed changes from the 2021 IPCC report to projected changes from the 2013 IPCC report, for the overlapping period 2007–2018, and find that they are highly consistent. Finally, we share some potential future research directions on improving sea-level projections.
Introduction
Present-day sea-level change (SLC) is primarily a consequence of human-induced climate change, which will impact people and communities all over the world. From a decision-making perspective, knowing how much the sea level will rise, and when, can help to decide which protective measures need to be taken at which point in time. Therefore, sea-level projections are among the most anticipated outcomes of the Intergovernmental Panel on Climate Change (IPCC) assessment reports (ARs). While sea-level extremes are also an important consideration for future coastal hazards, in this review we focus our attention on projections of mean sea level.
In the past 15 years, process-based sea-level projections (i.e., projections which use models to simulate the physical processes and interactions contributing to sea-level change) in the IPCC reports have developed from global-mean only (AR4, Meehl et al., Reference Meehl, Stocker, Collins and Zhao2007) to regional projections (AR5, Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). More recent reports focused on the Antarctic contribution (Special Report on Oceans and Cryosphere in a Changing Climate SROCC, Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019), and provided projections consistent with the assessed Equilibrium Climate Sensitivity (ECS) (AR6, Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). The research community has dedicated significant research effort and published many papers on improving the understanding and modelling of the different contributions to SLC, such as ice sheets, glaciers and sterodynamic changes (e.g., Gregory et al., Reference Gregory, Bouttes, Griffies, Haak, Hurlin, Jungclaus, Kelley, Lee, Marshall, Romanou, Saenko, Stammer and Winton2016; Nowicki et al., Reference Nowicki, Payne, Larour, Seroussi, Goelzer, Lipscomb, Gregory, Abe-Ouchi and Shepherd2016; The IMBIE Team, 2018, 2019; Hock et al., Reference Hock, Bliss, Marzeion, Giesen, Hirabayashi, Huss, Radic and Slangen2019). Since AR5, new global mean and regional projections have been published, using various methods: for instance based on fully coupled climate models (Slangen et al., Reference Slangen, Katsman, van de Wal, Vermeersen and Riva2012; Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014; Slangen et al., Reference Slangen, Carson, Katsman, van de Wal, Köhl, Vermeersen and Stammer2014a; Carson et al., Reference Carson, Köhl, Stammer, Slangen, Katsman, van de Wal, Church and White2015; Jackson and Jevrejeva, Reference Jackson and Jevrejeva2016; Buchanan et al., Reference Buchanan, Oppenheimer and Kopp2017; Palmer et al., Reference Palmer, Gregory, Bagge, Calvert, Hagedoorn, Howard, Klemann, Lowe, Roberts, Slangen and Spada2020), reduced-complexity models (Perrette et al., Reference Perrette, Landerer, Riva, Frieler and Meinshausen2013; Schleussner et al., Reference Schleussner, Lissner, Fischer, Wohland, Perrette, Golly, Rogelj, Childers, Schewe, Frieler, Mengel, Hare and Schaeffer2016; Nauels et al., Reference Nauels, Meinshausen, Mengel, Lorbacher and Wigley2017), semi-empirical models (Kopp et al., Reference Kopp, Kemp, Bittermann, Horton, Donnelly, Gehrels, Hay, Mitrovica, Morrow and Rahmstorf2016; Mengel et al., Reference Mengel, Levermann, Frieler, Robinson, Marzeion and Winkelmann2016; Bakker et al., Reference Bakker, Wong, Ruckert and Keller2017; Bittermann et al., Reference Bittermann, Rahmstorf, Kopp and Kemp2017; Goodwin et al., Reference Goodwin, Haigh, Rohling and Slangen2017; Wong et al., Reference Wong, Bakker, Ruckert, Applegate, Slangen and Keller2017; Jackson et al., Reference Jackson, Grinsted and Jevrejeva2018; Jevrejeva et al., Reference Jevrejeva, Jackson, Grinsted, Lincke and Marzeion2018), structured expert judgement (SEJ) (Bamber et al., Reference Bamber, Oppenheimer, Kopp, Aspinall and Cooke2019), or a mixture of methods (Grinsted et al., Reference Grinsted, Jevrejeva, Riva and Dahl-Jensen2015; Kopp et al., Reference Kopp, DeConto, Bader, Hay, Horton, Kulp, Oppenheimer, Pollard and Strauss2017; Le Bars et al., Reference Le Bars, Drijfhout and De Vries2017; Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a). There have also been a number of reviews, including a database of sea-level projections (Garner et al., Reference Garner, Weiss, Parris, Kopp RE, Horton RM, Overpeck and Arbor2018), reviews on developments following AR5 (Clark et al., Reference Clark, Church, Gregory and Payne2015; Slangen et al., Reference Slangen, Adloff, Jevrejeva, Leclercq, Marzeion, Wada and Winkelmann2017a), overviews of processes and timescales (Horton et al., Reference Horton, Kopp, Garner, Hay, Khan, Roy and Shaw2018a; Hamlington et al., Reference Hamlington, Gardner, Ivins, Lenaerts, Reager, Trossman, Zaron, Adhikari, Arendt, Aschwanden, Beckley, Bekaert, Blewitt, Caron, Chambers, Chandanpurkar, Christianson, Csatho, Cullather, DeConto, Fasullo, Frederikse, Freymueller, Gilford, Girotto, Hammond, Hock, Holschuh, Kopp, Landerer, Larour, Menemenlis, Merrifield, Mitrovica, Nerem, Nias, Nieves, Nowicki, Pangaluru, Piecuch, Ray, Rounce, Schlegel, Seroussi, Shirzaei, Sweet, Velicogna, Vinogradova, Wahl, Wiese and Willis2020), reviews on coastal sea-level change (e.g., Van de Wal et al., Reference Van de Wal, Zhang, Minobe, Jevrejeva, Riva, Little, Richter and Palmer2019) and reviews integrating risk and adaptation assessments (e.g., Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021).
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One thing that all sea-level projections have in common, despite the different approaches and methodologies, is an uncertainty that grows substantially through time. The uncertainties in regional sea-level projections over the coming years to decades result primarily from internal climate variability (see e.g., Palmer et al., Reference Palmer, Gregory, Bagge, Calvert, Hagedoorn, Howard, Klemann, Lowe, Roberts, Slangen and Spada2020, their Figure 11). On decadal to centennial timescales, uncertainties depend on the future forcings (such as greenhouse gas emissions) and the response of the climate system; and on the modelling uncertainty associated with simulating the different contributions to SLC. The forcing uncertainty can be assessed using different emissions or radiative forcing scenarios, varying from scenarios with net-zero CO2 emissions by 2050 to scenarios with a tripling of the present-day CO2 emissions by 2100. The modelling uncertainty can be relatively well quantified for some contributions, such as global mean thermal expansion. For other contributions, such as (multi)-century timescale ice mass loss of the Antarctic Ice Sheet, the uncertainty is characterised as ‘deep uncertainty’, which means that experts do not know or cannot agree on appropriate conceptual models or the probability distributions used (Lempert et al., Reference Lempert, Popper and Bankes2003; Kopp et al., Reference Kopp, Oppenheimer, O’Reilly, Drijfhout, Edwards, Fox-Kemper, Garner, Golledge, Hermans, Hewitt, Horton, Krinner, Notz, Nowicki, Palmer, Slangen and Xiao2022). These contributions are therefore a topic of much research and debate (e.g., Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019).
In addition to studies on future sea-level projections, much research has been focused on understanding past observations. A lot of progress has been made in the closing of the sea-level budget for the 20th century, which compares the sum of the observed contributions to the total observed changes, on global (e.g., Gregory et al., Reference Gregory, White, Church, Bierkens, Box, Van Den Broeke, Cogley JG. Fettweis, Hanna, Huybrechts, Konikow, Leclercq, Marzeion, Oerlemans, Tamisiea, Wada, Wake and Van De Wal2013; Chambers et al., Reference Chambers, Cazenave, Champollion, Dieng, Llovel, Forsberg, von Schuckmann and Wada2016; Cazenave et al., Reference Cazenave2018; Frederikse et al., Reference Frederikse, Landerer, Caron, Adhikari, Parkes, Humphrey, Dangendorf, Hogarth, Zanna, Cheng and Wu2020) and basin scales (e.g., Slangen et al., Reference Slangen, Van De Wal, Wada and Vermeersen2014b; Frederikse et al., Reference Frederikse, Riva, Kleinherenbrink, Wada, van den Broeke and Marzeion2016; Rietbroek et al., Reference Rietbroek, Brunnabend, Kusche, Schröter and Dahle2016; Frederikse et al., Reference Frederikse, Jevrejeva, Riva and Dangendorf2018; Wang et al., Reference Wang, Church, Zhang, Gregory, Zanna and Chen2021b). These budget studies have led to important advances in the understanding of sea-level change and its contributing processes on global and regional scales. In addition, the observations can be compared with model simulations (Church et al., Reference Church, Monselesan, Gregory and Marzeion2013c; Meyssignac et al., Reference Meyssignac, Slangen, Melet, Church, Fettweis, Marzeion, Agosta, Ligtenberg, Spada, Richter, Palmer, Roberts and Champollion2017; Slangen et al., Reference Slangen, Meyssignac, Agosta, Champollion, Church, Fettweis, Ligtenberg, Marzeion, Melet, Palmer, Richter, Roberts and Spada2017b; Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019) to test, understand and improve the model representation of the different processes. This has turned out to be challenging, especially for the earlier part of the 20th century: SROCC stated that only 51% of the 1901–1990 observed global mean sea-level (GMSL) change could be explained by models, due to ‘the inability of climate models to reproduce some observed regional changes’, in particular before 1970. The agreement between models and observations increased to 91% for 1971–2015 and 99% for 2006–2015 (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019).
It is also possible to evaluate past projections against observations that have been made since. For instance, for total SLC, Wang et al. (Reference Wang, Church, Zhang and Chen2021a) found an almost identical GMSL trend in the observations and AR5 projections for the period 2007–2018. Lyu et al. (Reference Lyu, Zhang and Church2021) compared observations and climate model output of ocean warming for the purpose of constraining projections. They found a high correlation for the Argo period (2005–2019) and concluded that the observational record over this period is currently the most useful constraint for projections of ocean warming. Such evaluations against the already realised SLC are important to provide further insights and build confidence in sea-level projections.
Here, we will first discuss ‘how we got here’: recent methodological developments in process-based sea-level projections for the 21st century, with a brief recap of the IPCC sea-level projection methods up to IPCC AR5, followed by a discussion of the key differences between AR5, SROCC and AR6 projections (section ‘Key advances in sea-level projections up to IPCC AR6’). Next, we discuss ‘where we are’, by evaluating AR5 projections of SLC (which start from 2007 onwards) against observational time series (up to 2018), both for total GMSL and for individual contributions (section ‘Comparison of the AR5 model simulations with observations’). Finally, we discuss ‘where we’re going’: how can sea-level projections be better tailored for coastal information (section ‘Moving towards local information’). Throughout this review, we adopt the sea-level terminology defined by Gregory et al. (Reference Gregory, Griffies, Hughes, Lowe, Church, Fukimori, Gomez, Kopp, Landerer, Le Cozannet, Ponte, Stammer, Tamisiea and van de Wal2019) and we refer to Box 9.1 of IPCC AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for a summary of the key drivers of SLC.
Key advances in sea-level projections up to IPCC AR6
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Here, we will first discuss ‘how we got here’: recent methodological developments in process-based sea-level projections for the 21st century, with a brief recap of the IPCC sea-level projection methods up to IPCC AR5, followed by a discussion of the key differences between AR5, SROCC and AR6 projections (section ‘Key advances in sea-level projections up to IPCC AR6’). Next, we discuss ‘where we are’, by evaluating AR5 projections of SLC (which start from 2007 onwards) against observational time series (up to 2018), both for total GMSL and for individual contributions (section ‘Comparison of the AR5 model simulations with observations’). Finally, we discuss ‘where we’re going’: how can sea-level projections be better tailored for coastal information (section ‘Moving towards local information’). Throughout this review, we adopt the sea-level terminology defined by Gregory et al. (Reference Gregory, Griffies, Hughes, Lowe, Church, Fukimori, Gomez, Kopp, Landerer, Le Cozannet, Ponte, Stammer, Tamisiea and van de Wal2019) and we refer to Box 9.1 of IPCC AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for a summary of the key drivers of SLC.
Key advances in sea-level projections up to IPCC AR6
There have been substantial methodological and scientific advances in sea-level projections since the publication of the IPCC First Assessment Report in 1990 (Warrick and Oerlemans, Reference Warrick and Oerlemans1990). The use of global climate models (GCMs) in IPCC sea-level projections dates back to the IPCC Third Assessment Report (Church et al., Reference Church, Gregory, Huybrechts, Kuhn, Lambeck, Nhuan, Qin and Woodworth2001). In IPCC AR4, climate models from the third phase of the Climate Model Intercomparison Project (CMIP3) were used as the ‘backbone’ of the process-based GMSL projections (Meehl et al., Reference Meehl, Stocker, Collins and Zhao2007), with a similar approach adopted for AR5 using the CMIP5 generation of climate models (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). A major change for the AR5 was the inclusion of regional projections (following Slangen et al., Reference Slangen, Katsman, van de Wal, Vermeersen and Riva2012). The IPCC Special Report on Global Warming of 1.5° for the first time assessed GMSL based on warming levels (Hoegh-Guldberg et al., Reference Hoegh-Guldberg, Jacob, Taylor, Bindi, Brown, Camilloni, Diedhiou, Djalante, Ebi, Engelbrecht, Guiot, Hijioka, Mehrotra, Payne, Seneviratne, Thomas, Warren, Zhou, Masson-Delmotte, Zhai, Pörtner and Waterfield2018). The SROCC added new information on the dynamical ice sheet contribution to the AR5 projections (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019). The main advance in AR6 was the use of physics-based emulators to ensure consistency of the sea-level projections with the AR6-assessed ECS and global surface air temperature (GSAT).
We will now discuss some of the key differences of the global mean and regional sea-level projections in IPCC AR6 relative to AR5 and SROCC, by explaining what has been done differently, why these changes were made, and what the effects are on the projections. We do not include the SR1.5 projections in this discussion (Hoegh-Guldberg et al., Reference Hoegh-Guldberg, Jacob, Taylor, Bindi, Brown, Camilloni, Diedhiou, Djalante, Ebi, Engelbrecht, Guiot, Hijioka, Mehrotra, Payne, Seneviratne, Thomas, Warren, Zhou, Masson-Delmotte, Zhai, Pörtner and Waterfield2018), as the SR1.5 report made a literature-based assessment of GMSL changes for 1.5° and 2°, but did not produce new projections.
Before we discuss the projections, we note that the interpretation and communication of the uncertainties in sea-level projections has varied across the different IPCC assessment reports (Kopp et al., Reference Kopp, Oppenheimer, O’Reilly, Drijfhout, Edwards, Fox-Kemper, Garner, Golledge, Hermans, Hewitt, Horton, Krinner, Notz, Nowicki, Palmer, Slangen and Xiao2022). IPCC reports use calibrated uncertainty language, in which the confidence level is a qualitative reflection of the evidence and agreement, whereas the likelihood metric is a quantitative measure of uncertainty, expressed probabilistically (Box 1.1, Chen et al., Reference Chen, Rojas, Samset, Cobb, Diongue Niang, Edwards, mori, Faria, Hawkins, Hope, Huybrechts, Meinshausen, Mustafa, Plattner, Tréguier, Masson-Delmotte, Zhai, Pirani and Zhou2021). For the medium confidence projections in AR5, the 5–95th percentile range of the model ensemble was interpreted as the likely range (the central range with about two-thirds probability, 17–83%), with the uncertainty range of all contributions inflated relative to the model spread to account for structural uncertainties arising from the CMIP5 model ensemble. For the sea-level projections in AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Section 9.6), the likely range was redefined as the central range with at least two-thirds probability, encompassing the outer 17th to 83rd percentiles of the probability distributions considered in a p-box (e.g., Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a). That is, the definition of likely range in AR5, SROCC and AR6 is comparable but not exactly the same, and the way of determining the range from the available information is different. The AR6 medium confidence projections include estimated distributions for each emissions scenario with two different methodological choices for the Antarctic ice sheet (see Table 1). AR6 also presented a set of lowconfidence projections, which include additional contributions from ice sheet processes and estimates for which there is less agreement and/or less evidence (see Table 1).
Table 1: High-level summary of the methods used in the AR5, SROCC and AR6 reports to project global mean and regional SLC (1° × 1° resolution) to 2100. Note: This is an adapted version of Table 9.7 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).
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Table 1: High-level summary of the methods used in the AR5, SROCC and AR6 reports to project global mean and regional SLC (1° × 1° resolution) to 2100. Note: This is an adapted version of Table 9.7 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).
The methodologies of the projections in AR5, SROCC and AR6 are briefly summarised in Table 1; for more details, we refer to Chapter 13 of AR5 (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a), Chapter 4 of SROCC (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019) and Chapter 9 of AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). We focus on three major elements of the projections that have changed: (1) the use of CMIP5 versus CMIP6 model output and consistency with the assessed ECS (section ‘Updated climate model information and the use of emulators’); (2) differences in the approaches to project the contributions to SLC (section ‘Differences in the projected contributions to SLC’); (3) the way the reports addressed potential outcomes outside the likely range (section ‘Sea-level projections outside the likely range’).
Updated climate model information and the use of emulators
The majority of the sea-level projections for the 21st century since AR5 have been based on CMIP5 climate model output (Taylor et al., Reference Taylor, Stouffer and Meehl2012), forced by Representative Concentration Pathways (RCP, Meinshausen et al., Reference Meinshausen, Smith, Calvin, Daniel, Kainuma, Lamarque, Matsumoto, Montzka, Raper, Riahi, Thomson, Velders and DPP2011), which are scenarios of future greenhouse gas concentrations and aerosol emissions. The projections in AR6 used information from CMIP6 climate models (Eyring et al., Reference Eyring, Bony, Meehl, Senior, Stevens, Stouffer and Taylor2016), which were forced by Shared Socioeconomic Pathways (SSP, O’Neill et al., Reference O’Neill, Kriegler, Riahi, Ebi, Hallegatte, Carter, Mathur and van Vuuren2014): scenarios of socio-economic development (including for instance population change, urbanisation and technological development) in combination with radiative forcing changes (GHG emissions and concentrations). These scenarios are noted as SSPx − y, where x denotes the SSP pathway (SSP1 sustainability, SSP2 middle-of-the-road, SSP3 regional rivalry, SSP4 inequality, SSP5 fossil fuel-intensive) and y the radiative concentration level in 2100 in W/m2. AR6 used five illustrative SSP scenarios: SSP1–1.9 (very low emissions), SSP1–2.6 (low emissions), SSP2–4.5 (intermediate emissions), SSP3–7.0 (high emissions) and SSP5–8.5 (very high emissions).
The ECS from the CMIP6 model ensemble has a higher average and a wider range compared to the CMIP5 model ensemble and compared to the AR6 assessment of ECS (Forster et al., Reference Forster, Storelvmo, Armour, Collins, Dufresne, Frame, Lunt, Mauritsen, Palmer, Watanabe, Wild, Zhang, Masson-Delmotte, Zhai, Pirani and Zhou2021). The consequences of this change in ECS distribution for projections of GMSL change were investigated by Hermans et al. (Reference Hermans, Gregory, Palmer, Ringer, Katsman and Slangen2021), who used CMIP6 data in combination with the AR5 methodology. They found that, while the projected change in GSAT median and range increased substantially from CMIP5 to CMIP6 (from 1.9 (1.1–2.6) K to 2.5 (1.6–3.5) K under SSP2-RCP4.5, see their Table S2 for additional scenarios), the upper end of the GMSL likely range projections at 2100 increased by only 3–7 cm across all scenarios (see their Figures 1 and 3), due to the delayed response of SLC to temperature changes. However, they also found an increase in the end-of-century GMSL rates of up to ~20%, suggesting that differences between CMIP5 and CMIP6-based GMSL projections could become substantially larger on longer time scales.
Figure 1: Comparison of 21st century projections of global mean SLC in AR5, SROCC and AR6. Total GMSL and individual contributions, between 1995 and 2014 and 2100 (m), median values and likely ranges of medium confidence projections, for (a) RCP2.6/SSP1–2.6 and (b) RCP8.5/SSP5–8.5. See also Table 9.8 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for comparative numbers of GMSL projections. AR6 low confidence projections for SSP1–2.6 and SSP5–8.5 in grey for Greenland, Antarctica and GMSL. Corrections for the differences in baseline period between AR5 (1986–2005) and AR6 (1995–2014) were done following IPCC AR6, Table 9.8.
Figure 2: Comparison of regional relative sea-level change w.r.t. the global mean sea-level change in AR5 and AR6 (2020–2100) (%), based on median values, for (a) IPCC AR5 RCP4.5, global mean of 0.46 m and (b) IPCC AR6 SSP2–4.5, global mean of 0.51 m.
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Figure 1: Comparison of 21st century projections of global mean SLC in AR5, SROCC and AR6. Total GMSL and individual contributions, between 1995 and 2014 and 2100 (m), median values and likely ranges of medium confidence projections, for (a) RCP2.6/SSP1–2.6 and (b) RCP8.5/SSP5–8.5. See also Table 9.8 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for comparative numbers of GMSL projections. AR6 low confidence projections for SSP1–2.6 and SSP5–8.5 in grey for Greenland, Antarctica and GMSL. Corrections for the differences in baseline period between AR5 (1986–2005) and AR6 (1995–2014) were done following IPCC AR6, Table 9.8.
Figure 2: Comparison of regional relative sea-level change w.r.t. the global mean sea-level change in AR5 and AR6 (2020–2100) (%), based on median values, for (a) IPCC AR5 RCP4.5, global mean of 0.46 m and (b) IPCC AR6 SSP2–4.5, global mean of 0.51 m.
Figure 3: Comparison of observations (IPCC AR6, available up to 2018) and projections (IPCC AR5, available from 2007) of GMSL change. (a) Total GMSL and (b-f) individual contributions in (m) with respect to the period 1986–2005; all uncertainties recomputed to represent the likely range. Text in panels compares rates (mm/yr) of observations for 2006–2018 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Table 9.5) to rates of projections for 2007–2018 (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a); rates rounded to nearest 0.1 mm/yr; time periods used for rates differ by 1 year, allowing for traceability to the IPCC reports. Note that AR5 included the Greenland peripheral glaciers in the glacier contribution, whereas AR6 included it in the Greenland contribution; we have therefore subtracted a Greenland peripheral glacier estimate of 0.1 mm/yr from the AR6 Greenland observations in (c) and added it to the AR6 glacier observations in (d), both for the time series and the rates (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a, Table 13.1; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b, Table 9.SM.2). The AR5 observed glacier change is added to (d) for reference (using the 1993–2010 linear rate from Table 13.1 of Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a).
One of the novel aspects of AR6 was the use of a physically-based emulator, which allowed for projections of 21st century GSAT and SLC that were consistent with the AR6 assessment of ECS (Forster et al., Reference Forster, Storelvmo, Armour, Collins, Dufresne, Frame, Lunt, Mauritsen, Palmer, Watanabe, Wild, Zhang, Masson-Delmotte, Zhai, Pirani and Zhou2021). The AR6 used a simple two-layer energy balance model (e.g., Geoffroy et al., Reference Geoffroy, Saint-Martin, Bellon, Voldoire, Olivié and Tytéca2013). Previous studies have used this two-layer model to successfully emulate CMIP5 model projections of GSAT and global mean thermosteric SLC to 2300 (Palmer et al., Reference Palmer, Harris and Gregory2018; Yuan and Kopp, Reference Yuan and Kopp2021). The AR6 emulator ensemble was constrained using four observational targets, including historical GSAT change and ocean heat uptake (Smith et al., Reference Smith, Nicholls, Armour, Collins, Forster, Meinshausen, Palmer, Watanabe, Masson-Delmotte, Zhai, Pirani and Zhou2021). The projected ocean heat uptake was translated to global mean thermosteric SLC using CMIP6-based estimates of expansion efficiency (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b). The GSAT changes were also used as input for the land-ice contributions to GMSL rise, which were generated with additional emulators applied to suites of coordinated community efforts for the ice sheet (LARMIP-2, Levermann et al., Reference Levermann, Winkelmann, Albrecht, Goelzer, Golledge, Greve, Huybrechts, Jordan, Leguy, Martin, Morlighem, Pattyn, Pollard, Quiquet, Rodehacke, Seroussi, Sutter, Zhang, Van Breedam, Calov, Deconto, Dumas, Garbe, Gudmundsson, Hoffman, Humbert, Kleiner, Lipscomb, Meinshausen, Ng, Nowicki, Perego, Price, Saito, Schlegel, Sun and Van De Wal2020; ISMIP6, Nowicki et al., Reference Nowicki, Payne, Larour, Seroussi, Goelzer, Lipscomb, Gregory, Abe-Ouchi and Shepherd2016) and glacier model (GlacierMIP2, Marzeion et al., Reference Marzeion, Hock, Anderson, Bliss, Champollion, Fujita, Huss, Immerzeel, Kraaijenbrink, Malles, Maussion, Radić, Rounce, Sakai, Shannon, van de Wal and Zekollari2020) simulations carried out for AR6.
Differences in the projected contributions to SLC
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Differences in the projected contributions to SLC
In AR5, the assessments of glacier and ice sheet contributions were based on a range of individual models and publications. The only difference in the SROCC projections with respect to AR5 was the reassessment of the Antarctic dynamics contribution, by replacing the AR5 Antarctic scenario-independent ice dynamic projections with scenario-dependent process-based model estimates (Levermann et al., Reference Levermann, Winkelmann, Nowicki, Fastook, Frieler, Greve, Hellmer, Martin, Meinshausen, Mengel, Payne, Pollard, Sato, Timmermann, Wang and Bindschadler2014; Golledge et al., Reference Golledge, Kowalewski, Naish, Levy, Fogwill and Gasson2015; Ritz et al., Reference Ritz, Edwards, Durand, Payne, Peyaud and Hindmarsh2015; Bulthuis et al., Reference Bulthuis, Arnst, Sun and Pattyn2019; Golledge et al., Reference Golledge, Keller, Gomez, Naughten, Bernales, Trusel and Edwards2019). This led to a decrease in 21st century GMSL change compared with AR5 for the RCP2.6 scenario, and an increase for the RCP8.5 scenario (medians and likely ranges; Figure 1a,b). However, the scenario-dependence in SROCC may have been amplified because two model estimates did not include accumulation changes (Levermann et al., Reference Levermann, Winkelmann, Nowicki, Fastook, Frieler, Greve, Hellmer, Martin, Meinshausen, Mengel, Payne, Pollard, Sato, Timmermann, Wang and Bindschadler2014; Ritz et al., Reference Ritz, Edwards, Durand, Payne, Peyaud and Hindmarsh2015), which are projected to increase with warming and partially counteract dynamic losses (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).
For the AR6 projections, statistical emulators were applied to the ISMIP6 and GlacierMIP2 outputs, using the Gaussian process model described in Edwards et al. (Reference Edwards, Nowicki, Marzeion, Hock, Goelzer, Seroussi, Jourdain, Slater, Turner, Smith, McKenna, Simon, Abe-Ouchi, Gregory, Larour, Lipscomb, Payne, Shepherd, Agosta, Alexander, Albrecht, Anderson, Asay-Davis, Aschwanden, Barthel, Bliss, Calov, Chambers, Champollion, Choi, Cullather, Cuzzone, Dumas, Felikson, Fettweis, Fujita, Galton-Fenzi, Gladstone, Golledge, Greve, Hattermann, Hoffman, Humbert, Huss, Huybrechts, Immerzeel, Kleiner, Kraaijenbrink, Le clec’h, Lee, Leguy, Little, Lowry, Malles, Martin, Maussion, Morlighem, O’Neill, Nias, Pattyn, Pelle, Price, Quiquet, Radić, Reese, Rounce, Rückamp, Sakai, Shafer, Schlegel, Shannon, Smith, Straneo, Sun, Tarasov, Trusel, Van Breedam, van de Wal, van den Broeke, Winkelmann, Zekollari, Zhao, Zhang and Zwinger2021). For LARMIP-2, results for Antarctic ice sheet dynamics were emulated using an impulse-response function model following (Levermann et al., Reference Levermann, Winkelmann, Albrecht, Goelzer, Golledge, Greve, Huybrechts, Jordan, Leguy, Martin, Morlighem, Pattyn, Pollard, Quiquet, Rodehacke, Seroussi, Sutter, Zhang, Van Breedam, Calov, Deconto, Dumas, Garbe, Gudmundsson, Hoffman, Humbert, Kleiner, Lipscomb, Meinshausen, Ng, Nowicki, Perego, Price, Saito, Schlegel, Sun and Van De Wal2020), augmented by a parametric surface-mass balance model following AR5. There were several motivations for using these emulators: (1) to constrain the projections to the assessed ECS range, an approach that represents a marked change from previous IPCC reports; (2) to be able to make projections across all five illustrative SSP scenarios of AR6, as the ice sheet and glacier contributions were mostly based on CMIP5 RCP scenarios; and (3) to sample modelling uncertainties more thoroughly, estimating probability distributions for the contributions. The use of simple climate models and emulators is a trade-off between a more complete exploration of the uncertainties which can be done due to the computational speed of the emulators (compared to the full ice sheet and glacier models, which are limited by constraints of computing and person time), and the potential biases introduced by the necessary assumptions of a simpler model (Edwards et al., Reference Edwards, Nowicki, Marzeion, Hock, Goelzer, Seroussi, Jourdain, Slater, Turner, Smith, McKenna, Simon, Abe-Ouchi, Gregory, Larour, Lipscomb, Payne, Shepherd, Agosta, Alexander, Albrecht, Anderson, Asay-Davis, Aschwanden, Barthel, Bliss, Calov, Chambers, Champollion, Choi, Cullather, Cuzzone, Dumas, Felikson, Fettweis, Fujita, Galton-Fenzi, Gladstone, Golledge, Greve, Hattermann, Hoffman, Humbert, Huss, Huybrechts, Immerzeel, Kleiner, Kraaijenbrink, Le clec’h, Lee, Leguy, Little, Lowry, Malles, Martin, Maussion, Morlighem, O’Neill, Nias, Pattyn, Pelle, Price, Quiquet, Radić, Reese, Rounce, Rückamp, Sakai, Shafer, Schlegel, Shannon, Smith, Straneo, Sun, Tarasov, Trusel, Van Breedam, van de Wal, van den Broeke, Winkelmann, Zekollari, Zhao, Zhang and Zwinger2021). The Gaussian process emulator performed well for the cumulative change in time, but did not account for temporal correlation, so the rates could not be estimated from the emulator. As a consequence, in contexts where rates were needed, AR6 used simpler parametric emulators, based on approaches used in AR5.
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A comparison of the GMSL projections to 2100 in the different reports reveals a number of differences (Figure 1a,b). In the land ice contributions, we see a narrowing of the likely ranges for glaciers (under both scenarios) and the Greenland ice sheet (under SSP5–8.5), and a widening of the Antarctic ice sheet likely range. The latter is wider as it is based on a p-box bounding distribution functions from the ISMIP6 emulator and LARMIP-2 (Table 1), where the presented likely range spans from the lowest 17th to the highest 83rd percentile of the considered methods. The ECS-constrained temperature projections in AR6 (section ‘Updated climate model information and the use of emulators’) used as input to the land ice emulators show a marked reduction in the width of the likely range at 2100 (~0.7 K for SSP1–2.6; ~1.9 K for SSP5–8.5) compared with the 21 CMIP5 models used as the basis of the AR5 sea-level projections (~1.6 K for RCP2.6; ~2.8 K for RCP8.5), which could also be one of the reasons for the reduced width of the glacier and Greenland likely ranges. The glacier range may also be slightly underestimated because each region is emulated independently, which means the projections do not account for covariances in the regional uncertainties apart from those associates with a common dependence on temperature (Marzeion et al., Reference Marzeion, Hock, Anderson, Bliss, Champollion, Fujita, Huss, Immerzeel, Kraaijenbrink, Malles, Maussion, Radić, Rounce, Sakai, Shannon, van de Wal and Zekollari2020; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Section 9.5). However, the AR5 glacier and Greenland uncertainties were open-ended (≥ 66% ranges) and essentially estimated with expert judgement, at a time of far less information from – and confidence in – these process-based models, so the narrowing range is also consistent with an improving evidence base. The land-water storage contribution is reduced in AR6 compared with AR5 due to the use of a different methodology which now links land-water storage changes to global population under SSP scenarios (Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014), in combination with a larger negative reservoir impoundment contribution from Hawley et al. (Reference Hawley, Hay, Mitrovica and Kopp2020).
AR5 used different methodologies for estimating the uncertainties in GMSL (Figure 1a,b) and regional SLC (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013b). In contrast, the AR6 GMSL (Figure 1a,b) and regional projected uncertainties are combined in the same way, with the different contributions all treated as conditionally independent given GSAT, which is an input for the emulator (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b). The total projected GMSL for SSP1–2.6 has increased in AR6 compared with RCP2.6 projections in AR5 and SROCC, with a similar likely range (Figure 1a), but with different relative contributions of each component. For SSP5–8.5, the AR6 GMSL projections are 4 cm lower than RCP8.5 in SROCC but 6 cm higher than RCP8.5 in AR5 (Figure 1b), due to differences in the model estimates included (from AR5 to SROCC) and in both models used and the methods used to combine the models (from SROCC to AR6) of the projected Antarctic contribution.
The regional projections (Figure 2) show that SLC is spatially highly variable, due to a combination of ocean dynamic changes, gravitational, rotational and deformation (GRD) effects in response to present-day mass changes, and long-term Glacial Isostatic Adjustment (GIA). There is an overall agreement in the patterns between AR5 and AR6. Some differences arise from the vertical land motion (VLM) contribution, which included only GIA in AR5 and also other VLM contributions, such as tectonics, compaction or anthropogenic subsidence, in AR6: compare for instance the larger ratios along the US East Coast ( Figure 2b) to the VLM contribution in Figure 9.26 from Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). The increased contribution from Antarctica compared to AR5, in combination with the ocean dynamics contribution, leads to a more widespread below-average SLC in the Antarctic Circumpolar Current region.
Sea-level projections outside the likely range
One of the key uncertainties in sea-level projections is the dynamic contribution of the ice sheets (i.e., processes related to the flow of the ice). AR5 assessed the likely dynamical contribution of the Antarctic Ice Sheet by 2100 at −2 to 18.5 cm, but also noted that ‘Based on current understanding, only the collapse of marine-based sectors of the Antarctic ice sheet, if initiated, could cause global mean sea level to rise substantially above the likely range during the 21st century. There is medium confidence that this additional contribution would not exceed several tenths of a metre of sea level rise during the 21st century’. An ice sheet estimate based on SEJ was available at the time of AR5 but this could not be supported by other lines of evidence (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). Including the SEJ estimates would have led to an assessment that could not be transparently linked to physical evidence, as the reasoning of the experts involved in the SEJ exercise is undocumented, and it was decided not to use it for the AR5 assessment.
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Sea-level projections outside the likely range
One of the key uncertainties in sea-level projections is the dynamic contribution of the ice sheets (i.e., processes related to the flow of the ice). AR5 assessed the likely dynamical contribution of the Antarctic Ice Sheet by 2100 at −2 to 18.5 cm, but also noted that ‘Based on current understanding, only the collapse of marine-based sectors of the Antarctic ice sheet, if initiated, could cause global mean sea level to rise substantially above the likely range during the 21st century. There is medium confidence that this additional contribution would not exceed several tenths of a metre of sea level rise during the 21st century’. An ice sheet estimate based on SEJ was available at the time of AR5 but this could not be supported by other lines of evidence (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). Including the SEJ estimates would have led to an assessment that could not be transparently linked to physical evidence, as the reasoning of the experts involved in the SEJ exercise is undocumented, and it was decided not to use it for the AR5 assessment.
After AR5, following for instance Sutton (Reference Sutton2019), low probability estimates were increasingly used in the context of risk assessment and to discuss less likely outcomes for risk-averse users (e.g., Le Cozannet et al., Reference Le Cozannet, Nicholls, Hinkel, Sweet, McInnes, Van de Wal, Slangen, Lowe and White2017b; Hinkel et al., Reference Hinkel, Church, Gregory, Gregory, Lambert, McInnes, Nicholls, Church, van der Pol and van de Wal2019; Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021). SROCC argued that stakeholders with a low risk tolerance might use the SEJ numbers (e.g., their Figure 4.2). Model results including marine ice cliff instability (MICI, Deconto and Pollard, Reference Deconto and Pollard2016) were not used in the main projections of SROCC because the too high surface melt rates led to an uncertain timing and magnitude in the simulated ice loss. In AR6, a set of low confidence projections was presented (shown in grey in Figure 1a,b) which build on the medium confidence projections. These projections include additional contributions for the ice sheets, estimated using a p-box approach (e.g., Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a), considering SEJ (Bamber et al., Reference Bamber, Oppenheimer, Kopp, Aspinall and Cooke2019) together with an improved model-based estimate for Antarctica which included MICI (DeConto et al., Reference DeConto, Pollard, Alley, Velicogna, Gasson, Gomez, Sadai, Condron, Gilford, Ashe, Kopp, Li and Dutton2021). It is important to note that the low confidence ranges represent the breadth of literature estimates available at the time, but that they are not incorporated in the assessed likely ranges.
The AR6 low confidence projections suggest that by 2100, under SSP1–2.6 ( Figure 1a), there is a potential Greenland contribution outside the likely range, based on SEJ. For Antarctica, the medium confidence SSP1–2.6 projections already include a wide range of values, so the impact of SEJ and MICI estimates in the lowconfidence projections is less distinct. Under SSP5–8.5 (Figure 1b), the upper values of the AR6 low confidence projections for both ice sheets are considerably larger than the corresponding medium confidence estimates. This reflects the deep uncertainty in the literature on the Antarctic contribution (see also Box 9.4 in Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). What is needed to reduce this deep uncertainty is primarily a better understanding of the physical processes. This will lead to more physically-based model projections with larger ensembles, which will allow for a better exploration of the uncertainties.
Comparison of the AR5 model simulations with observations
In the previous section, we discussed ‘how we got here’: the developments that led to the most recent IPCC projections. However, it is also relevant to see ‘where we are’, by comparing the observed sea-level change against sea-level projections for their overlapping period. We evaluate the assessed likely ranges of the AR5 projections (from 2007 onwards, Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a) against the assessed observational time series from AR6 (up to 2018, Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Table 9.5), both for the total GMSL and the individual contributions (Figure 3).
For GMSL, Antarctica, Greenland and thermal expansion, the observational timeseries are close to the centre of the projections and the estimated rates of change are highly consistent (Figure 3a,b,c,e). The observed glacier timeseries in AR6 is at the lower end of the projections, even though the observed rates entirely fall within the likely range of the projected rates (Figure 3d). It is worth noting that the AR5 included glaciers peripheral to the Greenland Ice Sheet in the glacier projections (their Table 13.5), which according to the observations in their Table 13.1 adds a contribution in the order of 0.1 mm/yr. In AR6, this was included in the Greenland contribution. To facilitate the comparison, we have included the observed Greenland peripheral glacier estimate in Figure 3d (Glaciers) and subtracted it from the observations in Figure 3c (Greenland), based on linear rates presented in Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a and Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a. In addition, the glacier contributions since AR5 suggest a smaller glacier contribution, both in observations and projections (for the observations: grey dashed line in Figure 3d based on Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a, Table 13.1 shows a higher rate than AR6, for the projections: Marzeion et al., Reference Marzeion, Leclercq, Cogley and Jarosch2015). The observed rate of land-water change is larger than the projected central value, but the observed time series, despite its interannual variability, mostly falls within the projected likely range. The observed rate of change is at the upper bound of the likely range projections (Figure 3f).
Wang et al. (Reference Wang, Church, Zhang and Chen2021a) also evaluated GMSL and regional projections from AR5 and SROCC against different tide gauge and altimetry time series for the period 2007–2018. They found that the GMSL trends for 2007–2018 from AR5 projections are almost identical to observed trends and well within the 90% confidence interval. They also showed significant local differences between observations and models, which could be improved with better VLM estimates and minimisation of the internal variability.
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Wang et al. (Reference Wang, Church, Zhang and Chen2021a) also evaluated GMSL and regional projections from AR5 and SROCC against different tide gauge and altimetry time series for the period 2007–2018. They found that the GMSL trends for 2007–2018 from AR5 projections are almost identical to observed trends and well within the 90% confidence interval. They also showed significant local differences between observations and models, which could be improved with better VLM estimates and minimisation of the internal variability.
A study by Lyu et al. (Reference Lyu, Zhang and Church2021) focused on ocean warming, with the purpose of constraining projections. They compared the observations of ocean temperature by the Argo array (2005–2019) with model simulations from the CMIP5 and CMIP6 databases. They found that (1) the range of CMIP6 has shifted upwards compared with CMIP5; (2) there is a high correlation between observations and models over the Argo period; (3) the emergent constraint indicates that the larger trend of thermosteric SLC in the CMIP6 archive needs to be taken with caution. This supports the AR6 approach, where an emulator was used to constrain the thermosteric SLC of CMIP6 models with the assessed ECS range (section ‘Updated climate model information and the use of emulators’), leading to thermosteric SLC projections similar to AR5 and the constrained Lyu et al. (Reference Lyu, Zhang and Church2021) projections.
Moving towards local information
AR5 was the first IPCC assessment report to show regional sea-level projections in addition to GMSL projections, by including the effects of changes in ocean density and circulation, GIA and GRD effects (Table 1). SROCC built on AR5 but explored regional changes in sea-level extremes in more depth. In AR6 as a whole, even stronger emphasis was put on regional climate changes and on using regional information for impacts and risk assessment, in particular in Chapter 10 (Doblas-Reyes et al., Reference Doblas-Reyes, Sörensson, Almazroui, Dosio, Gutowski, Haarsma, Hamdi, Hewitson, Kwon, Lamptey, Maraun, Stephenson, Takayabu, Terray, Turner, Zuo, Masson-Delmotte, Zhai, Pirani and Zhou2021), Chapter 12 (Ranasinghe et al., Reference Ranasinghe, Ruane, Vautard, Arnell, Coppola, Cruz, Dessai, Islam, Rahimi, Ruiz, Sillmann, Sylla, Tebaldi, Wang, Zaaboul, Masson-Delmotte, Zhai, Pirani and Zhou2021) and the Interactive Atlas (Gutiérrez et al., Reference Gutiérrez, Jones, Narisma, Alves, Amjad, Gorodetskaya, Grose, Klutse, Krakovska, Li, Martínez-Castro, Mearns, Mernild, Ngo-Duc, van den Hurk, Yoon, Masson-Delmotte, Zhai, Pirani and Zhou2021). The IPCC authors and the IPCC Technical Support Unit also collaborated with NASA to develop the NASA/IPCC Sea Level Projection Tool (https://sealevel.nasa.gov/ipcc-ar6-sea-level-projection-tool) to provide easy access to global and regional projections. As the need for more detailed sea-level information is becoming increasingly evident (e.g., Le Cozannet et al., Reference Le Cozannet, Nicholls, Hinkel, Sweet, McInnes, Van de Wal, Slangen, Lowe and White2017b; Hinkel et al., Reference Hinkel, Church, Gregory, Gregory, Lambert, McInnes, Nicholls, Church, van der Pol and van de Wal2019; Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021; Durand et al., Reference Durand, van den Broeke, Le Cozannet, Edwards, Holland, Jourdain, Marzeion, Mottram, Nicholls, Pattyn, Paul, Slangen, Winkelmann, Burgard, van Calcar, Barré, Bataille and Chapuis2022), we discuss a couple of potential future research avenues which may help to further improve sea-level projections on a regional to local scale.
High-resolution ocean modelling
Ocean dynamic SLC is a major driver of spatial sea-level variability, which is typically derived from CMIP5 and CMIP6 GCM simulations. However, the extent to which GCMs can provide local information is limited because of their relatively low atmosphere and ocean grid resolutions, which are constrained by computational costs. The typical ocean grid resolution of CMIP5 models is approximately 1° by 1° (~100 km). Although the ocean components of some CMIP6 models operate at a 0.25° resolution, the resolution of most CMIP6 models has not increased much relative to CMIP5, and the CMIP5 and CMIP6 simulations of ocean dynamic SLC show similar features (Lyu et al., Reference Lyu, Zhang and Church2020). These relatively coarse resolutions may lead to misrepresentations of ocean dynamic SLC, particularly in coastal regions in which small-scale and tidal processes and bathymetric features are important. Increasing the resolution of the GCMs requires significant additional computational resources as well as more explicit modelling of high-resolution processes that are currently parameterized.
As an alternative, GCMs can be dynamically downscaled using high-resolution atmosphere or ocean models. Emerging research demonstrates the value of dynamical downscaling for SLC simulations in coastal regions such as the Northwestern European Shelf (Figure 4; Hermans et al., Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020; Chaigneau et al., Reference Chaigneau, Reffray, Voldoire and Melet2022; Hermans et al., Reference Hermans, Katsman, Camargo, Garner, Kopp and Slangen2022), the Southern Ocean (Zhang et al., Reference Zhang, Church, Monselesan and McInnes2017), the Mediterranean Sea (Sannino et al., Reference Sannino, Carillo, Iacono, Napolitano, Palma, Pisacane and Struglia2022), the marginal seas in the Northwest Pacific Ocean (Liu et al., Reference Liu, Minobe, Sasaki and Terada2016; Kim et al., Reference Kim, Kim, Jeong, Lee, Byun and Cho2021), the marginal seas near China (Jin et al., Reference Jin, Zhang, Church and Bao2021) and the Brazilian continental shelf (Toste et al., Reference Toste, Assad and Landau2018), on both annual and sub-annual timescales. Additionally, dynamical downscaling can offer a framework in which local changes in tides, surges and waves can be resolved in conjunction with time-mean SLC and incorporated into sea-level projections (Kim et al., Reference Kim, Kim, Jeong, Lee, Byun and Cho2021; Chaigneau et al., Reference Chaigneau, Reffray, Voldoire and Melet2022), as it allows for modelling changes at higher temporal frequencies. Dynamical downscaling requires GCM output as boundary conditions, which means that the regional solutions due to the explicit modelling of higher resolution processes should always be considered in the context of the GCM model that is driving the regional model. For instance, for the South China Sea, Jin et al. (Reference Jin, Zhang, Church and Bao2021) found that ‘the downscaled results driven by ensemble mean forcings are almost identical to the ensemble average results from individually downscaled cases’. However, more extensive analysis of the uncertainties associated with dynamical downscaling remains to be done. As a result, the dynamical downscaling of ocean simulations has not yet been systematically applied in the context of regional and local sea-level projections.
Figure 4: Ocean dynamic SLC northwest of Europe, as simulated by (a) the CMIP5 GCM HadGEM2-ES and (b) dynamically downscaled using regional ocean model NEMO-AMM7, and by (c) the CMIP5 GCM MPI-ESM-LR and (d) dynamically downscaled, for the scenario RCP8.5 (2074–2099 minus 1980–2005). Figure adapted from Hermans et al. (Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020).
Vertical land motion
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Figure 4: Ocean dynamic SLC northwest of Europe, as simulated by (a) the CMIP5 GCM HadGEM2-ES and (b) dynamically downscaled using regional ocean model NEMO-AMM7, and by (c) the CMIP5 GCM MPI-ESM-LR and (d) dynamically downscaled, for the scenario RCP8.5 (2074–2099 minus 1980–2005). Figure adapted from Hermans et al. (Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020).
Vertical land motion
In addition to the ocean and ice contributions, relative SLC is affected by VLM (Table 1), which may amplify or even dominate the SLC experienced at coastal locations. AR5 and SROCC used GIA models to estimate the VLM contribution to SLC, whereas AR6 based its VLM estimate on the geological background rate at tide gauge stations, derived using the Gaussian Process Model from (Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014; Table 1). Neither method provides a satisfactory answer, given that the former excludes non-GIA VLM contributions, and the latter requires assumptions regarding the spatio-temporal extrapolation of the tide-gauge derived background rates to areas without tide gauge information by using a GIA model as a prior. AR6, therefore, stated that ‘there is low to medium confidence in the GIA and VLM projections employed in this Report. In many regions, higher-fidelity projections would require more detailed regional analysis’.
Work published after the IPCC AR6 literature deadline has provided new observation-based estimates of VLM for 99 coastal cities based on InSAR observations (Wu et al., Reference Wu, Wei and D’Hondt2022) and along the world’s coastlines using GNSS data (Oelsmann et al., Reference Oelsmann, Passaro, Dettmering, Schwatke, Sánchez and Seitz2021). However, even with better observational estimates, significant assumptions are required when extrapolating these into the future. Both AR5 and AR6 assume VLM rates remain constant over time, an assumption that is wrong in regions that are tectonically active (where VLM will be nonlinear and stochastic) or where VLM occurs in response to groundwater and gas extractions (which is strongly dependent on societal choices). A potential solution is to use expanded geological reconstructions of paleo sea level on millennial time scales to constrain long-term average trends (Horton et al., Reference Horton, Shennan, Bradley, Cahill, Kirwan, Kopp and Shaw2018b).
Conclusions and future perspectives
In this overview, we have discussed several aspects of sea-level projections: recent developments in the projections, how they compare against observations, and potential future research directions: ‘how we got here’ (section ‘Key advances in sea-level projections up to IPCC AR6’), ‘where we are’ (section ‘Comparison of the AR5 model simulations with observations’) and ‘where we’re going’ (section ‘Moving towards local information’).
Key differences between AR5, SROCC and AR6 include the use of new climate model information (CMIP6) and the use of emulators to constrain the projections to the AR6 assessment of Equilibrium Climate Sensitivity (section ‘Updated climate model information and the use of emulators’), new information for the different projected contributions to sea-level change (section ‘Differences in the projected contributions to SLC’), and the treatment of projections outside the likely range (section ‘Sea-level projections outside the likely range’).
The likely range projections of GMSL and regional SLC at 2100 show relatively modest changes from AR5 to SROCC and AR6, given approximately equivalent climate change scenarios (sections ‘Updated climate model information and the use of emulators’ and ‘Differences in the projected contributions to SLC’): under RCP2.6/SSP1–2.6 from 0.25–0.58 m (AR5) to 0.33–0.62 m (AR6); under RCP8.5/SSP5–8.5 from 0.49–0.95 m (AR5) to 0.63–1.01 m (AR6). Substantial reductions in the uncertainty of the Greenland and glacier contributions to GMSL at 2100 under SSP5–8.5 for AR6 are counterbalanced by an increase in the Antarctic uncertainty, which leads to relatively small changes in overall uncertainty at 2100 between AR5 and AR6.
In AR6, the explicit inclusion of low confidence projections highlighted the deep uncertainty associated with the dynamical ice sheet contribution (section ‘Sea-level projections outside the likely range’), which was communicated through the use of ‘low-likelihood high-impact’ storylines (IPCC, Reference Masson-Delmotte, Zhai, Pirani, Connors, Péan, Berger, Caud, Chen, Goldfarb, Gomis, Huang, Leitzell, Lonnoy, JBR, Maycock, Waterfield, Yelekçi, Yu and Zhou2021; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). Regional SLC projections based on the low confidence projections were also provided by AR6, but we highlight that more work is needed on understanding and physical modelling of the ice sheet contributions, and on the potential for different regional estimates associated with the partitioning of Greenland and Antarctic ice mass loss.
Our comparison of AR5 projections with observations for the period 2007–2018 shows that the rates of change agree within uncertainties for GMSL and for individual contributions (section ‘Comparison of the AR5 model simulations with observations’), which is in line with previous studies focusing on total sea-level change (Wang et al., Reference Wang, Church, Zhang and Chen2021a) and the ocean heat uptake contribution (Lyu et al., Reference Lyu, Zhang and Church2021). Monitoring the projections against observed changes is important as it can help to constrain future projections.
In terms of future developments of sea-level projections (section ‘Moving towards local information’), we highlight the need for dynamical ocean downscaling to represent processes missing in GCMs, such as tidal effects and local currents in shelf sea regions, to better estimate future ocean dynamic SLC. This would also improve simulations of key small-scale processes at the ocean-ice interface that affect the climatic drivers of ice sheets and therefore projections of their future evolution. It would also lead to a better quantification of the effects on mean SLC on, for example, tidal characteristics and wave propagations to understand the potential compounding effects on future coastal flood hazards. A second aspect that is relevant to relative sea-level projections, in particular in low-lying delta regions, is the need for improved VLM observational estimates and projections. This will particularly impact coastal SLC projections, as flood risks depend on (and in some parts of the world are dominated by) the movement of the land in addition to the changes in water level.
In this paper, we have focused on sea-level projections up to 2100. However, it is important to note that sea-level change does not stop in 2100. Currently, projections beyond 2100 are typically based on different methods compared with the projections up to 2100, due to a lack of model simulations and literature. For instance, in AR6 the time series were extended to 2150 assuming constant ice sheet rates post 2100 and the Gaussian process emulators were substituted with parametric fits. Unfortunately, the use of different methods tends to lead to discontinuities in the time series. To fill this gap, we need better understanding and process modelling of the different components, such that consistent methods can be used to generate long-term projections for the next IPCC assessment report and beyond. This will allow investigations of for instance the sea-level response to surface warming overshoot scenarios, or the inclusion of tipping points in sea-level projections (e.g., Lenton et al., Reference Lenton, Rockström, Gaffney, Rahmstorf, Richardson, Steffen and Schellnhuber2019). These are only some of the many potential research avenues associated with long-term sea-level projections, all of which are important to investigate given the long-lasting commitment and widespread consequences of future sea-level rise.
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Li et al. (2022)
Title:
The Impact of Horizontal Resolution on Projected Sea-Level Rise Along US East Continental Shelf With the Community Earth System Model
Key Points:
The high resolution (HR) Community Earth System Model reduces biases in dynamic sea level (DSL) and circulation on US east continental shelf
Compared to the low resolution model, the HR projects enhanced (reduced) trends of DSL rise along the US south (north) east continental shelf
Different DSL rise patterns are related to different Gulf Stream reductions under a weakening Atlantic Meridional Overturning Circulation
Corresponding author:
Dapeng Li
Citation:
Li, D., Chang, P., Yeager, S. G., Danabasoglu, G., Castruccio, F. S., Small, J., et al. (2022). The Impact of Horizontal Resolution on Projected Sea‐Level Rise Along US East Continental Shelf With the Community Earth System Model. Journal of Advances in Modeling Earth Systems, 14(5), e2021MS002868. doi:10.1029/2021ms002868
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021MS002868
Abstract
The Intergovernmental Panel on Climate Change Fifth Assessment Report lists sea-level rise as one of the major future climate challenges. Based on pre-industrial and historical-and-future climate simulations with the Community Earth System Model, we analyze the projected sea-level rise in the Northwest Atlantic Ocean with two sets of simulations at different horizontal resolutions. Compared with observations, the low resolution (LR) model simulated Gulf Stream does not separate from the shore but flows northward along the entire coast, causing large biases in regional dynamic sea level (DSL). The high resolution (HR) model improves the Gulf Stream representation and reduces biases in regional DSL. Under the RCP8.5 future climate scenario, LR projects a DSL trend of 1.5–2 mm/yr along the northeast continental shelf (north of 40° N), which is 2–3 times the trend projected by HR. Along the southeast shelf (south of 35° N), HR projects a DSL trend of 0.5–1 mm/yr while the DSL trend in LR is statistically insignificant. The different spatial patterns of DSL changes are attributable to the different Gulf Stream reductions in response to a weakening Atlantic Meridional Overturning Circulation. Due to its poor representation of the Gulf Stream, LR projects larger (smaller) current decreases along the north (south) east continental slope compared to HR. This leads to larger (smaller) trends of DSL rise along the north (south) east shelf in LR than in HR. The results of this study suggest that the better resolved ocean circulations in HR can have significant impacts on regional DSL simulations and projections.
Plain Language Summary
Projecting future sea-level rise has great socioeconomic value. Based on long-term global high-resolution Community Earth System Model simulations, we analyze future sea-level rise in the Northwest Atlantic Ocean. Two identical sets of simulations were conducted with different horizontal resolutions. Comparisons between the two sets of simulations show different sea-level rise projections along the US east continental shelf between the low-resolution (LR) and high-resolution (HR) models. At the northeast shelf, HR projects a sea-level rise of 0.8 mm/yr, less than half of the trend (1.7 mm/yr) projected by LR. At the southeast shelf, HR projects a sea-level rise of 0.6 mm/yr, while the trend in LR is statistically insignificant at only 0.15 mm/yr. We attribute the different sea-level rise projections to the different ocean circulations simulated in LR and HR. Under global warming, LR projects a decrease in Gulf Stream flow along the entire east continental slope, while the decrease in Gulf Stream strength is confined to the southeast continental slope in HR. This study provides an explanation for the discrepancy in regional sea-level rise projections between low- and high-resolution climate models and thus improves our understanding of projected future sea-level rise.
Introduction
Sea-level rise has been listed as one of the major impacts of global warming by the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (Collins et al., 2013). Based on an analysis of an urban protection data set, Hallegatte et al. (2013) predicted an increase in the cost of global flooding from ∼$6 billion/year in 2005 to $60–63 billion/year in 2050 due to future sea-level rise and land subsidence. With ∼41% of global population residing in coastal areas (Martínez et al., 2007), understanding future coastal sea-level rise is of great socioeconomic importance.
The US east coast has been recognized as one of the hot spots for future sea-level rise (Little et al., 2019; Yin et al., 2009). Based on Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model (CM) global simulations at 1˚ horizontal resolution, Yin et al. (2009) reported ∼20 cm future dynamical sea level (DSL) rise off the US northeast coast. By decomposing the DSL rise into local steric height and mass transport components, they found: (a) negative and positive (referenced to global mean) local steric height increases in coastal and open ocean regions; (b) a large cancellation between the negative local steric height and the positive mass transport in coastal regions. Studies also indicate that DSL along the US east coast is related to the Atlantic Meridional Overturning Circulation (AMOC). Based on “hosing” experiments (in which freshwater forcing is artificially applied at the subpolar North Atlantic Ocean), Levermann et al. (2005) first showed DSL rises near the North America coasts under a weakening AMOC. They attribute the changes in DSL to changes in geostrophic circulation (Levermann et al., 2005). Near the US northeast coasts, the same DSL and AMOC relation has been repeatedly documented in subsequent climate simulations forced by future global warming scenarios (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009). By comparing 25 different models (at ∼1˚ horizontal resolution) participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5), Little et al. (2019) showed that most models exhibit DSL rises near the US northeast coast with decreasing AMOC. However, large uncertainty exists in projected future DSL rises given the spread across different models (Little et al., 2019).
Most climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1˚) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1˚) and high-resolution (0.1˚ ocean and sea ice; and 0.25˚ atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.
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Most climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1˚) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1˚) and high-resolution (0.1˚ ocean and sea ice; and 0.25˚ atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.
The refinement in model horizontal resolution improves sea level simulations. Higginson et al. (2015) suggested that models with coarse resolution may produce erroneous coastal sea level due to inadequate model resolution. By comparing global ocean sea-ice simulations at four different horizontal resolutions (2˚, 1˚, 0.5˚, and 0.25˚), Penduff et al. (2010) showed that the 0.25˚ resolution model can capture sea-level variability more realistically than the others in ocean eddy active regions. Thus, the impacts of model horizontal resolution on future sea-level change deserve focused exploration (Little et al., 2019). In this study, we examine the benefits of HR climate simulations by analyzing the projected sea level change in the Northwest Atlantic Ocean. The novelty of this work lies in the fact that the pair of HR and LR CESM simulations analyzed in this work are much longer than those analyzed in previous studies. They consist of a 500-year preindustrial control (CTRL) simulation and a 250-year (1850–2100) historic and future transient (TNST) climate simulation branched from CTRL (Chang et al., 2020). These multi-century simulations completed by the International Laboratory for High-Resolution Earth System Prediction (iHESP) are much longer than the simulation period (1950–2050, 100 years) specified in the High Resolution Model Intercomparison Project (HighResMIP, Haarsma et al., 2016). The long integration time reduces model drift and thus potentially improves the fidelity of simulation results. The objectives of this work are to (a) compare LR and HR CESM with observations to validate model results, (b) estimate the long-term sea-level trends along the US east continental shelf in HR and LR, (c) explore how refinement in model resolution impacts ocean circulation and sea-level projections. The reason we focus on ocean circulation is because previous studies have shown DSL rises near the US east coast are associated with a weakening AMOC (Levermann et al., 2005; Little et al., 2017; Yin et al., 2009). However, previous sea-level projections near the US east coasts are all based on LR models. Here we revisit this issue and compare HR and LR projected sea-level rise. Although the resolution of HR is much higher than that of LR (see Table 1 for details), HR is still too coarse to fully resolve small scale dynamical processes near the coasts. Regional downscaling with higher resolution is needed to simulate the full range of coastal dynamics relevant to sea-level rise. The manuscript is structured in five sections. Sections 2 and 3 describe data and methods, respectively. Section 4 presents results and discussion, followed by a summary in Section 5.
Table 1: Four 250-Year CESM Simulations Analyzed in This Study
Resolution | TNST/CTRL | Nominal horizontal resolution for ocean and sea-ice (atmosphere and land) | Vertical layers for ocean (atmosphere) | Climate forcing
LR TNST 1 (1) 60 (30) 1850–2005: Historic forcing, 2006–2100: RCP 8.5
LR CTRL 1 (1) 60 (30) 251-500 model year: Climate forcing of 1850
HR TNST 0.1 (0.25) 62 (30) 1850–2005: Historic forcing, 2006–2100: RCP 8.5
HR CTRL 0.1 (0.25) 62 (30) 251-500 model year: Climate forcing of 1850
Note. LR and HR stand for low and high resolution, respectively. TNST and CTRL stand for historic/future-transient and pre-industrial control simulations, respectively. TNST simulations were branched from respective CTRL simulations at year 250.
Data
CESM CTRL and TNST Climate Simulations
A comprehensive overview of the CESM CTRL and TNST climate simulations completed as a part of the iHESP partnership is presented in Chang et al. (2020). Here, we present a brief summary of the CESM simulations (Table 1). The CESM CTRL and TNST simulations are designed following the CMIP5 protocol (Taylor et al., 2012). The CTRL experiment is a 500-year simulation forced with perpetual climate forcing for year 1850. The TNST simulation is branched from the CTRL simulation at year 250 and forced with historic climate forcing from 1850 to 2005 and RCP 8.5 emission scenario climate forcing from 2,006 to 2,100. The model code base is CESM1.3 and the component models include the Parallel Ocean Program version 2 (POP2; Danabasoglu et al., 2012; Smith et al., 2010) for the ocean, the spectral element dynamical core (SE-dycore) Community Atmosphere Model version 5 (CAM5; Neale et al., 2012) for the atmosphere, the Community Land Model version 4 (Lawrence et al., 2011) for the land, and the Community Ice Code version 4 (Hunke & Lipscomb, 2008) for the sea ice. For HR CESM, the nominal horizontal resolutions are 0.1˚ for the ocean and sea ice and 0.25˚ for the atmosphere and land, with 62 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. For LR CESM, the nominal horizontal resolution is 1° for all the component models with 60 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. Both POP2 and CAM5 utilize stretched vertical grids.
For global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field “x” as: ∆ x = (x(TNST)2 – x(TNST)1) – (x(CTRL)2 – x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.
Observational Datasets
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For global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field “x” as: ∆ x = (x(TNST)2 – x(TNST)1) – (x(CTRL)2 – x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.
Observational Datasets
Five observational datasets are used to evaluate model results. The first is the sea surface height (SSH) above geoid obtained from satellite altimeters between 1993 and 2019 (Taburet et al., 2019). It includes data observed from all altimeter missions, and the temporal and spatial resolutions are daily and 0.25˚, respectively. The second is the climatological mean near-surface velocity from drifters (Laurindo et al., 2017). The time period for the climatological mean is 1979–2020 and the spatial resolution is 0.25˚. The third data set is the World Ocean Atlas (WOA) climatological mean temperature and salinity (Locarnini et al., 2018; Zweng et al., 2019). The time period for climatological mean is 2005–2017 and the spatial resolution is 0.25. The fourth data set is the ETOPO5 bathymetry with a spatial resolution of 5 min (NGDC, 1993). The four observational data sets above may not be fully representative at the coasts due to their resolutions and/or lack of measurements. Therefore, they can only be used to compare LR and HR simulation in the open ocean off the coast. The last data set is AMOC measured by the RAPID-MOC array at 26.5° N (McCarthy et al., 2015). The measurements started from April 2004 and are still in progress. All CESM simulations and observational data sets are publicly available and the access to the datasets is provided in the acknowledgment section.
Methods
SSH Decomposition
The methods to decompose SSH (η) are discussed in detail in Griffies et al. (2014) and Griffies and Greatbatch (2012). Here, we summarize the key equations in this section. More detailed information of the relevant equations and derivations is presented in the Supporting Information.
For a hydrostatic fluid, η tendency can be decomposed as:
urn:x-wiley:19422466:media:jame21583:jame21583-math-0024 (1)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0025 is the gravitational acceleration, urn:x-wiley:19422466:media:jame21583:jame21583-math-0026 is the surface density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0027 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0028 are the pressure at the surface and the bottom, urn:x-wiley:19422466:media:jame21583:jame21583-math-0029 is the water depth, urn:x-wiley:19422466:media:jame21583:jame21583-math-0030 is the in-situ density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0031 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0032 are the vertical and time coordinates, respectively (Equation (13) in Griffies et al., 2014). The first term on the right-hand side of Eq (1) measures sea-level change associated with mass change and it’s related to barotropic mass transport and surface mass flux (see Equations (47–49) in Griffies et al. (2014) and the Supporting Information for details). The second term on the right-hand side of Equation (1) measures sea-level change associated with local density change. This decomposition was first used by Gill and Niller (1973) to analyze sea-level fluctuation. Landerer et al. (2007) and Yin et al. (2009) later used this decomposition to interpret climate models simulated sea-level patterns under global warming.
For the POP2 model, which uses the Boussinesq approximation and zero surface water flux, SSH explicitly computed by the model is the DSL (Griffies et al., 2014). DSL (urn:x-wiley:19422466:media:jame21583:jame21583-math-0033) is defined as the anomaly from the global mean sea level: urn:x-wiley:19422466:media:jame21583:jame21583-math-0034, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0035 is the globally averaged sea level (Griffies et al., 2014), and urn:x-wiley:19422466:media:jame21583:jame21583-math-0036 is zero at every time step in POP2. Thus, all terms in Equation (1) should be interpreted as anomalies from the global mean when decomposing the POP2 SSH field. Since the bottom pressure is not available from POP2 output, we estimate the mass transport term as the residual between SSH and local steric height.
Boussinesq Approximation and Sterodynamic Sea-Level
Many ocean models including POP2 employ the Boussinesq approximation which conserves the volume rather than the mass of a fluid parcel. Greatbatch (1994) showed that Boussinesq models do not account for sea-level changes associated with the net expansion (or contraction) of the global ocean. Further comparison between Boussinesq and non-Boussinesq models shows: (a) very similar large-scale sea level patterns (see Figure 3 in Griffies & Greatbatch, 2012); (b) corrections are needed in Boussinesq models to study the impact on earth rotation and geoid associated with water mass redistribution (Bryan, 1997; Kopp et al., 2010). For assessing future sea-level change with a Boussinesq model, the only correction required is to add a globally uniform, time-varying factor known as the global mean steric sea-level (Greatbatch, 1994; Griffies et al., 2014). Since this correction is globally uniform, it has no dynamical effects (Greatbatch, 1994).
The global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):
urn:x-wiley:19422466:media:jame21583:jame21583-math-0039
(2)
urn:x-wiley:19422466:media:jame21583:jame21583-math-0040
(3)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).
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The global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):
urn:x-wiley:19422466:media:jame21583:jame21583-math-0039
(2)
urn:x-wiley:19422466:media:jame21583:jame21583-math-0040
(3)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).
The sterodynamic sea-level changes only account for changes in sea-level associated with ocean circulation and density changes (Gregory et al., 2019), while the actual sea-level can be influenced by other processes such as glacial melting, changes in land-water storage, and vertical land motion. The current version of CESM does not include these processes. Thus, sea-level changes associated with these processes are not considered in this study.
Externally Forced Sea-Level Changes
In this study, we are interested in the externally forced sea-level changes. By referencing TNST to CTRL simulations, sea-level changes in response to anthropogenic climate forcing can be extracted (a schematic is presented in Figure S1 in the Supporting Information S1). While internal variability can give rise to large decadal fluctuations in sea-level in the North Atlantic Ocean (Chafik et al., 2019; Griffies & Bryan, 1997; Yeager, 2020), externally forced sea-level changes are expected to manifest as robust long-term trends. Hence we use linear trend analysis with significance tests to identify externally forced sea-level changes. Given that externally forced sea-level changes may not necessarily be linear with time, we also examine sea-level differences between present and future time periods. The two analysis methods give very similar spatial patterns of sea-level response to the RCP8.5 CO2 emission scenario.
Results and Discussion
Evaluation of Model Simulations Against Observations
We first compare the model results with the existing observations before discussing future sea-level projections. Figure 1 shows DSL mean and variance from the satellite observations, HR, and LR simulations. For the mean DSL, HR shows two major improvements over LR: (a) HR reduces mean DSL bias along the entire US east continental shelf; and (b) HR produces more realistic mean DSL patterns along the Gulf Stream extension than LR (Figures 1a–1c). Along the northeast continental shelf (north of Cape Hatteras, marked as the blue star in Figures 1a–1c), HR reduces the negative DSL bias of ∼40 cm in LR. Along the southeast shelf (south of Cape Hatteras), HR reduces the positive DSL bias of ∼20 cm in LR (Figures 1a–1c). In addition, HR improves the Gulf Stream separation point over LR, although the overshooting issue still exists. The Gulf Stream separation point was determined from visual inspection. A non-biased method is to select a (fixed) DSL/SSH isoline and quantify the separation latitude, for example, as was done for the East Australian Current (Cetina-Heredia et al., 2014). Observations show that the Gulf Stream leaves the US east coast near Cape Hatteras at 35° N (Figure 1a). HR simulated Gulf Stream meanders past 35° N and separates from the coast close to 40° N, while LR simulated Gulf Stream does not show a clear separation from the coasts (Figures 1b-1c). The attachment of the Gulf Stream to the coast is a common issue in coarse resolution ocean model simulations (Chassignet & Marshall, 2008; Dengg et al., 1996; Saba et al., 2016; Schoonover et al., 2017). A realistic Gulf Stream separation has been found when model horizontal resolution increases up to 1/50urn:x-wiley:19422466:media:jame21583:jame21583-math-0048 (equivalent to 1.5 km in mid latitudes), and the effects of submesocale processes are explicitly represented (Chassignet & Xu, 2017). Despite this shortcoming, the simulated mean DSL along the Gulf Stream extension is much closer to observations in HR than in LR. For DSL variance, HR and the observations show similar spatial patterns along the continental shelf with large variance in the south and small variance in the north, even though the magnitudes in HR are larger than observations (Figures 1d-1e). In contrast, LR produces opposite spatial patterns with small (large) variance along the south (north) east shelf (Figure 1f). In the Gulf Stream extension region, the variance in HR is closer to observations than LR (Figures 1d–1f). This improvement is likely attributed to the better representation of oceanic mesoscale eddies in HR, which has been listed as one of the existing problems for coarse resolution climate model projections of future sea-level change (Fasullo & Nerem, 2018).
Figure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)–(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993–2019. The blue star in (a)–(c) denotes Cape Hatteras.
DSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a–2c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40–60 cm/s, less than half of the observed values of 120–140 cm/s. In contrast, HR simulated current speed is ∼120 cm/s or greater (Figure 2b), much closer to the observations. At ∼40° N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d–2f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10–20 cm/s, much less than the current speed of ∼50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.
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Figure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)–(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993–2019. The blue star in (a)–(c) denotes Cape Hatteras.
DSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a–2c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40–60 cm/s, less than half of the observed values of 120–140 cm/s. In contrast, HR simulated current speed is ∼120 cm/s or greater (Figure 2b), much closer to the observations. At ∼40° N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d–2f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10–20 cm/s, much less than the current speed of ∼50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.
Figure 2: Left column: mean near surface velocity from drifter observations (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: mean near surface velocity from drifter observations (d), HR (e) and LR (f) zoomed into the US northeast continental shelf and slope. The velocity is sampled at 15-m depth. The time period for the climatological mean is 1979–2020. Red star in (d) indicates Boston, Massachusetts. For clarity, vectors are plotted at every four grid points in (a), every 10 grid points in (b), and every grid point in (c) to approximate a spatial resolution of 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0050 (the resolutions of drifter, HR and LR are 0.25urn:x-wiley:19422466:media:jame21583:jame21583-math-0051, 0.1urn:x-wiley:19422466:media:jame21583:jame21583-math-0052 and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0053, respectively). To highlight small-scale circulations, vectors are plotted on every 2 grid points in (d), every 5 grid points in (e), and every grid point in (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0054 for both observations (d) and HR (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0055 for LR (f).
In addition to improved DSL and ocean circulations, HR reduces biases in near surface temperature and salinity along the northeast continental shelf (Figure 3). Compared to the WOA climatology, HR reduces the warm temperature and high salinity biases of LR in the Gulf of Maine (Figure 3). These bias reductions may be attributed to the improved ocean circulation in HR (Figures 2d–2f). In LR, the overshooting Gulf Stream brings warm and saline water to the Gulf of Maine, causing ∼4° C bias in near surface temperature and ∼3 g/kg bias in near surface salinity (Figure 3). In HR, the southwestward shelf current transports cold and fresh water from the Gulf of St. Lawrence and the Labrador Sea to the Gulf of Maine, reducing the temperature and salinity biases (Figure 3). Although HR improves surface salinity in the Gulf of Maine, it shows a negative salinity bias (∼−1 g/kg) in the Gulf of St. Lawrence (Figures 3d–3f). The low salinity water there may explain the negative salinity bias in the Gulf of Maine as southwestward shelf currents move from the Gulf of St. Lawrence to the Gulf of Maine.
Figure 3: Left column: mean temperature at 15-m depth from World Ocean Atlas (WOA), (a), high resolution (HR) (b), and low resolution (LR) (c). Right column: mean salinity at 15-m depth from WOA (d), HR (e) and LR (f). Arrows are the mean velocities at 15-m depth from drifter observations (a), (d), HR (b), (e), and LR (c), (f). The averaging time period for temperature and salinity is 2005–2017. Red star indicates Boston, Massachusetts. Vectors are plotted on every two grid points in (a), (d), every 5 grid points in (b), (e), and every grid point in (c), (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0057 for both drifter (a), (d) and HR (b), (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0058 for LR (c), (f).
Projected Future Sea-Level Rise
Under the future RCP 8.5 emission scenario, both LR and HR project increasing DSL trends along the US east continental shelf but with different amplitudes (Figures 4a and 4d). Along the northeast shelf (north of 40° N), LR projects a DSL trend of 1.5–2 mm/yr, more than double the DSL trend of 0.5–1 mm/yr projected by HR. Along the southeast shelf (south of 35° N), HR shows a DSL trend of 0.5–1 mm/yr, while LR shows a statistically insignificant trend of less than 0.5 mm/yr. Although LR and HR project different DSL trends along the US east shelf, the global mean thermosteric sea-level rise is in close agreement between the two models (Figure 5). This is consistent with the finding by Van Westen et al. (2020) and may be attributed to the fact that the global mean thermosteric sea-level rise is related to ocean heat uptake, which is largely determined by the RCP8.5 emission scenario specified in LR and HR. Between 2,001 and 2,100, LR and HR project a similar average trend of ∼3 mm/yr for global mean thermosteric sea-level rise (Figure 5).
Figure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.
Figure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.
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Figure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.
Figure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.
Figures 4b–4e, 4f show the trends of local steric height and mass transport components (both are relative to global mean, see Section 3) in the Northwest Atlantic Ocean. For both LR and HR, negative and positive local steric height trends mostly occur in continental shelf and open ocean regions, respectively. This indicates that the local steric height increase is lower than the global mean in continental shelf and greater than the global mean in the open ocean. This is because the local steric height is a depth integral (Equation (3)), so that the steric response increases with water depth. The negative local steric height trends in continental shelf are compensated by positive mass transport trends (Figures 4c and 4f). These are consistent with the model simulation results reported by Yin et al. (2009). Different contributions of local steric height and mass transport to DSL are noted between LR and HR (Figure 4). Here we choose two regions (marked as the 3° × 3° black boxes in Figures 4a and 4d) to analyze the difference between LR and HR. At the northeast shelf near Boston, Massachusetts (highlighted as the red star in Figure 4), the larger increases in mass transport and the smaller decreases in local steric height lead to larger increases in DSL in LR (Figure 4, Table 2). We further quantify the relative contributions of mass transport and local steric height to the difference in DSL trends between LR and HR. At the northeast shelf box region, LR and HR project DSL rises of 1.66 and 0.8 mm/yr, respectively (Table 2, Figure 6a). The difference in projected DSL rise (0.86 mm/yr) results from the difference in local steric height and mass transport (Figures 6b and 6c). Between LR and HR, the difference in local steric height is 0.55 mm/yr (see the fourth row in Table 2), accounting for 64% of the DSL difference (0.86 mm/yr). The difference in mass transport accounts for the remaining 36% of the DSL difference. The same analysis performed for the southeast shelf box region reveals the difference in mass transport (0.32 mm/yr) accounts for 65% of the DSL trend difference (0.49 mm/yr), and the difference in local steric height accounts for the remaining (Table 2, Figures 6d–6f). Because the mass transport is estimated as the residual between DSL and local steric height (see Section 3), we next focus on comparing the differences in local steric height between LR and HR.
Table 2: Contributions of Local Steric Height and Mass Transport to Dynamic Sea Level (DSL) Trends on the Northeast Shelf Near Boston, Massachusetts and on the Southeast Shelf Near Jacksonville, Florida
Boston, Massachusetts DSL Local steric height Mass transport
LR 1.66 urn:x-wiley:19422466:media:jame21583:jame21583-math-0064 0.19 −2.55 urn:x-wiley:19422466:media:jame21583:jame21583-math-0065 0.11 4.22 urn:x-wiley:19422466:media:jame21583:jame21583-math-0066 0.20
HR 0.80 urn:x-wiley:19422466:media:jame21583:jame21583-math-0067 0.26 −3.10 urn:x-wiley:19422466:media:jame21583:jame21583-math-0068 0.23 3.91 urn:x-wiley:19422466:media:jame21583:jame21583-math-0069 0.16
LR–HR 0.86 0.55 0.31
Jacksonville, Florida DSL Local steric height Mass transport
LR 0.15 urn:x-wiley:19422466:media:jame21583:jame21583-math-0070 0.20 −2.74 urn:x-wiley:19422466:media:jame21583:jame21583-math-0071 0.14 2.89 urn:x-wiley:19422466:media:jame21583:jame21583-math-0072 0.14
HR 0.64 urn:x-wiley:19422466:media:jame21583:jame21583-math-0073 0.29 −2.57 urn:x-wiley:19422466:media:jame21583:jame21583-math-0074 0.14 3.21 urn:x-wiley:19422466:media:jame21583:jame21583-math-0075 0.21
HR–LR 0.49 0.17 0.32
Note. The trends and 95% confidence intervals are computed with the time series in Figure 6 from 2,001 to 2,100. The unit is mm/yr.
Figure 6: Time series of dynamic sea level, local steric height and mass transports on the northeast shelf near Boston, Massachusetts (a–c) and on the southeast shelf near Jacksonville, Florida (d–f). The values are spatially averaged within the boxes highlighted in Figures 4a and 4d. Thin and thick lines are yearly mean and 10-year running mean, respectively. Shaded areas in (a–f) are from 2,001 to 2,100, when Atlantic Meridional Overturning Circulation strength starts to decrease (see Figure 9d).
Two factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a–7c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.
Figure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.
Figure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001–2,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.
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Two factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a–7c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.
Figure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.
Figure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001–2,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.
To study the impact of bathymetry on local steric height, we integrate HR projected density changes (urn:x-wiley:19422466:media:jame21583:jame21583-math-0076) from the surface to the depths used in LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0077) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0078), respectively (so the only difference is bathymetry between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0079 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0080 has a shallow bias and urn:x-wiley:19422466:media:jame21583:jame21583-math-0081 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0082 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0083 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0084 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0085 = 8.4 cm. Thus, if LR projects same density change as HR and the only difference is bathymetry, then the bias in LR bathymetry can lead up to 50% difference in local steric height changes in that region. To study the impact of density on local steric height, we integrate the projected density changes of LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0086) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0087) from the surface to urn:x-wiley:19422466:media:jame21583:jame21583-math-0088 (so the only difference is density between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0089 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0090 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0091 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0092 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0093 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0094 = 8.3 cm. Thus, if HR uses the same bathymetry as LR and the only difference is density changes, then the difference in density projections can cause ∼50% difference in local steric height changes in that region.
Both temperature and salinity changes contribute to density changes. In the Gulf of Maine box region, HR projects a 5° C increase in surface temperature from 2001 to 2100, ∼40% larger than the temperature increase (3.6° C) projected by LR (Figure 8b). The enhanced warming projected by HR is consistent with Saba et al. (2016), who showed larger warming rates along the Northwest Atlantic shelf in climate models with higher horizontal resolutions. In addition to enhanced warming, HR also projects larger salinity increases in the entire water column than LR (Figure 8c). The large salinity increases partially compensate the density decreases due to high temperature, leading to reduced density decreases (even density increases at 70 m depth) in HR than that in LR (Figure 8). Note that the density increases near 70 m in HR (Figure 8a) contribute negatively to the local steric height changes.
Associations With AMOC
Previous studies have related DSL changes in the North Atlantic Ocean to AMOC (Chafik et al., 2019; Little et al., 2017; Yin et al., 2009). We start by comparing AMOC overturning streamfunctions between LR and HR. For the mean states (the mean states were computed as the averages over the last 100 years (400–500) of the control simulations, Figures 9a and 9b), differences are noted (a) below 3,000-m depth in the Atlantic basin, and (b) in mid latitudes (∼40°N) between 800 and 1,400 m depth. The former difference may be related to the Nordic Seas overflow parameterization (Danabasoglu et al., 2010), which is used in LR and disabled in HR. At ∼40°N and between 800 and 1,400 m depth, the mean AMOC transport in LR (20–22 Sv, 1 Sv = 106 m3/s) is stronger than that (mostly 16–20 Sv) in HR. One factor that may explain such difference is the mixed layer depth (MLD) bias in the north Atlantic deep water formation regions. By comparing LR, HR and observed MLD, Chang et al. (2020) showed LR contains large positive bias in the north Atlantic deep water formation regions such as Labrador Sea (see their Figure 15). MLD bias there may affect deep water formation and AMOC variability (Yeager et al., 2021). Exploring the impacts of MLD and deep water formation on AMOC is beyond the scope of this work. A study assessing the contributions of the Labrador Sea water formation to AMOC can be found in Yeager et al. (2021).
Figure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401–500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5°N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5°N and 1000-m depth.
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Figure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401–500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5°N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5°N and 1000-m depth.
Figure 9c presents the climatological mean (1986–2005) AMOC overturning streamfunctions at 26.5°N. Compared to the RAPID observations (Smeed et al., 2014, 2018), LR and HR show realistic vertical structures in the upper 2,000 m, with the maximum values at 1,000-m depth. Below 3,000-m depth, model biases are evident and LR is in closer agreement with observations than HR. The large differences between HR and observations maybe related to the aforementioned overflow parameterization (Chang et al., 2020; Danabasoglu et al., 2010). By comparing AMOC simulations from multiple global models, Danabasoglu et al. (2014) showed that large biases between models and RAPID observations at depth are common if the overflows are not parameterized. Under the RCP8.5 emission scenario, LR and HR project similar reductions of AMOC strength (∼8 Sv) from 2,001 to 2,100 (Figure 9d, AMOC strength is defined as the AMOC overturning streamfunction at 26.5°N and 1,000-m depth).
As the AMOC strength decreases, LR and HR project weakened Gulf Stream currents but with different amplitudes (Figure 10). LR projects a decrease in near surface current speed along the entire US east continental slope with the largest decrease occurring at 40° N. For HR, the current speed decreases are mainly confined along the southeast continental slope. The spatial patterns of current speed trends are related to the mean ocean circulation (Figure 2). LR simulated Gulf Stream does not have a clear separation point from the shore, and it moves northward along the entire continental slope (Figures 2c and 2f). As a result, the weakening Gulf Stream currents affect the entire east continental slope. HR simulated Gulf Stream leaves US east continental slope at ∼40° N (Figure 2b), so the effects of weakening Gulf Stream are mainly confined along the southeast slope. For 1 Sv of AMOC reduction, HR projects a larger decrease in Gulf Stream currents at the southeast continental slope compared to LR (Figure 10, Figures 11a, 11b). In addition to the large Gulf Stream reductions, HR shows narrow bands of enhanced current speed on the landside of the Gulf Stream. The increases in current speed are associated with the shift of Gulf Stream path. At 31.5° N, the mean Gulf Stream currents (indicated by the 80 and 120 cm/s velocity contours in Figure 11d) slightly shift toward the continental slope as the Gulf Stream weakens. LR also shows enhanced current speed on the landside of Gulf Stream but the enhancements are only noticed in a few grid points. At 31.5° N, the continental slope and shift in Gulf Stream path are completely absent in LR (Figure 11c).
Figure 10: Regressions of velocity speed at 15-m depth on Atlantic Meridional Overturning Circulation strength from low resolution (a) and high resolution (b). Regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). Green lines in (a) denote the cross sections for Figure 11.
Figure 11: Top panel: Regressions of velocity speed on Atlantic Meridional Overturning Circulation strength across 31.5° N from low resolution (LR) (a) and high resolution (HR) (b). Bottom panel: velocity speed averaged during historical time (2,001–2,020, solid contours) and future time (2,081–2,100, dashed contours) across 31.5° N from LR (c) and HR (d). The cross-section is highlighted as the green line in Figure 10a. In (a)–(b), regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). In (c)–(d), contours with same color have the same velocity speed and the unit of contour labels is cm/s.
Based on geostrophic balance (e.g., urn:x-wiley:19422466:media:jame21583:jame21583-math-0103, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0104 is the meridional geostrophic velocity, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0105 is the Coriolis parameter), large DSL gradient exists across the Gulf Stream. As the AMOC strength decreases, the weakened Gulf Stream currents reduce the DSL gradient across the Gulf Stream. This can lead to DSL rises on the landside of the Gulf Stream and DSL decreases in the open ocean. Compared to HR, LR projects larger current speed decreases along the northeast continental slope, and smaller current speed decreases along the southeast continental slope (Figure 10). This will lead to larger DSL rises along the northeast shelf and smaller DSL rises along the southeast shelf, in line with the projected DSL trends shown in Figures 4a and 4d. In addition to the different Gulf Stream reductions between LR and HR, the landward shift in the Gulf Stream path projected by HR can also affect regional DSL patterns in the future. These suggest that the better resolved Gulf Stream in HR can have significant impacts on regional DSL projections.
Here we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.
Summary and Conclusions
In this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.
HR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region
Both LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)
Compared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40° N), and larger trends of DSL rise along the southeast shelf (south of 35° N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC
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Here we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.
Summary and Conclusions
In this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.
HR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region
Both LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)
Compared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40° N), and larger trends of DSL rise along the southeast shelf (south of 35° N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC
The improved ocean circulation associated with refined horizontal resolution has been reported in numerous studies (Chassignet et al., 2020; Saba et al., 2016; van Westen et al., 2020). Here we show that the HR CESM simulates realistic Gulf Stream currents along the southeast continental slope and southwestward shelf currents along the northeast shelf. The southwestward shelf currents carry cold and fresh water from the Labrador Sea to Gulf of Maine, reducing warm temperature and high salinity bias. These results are consistent with Saba et al. (2016), who showed improved regional circulations and reduced temperature and salinity bias in the HR GFDL CM simulations. In addition to reduced biases in ocean circulation, HR better resolves small scale features of bathymetry and coastline. These make HR more suitable for regional sea-level study than LR. Jean-Michel et al. (2021) reported a global reanalysis product with a horizontal resolution of 1/12urn:x-wiley:19422466:media:jame21583:jame21583-math-0108 called GLORYS12. Such HR data products provide valuable information for regional studies.
In response to a weakening AMOC under global warming, both LR and HR models project decreasing Gulf Stream currents but at different spatial locations. The weakening Gulf Stream currents occur along the entire east continental slope in LR, while they are confined along the southeast continental slope in HR. The difference in Gulf Stream changes is related to the mean ocean circulation patterns. Compared with observations, LR simulated Gulf Stream does not show a clear separation from the shore. Thus, the weakening Gulf Stream currents affect the entire east continental slope. In contrast, HR simulated Gulf Stream leaves the shore at ∼40° N (HR still contains bias given the observed separation point at ∼35° N), so the effects of weakening Gulf Stream are confined along the southeast continental slope. The decreasing Gulf Stream currents can lead to DSL rise on the landside of the Gulf Stream through geostrophic balance. In this study, we focus on the contribution of ocean circulation to DSL. In addition to ocean circulation, sea-level can be influenced by many other processes such as coastal trapped waves (Hughes et al., 2019) and atmospheric forcing (Chafik et al., 2019; Llovel et al., 2018). Based on observational and reanalysis data, Chafik et al. (2019) demonstrated a high correlation between along-shelf winds and sea level along the European coast. Yin et al. (2020) analyzed GFDL simulations and showed the Gulf of Mexico coasts, particularly New Orleans, are most vulnerable to storm related extreme sea-level under global warming. Here we do not consider atmospheric forcing because the role of atmospheric variability on low frequency sea-level changes is still in debate. Woodworth et al. (2014) argued winds can generate low frequency sea-level changes near the coasts, while Little et al. (2019) suggested atmospheric forcing dominates high frequency sea-level variability. The low frequency sea-level variability is mainly associated with AMOC reductions (Little et al., 2017; Yin et al., 2009). Future work is encouraged to explore how atmospheric variability impacts future sea-level changes. Due to the volume conservation constraint in the ocean model used here, the simulated DSL changes do not account for global mean sea-level changes due to volume expansion or contraction. The global mean sea-level change can be estimated with the globally averaged steric height (Greatbatch, 1994; Yin et al., 2010). Under the future RCP 8.5 emission scenario, LR and HR models project similar global mean thermosteric sea-level rise of ∼3 mm/yr from 2,001 to 2,100. Including the global mean thermosteric sea-level rise, HR projects a sterodynamic sea-level rise of 3.5–4 mm/yr along the east shelf. In contrast, LR projects a smaller trend (3–3.5 mm/yr) along the southeast shelf, and a larger trend (4.5–5 mm/yr) along the northeast shelf. These trends do not account for sea-level rise due to glacial melting. Thus, future work may focus on exploring the contributions of glacial melting to sea-level rise. Recent studies have consistently shown that HR climate models produce overall more realistic simulations than LR models (Chang et al., 2020; Griffies et al., 2015; Saba et al., 2016; Small et al., 2014; van Westen et al., 2020). Higher horizontal resolutions enable to resolve more baroclinic modes. These baroclinic modes contains vertical structures and therefore high vertical resolutions become important. Stewart et al. (2017) showed increasing vertical resolutions can lead to ∼ 30% increases in SSH variance south of 40° S. The benefits of HR models can not only be used to learn physical mechanisms but also to diagnose parametrization schemes (Bachman et al., 2020). However, due to high computing costs, HR model ensembles and future projections are still scarce. As of now, only 7 models have completed and published their HR simulation results following CMIP6 HighResMIP protocol (Haarsma et al., 2016). We encourage future efforts to focus on creating more ensembles and simulating different future climate scenarios to improve the robustness of future projections. Another option to reach this goal would be to reduce LR models biases with accurate subgrid parameterizations. Recent advancement of machine learning may help solve this problem (Guillaumin & Zanna, 2021).
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Bamber et al. (2019)
Title:
Ice sheet contributions to future sea-level rise from structured expert judgment
Key Points:
Potential contributions of ice sheets to future sea-level rise (SLR) remain the largest source of uncertainty in SLR projections
For a +2 °C temperature scenario, consistent with the Paris Agreement, the study estimates a median SLR contribution of 26 cm by 2100, with a 95th percentile value of 81 cm. For a +5 °C temperature scenario, more consistent with unchecked emissions growth, the corresponding values are 51 cm and 178 cm, respectively.
Beyond 2100, uncertainty and projected SLR increase rapidly. For the +5 °C scenario, the 95th percentile ice sheet contribution by 2200 is 7.5 m due to instabilities in both West and East Antarctica.
Scenarios of 21st century global total SLR exceeding 2 m should be used for planning purposes.
Keywords:
sea-level rise, climate predictions, ice sheets, Greenland, Antarctica
Corresponding author:
Jonathan L. Bamber
Citation:
Bamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2019). Ice sheet contributions to future sea-level rise from structured expert judgment. Proceedings of the National Academy of Sciences, 116(23), 11195–11200. doi:10.1073/pnas.1817205116
URL:
https://www.pnas.org/doi/full/10.1073/pnas.1817205116
Significance
Future sea level rise (SLR) poses serious threats to the viability of coastal communities, but continues to be challenging to project using deterministic modeling approaches. Nonetheless, adaptation strategies urgently require quantification of future SLR uncertainties, particularly upper-end estimates. Structured expert judgement (SEJ) has proved a valuable approach for similar problems. Our findings, using SEJ, produce probability distributions with long upper tails that are influenced by interdependencies between processes and ice sheets. We find that a global total SLR exceeding 2 m by 2100 lies within the 90% uncertainty bounds for a high emission scenario. This is more than twice the upper value put forward by the Intergovernmental Panel on Climate Change in the Fifth Assessment Report.
Abstract
Despite considerable advances in process understanding, numerical modeling, and the observational record of ice sheet contributions to global mean sea-level rise (SLR) since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change, severe limitations remain in the predictive capability of ice sheet models. As a consequence, the potential contributions of ice sheets remain the largest source of uncertainty in projecting future SLR. Here, we report the findings of a structured expert judgement study, using unique techniques for modeling correlations between inter- and intra-ice sheet processes and their tail dependences. We find that since the AR5, expert uncertainty has grown, in particular because of uncertain ice dynamic effects. For a +2 °C temperature scenario consistent with the Paris Agreement, we obtain a median estimate of a 26 cm SLR contribution by 2100, with a 95th percentile value of 81 cm. For a +5 °C temperature scenario more consistent with unchecked emissions growth, the corresponding values are 51 and 178 cm, respectively. Inclusion of thermal expansion and glacier contributions results in a global total SLR estimate that exceeds 2 m at the 95th percentile. Our findings support the use of scenarios of 21st century global total SLR exceeding 2 m for planning purposes. Beyond 2100, uncertainty and projected SLR increase rapidly. The 95th percentile ice sheet contribution by 2200, for the +5 °C scenario, is 7.5 m as a result of instabilities coming into play in both West and East Antarctica. Introducing process correlations and tail dependences increases estimates by roughly 15%.
Introduction
Global mean sea-level rise (SLR), which during the last quarter century has occurred at an accelerating rate (1), averaging about +3 mm⋅y−1, threatens coastal communities and ecosystems worldwide. Adaptation measures accounting for the changing hazard, including building or raising permanent or movable structures such as surge barriers and sea walls, enhancing nature-based defenses such as wetlands, and selective retreat of populations and facilities from areas threatened by episodic flooding or permanent inundation, are being planned or implemented in several countries. Risk assessment for such adaptation efforts requires projections of future SLR, including careful characterization and evaluation of uncertainties (2) and regional projections that account for ocean dynamics, gravitational and rotational effects, and vertical land motion (3). During the nearly 40 y since the first modern, scientific assessments of SLR, understanding of the various causes of this rise has advanced substantially. Improvements during the past decade include closing the historic sea-level budget, attributing global mean SLR to human activities, confirming acceleration of SLR since the nineteenth century and during the satellite altimetry era, and developing analytical frameworks for estimating regional and local mean sea level and extreme water level changes. Nonetheless, long-term SLR projections remain acutely uncertain, in large part because of inadequate understanding of the potential future behaviors of the Greenland and Antarctic ice sheets and their responses to future global climate change. This limitation is especially troubling, given that the ice sheet influence on SLR has been increasing since the 1990s (4) and has overtaken mountain glaciers to become the largest barystatic (mass) contribution to SLR (5). In addition, for any given future climate scenario, the ice sheets constitute the component with the largest uncertainties by a substantial margin, especially beyond 2050 (6).
Advances since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (7) include improved process understanding and representation in deterministic ice sheet models (8, 9), probabilistic projections calibrated against these models and the observational record (10), and new semiempirical models, based on the historical relationship between temperature and sea-level changes. Each of these approaches has limitations that stem from factors including poorly understood processes, poorly constrained boundary conditions, and a short (∼25 y) satellite observation record of ice sheets that does not capture the time scales of internal variability in the ice sheet climate system. As a consequence, it is unclear to what extent recent observed ice sheet changes (11) are a result of internal variability (ice sheet weather) or external forcing (ice sheet climate).
Where other methods are intractable for scientific or practical reasons, structured expert judgement (SEJ), using calibrated expert responses, provides a formal approach for estimating uncertain quantities according to current scientific understanding. It has been used in a wide range of applications, including natural and anthropogenic hazards such as earthquakes, volcanic eruptions, vector-borne disease spread, and nuclear waste security (12). That said, it should not be regarded as a substitute for fundamental research into driving processes, but instead as a source of complementary insights into the current state of knowledge and, in particular, the extent of the uncertainties (12). An SEJ study conducted in advance of the AR5 (13) (hereafter BA13) provided valuable insights into the uncertainties around ice sheet projections, as assessed at that time.
Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14–16), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.
Here, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts’ uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts’ judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).
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Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14–16), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.
Here, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts’ uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts’ judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).
The participating experts quantified their uncertainties for three physical processes relevant to ice sheet mass balance: accumulation, discharge, and surface runoff. 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) stabilized in 2100 at +2 °C above preindustrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H) stabilized at +5 °C (SI Appendix, Fig. S1). The experts generated values for four dates: 2050, 2100, 2200, and 2300. Experts also quantified the dependence between accumulation, runoff, and discharge within each of the three ice sheets, and between each ice sheet for discharge only, for the H scenario in 2100. We used temperature trajectories rather than emissions scenarios to isolate the experts’ judgements about the relationship between global mean surface air temperature change and ice sheet changes from judgements about climate sensitivity.
An important and unique element of SEJ2018 was the elicitation of intra- and inter-ice sheet dependencies (SI Appendix, Note 1.5). Two features of dependence were elicited: a central dependence and an upper tail dependence. The former captures the probability that one variable exceeds its median given that the other variable exceeds its median, whereas the latter captures the probability that one variable exceeds its 95th percentile given that the other exceeds its 95th percentile. It is well known that these two types of dependence are, in general, markedly different, a property that is not captured by the usual Gaussian dependence model. The latter always imposes tail independence, regardless of the degree of central dependence, and can produce large errors when applied inappropriately (24). For example, if GrIS discharge exceeds its 95th percentile, what is the probability that runoff will also exceed its 95th percentile? This probability may be substantially higher than the independent probability of 5%, and ignoring tail dependence may lead to underestimating the probability of high SLR contributions. On the basis of each expert’s responses, a joint distribution was constructed to capture the dependencies among runoff, accumulation, and discharge for GrIS, WAIS, and EAIS, with dependence structures chosen, per expert, to capture central and tail dependences (Methods and SI Appendix, Note 1.5). In BA13, heuristic dependency values were applied on the basis of simple assumptions about the response of processes to a common forcing.
To help interpret the findings, experts were also asked to provide qualitative and rank-order information on what they regard to be the leading processes that could influence ice dynamics and surface mass balance (snowfall minus ablation); henceforth, this is termed the descriptive rationale. Further details can be found in the SI Appendix. The combined sea-level contribution from all processes and ice sheets was determined assuming either independence or dependence. Here, we focus on the findings with dependence; we examine the effect of the elicited dependencies and the approach taken in SI Appendix, Note 1.5.
The ice sheet contributions were expressed as anomalies from the 2000–2010 mean states, which were predefined (SI Appendix, Table S7). The baseline sea-level contribution for this period was prescribed as 0.76 mm⋅y−1 (0.56, 0.20, and 0.00 mm⋅y−1 for GrIS, WAIS, and EAIS, respectively) and has been added to the elicited values discussed here. This is close to an observationally derived value of 0.79 mm⋅y−1 for the same period, which was published subsequently to the SEJ workshops (4).
Results and Discussion
Fig. 1 shows the probability density functions (PDFs) for both temperature trajectory scenarios for the combined ice sheet contributions, assuming some dependencies exist between ice sheet processes, as elicited from the expert group (SI Appendix, Note 1.5). The associated numerical values are detailed in Table 1, and plots for all four epochs are provided in SI Appendix, Fig. S2. They display similar characteristics to Fig. 1. The PDFs were generated using Monte Carlo sampling from the intrinsic range obtained from the expert responses (22). All PDFs are non-Gaussian and exhibit an extended upper tail, especially for the H temperature scenario. We believe this reflects the experts’ joint view that large amplitude, nonlinear instabilities could be triggered at this higher temperature, even by 2050. For example, for 2050, the median [and likely range, defined as the 17–83% probability range, as in the AR5 (25)] of the ice sheet contributions are 10 cm (5–18 cm) for the L scenario and 12 cm (6–24 cm) for the H scenario. The tail behavior is discussed further in SI Appendix, Note 1.1. By 2100, the differences between the scenarios grow larger, with projected contributions of 26 cm (12–53 cm) and 51 cm (22–113 cm; Fig. 2 and Table 1).
Fig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm⋅a−1 is included. Note that there is more than a factor five change in the x axis scales.
Table 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000–2010 of 0.76 mm y−1. The AR5-defined likely range (17–83%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.
Year and ice sheet Low High
Mean ± SD 50% 5–95% 17–83% Mean ± SD 50% 5–95% 17–83%
2050
PW01 SLR 11 ± 8 10 1–27 5–18 15 ± 12 12 1–38 6–24
GrIS 7 ± 5 5 2–18 3–11 9 ± 7 6 2–27 4–14
WAIS 7 ± 8 5 0–23 1–7 5 ± 6 4 0–18 1–10
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Fig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm⋅a−1 is included. Note that there is more than a factor five change in the x axis scales.
Table 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000–2010 of 0.76 mm y−1. The AR5-defined likely range (17–83%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.
Year and ice sheet Low High
Mean ± SD 50% 5–95% 17–83% Mean ± SD 50% 5–95% 17–83%
2050
PW01 SLR 11 ± 8 10 1–27 5–18 15 ± 12 12 1–38 6–24
GrIS 7 ± 5 5 2–18 3–11 9 ± 7 6 2–27 4–14
WAIS 7 ± 8 5 0–23 1–7 5 ± 6 4 0–18 1–10
EAIS 0 ± 2 0 −4–4 −2–1 0 ± 4 0 −6–7 −3–2
2100
PW01 SLR 32 ± 25 26 3–81 12–53 67 ± 56 51 7–178 22–112
GrIS 19 ± 16 13 2–57 7–31 33 ± 30 23 2–99 10–60
WAIS 13 ± 16 8 −3–44 2–23 27 ± 33 18 −5–93 3–46
EAIS 3 ± 6 0 −8–12 −3–4 6 ± 17 2 −11–46 −4–11
2200
PW01 SLR 89 ± 72 72 5–231 30–149 204 ± 260 130 5–750 40–251
GrIS 49 ± 47 34 5–149 19–79 77 ± 69 55 3–216 23–122
WAIS 37 ± 45 26 −24–128 1–76 80 ± 113 51 −25–324 −3–138
EAIS 4 ± 15 2 −15–34 −6–10 48 ± 158 6 −29–398 −10–19
2300
PW01 SLR 155 ± 137 120 0–426 47–259 310 ± 322 225 14–988 87–466
GrIS 78 ± 75 55 7–237 30–145 130 ± 117 98 7–349 39–225
WAIS 67 ± 88 44 −47–248 6–131 117 ± 136 83 −36–384 7–228
EAIS 10 ± 41 3 −29–96 −8–24 63 ± 195 10 −53–498 −14–51
Fig. 2: Median and likely range (17th–83rd percentile as used in the AR5) estimates of the ice sheet SLR contributions for different temperature scenarios and different studies. AR5 RCP ice sheet contributions are shown for RCP 2.6 and RCP 8.5 by combining contributions from the different sources (gray bars). BA13 is shown for the elicited temperature increase of 3.5 °C by 2100 (orange bar). This study (SEJ2018, in blue) is shown for the L and H temperature scenarios using solid lines. Dashed lines are interpolated from the L and H findings, using stochastic resampling of the distributions assuming a linear relationship between pairs of L and H samples.
The relative contribution of each ice sheet to total SLR (used here to refer to the sum of the three ice sheet contributions) depends on the temperature scenario. To demonstrate this, we compare the mean projections for the three ice sheets for the overall 2100 H distribution, for the same distribution conditional on the total contribution being above the median total projection (>51 cm), and the same distribution conditional on the total being above the 90th percentile (>141 cm). In the unconditional distribution, GrIS dominates the mean projection, contributing 33 cm (49%) of the 67-cm total, compared with 27 cm for WAIS and 6 cm for EAIS: proportions that approximately mirror the present-day contributions (4). The GrIS share declines for larger total contributions. For the mean of the upper half of total SLR projections, GrIS contributes 49 cm (46%) of 106 cm total compared with 44 cm for WAIS and 13 cm for EAIS; for the mean of the top decile, GrIS contributes 60 cm (30%) of the 194-cm total compared with 95 cm for WAIS and 39 cm for EAIS.
Statistically, the declining GrIS share and declining GrIS/AIS ratio reflect a higher mean estimate but slightly less skewed distribution for GrIS than for WAIS, and a long tail for EAIS (Fig. 3), as well as the assessed dependence structure between different terms. Physically, this is likely a result of the role of highly nonlinear dynamic processes coming into play for marine sectors of the AIS that are needed to achieve the higher values of total SLR, whereas at lower total SLR values, more linear processes dominate. It is also noteworthy that the fifth percentiles for both temperature scenarios and for all epochs are less than their current values, suggesting a scenario in which increased snowfall, primarily over the AIS (Table 1), plausibly compensates for any changes in ice dynamics and enhanced melting over the GrIS.
Fig. 3: Individual ice sheet contributions to SLR for 2100 L (A) and H (B) temperature scenarios, assuming dependences between the ice sheets in terms of the processes of accumulation, runoff, and discharge. PDFs were generated from 50,000 realizations of the relevant SEJ distributions. Horizontal bars indicate the fifth, 50th, and 95th percentile values (i.e., the 90% credible range). Also shown are the likely range (17th–83rd percentile) as defined in the AR5 and the total AIS contribution (WAIS plus EAIS assuming the inter ice sheet dependencies elicited). Note that this is not simply the sum of WAIS and EAIS contributions because of inter-ice sheet dependencies. The AIS values are compared with a recent emulator approach (30) in SI Appendix, Fig. S11.
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Statistically, the declining GrIS share and declining GrIS/AIS ratio reflect a higher mean estimate but slightly less skewed distribution for GrIS than for WAIS, and a long tail for EAIS (Fig. 3), as well as the assessed dependence structure between different terms. Physically, this is likely a result of the role of highly nonlinear dynamic processes coming into play for marine sectors of the AIS that are needed to achieve the higher values of total SLR, whereas at lower total SLR values, more linear processes dominate. It is also noteworthy that the fifth percentiles for both temperature scenarios and for all epochs are less than their current values, suggesting a scenario in which increased snowfall, primarily over the AIS (Table 1), plausibly compensates for any changes in ice dynamics and enhanced melting over the GrIS.
Fig. 3: Individual ice sheet contributions to SLR for 2100 L (A) and H (B) temperature scenarios, assuming dependences between the ice sheets in terms of the processes of accumulation, runoff, and discharge. PDFs were generated from 50,000 realizations of the relevant SEJ distributions. Horizontal bars indicate the fifth, 50th, and 95th percentile values (i.e., the 90% credible range). Also shown are the likely range (17th–83rd percentile) as defined in the AR5 and the total AIS contribution (WAIS plus EAIS assuming the inter ice sheet dependencies elicited). Note that this is not simply the sum of WAIS and EAIS contributions because of inter-ice sheet dependencies. The AIS values are compared with a recent emulator approach (30) in SI Appendix, Fig. S11.
Direct comparison with the AR5 is complicated by the use of different external forcings. Our L scenario is slightly warmer than the median projection for Representative Concentration Pathway (RCP) 2.6, and cooler than the median projection for RCP 4.5 at 2100 (2081–2100 global mean warming of +1.9 °C compared with medians of +1.6 °C and +2.4 °C, for RCP 2.6 and RCP 4.5, respectively), whereas our H scenario is roughly comparable to the median projection for RCP8.5 (2081–2100 global mean warming of +4.5 °C compared with a median of +4.3 °C for RCP 8.5), although with different trajectories (SI Appendix, Fig. S1). Our two temperature scenarios were chosen to assess the potential consequences, in terms of SLR, of the goal of the COP21 Paris agreement to keep global temperatures below +2 °C above preindustrial and of a scenario closer to business as usual, as opposed to matching a specific RCP. For comparison, the AR5 likely range ice sheet SLR contribution for RCP8.5 at 2100 is 6–35 cm, with a median of 19 cm (7) (Fig. 2). As mentioned, comparing our findings with those from the AR5 requires transforming temperatures and percentiles to match those used in the AR5. Nonetheless, given these caveats, it is clear the SEJ median and upper value of the likely range (83rd percentile) are statistically significantly larger than the corresponding AR5 values (Fig. 2). Our likely range upper bound is almost three times the AR5 value for RCP 8.5 (94 vs. 35 cm, estimated by summing the individual components considered in the AR5 and, hence, assuming perfect dependence). This is driven, primarily, by larger uncertainty ranges for the WAIS and GrIS contributions (Fig. 3), possibly resulting from experts’ consideration of the aforementioned nonlinear processes. We note also that the uncertainties have grown substantially in comparison with BA13, where the elicited temperature increase above preindustrial was +3.5 °C (indicated by the orange line in Fig. 2). In comparison, our current findings result in a larger uncertainty range at a lower temperature increase (Fig. 2). There has been recent consideration of the benefits of limiting warming to +1.5 °C (26) and what difference this would make compared with the Paris Agreement +2 °C. The reduction in the sea-level contribution from the ice sheets at this lower temperature for our study is broadly in line with the findings of the Intergovernmental Panel on Climate Change Special Report on 1.5 °C, which obtained a value of 10 cm reduction in global mean sea level from all sources (26).
Another important point is the positive skews of the distributions, which result in long upper tails that are less apparent in the AR5 values (limited to the likely range). For example, the median values obtained here and in the AR5 for RCP2.6 differ by 8 cm (Fig. 2), but the 83rd percentile from the SEJ is about 100% larger (51 vs. 25 cm). This becomes even more important if considering probabilities beyond the likely range defined in the AR5, such as the very likely range (the 90th percentile confidence interval). This is apparent from the values in Table 1. Kurtosis provides a quantitative measure of tail behavior and is discussed in SI Appendix, Note 1.1.
Fig. 3 illustrates the PDFs for 2100 L and H temperature trajectories for each ice sheet. The 90% credible intervals for the GrIS and WAIS (approximately equivalent to the very likely range in Intergovernmental Panel on Climate Change terminology) are broadly similar to one another in both scenarios (c.f. the 90% credible interval bars in Fig. 3 A and B). For the 2100 L and H scenarios, the EAIS uncertainty ranges are about a factor of three and two smaller, respectively. Median values for the GrIS and WAIS are broadly comparable (13/8 cm for L and 23/18 cm for H), whereas the EAIS median values are 0 and 2 cm for L and H, respectively. Both the WAIS and GrIS show a strong skew with a long positive tail, which is absent for the EAIS for 2100 L but begins to emerge for 2100 H. There is, consequently, a substantial difference between the high-end, 95th percentile values considered here versus the 83rd percentile value presented in the AR5, which is far more pronounced than differences between the fifth and 17th percentiles (Fig. 3). For WAIS under 2100 H, the difference between the 83rd and 95th percentile is a factor two (Fig. 3 and Table 1), and a factor four for the EAIS. This is also seen when considering the total SLR from the ice sheets. For 2200 H, the 83rd and 95th percentiles are 251 and 750 cm, respectively (Table 1). By limiting consideration only to the likely range, the AR5 results miss this tail behavior, which is a critical component of risk management.
The present SEJ demonstrates a shift in expert opinion since BA13 (i.e., in 2012), when it was found that the GrIS had the narrowest 90% credible range but the largest median SLR rate (13). Here, the GrIS still has the largest median value (for both L and H), but the upper tail of the distribution is now comparable to that of the WAIS (Fig. 3A). It is difficult to determine the basis for this, but we note that the experts overwhelmingly believe that the recent (last 2 decades) acceleration in mass loss from the GrIS is predominantly a result of external forcing, rather than internal variability. Of the 22 experts, 18 judge the acceleration is largely or entirely a result of external forcing (SI Appendix, Fig. S9A and Table S6). This is an important and statistically significant shift from the findings in BA13. In contrast, for the WAIS, opinion remains divided, with seven experts indicating their view that it is largely a result of internal variability, seven placing more weight on external forcing, and eight giving equal weights to each. This reflects the earlier conclusions of BA13.
The findings of SEJ2018 cannot be directly compared with BA13 because the target questions differ, as do the temperature scenarios. The closest comparison that can be made between SEJ2018 and BA13 is for the latter’s cumulative 5/50/95% SLR values of 10/29/84 cm for 2010–2100, which comprised two-thirds from GrIS, one-third from WAIS, and a negligible amount from EAIS, for a temperature increase based on experts’ judgement of +3.5 °C (13). For SEJ2018, we obtain −5/18/73 cm for +2 °C rise and −1/43/170 cm for +5 °C rise (integrated over 2000–2100). Fig. 2 compares the likely range in BA13 and the various temperature markers used here and in the AR5. It is evident that opinion has shifted toward a stronger ice sheet response and a larger credible range, for a given temperature change, than was considered plausible by the experts 6 y ago.
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The present SEJ demonstrates a shift in expert opinion since BA13 (i.e., in 2012), when it was found that the GrIS had the narrowest 90% credible range but the largest median SLR rate (13). Here, the GrIS still has the largest median value (for both L and H), but the upper tail of the distribution is now comparable to that of the WAIS (Fig. 3A). It is difficult to determine the basis for this, but we note that the experts overwhelmingly believe that the recent (last 2 decades) acceleration in mass loss from the GrIS is predominantly a result of external forcing, rather than internal variability. Of the 22 experts, 18 judge the acceleration is largely or entirely a result of external forcing (SI Appendix, Fig. S9A and Table S6). This is an important and statistically significant shift from the findings in BA13. In contrast, for the WAIS, opinion remains divided, with seven experts indicating their view that it is largely a result of internal variability, seven placing more weight on external forcing, and eight giving equal weights to each. This reflects the earlier conclusions of BA13.
The findings of SEJ2018 cannot be directly compared with BA13 because the target questions differ, as do the temperature scenarios. The closest comparison that can be made between SEJ2018 and BA13 is for the latter’s cumulative 5/50/95% SLR values of 10/29/84 cm for 2010–2100, which comprised two-thirds from GrIS, one-third from WAIS, and a negligible amount from EAIS, for a temperature increase based on experts’ judgement of +3.5 °C (13). For SEJ2018, we obtain −5/18/73 cm for +2 °C rise and −1/43/170 cm for +5 °C rise (integrated over 2000–2100). Fig. 2 compares the likely range in BA13 and the various temperature markers used here and in the AR5. It is evident that opinion has shifted toward a stronger ice sheet response and a larger credible range, for a given temperature change, than was considered plausible by the experts 6 y ago.
The rather high median and 95% values for 2100 SLR (Fig. 2 and Table 1), found here, likely reflect recent studies that have explored, in particular, AIS sensitivity to CO2 forcing during previous warm periods (27, 28) and new positive feedback processes such as the Marine Ice Cliff Instability (19), alongside the increasing evidence for a secular trend in Arctic climate (29) and subsequent increasing GrIS mass loss (4). A recent study (30) has used an emulator approach to reexamine the potential role of the Marine Ice Cliff Instability in explaining past sea level and how this affects projections, and we can compare our AIS results with the projections reported in ref. 30. Our results lie between the emulation with Marine Ice Cliff Instability and without, lying closer to the latter for the median values (SI Appendix, Fig. S11). Uncertainties for the H temperature scenario grow rapidly beyond 2100, with 90th percentile credible ranges of −10 to 740 cm and −9 to 970 cm for 2200 and 2300, respectively. Limiting projections to the likely range largely obscures the real, and potentially critical, extent of the deep uncertainties evident in this study.
Global Total SLR Projections
To place these results in the context of total SLR projections, including contributions from ocean thermal expansion, glaciers, and land-water storage, we use a probabilistic SLR projection framework (3). Specifically, we substitute Monte Carlo samples from the PW01 joint probability distribution in SEJ2018 for the ice sheet values used in Kopp et al. (3), while keeping the remaining projections for other components of SLR. For thermal expansion and glaciers, these projections are driven by CMIP5 model projections, using an approach similar to that of AR5. For land-water storage, the projections are based on semiempirical relationships among population, dam construction, and groundwater withdrawal (3). We combine the L scenario ice sheet projections with the other components from the +2.0 °C scenario developed by Rasmussen et al. (31), and for the H scenario with those for RCP 8.5 from Kopp et al. (3).
Compared with other SLR projections for 2050 developed over the last 6 y (32), the 2050 L projections are broadly comparable (very likely range of 16–49 cm), whereas the 2050 H projections are somewhat fatter tailed, with the very likely range extending up to 61 cm (Table 2). This compares with the 20 studies compiled by Horton et al. (32), which spanned from 12 cm at the low end of fifth percentile projections to 48 cm at the high end of 95th percentile projections. There are relatively few +2 °C studies to compare with our 2100 L projections, but those that are compiled in Horton et al. (32) range from 0.2 m at the low end of fifth percentile projections to 1.1 m at the high end of the 95th percentile projections. The SEJ2018 distributions fall on the high side of this range, with a median projection of 0.7 m and a 90th percentile range of 0.4–1.3 m.
Table 2: Total global-mean sea-level rise projections. Produced by combining PW01 ice sheet projections with thermal expansion, glacier, and land water storage distributions from Kopp et al (3).
Centimeters above 2000 CE 50% 17–83% 5–95% 1–99%
2050 L 30 22–40 16–49 10–61
2050 H 34 26–47 21–61 16–77
2100 L 69 49–98 36–126 21–163
2100 H 111 79–174 62–238 43–329
The 2100 H projections fall within the existing range of RCP 8.5 projections, which have extended upward in recent years, substantially beyond the AR5 range. The 2100 H median projection of 1.1 m falls midway between the AR5 projection of 0.7 m and the 1.5 m that Kopp et al. (6) projected using the Antarctic ice sheet projections of DeConto and Pollard (19), which provided an initial attempt at explicit, continental-scale physical modeling of ice shelf hydrofracturing and marine ice cliff instability. The very likely range of 0.6–2.4 m falls within the 0.4–2.4-m low-fifth percentile to high-95th percentile range in the compilation of Horton et al. (32). This comparison emphasizes the skewness of the expert distribution: although the median projection falls in the middle of recently published projections, the 95th percentile tracks the high end of published projections. Although none of these studies is entirely independent of the others, taken together, they provide strong support for recent coastal planning scenarios that anticipate SLR well above the AR5 range (33–35).
Conclusions
This study suggests that experts’ judgments of uncertainties in projections of the ice sheet contribution to SLR have grown during the last 6 y and since publication of the AR5. This is likely a consequence of a focused effort by the glaciological community to refine process understanding and improve process representation in numerical ice sheet models. It may also be related to the observational record, which indicates continued increase in mass loss from both the AIS and GrIS during this time. This negative learning (36, 37) may appear a counter intuitive conclusion, but is not an uncommon outcome: as understanding of the complexity of a problem improves, so can uncertainty bounds grow. We note that for risk management applications, consideration of the upper tail behavior of our SLR estimates is crucial for robust decision making. Limiting attention to the likely range, as was the case in the Intergovernmental Panel on Climate Change AR5, may be misleading and will likely lead to a poor evaluation of the true risks. We find it plausible that SLR could exceed 2 m by 2100 for our high-temperature scenario, roughly equivalent to business as usual. This could result in land loss of 1.79 M km2, including critical regions of food production, and displacement of up to 187 million people (38). A SLR of this magnitude would clearly have profound consequences for humanity.
Materials and Methods
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Conclusions
This study suggests that experts’ judgments of uncertainties in projections of the ice sheet contribution to SLR have grown during the last 6 y and since publication of the AR5. This is likely a consequence of a focused effort by the glaciological community to refine process understanding and improve process representation in numerical ice sheet models. It may also be related to the observational record, which indicates continued increase in mass loss from both the AIS and GrIS during this time. This negative learning (36, 37) may appear a counter intuitive conclusion, but is not an uncommon outcome: as understanding of the complexity of a problem improves, so can uncertainty bounds grow. We note that for risk management applications, consideration of the upper tail behavior of our SLR estimates is crucial for robust decision making. Limiting attention to the likely range, as was the case in the Intergovernmental Panel on Climate Change AR5, may be misleading and will likely lead to a poor evaluation of the true risks. We find it plausible that SLR could exceed 2 m by 2100 for our high-temperature scenario, roughly equivalent to business as usual. This could result in land loss of 1.79 M km2, including critical regions of food production, and displacement of up to 187 million people (38). A SLR of this magnitude would clearly have profound consequences for humanity.
Materials and Methods
Experts were convened in two separate 2-d workshops, one in Washington, DC, drawing on experts working in North America, followed by one near London, drawing on European experts. The experts were notified in advance of the objectives of the exercise and received examples of questions to be asked, along with a description of the method to be applied for analyzing their responses (SI Appendix, Note 4). To minimize misunderstandings and ambiguities and to clarify issues and aspects of the problem, group discussion of the target questions was allowed before experts individually (and privately) completed each of the three categories of questions. These comprised seed questions used for calibration of the experts, target questions for eliciting judgments on topics for which our goal was to quantify uncertainties, and a set of descriptive rationale questions, through which experts could articulate or summarize their reasoning about the target items (SI Appendix, Note 3). The period for answering questions was unlimited, but in practice was about 6–8 h overall. At the conclusion of the first day, responses were collated and preliminary probability distributions were developed from EW and from performance weights combination solutions, using the Classical Model Decision Maker approach (22). These preliminary outcomes were presented to the experts on the second day, and they were given an opportunity to discuss and, if they wished, to revise their initial judgments. Although a broad discussion revealed what motivated many of the responses and provided a basis for our interpretation here of the key contributory factors, few experts changed any of their responses after this provisional presentation.
After the elicitation, the target item uncertainty distributions were recalculated with the Classical Model to conform to the goal of achieving optimal statistical accuracy with minimal credible bounds (e.g., high informativeness). This is accomplished by forming a weighted combination of those experts for which the hypothesis that their probabilistic assessments were statistically accurate would be not rejected at the 0.01 level (denoted PW01). The threshold 0.01 was chosen to achieve robust representation of experts from both workshops while enforcing standard scientific constraints on statistical hypotheses. On this basis, the judgments of six US and two European experts were preferred, and the outcomes of pooling their judgments are shown in SI Appendix, Table S1, for each of the temperature scenarios. Instead of choosing a statistical rejection threshold based on standard hypothesis testing, the Classical Model also allows choosing an optimal threshold that maximizes the statistical accuracy and informativeness of the resulting combination. The effect of this optimization is a moderate reduction in the 90th percentile credible range relative to the PW01 combination.
The Classical Model Decision Maker combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P value drops below some threshold (22). This means that, with such a cutoff, an expert receives their maximal expected weight in the long run by, and only by, stating percentiles that reflect their true beliefs. The weight of an expert is determined by his/her statistical accuracy and informativeness. For comparison, an equally weighted combination of the eight preferred experts (denoted EW01) is formed. EW01’s credible intervals are wider than those of PW01 (SI Appendix, Note 1.1). We use PW01 here to provide robust representation from both panels, as explained here. All combinations concern the experts’ joint distributions, based on the elicited dependence information. Expert scoring is shown in SI Appendix, Table S3, where further details can be found. Rutgers, Princeton University, and Resources for the Future (RFF) considered this study to be exempt from requiring informed consent.
Supplementary Information
Determining expert quantiles
Thirteen experts participated in the expert elicitation on contribution to sea level rise from ice sheets, held at RFF, Washington DC, USA on Jan 25-26. Nine experts participated in a similar elicitation held near London, UK on Feb 20-21, 2018. The two elicitations used the same elicitation protocol. The assessments concerned Accumulation, Runoff and Discharge for GrIS, WAIS and EAIS for the time temperature scenarios shown in Figure S1. Experts were chosen based on whether they were research active in the topic, assessed on their publications over the last ~5 years and involvement in related initiatives such as NASA SeaRise, Delta Commission (Netherlands Govt), EU Ice2Sea project, Ice Sheet MIPS etc. A working minimum group size, from previous experience, is about six experts and more than 20 provides diminishing returns in terms of the performance of the synthetic pooled expert. We also wished to obtain a balance in age, gender and specialism within the broad field of ice sheets and SLR and to avoid accessing multiple experts from the same group. In addition to the 22 that participated, nine experts were invited who could not attend (4) or did not wish to (5).
The participating experts are listed below
US elicitation: Robert Bindschadler, Rob DeConto, Natalya Gomez, Ian Howat, Ian Joughin, Shawn Marshall, Sophie Nowicki, Stephen Price, Eric Rignot, Ted Scambos, Christian Schoof, Helene Seroussi, Ryan Walker
EU elicitation: Gaël Durand, Johannes Fuerst, Hilmar Gudmundsson, Anders Levermann, Frank Pattyn, Catherine Ritz, Ingo Sasgen, Aimee Slangen, Bert Wouters
The assessments were combined using equal weighting and performance-based weighting. In the EU expert panel, one expert provided judgments based on a conceptual interpretation of the three processes, Accumulation, Runoff and Discharge, that differed significantly from the definitional framework outlined in the questionnaire; the expert acknowledged this to be the case upon enquiry, and their judgments were not included in subsequent processing. In the US panel one expert misinterpreted the baseline values, as a result, their uncertainty judgments contained systematic discrepancies in relation to others in the panel. Unfortunately, there was not an opportunity to re-visit and correct this expert’s evaluations in a timely manner, and so the relevant inputs were removed from the analysis reported here.
The combined assessments were convolved to obtain the overall ice sheet contribution to global sea level rise using dependence information provided by the experts
Overall Results
In this exercise experts quantified their 5th, 50th and 95th percentiles for accumulation, for discharge and for runoff for each of GrIS, WAIS and EAIS as anomalies from the 2000-2010 baseline trend (see Supplementary note 5).
They also quantified their dependence between these quantities at 2100 with 5˚ C warming with respect to pre-industrial. This same dependence structure was applied for all other scenarios. As an extension, more articulated dependence structures could be elicited for the different scenarios and applied to the present assessments. In the terminology of SEJ, a Decision Maker (DM) is a “synthetic pooled expert” that is some weighted combination of experts. Equal Weights (EW) is sometime referred to as “one person one vote”. Performance Weighting (PW) is where experts are weighted based on measures of their informative and accuracy quantified using a set of calibration questions or items (described in greater detail in SI Note 1.2).
The results with Performance Weighting (PW) are shown in Table S1 in yellow. For the final results, it was decided to use the performance weighted combination of all experts whose statistical accuracy (P- value) was greater than 0.01 (PW01). EW denotes Equal Weighted combinations.
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EU elicitation: Gaël Durand, Johannes Fuerst, Hilmar Gudmundsson, Anders Levermann, Frank Pattyn, Catherine Ritz, Ingo Sasgen, Aimee Slangen, Bert Wouters
The assessments were combined using equal weighting and performance-based weighting. In the EU expert panel, one expert provided judgments based on a conceptual interpretation of the three processes, Accumulation, Runoff and Discharge, that differed significantly from the definitional framework outlined in the questionnaire; the expert acknowledged this to be the case upon enquiry, and their judgments were not included in subsequent processing. In the US panel one expert misinterpreted the baseline values, as a result, their uncertainty judgments contained systematic discrepancies in relation to others in the panel. Unfortunately, there was not an opportunity to re-visit and correct this expert’s evaluations in a timely manner, and so the relevant inputs were removed from the analysis reported here.
The combined assessments were convolved to obtain the overall ice sheet contribution to global sea level rise using dependence information provided by the experts
Overall Results
In this exercise experts quantified their 5th, 50th and 95th percentiles for accumulation, for discharge and for runoff for each of GrIS, WAIS and EAIS as anomalies from the 2000-2010 baseline trend (see Supplementary note 5).
They also quantified their dependence between these quantities at 2100 with 5˚ C warming with respect to pre-industrial. This same dependence structure was applied for all other scenarios. As an extension, more articulated dependence structures could be elicited for the different scenarios and applied to the present assessments. In the terminology of SEJ, a Decision Maker (DM) is a “synthetic pooled expert” that is some weighted combination of experts. Equal Weights (EW) is sometime referred to as “one person one vote”. Performance Weighting (PW) is where experts are weighted based on measures of their informative and accuracy quantified using a set of calibration questions or items (described in greater detail in SI Note 1.2).
The results with Performance Weighting (PW) are shown in Table S1 in yellow. For the final results, it was decided to use the performance weighted combination of all experts whose statistical accuracy (P- value) was greater than 0.01 (PW01). EW denotes Equal Weighted combinations.
Total ice-sheet SLR is the sum of SLR from all three ice sheets: however, this is a sum of stochastic variables. For 2300H the total mean of 287 cm is the sum of 63 cm, 113 cm and 111 cm, but the quantiles do not sum in this way. For 2300H, the total 95th percentile, 966cm, is smaller than 498 cm + 332 cm + 378 cm = 1208 cm. Adding stochastic variables requires knowledge of their joint distribution. The quantiles will add only if the variables are completely rank dependent (sometimes called co- monotonic). In this case one variable is at or above its 95th percentile if and only if the others are as well. The chance of that happening is then 5%, which means that the sum of the 95th percentiles is exceeded with probability 5%. If the variables are independent, then the chance that all three are at or above their respective 95th percentiles is 0.053 = 0.000125. In this case the 95th percentile will be much lower than the sum of the separate 95th percentiles. In fact, if the three ice sheets are independent the 95th percentile of PW01 (Figure S9b) is 823 cm. The difference 966 cm − 823 cm reflects the effect of the dependence.
The choice of a cutoff for statistical accuracy (P-value) beneath which experts are unweighted is imposed by the theory of strictly proper scoring rules (see Supplementary Information section 1.2). The scoring rule theory does not say what this cutoff should be, only that there should be some positive lower bound to the admissible statistical accuracy scores. Optimal performance weighting (PWOpt) chooses a cutoff which optimizes the scores of the resulting combination. PW01 reflects the choice to include all those experts who have acceptable statistical accuracy so as to ensure wider representation. The distributions of PW01 are somewhat wider than those of PWOpt. With the optimal cutoff of 0.399, only experts 3 and 14 are weighted. Cutoff = 0.01 forms a weighted combination of eight experts whose statistical accuracy is above 0.01; these are experts 3,6,8,9,12,14,24 and 27. EW01 forms an equal weighted combination of these same eight experts. All combinations concern the experts’ joint distributions based on the elicited dependence information.
Expert Scoring
The expert judgment methodology applied here is termed the “Classical Model” because of its analogy to classical hypothesis testing (1). The key idea is that experts are treated as statistical hypotheses. Experts were given a PowerPoint presentation to explain the basic features of the method (see SI Section 8), on which this section is based. Expert scoring is shown in Table S2. For detailed explanations please refer to (2), especially the online supplementary material (Appendix A).
An expert’s statistical accuracy is the P-value (column 2 in Table S2) at which we would falsely reject the hypothesis that an expert’s probability assessments are statistically accurate. Roughly, an expert is statistically accurate if, in a statistical sense, 5% of the realizations fall beneath his/her 5th percentile, 45% of the realizations fall between the 5th and 50th percentile, etc. High values (near 1) are good, low values (near 0) reflect low statistical accuracy. An expert’s informativeness is measured as the Shannon relative information in the expert’s distribution relative to a uniform background measure over an interval containing all experts’ percentile assessments and the realizations, variable-wise. Columns 3 and 4 give the average information scores for each expert for all variables (column 3) and all calibration variables (column 4). The number of calibration variables is shown in column 5 for each expert (in this case all experts assessed all 16 calibration variables). The product of columns 2 and 4 is the combined score for each expert. Note that statistical accuracy scores vary over seven orders of magnitude whereas information scores vary within a factor three. Therefore, by design, the ratios of the products of combined scores are dominated by the statistical accuracy. If an expert’s P-value is above a cut-off value (in this case P=0.01) then the expert is weighted with weight proportional to the combined score. Normalized weights for weighted experts are shown in column 6.
A combination of the experts’ distributions is termed a “decision maker” (DM). Column 7 gives each expert’s Shannon relative information with respect to the equal weight (EW) DM (1). These dimensionless numbers indicate the divergence among the experts themselves and are compared with perturbations caused by dropping a single expert or a single calibration variable (Supplementary Tables 3 and 4). Note that the scores in column 7 are somewhat smaller than the scores in column 3. This suggests that EW is somewhat more informative than the background measure, relative to which the experts’ informativeness is measured in column 3.
Other DMs in Table 2, besides EW, are PW01, the performance weighted combination of the eight weighted experts, and PWOpt, the performance weighted combination with the cutoff chosen to optimize the combined score of the DM. Indeed, the combined score of PWOpt (0.4914) is (only) slightly greater than that of PW01 (0.4795). As is typical in such studies, the information of EW is about half that of PWOpt. Very roughly, this translates to EW’s average 90% confidence bands being twice as large as those of PWOpt. Similarly, EW’s statistical accuracy (P-value) is inferior to that of PWOpt. This is an “in-sample” comparison since DM’s are compared on the same set over which PWOpt is optimized. For “out-of-sample” comparisons see below.
Six of the 13 US experts had a statistical accuracy score above 0.01. This is a high number for SEJ studies, especially considering the fact that 16 calibration variables were used, constituting a more powerful statistical test than the traditional number of ten calibration items. Two of the eight EU experts had a statistical accuracy score above 0.01, which is in line with most SEJ studies. There is very little difference between the scores of PWOpt and PW01, though there are modest differences in SLR predictions (see Table S1). A scoring system is asymptotically strictly proper if and only if an expert obtains his/her highest expected score in the long run by, and only by, stating percentiles corresponding to his/her true beliefs. The combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P-value drops below some threshold (1). If (s)he tries to game the system to maximize his/her expected weight, (s)he will eventually figure out that (s)he must say exactly what (s)he thinks. Honesty is the only optimal strategy. The theory does not say what the cut-off value should be, so that is often chosen by optimization.
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Other DMs in Table 2, besides EW, are PW01, the performance weighted combination of the eight weighted experts, and PWOpt, the performance weighted combination with the cutoff chosen to optimize the combined score of the DM. Indeed, the combined score of PWOpt (0.4914) is (only) slightly greater than that of PW01 (0.4795). As is typical in such studies, the information of EW is about half that of PWOpt. Very roughly, this translates to EW’s average 90% confidence bands being twice as large as those of PWOpt. Similarly, EW’s statistical accuracy (P-value) is inferior to that of PWOpt. This is an “in-sample” comparison since DM’s are compared on the same set over which PWOpt is optimized. For “out-of-sample” comparisons see below.
Six of the 13 US experts had a statistical accuracy score above 0.01. This is a high number for SEJ studies, especially considering the fact that 16 calibration variables were used, constituting a more powerful statistical test than the traditional number of ten calibration items. Two of the eight EU experts had a statistical accuracy score above 0.01, which is in line with most SEJ studies. There is very little difference between the scores of PWOpt and PW01, though there are modest differences in SLR predictions (see Table S1). A scoring system is asymptotically strictly proper if and only if an expert obtains his/her highest expected score in the long run by, and only by, stating percentiles corresponding to his/her true beliefs. The combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P-value drops below some threshold (1). If (s)he tries to game the system to maximize his/her expected weight, (s)he will eventually figure out that (s)he must say exactly what (s)he thinks. Honesty is the only optimal strategy. The theory does not say what the cut-off value should be, so that is often chosen by optimization.
In the Classical Model, the optimization works as follows: starting with a cutoff beneath the lowest P- value includes all experts with weight proportional to their combined scores. The combined score of the resulting DM is stored. Taking the expert with the lowest P-value, we next exclude that expert, normalize the remaining combined scores, compute the resulting DM, apply this DM to the calibration variables and store the resulting DM’s combined score. Then we remove the next lowest P-value expert and repeat. With N expert P-values this results in N-1 different DM’s. We choose the DM whose combined score is the highest. In this case, setting the cut-off at 0.399 and retaining experts 3 and 14 produced the highest scoring DM. With this scoring system it is impossible that a weighted expert has a lower P-value than an unweighted expert, even though doing so might produce a higher DM score. This system can thus be regarded as optimal weighting under a strictly proper scoring rule constraint. The theory was developed in the 1980s and is detailed in (1) and (2).
The Classical Model has been applied in hundreds of expert panels and has been validated both in- and out-of-sample (2-5). In the absence of observations of the variables of interest, out-of-sample validation comes down to cross-validation whereby the calibration variables are repeatedly separated into subsets of training- and test variables. The PW model is initialized on the training variables and scored on the test variables. The superiority of PW over EW in terms of statistical accuracy and informativeness has been demonstrated using this approach.
Robustness on Experts
Robustness on experts examines the effect on the PW01 “decision maker” (i.e. the synthetic pooled expert) of losing individual experts. Experts are removed one at a time and PW01 is recomputed. Table S3 shows the resulting information and P-values of the “perturbed” PW01. The rightmost column of Table S4 shows the divergence among the experts themselves. Comparison with the rightmost column of table S3 shows that the scoring results are very robust against loss of a single expert.
A more complete sense of robustness would examine the effect of the method of recruitment of experts and of the elicitation team. Before the Classical Model was adopted for the European uncertainty analysis of accident consequence codes for nuclear power plants (6), the authorities in Brussels required that parallel elicitations be carried out using the same elicitation protocol, but with different elicitation teams independently recruiting different experts. The findings in this case indicate a strong convergence of elicitation results from the two groups (6). Such an approach is generally far beyond the budgets of most applications. However, the results here (Table S1) show good general agreement on SLR between the US and European panels who were elicited separately. A different type of robustness is gleaned from the 14 year running expert judgment assessments of risks from the Montserrat volcano (7). Those assessments concerned a consistent elicitation method, applied to the same variables under changing conditions, with some exchanging of participating experts over elicitations. The approach showed good consistency of performance for volcanic hazard assessment purposes, over more than seventy repeat elicitations.
Robustness on Items
Seed variables are removed one at a time and PW01 is recomputed. These scores are extremely robust against loss of a seed variable. Comparing the rightmost columns of Supplementary Tables 3 and 5 shows that the perturbation caused by loss of a single calibration variable is very small relative to the divergence among the experts themselves.
Dependence Elicitation
Dependence and especially tail dependence are unfamiliar concepts for many scientists. A PowerPoint presentation was given to the experts, before the elicitation, to introduce these notions, where the reader can find precise definitions (see Supplementary Section 8 for links). Figure S6 from the presentation shows how aggregation affects uncertainty. 3 sigma or one in 1000 upper tail events are depicted for the sum of 10 zero mean normal variables. If the variables have a pairwise correlation of 0.5, the distribution dilates such that the 3 sigma event coincides with the sigma event of the sum of independent Normals. If this pairwise correlation is realized with an upper tail dependent copula, the 3 sigma event coincides with the 7 sigma event for independent Normals. Thus an event whose probability is 1/1000 (3 sigma will appear to be an event with probability 1.28*10^{-12} (7 sigma)) when tail dependence is present but ignored.
The dependence elicitation for pairs of variables was accomplished by eliciting conditional exceedance probabilities: for central correlation, experts answered: “what is the probability that variable X exceeds its median given that variable Y has exceeded its median?”. Numerical and verbal answers were accepted (Table S8). For upper tail dependence, “median” was replaced by “95th percentile” in the above question and verbal responses were elicited as indicated in Table S8.
Three random variables (Runoff, Discharge and Accumulation) for each of the three ice sheets yield 36 pairs of variables. Potential dependences between ice sheets were also identified. Based on judgments of size and relevance, the analysis team pared this down to 10 pairs corresponding to the colored nodes in Figure S8, in addition to 3 inter-ice sheet relations. This structure is a “dependence vine” for determining a high dimensional joint distribution based on bivariate and conditional bivariate distributions. Unspecified (conditional) bivariate distributions are conditionally independent, making it easy to extend a partially specified structure to the minimally informative realization of the specified structure.
The basic “dependence vine” for expert 14, as an example, is shown in Figure S8. The ellipses represent the variables (GA = Greenland Accumulation; WD = West Antarctica Discharge; etc). The dependences, represented by arcs, are quantified by assessing exceedance probabilities. The colored nodes are those between which dependence is assessed. Conditional independence is assumed elsewhere. Calculations and sampling were performed with the freeware UNINET. This exposition of vine theory is necessarily incomplete; a Wiki page provides more background and references. A full exposition is in (8, 9).
For each of the eight experts with P-value > 0.01, a comparable regular vine was constructed using the dependence information elicited from each individual expert. These eight joint distributions were combined with the various weighting schemes shown in Table S2.
From expert quantiles to SLR
The procedure of going from expert quantiles to distributions for SLR is as follows (for detailed information see (2), especially the online supplementary material Appendix A):
For each variable we determine an “intrinsic range” (IR), the smallest interval that contains all expert assessments plus the realization (in case of seed variables) + a 10% overshoot below and above (10% is a parameter that can be adjusted in the code)
We put a background measure on each IR. In the code the user can choose between the uniform and log-uniform background measure. Log-uniform is indicated when experts reason in orders of magnitude. In this case all background measures are uniform. Other choices could be made but would require re-coding.
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Three random variables (Runoff, Discharge and Accumulation) for each of the three ice sheets yield 36 pairs of variables. Potential dependences between ice sheets were also identified. Based on judgments of size and relevance, the analysis team pared this down to 10 pairs corresponding to the colored nodes in Figure S8, in addition to 3 inter-ice sheet relations. This structure is a “dependence vine” for determining a high dimensional joint distribution based on bivariate and conditional bivariate distributions. Unspecified (conditional) bivariate distributions are conditionally independent, making it easy to extend a partially specified structure to the minimally informative realization of the specified structure.
The basic “dependence vine” for expert 14, as an example, is shown in Figure S8. The ellipses represent the variables (GA = Greenland Accumulation; WD = West Antarctica Discharge; etc). The dependences, represented by arcs, are quantified by assessing exceedance probabilities. The colored nodes are those between which dependence is assessed. Conditional independence is assumed elsewhere. Calculations and sampling were performed with the freeware UNINET. This exposition of vine theory is necessarily incomplete; a Wiki page provides more background and references. A full exposition is in (8, 9).
For each of the eight experts with P-value > 0.01, a comparable regular vine was constructed using the dependence information elicited from each individual expert. These eight joint distributions were combined with the various weighting schemes shown in Table S2.
From expert quantiles to SLR
The procedure of going from expert quantiles to distributions for SLR is as follows (for detailed information see (2), especially the online supplementary material Appendix A):
For each variable we determine an “intrinsic range” (IR), the smallest interval that contains all expert assessments plus the realization (in case of seed variables) + a 10% overshoot below and above (10% is a parameter that can be adjusted in the code)
We put a background measure on each IR. In the code the user can choose between the uniform and log-uniform background measure. Log-uniform is indicated when experts reason in orders of magnitude. In this case all background measures are uniform. Other choices could be made but would require re-coding.
For each expert and each variable, we fit a density that is minimally informative with respect to the background measure and complies with the expert’s quantile assessments. For the uniform background, this is a piecewise uniform density. This density “adds as little as possible” to the expert’s assessment. Note that fitting a two-parameter family such as the Gaussian distribution will often be unable to match 3 quantiles.
4) ASSUMING INDEPENDENCE
a. With N experts we form the EW combination by simple averaging of the experts’ densities. DO NOT average the quantiles; that can give a very overconfident result.
b. With PW, we take a weighted average of densities.
c. Simple Monte Carlo sampling is used to build a distribution for SLR. For each ice sheet we sample D, R and A and store D+R-A.
d. Monte Carlo sampling is used to build a distribution of total SLR as SLRGr + SLREAIS + SLRWAIS. Again, do not sum the quantiles.
WITH DEPENDENCE, we build a joint density for each expert based on the elicited exceedance probabilities. This cannot be done with generic software. XL add-ons like @Risk and Crystal Ball impose the assumption of the Gaussian copula. Based on a pilot elicitation with the 2012 experts, we anticipated that tail dependence could be significant, rendering the Gaussian copula inappropriate. For each expert we obtain a distribution for total SLR, and we take a weighted average of these densities to find the combined distribution for SLR. Each expert’s total SLR distributions incorporates his/her dependence.
Steps (1) – (3) can be done with freeware EXCALIBUR (EXpert CALIBRation). Step (4) can be done with Freeware UNICORN (UNCertainty analysis wIth CORelatioNs)– which has limited dependence modeling capability). Step (5) uses freeware UNINET which is much more powerful. All these programs can be downloaded from http://www.lighttwist.net/wp/.
Experts’ rationales
This section summarizes and collates the expert responses to the rationale questionnaire that is reproduced in supplementary note 6. For description of the process considered see note 6.
It is apparent that SEJ2018 value spreads for Antarctic Ice Sheet contribution to sea level rise in 2100CE lie above Edwards et al (2019)(10) no-MICI but are substantially lower than the 50th and 95th percentile MICI values obtained using the emulator in (10).
Briefing note sent to experts prior to elicitation
The following briefing note was sent to all experts prior to the elicitation:
Eliciting Ice Sheets’ Contribution to Sea Level Rise
Sept 28, 2017
Introduction: Probabilistic prediction for Ice Sheet contributions to Sea Level Rise
With global warming, ice sheets in Greenland and Antarctica are likely to become the primary agents of Sea Level Rise (SLR) in the coming decades and centuries. In their normally slow, march to the sea, glaciers draining the ice sheets exhibit dynamics which are highly variable from place to place, with neighboring glaciers or ice streams responding in markedly different ways to the same external forcing. Dynamic models must account for things like bedrock properties (including slipperiness and topography), ice shelf buttressing, precipitation, melt water effects on ice stiffness, grounding line migration, ocean currents, and ice cliff instability. Some of these features are directly observable, many are not.
Glaciologists focusing on individual glaciers must contend with many uncertainties when predicting future ice mechanics and dynamics out to, say 2100CE, or even 2300CE. Point predictions, whatever their pedigree, are of limited value when the uncertainties are very large. Scientists must therefore make probabilistic predictions; they must say, in effect “My best estimate is a +0.2mm contribution to SLR by 2100CE from this particular glacier, and I am 90% confident the contribution will be between - 3mm and +6mm”. A narrative might explain, say, “the contribution could actually be negative (the ice sheet would actually grow) if warming and changing atmospheric and ocean circulation increased winter precipitation inland while leaving the buttressing ice shelves largely intact; a very high contribution might result if increased storminess and shifting ocean currents break up ice shelves or summer coastal precipitation causes increased calving and instability”. Capturing the narrative behind the uncertainty assessments is essential for understanding and communicating our current state of knowledge.
That is the easy part. Judging the cumulative future effects of the main ice sheets on sea level rise raises a host of new questions and methodological challenges, lying further outside most physical scientists’ comfort zone. What might be the joint impacts of ice sheet responses on SLR if extreme conditions were encountered under global climate change?
A proof of concept
We describe a proof-of-concept demonstration for using expert judgments to constrain quantitative estimates of dependences in potentially correlated processes that affect the ice sheet (2), and indicate some preliminary trial results. We also explore the influence on these results of different ways of combining expert judgments (3).
A talk on this subject was given at the Banff research center in 2013 by Roger Cooke and can be streamed from http://www.birs.ca/events/2013/5-day-workshops/13w5146/videos/watch/201305221037-Cooke.html
A talk on performance weighting was given at the Centers for Disease Control and Prevention in Atlanta GA on May 23, 2017 by Willy Aspinall, and may be streamed at https://www.youtube.com/watch?v=FPC-h-br8i8&feature=youtu.be
A recent study extending (Bamber and Aspinall, 2013, henceforth B&A) made a first pass at assessing dependences between macro process variables relating to the Greenland, West Antarctica and East Antarctica ice sheets. Estimates of contributions to SLR were based on the B&A protocol. A typical question was
In the case of Greenland, for a global mean annual Surface Average Temperature rise of 3°C by 2100 with respect to pre-industrial, what will be the integrated contribution, in mm to SLR relative to 2000- 2010 of the following:
i) accumulation
5% value: ___________ 95% value: ___________ 50%value: ____________
ii) runoff
5% value: ___________ 95% value: ___________ 50%value: ____________
iii) discharge
5% value: ___________ 95% value: ___________ 50%value:: ____________
Similar questions were directed to West and East Antarctica, and to different temperatures, out to 2200.
The dependence elicitation was based on exceedance probabilities, as pioneered in the 1990’s by uncertainty analyses for nuclear power plants in the US and in Europe. Whereas the earlier nuclear work used only the 50% exceedance probabilities, our ice sheet follow-on study asked also for 95% exceedance probabilities.
Within ice sheet process dependencies to 2100CE
Greenland Ice Sheet, 2100 3°C warming
Given discharge >= your 50% value, what is probability that runoff also >= your 50% =____
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A talk on this subject was given at the Banff research center in 2013 by Roger Cooke and can be streamed from http://www.birs.ca/events/2013/5-day-workshops/13w5146/videos/watch/201305221037-Cooke.html
A talk on performance weighting was given at the Centers for Disease Control and Prevention in Atlanta GA on May 23, 2017 by Willy Aspinall, and may be streamed at https://www.youtube.com/watch?v=FPC-h-br8i8&feature=youtu.be
A recent study extending (Bamber and Aspinall, 2013, henceforth B&A) made a first pass at assessing dependences between macro process variables relating to the Greenland, West Antarctica and East Antarctica ice sheets. Estimates of contributions to SLR were based on the B&A protocol. A typical question was
In the case of Greenland, for a global mean annual Surface Average Temperature rise of 3°C by 2100 with respect to pre-industrial, what will be the integrated contribution, in mm to SLR relative to 2000- 2010 of the following:
i) accumulation
5% value: ___________ 95% value: ___________ 50%value: ____________
ii) runoff
5% value: ___________ 95% value: ___________ 50%value: ____________
iii) discharge
5% value: ___________ 95% value: ___________ 50%value:: ____________
Similar questions were directed to West and East Antarctica, and to different temperatures, out to 2200.
The dependence elicitation was based on exceedance probabilities, as pioneered in the 1990’s by uncertainty analyses for nuclear power plants in the US and in Europe. Whereas the earlier nuclear work used only the 50% exceedance probabilities, our ice sheet follow-on study asked also for 95% exceedance probabilities.
Within ice sheet process dependencies to 2100CE
Greenland Ice Sheet, 2100 3°C warming
Given discharge >= your 50% value, what is probability that runoff also >= your 50% =____
Given discharge >= your 95% value, what is probability that runoff also >= your 95% =____
Given accumulation >= your 50% value, what is probability that discharge also >= your 50% =____
Given accumulation >= your 50% value, what is probability that runoff also >= your 50% =____
In answering questions concerning the 95% exceedances, the experts had to consider whether factors likely to produce extreme values in one variable would also produce extreme values in the other.
An extensive procedures guide for structured expert judgment emerging from these nuclear studies has informed many subsequent applications, including B&A. Following the Classical Model for structured expert judgment (Cooke 1991; Cooke and Goossens 2008), calibration variables from the experts’ field were used by B&A to score the experts’ statistical accuracy and informativeness. True values of calibration variables are known post hoc, they preferably concern near term future measurements, but can also involve unfamiliar intersections of past data or literature. An illustrative calibration variable from B&A was
There are nine main glacier/ice caps on Iceland. What was their 2009/2010 average climatic balance Bclim, in Kg/m2? (please indicate gain by +value, loss by -value)
5% value: ___________ 95% value: ___________ 50%value: ____________
Based on extensive experience with the Classical Model, an equally weighted combination of experts tends to give statistically accurate assessments exhibiting wide confidence bounds (low information). The goal of the Classical Model is to demonstrate high statistical accuracy with narrow confidence bounds. This is accomplished by differentially weighting the experts so as to favor those with high statistical accuracy and high information. Recent background on the Classical Model for climate uncertainty quantification may be found here. Other recent applications are summarized here, a Wikipedia page gives some background, and an extensive study of out-of-sample validation with complete mathematical exposition in supplementary material is here.
Dependence and aggregation
The SLR contribution of, say, the Jakobshaven glacier in western Greenland up to 2100CE is a random variable; it can be described mathematically by giving a range of possible values and a probability that each value would be realized. Quantifying the uncertainty in the contribution to SLR from the Greenland and Antarctic ice sheets involves adding together hundreds of random variables. Adding random variables is not like adding ordinary numbers. In adding two random variables, say the Jakobshaven and the Petermann glaciers’ contributions to SLR by 2100CE, we must consider all possible combinations of values for Jakobshaven and for Petermann, and consider the probability that these values arise together. Suppose the contribution from Jakobshaven were very large. According to the above narrative, that suggests certain influencing factors are in play; how would these influences affect the Petermann glacier, 1274 km to the north? If they would also tend to induce high contribution values for the Petermann, then this could indicate a positive dependence between the SLR contributions of the two glaciers. If, on the contrary, the drivers of elevated ice mass loss in the west of Greenland were conducive to more stable conditions in the north, then the interglacier dependence might be negative.
The more random variables we aggregate, the more important the effects of long range, global correlations can become, a feature which our intuitions easily under-appreciate. A neglected weak global correlation of = 0.2 when summing 500 normal variables underestimates the confidence interval of the sum by an order of magnitude. Global correlations also amplify the correlation of aggregations. In the above example, the correlation between the sum of the first 250 variables and the sum of the second 250 variables is 0.992. In contemplating the uncertainty in the effects of hundreds of glaciers, we must consider the overall effects of these dependencies.
Tail Dependence
The correlation coefficient represents a sort of average association between two random variables. This often yields an adequate measure of their association, but not always. The linkage between two variables may be primarily due to factors driving the extreme values, not the more mundane, central values.
For example, under normal conditions it may be that the mass loss at Jakobshaven and at Petermann vary according to local weather conditions, which are largely uncorrelated. However, very large mass loss at Jakobshaven would implicate large scale warming factors, which in turn could imply large mass loss at Petermann as well. In such cases one speaks of positive tail dependence between the two variables, here glacier processes. Tail dependence can be positive or negative, can affect the upper or lower tails of distributions, or both, and bears no direct relation to the ordinary correlation. Thus, two Gaussian variables are always tail independent. Given that one of them exceeds its rth percentile, the probability that the second also exceeds its own rth percentile tends toward the independent value of (100-r)% as r tends to 100% regardless of the correlation, provided it is strictly between 1 and −1.
In other words, a very high value of one variable tends not to entrain a high value of the other with two Gaussian variables, but this will not be true for variables characterized by other distributions.
Results
The calculations were performed by Aspinall and Cooke defining a regular vine, using the experts’ responses. Regular vines capture dependence in terms of nested bivariate and conditional bivariate distributions on the ranks of random variables, called copulae. The copulae are chosen to mimic the elicited exceedance probabilities. Our highest weighted experts evinced tail dependence between Greenland Discharge and Greenland Runoff, between West Antarctica Discharge and West Antarctica Runoff, and between West Antarctica Discharge and East Antarctica Discharge. Although the actual values of tail dependence varied between experts, they were comparable in magnitude. Other variables exhibited median dependence without tail dependence.
Table 1 presents the overall results for the case of +3˚C global warming by 2100CE, and enables us to gauge the effects of dependence and of performance weighting. “EW” denotes the combination based on equal weighting of all nine experts, “PW” denotes the optimal performance weighting in which two experts were weighted, based on statistical accuracy and informativeness4. “Indep” signifies that experts’ dependence information was not used. The contribution to SLR was computed, per ice sheet, as Runoff + Discharge − Accumulation as if these were independent random variables. “tail indep” signifies that tail dependence was ignored and dependence was based only on the 50% exceedance probabilities. “tail dep” includes the information on tail dependence.
Table 1: “EW” denotes the combination based on equal weighting of all experts, “PW” denotes the optimal performance weighting in which the experts were weighted. “Indep” signifies that no dependence information was used. “tail indep” signifies that dependence was based only on the 50% exceedance probabilities. “tail dep” includes the information on tail dependence.
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In other words, a very high value of one variable tends not to entrain a high value of the other with two Gaussian variables, but this will not be true for variables characterized by other distributions.
Results
The calculations were performed by Aspinall and Cooke defining a regular vine, using the experts’ responses. Regular vines capture dependence in terms of nested bivariate and conditional bivariate distributions on the ranks of random variables, called copulae. The copulae are chosen to mimic the elicited exceedance probabilities. Our highest weighted experts evinced tail dependence between Greenland Discharge and Greenland Runoff, between West Antarctica Discharge and West Antarctica Runoff, and between West Antarctica Discharge and East Antarctica Discharge. Although the actual values of tail dependence varied between experts, they were comparable in magnitude. Other variables exhibited median dependence without tail dependence.
Table 1 presents the overall results for the case of +3˚C global warming by 2100CE, and enables us to gauge the effects of dependence and of performance weighting. “EW” denotes the combination based on equal weighting of all nine experts, “PW” denotes the optimal performance weighting in which two experts were weighted, based on statistical accuracy and informativeness4. “Indep” signifies that experts’ dependence information was not used. The contribution to SLR was computed, per ice sheet, as Runoff + Discharge − Accumulation as if these were independent random variables. “tail indep” signifies that tail dependence was ignored and dependence was based only on the 50% exceedance probabilities. “tail dep” includes the information on tail dependence.
Table 1: “EW” denotes the combination based on equal weighting of all experts, “PW” denotes the optimal performance weighting in which the experts were weighted. “Indep” signifies that no dependence information was used. “tail indep” signifies that dependence was based only on the 50% exceedance probabilities. “tail dep” includes the information on tail dependence.
Ice sheet contribution to SLR by 2100CE with +3˚C warming [mm] mean stdev 5% 50% 95% Expert combination method EW indep 615 270 238 581 1120 PW Indep 335 200 71 307 719 PW tail indep 337 216 64 305 749 PW tail dep 338 229 71 292 785 The largest effect is wrought by using performance-based weighting instead of expert equal weighting. The mean SLR of “EW indep” is nearly twice that of the PW combinations, and the 5- 50- and95- percentiles are substantially shifted upwards, relative to any of the alternative combinations. Focusing on the PW combinations, the effect of including dependence information is most visible in the 95th percentiles; the corresponding means are notably consistent. Including ice sheet inter-dependence, without tail dependence, raises the 95th percentile by +37 mm relative to the independent case; including tail dependence raises this percentile by +66mm relative to the independent case.
These are “linear pooling methods”; other methods have also been proposed for ice sheet uncertainty quantification, for a discussion see Bamber et al (2016).
Conclusions
Predicting the cumulative effect of ice sheets on Sea Level Rise by 2100CE involves large uncertainties. Developing science-based quantifications of these uncertainties obliges scientists to venture outside their comfort zone of deterministic model-based predictions and deal with expert subjective uncertainty assessments. Adding information on dependence and tail dependence increased the values of the upper tail 95th percentiles of the performance weight combination. However, that increase effect was dominated by the reduction in SLR predictions produced by restricting the elicitation solution to our statistically accurate experts.
Reference values for ice-sheet processes
In the elicitation workshops, there was extensive discussion of how to define ice sheet contributions to sea level over future periods of time in relation to the temperature rise trajectories shown in Fig. S1. It was agreed that the ice sheet contributions would be expressed as anomalies from the 2000-2010 mean mass change states, as pre-defined in Table S7. On this basis, the net baseline sea-level contributions for this period were prescribed as 0.76 mm yr-1 for overall SLR, and 0.56, 0.20, and 0.00 mm yr-1 for GrIS, WAIS, and EAIS, respectively. (The resulting joint contribution of the three ice sheets is close to an observationally-derived value of 0.79 mm yr-1 for the same period, which was published subsequently to the SEJ workshops (4)).
For the SLR results presented in the main text, baseline contributions – integrated over the relevant time periods (i.e. from 2000CE to 2050CE; 2100CE; 2200CE and 2300CE) – have been added to the elicited SLR values reported in Supplementary note 1.
Table S8: Reference probabilities assumed for estimating central and tail dependencies.
Prompts for discussion of rationales
Some of the questions below give you options for answering that are not independent (e.g., on the second question, buttressing is not independent of hydrofracturing). In such cases, indicate the option that best captures your overall judgment. In cases where you feel more than one answer is absolutely necessary to best characterize your judgment, feel free to fit in more than one response. Where changes are referred to and a future period is specified, these are for the difference between the future period and the base period, 2000-2010.
Mass change observations and assumptions
Are the recent ~decadal trends in mass balance largely due to internal variability of the atmosphere/ice/ocean/climate system or anthropogenic forcing, for each ice sheet overall?
Sheet: GrIS WAIS EAIS
IV EF IV EF (no trend) (no trend)
Dynamical processes
How will changes in near-field gravitational and vertical land motion due to past and future ice sheet unloading affect marine ice sheet instability: Decrease instability (D), Increase instability (I), or No significant change (N)?
Sheet GrIS WAIS EAIS
D I N
Among buttressing by ice shelves (B), basal traction (BT), transverse stresses (TS), hydrofracturing (HF), ice cliff instability (IC), and dissipation after iceberg formation at exit gates (DI), which one will be the most important for controlling the overall 21st, 22nd, and 23rd century discharge rate and grounding line migration for key ice streams and outlet glaciers (recognizing time variations in the role of each)? Key ice streams are those that you expect to control overall discharge for that ice sheet.
2°C scenario: Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd B BT TS HF IC DI
5°C scenario: Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd B BT TS HF IC DI
Surface mass balance
Between atmospheric circulation/moisture transport changes (AM) and albedo changes (AC), which do you consider more important for determining surface mass balance of grounded ice during the 21st, 22nd, and 23rd century.
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC
Among changes in summer sea ice extent (SI), atmospheric circulation/moisture transport changes (AM), and albedo changes (AC), which do you consider most important for determining surface mass balance and rate of thinning of ice shelves in 21st, 22nd, and 23rd century?
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC
Ocean processes
Among Antarctic circumpolar current changes (ACC), changes in intrusion of circumpolar deep water onto continental shelf (CDW), and changes in AMOC (MOC), which do you consider will have the largest effect on sub-shelf basal melt rates during the 21st, 22nd, and 23rd century?
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC
Polar Amplification
Please provide the polar amplification factor (e.g., 1.5x, 2x) or range of factors that you used in your estimates.
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Surface mass balance
Between atmospheric circulation/moisture transport changes (AM) and albedo changes (AC), which do you consider more important for determining surface mass balance of grounded ice during the 21st, 22nd, and 23rd century.
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC
Among changes in summer sea ice extent (SI), atmospheric circulation/moisture transport changes (AM), and albedo changes (AC), which do you consider most important for determining surface mass balance and rate of thinning of ice shelves in 21st, 22nd, and 23rd century?
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC
Ocean processes
Among Antarctic circumpolar current changes (ACC), changes in intrusion of circumpolar deep water onto continental shelf (CDW), and changes in AMOC (MOC), which do you consider will have the largest effect on sub-shelf basal melt rates during the 21st, 22nd, and 23rd century?
2°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC
5°C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC
Polar Amplification
Please provide the polar amplification factor (e.g., 1.5x, 2x) or range of factors that you used in your estimates.
2050 2100 2200 2300 1.5°C 2.0°C 2°C 5°C 2°C 5°C 2°C 5°C North South
Low-probability, high-consequence scenarios
Are there high-outcome scenarios above the 95% values you provided that deserve attention? If so, what are they?
Ambiguity relating to discharge versus sea level contribution
The questionnaire provided to experts asked for their estimate of changes in discharge (defined as the ice flux across the grounding line) that would contribute to SLR. For ice grounded below sea level, such as in large sectors of the WAIS and parts of the EAIS, the change in volume of discharge and the sea level contribution are not the same quantity. This is because it is only the volume above flotation (VAF) that contributes to SLR, while the change in discharge includes ice below flotation that will be displaced by sea water.
This issue was identified during the second SEJ workshop held in Europe and to address it we asked all experts what value they were using for discharge: total discharge or VAF (the same as sea level equivalent). Of the 22 experts, four stated they had calculated total discharge and the rest VAF. Of these four, one had a high calibration score and a strong weighting in the PW01 solutions and a correction to these discharge values for the WAIS and EAIS were considered necessary. To do this, we utilized the output of a thermomechanical ice sheet model coupled to a solid earth deformation model in a climate forced deglaciation experiment (11, 12) and calculated the ratio of total discharge to VAF. This is shown in Figure S12 alongside the gradients for the ratio for the WAIS, EAIS and AIS. For the WAIS, the ratio changes after a volume loss of about 1 m sea level equivalent (SLE), while for the EAIS it is relatively constant. For the EAIS discharge we used a constant ratio, while for the WAIS it varied as a function of the discharge anomaly. The change in gradient is only significant for the 2300 L and H and 2200 H scenarios, where WAIS discharge anomaly exceeds 1 m for this expert.
Figure S12: The ratio of volume above flotation to total ice discharge for a present-day deglaciation experiment for the Antarctic ice sheet. Fig a) AIS, b) WAIS, c) EAIS. Blue dots represent the first 400 years, red dots are for the remaining 20 Kyr.
Elicitation questions
The Elicitation questions are available as a pdf and Excel file at https://doi.org/10.5523/bris.23k1jbtan6sjv2huakf63cqgav
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Yuan and Kopp (2021)
Title:
Emulating Ocean Dynamic Sea Level by Two-Layer Pattern Scaling
Key Points:
An emulator for DSL changes is developed based on a two-layer energy balance model and a two-layer pattern scaling technique
The two-layer emulator can better capture the evolution of DSL in corresponding coupled GCMs than scaling of global mean surface temperature
The two-layer emulator allows estimation of the probability of future DSL changes in various emission scenarios over multiple centuries
Corresponding author:
Yuan
Citation:
Yuan, J., & Kopp, R. E. (2021). Emulating ocean dynamic sea level by two-layer pattern scaling. Journal of Advances in Modeling Earth Systems, 13, e2020MS002323, https://doi.org/10.1029/2020MS002323
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020MS002323
Abstract
Ocean dynamic sea level (DSL) change is a key driver of relative sea level (RSL) change. Projections of DSL change are generally obtained from simulations using atmosphere-ocean general circulation models (GCMs). Here, we develop a two-layer climate emulator to interpolate between emission scenarios simulated with GCMs and extend projections beyond the time horizon of available simulations. This emulator captures the evolution of DSL changes in corresponding GCMs, especially over middle and low latitudes. Compared with an emulator using univariate pattern scaling, the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, with a reduction in global-averaged error during 2271-2290 of 36%, 24%, and 34% in RCP2.6, RCP4.5, and RCP8.5, respectively. Using the emulator, we develop a probabilistic ensemble of DSL projections through 2300 for four scenarios: Representative Concentration Pathway (RCP) 2.6, RCP 4.5, RCP 8.5, and Shared Socioeconomic Pathway (SSP) 3-7.0. The magnitude and uncertainty of projected DSL changes decrease from the high-to the low-emission scenarios, indicating a reduced DSL rise hazard in low- and moderate-emission scenarios (RCP2.6 and RCP4.5) compared to the high-emission scenarios (SSP3-7.0 and RCP8.5).
Plain Language Summary
As climate warms, sea-level rise poses a major threat to coastal communities and ecosystems. A key driver of local sea level change is ocean dynamic sea level change, which is associated with changes in ocean density and circulation. The primary tools used to project changes in dynamic sea level are atmosphere-ocean general circulation models, which are computationally expensive. Here we develop an emulator for dynamic sea level changes that is, built upon a two-layer energy balance model. Considering both the rapid response of well-mixed surface layer and the delayed response of the deep ocean to forcing, the emulator facilitates the estimation of probability distributions of future dynamic sea level change under different emission scenarios and the extension of projections beyond the time horizon of available simulations from some atmosphere-ocean general circulation models. This emulator captures the evolution of dynamic sea level changes in the atmosphere-ocean general circulation models to which it is tuned, including the non-linear and non-stationary relationship between the dynamic sea level and global warming. The emulator thus facilitates the estimation of future local sea-level changes.
Introduction
Sea-level rise impacts coastal communities and ecosystems through permanent inundation, increasingly common tidal flooding, and increasingly frequent and severe storm-driven flooding. Global-mean sea level (GMSL) is rising at an accelerating rate, and under most scenarios is projected to continue accelerating over the 21st century (Oppenheimer et al., 2019). Regional relative sea level (RSL) change differs from global-mean sea-level change due to a variety of processes operating on diverse timescales, including the gravitational, rotational, and deformational effects associated with mass redistribution and ocean dynamic effects associated with changes in surface winds, ocean currents, and heat and freshwater fluxes (Gregory et al., 2016, 2019; Kopp et al., 2015; Perrette et al., 2013; Stammer et al., 2013).
Atmosphere-ocean general circulation models (GCMs) are the primary tool used to project ocean dynamic sea level (DSL) change, but the computational demands of these models limit the utility of GCM ensembles for estimating the likelihood of different levels of future sea-level change. Ensembles such as the Coupled Model Intercomparison Project Phase 5 (CMIP5, Landerer et al., 2014; Taylor et al., 2012) are composed of models contributed based on voluntary effort, not the product of systematic experimental design; as such, they are an “ensemble of opportunity” rather than a probabilistic ensemble (Tebaldi & Knutti, 2007). The CMIP future projection experiments are driven by a small number of forcing scenarios - Representative Concentration Pathways (RCPs) in the case of CMIP5 - and model simulations are of different lengths; some simulations run the RCPs to the year 2100, while others extend these to 2300.
The computationally intensive nature of GCMs makes it challenging to produce large perturbed-physics ensembles that represent uncertainties in key feedback parameters, as well as to simulate forcing conditions intermediate between the RCPs. Simple climate models (SCMs) provide an alternative tool for estimating the uncertainties of future projections at the global scale, as they can capture the overall physics of climate evolution and can be run very fast even on a personal computer (Held et al., 2010; Meinshausen et al., 2011; Millar et al., 2017; Perrette et al., 2013). However, SCMs represent the climate at a highly aggregated (e.g., global or hemispheric) scale, and thus cannot produce spatial patterns of climate change at each time step.
Pattern scaling approaches are often used to translate the global mean surface air temperature (GSAT) change into regional-scale changes for impact analysis (Mitchell, 2003; Rasmussen et al., 2016; Santer, 1990; Tebaldi & Arblaster, 2014; Tebaldi et al.,2011). Generally speaking, pattern scaling uses a simple statistical model (often, linear regression) to relate local climatic changes to a variable such as GSAT change, assum.ing the patterns of local response to external forcing remain constant under increased forcing (Tebaldi & Arblaster, 2014).
Some previous studies use the pattern scaling approach to estimate the uncertainty in DSL projections (Bilbao et al., 2015; M. D. Palmer et al., 2020; Perrette et al., 2013). For example, Perrette et al. (2013) regressed DSL change on GSAT. At New York City, they found that r2 values across models vary between 0.02 and 0.85, and also that the linear relationship between DSL and GSAT becomes weaker after the 21st century. Bilbao et al. (2015) examined the relationship between DSL and several variables, including GSAT, global-mean sea-surface temperature, ocean volume mean temperature, and global-mean thermosteric sea-level rise (GMTSLR). They found that GSAT performed best in predicting 21st-century DSL change in a high emissions scenario (RCP 8.5), while ocean-volume mean temperature and GMTSLR performed better in lower emissions scenarios (RCP 2.6 and 4.5). They speculated that this difference reflects a more important role for surface warming relative to deep warming in a more strongly forced scenario. They found that, across models and scenarios, area-weighted average root mean square error in pattern-scaled 2081–2100 DSL change ranged from ~1 to 3 cm.
Building upon Bilbao et al. (2015)’s speculation about the relative importance of shallow and deep warming under different scenarios, we developed a bivariate pattern scaling, which uses a multiple linear regression with two predictors: GSAT and global-mean deep ocean temperature change. The two temperature changes can be generated by a two-layer energy-balance model (2LM) (Held et al., 2010; Winton et al., 2010), which has proved to be a useful tool for understanding the responses of climate system to climate forcing (Geoffroy et al, 2013a, 2013b). Shallow and deep temperatures from a 2LM have previously been employed in an emulator to extend 21st century CMIP5 projections of GMTSLR to 2300 (M. D. Palmer et al., 2018), and M. D. Palmer et al. (2020) used GSAT from the two-layer model and univariate pattern scaling (based on GSAT) to emulate CMIP5 projections of DSL change.
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Building upon Bilbao et al. (2015)’s speculation about the relative importance of shallow and deep warming under different scenarios, we developed a bivariate pattern scaling, which uses a multiple linear regression with two predictors: GSAT and global-mean deep ocean temperature change. The two temperature changes can be generated by a two-layer energy-balance model (2LM) (Held et al., 2010; Winton et al., 2010), which has proved to be a useful tool for understanding the responses of climate system to climate forcing (Geoffroy et al, 2013a, 2013b). Shallow and deep temperatures from a 2LM have previously been employed in an emulator to extend 21st century CMIP5 projections of GMTSLR to 2300 (M. D. Palmer et al., 2018), and M. D. Palmer et al. (2020) used GSAT from the two-layer model and univariate pattern scaling (based on GSAT) to emulate CMIP5 projections of DSL change.
In this study, we develop an emulator for DSL changes using both GSAT and deep-ocean temperature change projected by a 2LM. Here we drive the 2LM with radiative forcings from the Finite Amplitude Impulse Response model (FaIR), a SCM which includes a reduced-complexity carbon cycle and calculates atmospheric CO2 concentrations, radiative forcing and temperature changes based on emissions (Millar et al., 2017; Smith et al., 2017, 2018). FaIR was designed to more accurately reflect the temporal evolution of GSAT in response to a pulse emission, and it has been used in previous studies to produce observation-constrained future projections (Millar et al., 2017; Smith et al., 2017, 2018). In this study, we develop an emulator for GMTSLR and DSL change using surface and deep-ocean temperature changes generated by the FaIR-2LM (Section 2.2). As the univariate pattern scaling fails to capture the delayed response of the deep ocean to warming, we employ FaIR-2LM and two-layer pattern scaling to project future DSL changes, taking into account uncertainty in climate sensitivity, and demonstrate their ability to interpolate between climate scenarios run by GCMs. Compared to M. D. Palmer et al. (2018, 2020), which also use a 2LM to emulate GMTSLR or DSL projections, our approach differs in: (1) employing radiative forcings calculated based on emissions; (2) applying a format of 2LM considering efficacy factor of deep ocean heat uptake; (3) using both surface and deep-ocean temperature for pattern scaling (more details are described in supporting information).
Section 2 describes data and methodology, including the details of FaIR-2LM, the calibration of the FaIR.2LM based on selected CMIP5 GCMs, the two-layer pattern scaling methodology, and the application of this system to emulate DSL projections. Section 3 evaluates the performance of the two-layer pattern scaling. Section 4 shows the resulting ensemble of DSL projections. Finally, Section 5 discusses and summarizes the results.
Data and Methods
Data
We use the zos variable from five CMIP5 general circulation models (GCMs) in RCP 2.6, 4.5, and 8.5 sce.narios: MPI-ESM-LR, bcc-csm1-1, HadGEM2-ES, GISS-E2-R, IPSL-CM5A-LR. These five GCMs are used because they were used to calibrate the parameters of the 2LM by Geoffroy et al. (2013) and provide multi-century data (to 2300) for zos in all three scenarios. DSL is taken as zos with its global mean removed, consistent with the definition of Gregory et al. (2019). The drift is removed from DSL by subtracting a linear function of time fitted to the pre-industrial control simulation from each scenario experiments, at each grid point. In addition, we remove the climatology in a baseline period (1986-2005) from DSL. The global mean surface air temperature (GSAT) and GMTSLR from the five models in the three scenarios are also used to evaluate the performance of FaIR-2LM.
FaIR-Two Layer Model (FaIR-2LM) and Calibration
This study develops a hybrid SCM model by replacing the temperature module in FaIR 1.3 (Smith et al., 2018) with a 2LM. In FaIR 1.3, GSAT changes are the sum of two components, representing fast and slow responses to effective radiative forcing (ERF) (Equation 22 in Smith et al., 2018). The fast and slow components of temperature changes in FaIR 1.3 mathematically depend on multiple coefficients (e.g., thermal response timescales) that are obtained from the ensemble mean of multiple CMIP5 models (Geoffroy, et al., 2013b). Since these components do not have an unambiguous physical meaning, it is challenging to link them to sea-level change. Therefore, we replace the temperature module in FaIR 1.3 by the 2LM to construct FaIR.2LM. In each step of FaIR-2LM, the 2LM is driven by radiative forcing from FaIR 1.3, and produces the GSAT anomaly, which feeds back to the FaIR carbon cycle (Figure S1).
Figure S1: Schematic diagram of the FaIR-2LM (modified from Figure 1 of Smith et al. 2018).
We employ a 2LM that includes an efficacy term for deep ocean heat uptake (Geoffroy, et al., 2013a; Held et al., 2010; Winton et al., 2010):
C frac{dT}{dt} = mathcal{F} - lambda T - epsilon gamma (T - T_0) (1)
C_0 frac{dT_0}{dt} = gamma (T - T_0) (2)
where mathcal{F} denotes the adjusted radiative forcing, C and C_0 are the heat capacity of the well-mixed upper layer and the deep ocean layer, respectively, and T and T_0 represent the global mean temperature anomalies of the upper and lower layer, respectively. Following Equation 22 in Geoffroy, et al. (2013b) and using C = 8.2 W yr m^{-2} K^{-1} and C_0 = 109 W yr m^{-2} K^{-1} based on an average across multiple CMIP5 GCMs (Geoffroy, et al., 2013a), we estimate the average depths of the upper layer and lower layer are 86 m and 1141 m, respectively. T is equivalent to GSAT perturbation (Held et al., 2010). lambda is the parameter for climate feedback, gamme is the coefficient of deep ocean heat uptake, and epsilon is the efficacy factor of deep ocean heat uptake, which represents the uneven spatial distribution of heat exchanges between the two layers.
To calibrate FaIR-2LM, we adjust parameter settings (listed in Table 1) based on previous studies (Forster et al., 2013; Geoffroy, Saint-Martin, et al., 2013a; Zelinka et al., 2014). The radiative forcing in FaIR-2LM is driven by the default emission trajectory for each scenario in FaIR 1.3, but scaled by two parameters determined for each GCM: (1) the radiative forcing of CO_2 doubling (F_{2 times CO_2}) reported by Forster et al. (2013), and (2) the present-day aerosol forcing (a*f_{pd}) estimated in previous studies (Forster et al., 2013; Zelinka et al., 2014), or -0.9 W m^{-2} - the median of range estimated by the Fifth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR5) (Stocker et al., 2013) - for models not reported in previous studies. The five parameters in Equations 1 and 2 (i.e., lambda, gamma, epsilon, C, C_0) are the same as those in Geoffroy et al. (2013) for the corresponding GCMs.
Table 1: FaIR-2LM Parameters adjusted to match the GSAT in CMIP5 GCMs. \(\lambda\) (W m-2 K-1), \(\gamma\) (W m-2 K-1), \(\epsilon\), C (W yr m-2 K-1), and \(C_0\) (W yr m-2 K-1) are reported by Geoffroy et al. (2013). The units for \(F_{2 \times CO_2}\) and \(af_{pd}\) are W m-2.
CMIP5 GCMs
\(\lambda\)
\(\gamma\)
\(\epsilon\)
C
\(C_0\)
\(F_{2 \times CO_2}\)
\(af_{pd}\)
bcc-csm1-1
1.28
0.59
1.27
8.4
56
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To calibrate FaIR-2LM, we adjust parameter settings (listed in Table 1) based on previous studies (Forster et al., 2013; Geoffroy, Saint-Martin, et al., 2013a; Zelinka et al., 2014). The radiative forcing in FaIR-2LM is driven by the default emission trajectory for each scenario in FaIR 1.3, but scaled by two parameters determined for each GCM: (1) the radiative forcing of CO_2 doubling (F_{2 times CO_2}) reported by Forster et al. (2013), and (2) the present-day aerosol forcing (a*f_{pd}) estimated in previous studies (Forster et al., 2013; Zelinka et al., 2014), or -0.9 W m^{-2} - the median of range estimated by the Fifth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR5) (Stocker et al., 2013) - for models not reported in previous studies. The five parameters in Equations 1 and 2 (i.e., lambda, gamma, epsilon, C, C_0) are the same as those in Geoffroy et al. (2013) for the corresponding GCMs.
Table 1: FaIR-2LM Parameters adjusted to match the GSAT in CMIP5 GCMs. \(\lambda\) (W m-2 K-1), \(\gamma\) (W m-2 K-1), \(\epsilon\), C (W yr m-2 K-1), and \(C_0\) (W yr m-2 K-1) are reported by Geoffroy et al. (2013). The units for \(F_{2 \times CO_2}\) and \(af_{pd}\) are W m-2.
CMIP5 GCMs
\(\lambda\)
\(\gamma\)
\(\epsilon\)
C
\(C_0\)
\(F_{2 \times CO_2}\)
\(af_{pd}\)
bcc-csm1-1
1.28
0.59
1.27
8.4
56
3.23
-0.9
GISS-E2-R
2.03
1.06
1.44
6.1
134
3.78
-0.9
HadGEM2-ES
0.61
0.49
1.54
7.5
98
2.93
-1.23
IPSL-CM5A-LR
0.79
0.57
1.14
8.1
100
3.1
-0.68
MPI-ESM-LR
1.21
0.62
1.42
8.5
78
4.09
-0.9
GSAT produced by the calibrated FaIR-2LM is compared with that from the corresponding GCMs in the three scenarios (Fig. S2). For the five GCMs, the GSAT simulated by FaIR-2LM is close to the GSAT from the corresponding GCM, with the root mean square error (RMSE) determined over the entire simulation period in a range of 0.15-0.23 K for RCP2.6, 0.14-0.32 K for RCP4.5, and 0.20-0.43 K for RCP8.5.
GMTSLR is driven by the thermal expansion of sea water volume due to the increase in ocean heat uptake. To calibrate GMTSLR in FaIR-2LM to match a specific GCM, we first correct the drift in the GCM’s GMTSLR field by removing the linear trend in the pre-industrial control simulation, assuming the drift is not sensitive to the external forcing (Hobbs et al., 2016).
Then, we emulate GMTSLR based on the T and T_0 from FaIR-2LM following the approach described in Kuhlbrodt and Gregory (2012):
{GMTSLR} = sigma times (C Delta T + C_0 Delta T_0) (3)
where sigma is the expansion efficiency of heat in units of 10^{-24} m J^{-1}. The sigma value is calibrated by optimizing GMTSLR emulated from FaIR-2LM to match the GMTSLR simulated from the corresponding GCM.
Two-Layer Pattern Scaling
Univariate pattern scaling is based on a linear relation between regional changes in a climate variable (DSL for this study) and global mean responses of climate change, such as GSAT (T):
DSL(t,x,y) = alpha(x,y) T(t) + b(x,y) + epsilon(t,x,y) (4)
where x and y denote longitudes and latitudes, t represents the time, b is an intercept term, and epsilon is the residual term. Here, alpha captures the scaling relationship between DSL and GSAT (Figure 1). The five GCMs agree that the linear response of DSL to surface warming is positive over the Arctic and sub-polar Atlantic, and negative over the southeastern Pacific and the southern areas of Southern Ocean.
Figure 1: Changes in DSL in response to changes in deep ocean temperature (first column) and global-mean surface air temperature (second column) in bivariate pattern scaling. The third column is the response of DSL changes to global-mean surface air temperature in univariate pattern scaling. The first five rows display the maps of slopes obtained from a GCM over the period of 1981-2300. The sixth row shows the multi-model mean of slopes. The areas where the slopes from the five models agree in sign are hatched. White areas are lands. Units are m K^{-1}.
In the bivariate pattern scaling approach, we regress the DSL anomaly on both T (GSAT anomaly) and T_0 (deep-ocean temperature anomaly) from FaIR-2LM:
DSL(t_i,x,y) = alpha(x,y) T(t_i) + beta(x,y) T_0(t_i) + b(x,y) + epsilon(t,x,y) (5)
where t_i denotes years in three scenarios, i = 1, 2, 3. For each GCM, we estimate the fields of alpha, beta, b, and epsilon by regressing projections from all three emissions scenarios (RCPs 2.6, 4.5, and 8.5) on T and T_0 on a grid cell-by-grid cell basis. alpha represents changes in zos in response to changes in surface temperature in the period 1981–2300, while beta represents the response of changes in zos to changes in deep-ocean temperature at the same period (Figure 1). Consistent with the univariate scaling pattern, the five GCMs agree that the upper-layer response, represented by alpha, is positively correlated with warming over the most areas of Arctic and northern edge of the Southern Ocean, and negatively correlated with warming over the southeastern Pacific and the southern areas of Southern Ocean. The deep-layer response represented by beta is positively correlated with warming over the Indian and tropical and southern Pacific Oceans, and negatively correlated with warming over most areas of the Southern Ocean and Arctic. These reflect opposite behaviors between rapid and sustained changes in DSL over the Arctic, the Indian and tropical and southern Pacific Oceans, and a consistent DSL fall in both rapid and sustained changes over the Southern Ocean.
There is little agreement on either surface- or deep-layer slopes across the five GCMs over most parts of the Atlantic basin (Figure 1). This may reflect limited skill in simulating strong western boundary currents (e.g., the Atlantic Meridional Overturning Circulation (AMOC)) in the GCMs, which have a relatively coarse (~1˚) spatial resolution in ocean component (Small et al., 2014) and so poorly capture non-linear mesoscale processes in the ocean current (Hallberg, 2013). Near the eastern coast of North America, DSL is closely related to AMOC (Goddard et al., 2015), which is expected to weaken in a warming climate (Caesar et al., 2018). Low skill in capturing AMOC behavior can affect the DSL projections in the Atlantic basin as well as its coasts (van Westen et al., 2020). As the coefficients of pattern scaling depend on the simulations by the GCMs, they also do not explicitly resolve the non-linear mesoscale process of the ocean current. Therefore, we should interpret the DSL changes predicted by the two-layer emulator with cautions over the regions where non-linear mesoscale effects of ocean current are strong.
Projecting DSL Using FaIR-2LM and Patterns
We use two steps to generate a probabilistic ensemble of DSL projections. First, we generate an ensemble of surface and deep-ocean temperature pairs using FaIR-2LM. The planetary energy balance at the top of the atmosphere (Zelinka et al., 2020) is:
\[N = \mathcal{F} + \lambda T (6)\]
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There is little agreement on either surface- or deep-layer slopes across the five GCMs over most parts of the Atlantic basin (Figure 1). This may reflect limited skill in simulating strong western boundary currents (e.g., the Atlantic Meridional Overturning Circulation (AMOC)) in the GCMs, which have a relatively coarse (~1˚) spatial resolution in ocean component (Small et al., 2014) and so poorly capture non-linear mesoscale processes in the ocean current (Hallberg, 2013). Near the eastern coast of North America, DSL is closely related to AMOC (Goddard et al., 2015), which is expected to weaken in a warming climate (Caesar et al., 2018). Low skill in capturing AMOC behavior can affect the DSL projections in the Atlantic basin as well as its coasts (van Westen et al., 2020). As the coefficients of pattern scaling depend on the simulations by the GCMs, they also do not explicitly resolve the non-linear mesoscale process of the ocean current. Therefore, we should interpret the DSL changes predicted by the two-layer emulator with cautions over the regions where non-linear mesoscale effects of ocean current are strong.
Projecting DSL Using FaIR-2LM and Patterns
We use two steps to generate a probabilistic ensemble of DSL projections. First, we generate an ensemble of surface and deep-ocean temperature pairs using FaIR-2LM. The planetary energy balance at the top of the atmosphere (Zelinka et al., 2020) is:
\[N = \mathcal{F} + \lambda T (6)\]
where N is the radiative imbalance at the top of the atmosphere. The equilibrium climate sensitivity (ECS) is given by T when N = 0, and mathcal{F} = F_{2 times CO_2}. Therefore, lambda is related to F_{2 times CO_2} and ECS by
lambda = - F_{2 times CO_2} / ECS (7)
The uncertainty of F_{2 times CO_2} is small relative to the spread of lambda, while ECS largely determine the uncertainty of lambda. Therefore, we adopt the best estimation in the Intergovernmental Panel on Climate Change Fifth Assessment Report (AR5) for F_{2 times CO_2} = 3.71 W m^{-2} (Collins et al., 2013). We produce initial distributions of ECS, gamma, and gamma_{epsilon} based on the literature constraints (Figure S4) outlined below:
ECS: Based on multiple lines of evidence, the uncertainties of ECS estimated by AR5 are likely in the range 1.5˚C-4.5˚C with high confidence, extremely unlikely less than 1˚C and very unlikely greater than 6˚C (Collins et al., 2013). In the AR5 terminology, likely denotes a probability of at least 66%, very unlikely a probability of less than 10%, and extremely unlikely a probability of less than 5% (Mastrandrea et al., 2010). Therefore, we construct a log-normal distribution for ECS with parameters optimized to match a 5th percentile of 1˚C, a 17th percentile of 1.5˚C, an 83rd percentile of 4.5˚C, and a 90th percentile of 6˚C.
gamma: We treat gamma as normally distribution, with mean 0.67 W m^{-2} K^{-1} and standard deviation 0.15 W m^{-2} K^{-1} derived from the 16 GCMs in the CMIP5 archive (Geoffroy et al., 2013).
gamma_{epsilon}: As the efficacy factor of heat uptake is related to deep-ocean heat uptake (Held et al., 2010), we use gamma_{epsilon} instead of epsilon to maintain the covariance between gamma and epsilon. We calculate the mean of 0.86 W m^{-2} K^{-1} and standard deviation 0.29 W m^{-2} K^{-1} of gamma_{epsilon} based on the products of gamma and epsilon from 16 GCMs in CMIP5 archive (Geoffroy, et al., 2013a). The distribution of gamma_{epsilon} is constructed as a normal distribution with the multi-model mean and the multi-model standard deviation.
TCR: Under a zero-layer approximation which considers the 1%/yr increase in CO_2 until doubling scenario occurring on a timescale long enough that the upper ocean is in approximate equilibrium and short enough that the deep-ocean temperature has not yet responded substantially, Transient Climate Response (TCR) can be obtained by (Jimenez-de-la-Cuesta & Mauritsen, 2019):
{TCR} = - frac{F_{2 times CO_2}}{lambda - gamma_{epsilon}} (8)
Uncertainty in the TCR can be constrained adequately by varying only lambda and gamma_{epsilon} under the zero-layer approximation. Therefore, although there are significant uncertainties of C and C_0 among GCMs, we use fixed values because the uncertainties of these parameters are not necessary to represent uncertainty in the TCR. In this study, we set C = 8.2 W m^{-2} K^{-1} and C_0 = 109 W m^{-2} K^{-1} based on the multi-model mean of GCMs from Coupled Model Intercomparison Project Phase 5 (CMIP5) archive (Geoffroy, et al., 2013a).
We then generate a 100,000-member ensemble of ECS, gamma and gamma_{epsilon} based on these distributions via Monte Carlo sampling. As gamma_{epsilon}} should be larger than 0, we discard parameter sets in which gamma_{epsilon}} < 0 or gamma_{epsilon}} > 2 times 0.86 to keep the mean of gamma_{epsilon}} in parameter sets to be 0.86 W m^{-2} K^{-1}. Therefore, 99734 parameter sets are kept. An ensemble of lambda is then computed by the best estimation of F_{2 times CO_2} and the ensemble of ECS based on Equation 6 (Figure S4). The median (central 66% range) of lambda is −1.39 (−2.4 to −0.8) W m^{-2} K^{-1}. As the likely range of ECS estimated by AR5 is equivalent to the central 90% range of ECS estimated by CMIP5 GCMs, the uncertainty range of lambda estimated by FaIR-2LM is larger than that estimated by ensemble of GCMs (Geoffroy et al., 2013). The spread of TCR is estimated as a diagnostic by substituting the ensemble of lambda, gamma_{epsilon}, and best estimation of F_{2 times CO_2} into Equation 8. The uncertainty of TCR is in a central 66% range of 1.1–2.3˚C, with a 95th percentile of 2.9˚C. This is consistent with but slightly narrower than the TCR estimated by AR5, which is likely between 1˚C and 2.5˚C, and is extremely unlikely greater than 3˚C.
We apply Latin hypercube sampling (LHS, Stein, 1987) to the parameter sets of lambda, gamma, gamma_{epsilon} by sampling 1,000 sets from the 99,734 parameter sets. For each parameter, LHS divides the probability density function of the 99,734 samples into 1,000 portions that have equal area. A sample is taken from each portion randomly so that the 1,000 sample sets cover the multidimensional distribution of the three parameters. Finally, we applied 1,000 parameter sets together with the fixed parameters (F_{2 times CO_2}, C, C0) to the FAIR-2LM and generate a 1,000-member probabilistic ensemble of temperature pair time-series.
We compare the spread in GSAT projected by FaIR-2LM with the likely ranges estimated by AR5 for four different periods (Collins et al., 2013) (Table 3 and Figure S5). The mean of the probabilistic ensemble is slightly lower than the mean estimate of GSAT from AR5 in all four periods of RCP2.6 and RCP4.5, and in the 21st century for RCP8.5. Compared with AR5 likely ranges, the central 66% probability range of GSAT from FaIR-2LM is generally consistent: narrower in all four periods of RCP2.6, narrower in the first two periods but wider in the last two periods in RCP4.5, and wider in the first two periods but narrower in the last two periods in RCP8.5.
We project GMTSLR based on Equation 3 using the probabilistic ensemble of surface and deep-ocean temperature projections from FaIR-2LM. The C, C_0 and expansion efficiency of heat sigma (0.113 times 10^{-24 m}) used here are adopted from the multi-model ensemble mean of CMIP5 archive (Geoffroy, et al., 2013a; Kuhlbrodt & Gregory, 2012).
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We apply Latin hypercube sampling (LHS, Stein, 1987) to the parameter sets of lambda, gamma, gamma_{epsilon} by sampling 1,000 sets from the 99,734 parameter sets. For each parameter, LHS divides the probability density function of the 99,734 samples into 1,000 portions that have equal area. A sample is taken from each portion randomly so that the 1,000 sample sets cover the multidimensional distribution of the three parameters. Finally, we applied 1,000 parameter sets together with the fixed parameters (F_{2 times CO_2}, C, C0) to the FAIR-2LM and generate a 1,000-member probabilistic ensemble of temperature pair time-series.
We compare the spread in GSAT projected by FaIR-2LM with the likely ranges estimated by AR5 for four different periods (Collins et al., 2013) (Table 3 and Figure S5). The mean of the probabilistic ensemble is slightly lower than the mean estimate of GSAT from AR5 in all four periods of RCP2.6 and RCP4.5, and in the 21st century for RCP8.5. Compared with AR5 likely ranges, the central 66% probability range of GSAT from FaIR-2LM is generally consistent: narrower in all four periods of RCP2.6, narrower in the first two periods but wider in the last two periods in RCP4.5, and wider in the first two periods but narrower in the last two periods in RCP8.5.
We project GMTSLR based on Equation 3 using the probabilistic ensemble of surface and deep-ocean temperature projections from FaIR-2LM. The C, C_0 and expansion efficiency of heat sigma (0.113 times 10^{-24 m}) used here are adopted from the multi-model ensemble mean of CMIP5 archive (Geoffroy, et al., 2013a; Kuhlbrodt & Gregory, 2012).
A projection of DSL is constructed as follows: 1) a pair of alpha and beta is randomly picked with replacement from the pool of two-layer patterns produced in Section 2.3; 2) a temperature pair from the 1000 members is combined with the pair of alpha and beta in an equation:
{DSL}(t, x, y) = alpha(x, y) T(t) + beta(x, y) T_0(t) + b(x, y) (9)
Evaluation of Two-Layer Pattern Scaling
To evaluate the prediction skill of the two-layer pattern scaling, we compare the DSL changes simulated from a GCM with the DSL changes emulated by the two-layer pattern scaling (widehat{{DSL}}) based on FAIR-2LM using the key parameters (i.e. parameters in Table 1) in the same GCM. Two metrics are used: (1) absolute values of the residual differences between widehat{{DSL}} changes and DSL changes during a period at each grid point, and (2) global average of the absolute values obtained from the metric 1 (Table S1). These two metrics are applied to both bivariate pattern scaling and univariate pattern scaling, to examine the improvement of bivariate approach comparing with the univariate approach.
In 2271-2290, for instance, the global-averaged climatology of | DSL - widehat{{DSL}} | (score obtained by the second metric) from the two-layer pattern scaling is less than that from the univariate pattern scaling (bottom row Figure 2), with a reduction of 36%, 24%, and 34% in RCP2.6, RCP4.5, and RCP8.5, respectively. The spatial pattern of R = DSL - widehat{{DSL}} is derived from both approaches are various across GCMs (Figures S6-S10). The 5-model ensemble averaged climatology of | R | in both approaches is higher over high latitudes (e.g., Arctic, subpolar Northern Atlantic, Southern Ocean) than over middle to low latitudes, but is generally lower in two-layer pattern scaling than in univariate pattern scaling (first two rows Figure 2). As the pattern-scaling method cannot resolve DSL change due to unforced variability, the relatively large | R | over the high latitudes may be due to the relatively high unforced variability over these regions (Bilbao et al., 2015).
We further compare the time evolution of widehat{{DSL}} predicted by the two-layer pattern scaling approaches with the evolution of DSL in corresponding GCMs through the period 1981-2290. As case studies, we pick two grid cells: one in the western Pacific near the Philippines (14.5˚N, 127˚E), and the other over the North Atlantic near the coast of New York City [NYC] (40˚N, 73˚W) (solid black dots in Figure 2). The grid point near the Philippines is selected because it is in the tropical Pacific, where DSL rise associated with the deep ocean temperature rise is strongest, while the grid point near the NYC is selected represent a coastal area that some projections find experiences significant DSL changes in response to changes in AMOC.
Figure 2: Differences between DSL simulated by GCMs (zos) and DSL (widehat{{zos}}) predicted by univariate pattern scaling (univariate, first row) and two-layer pattern scaling (two-layer, second row) over the period 2271-2290 for the ensemble mean of 5 GCMs in three scenarios: RCP2.6, RCP4.5, RCP8.5 (Units: m). The third row shows the global mean of the | {zos} - (widehat{{zos}} | in 1TS and 2TS, respectively. Black dots on maps denote the two grid cells used for the plot in Figure 3.
At the western Pacific grid cell, in RCP 2.6, the relationship between DSL and GSAT anomaly displays a hook-like shape, indicating continued rise in DSL as GSAT stabilizes and declines in response to negative emissions (Figure 3a). The delayed adjustment of DSL may be due to the continuous warming of deep layer (T_0) when GSAT is stabilized, because the ocean is not yet equilibrated with the elevated forcing. In response to changes in T_0, the deep ocean density is still changing even without changing circulation in the deep ocean (England, 1995), so DSL continues to change. This hook-like shape is captured by the two-layer pattern scaling approach but not by the univariate pattern scaling. Compare to the DSL simulated by a GCM, the RMSE of the predicted DSL is smaller if using the two-layer pattern scaling approach than using the univariate pattern scaling approach. The average RMSE across the five GCMs is reduced 26% if we use the approach from the two-layer pattern scaling instead of the univariate pattern scaling (Table 3). Across the five GCMs, although the relationship between DSL and GSAT is diverse in RCP4.5 and RCP8.5, DSL projected by the two-layer technique is consistently closer than that predicted by the univariate technique to the DSL simulated by the GCMs. The sole exception is for bcc-csm1-1 in RCP8.5, for which the simulated DSL projection is quite linearly associated with GSAT. The average of RMSEs across the 5 GCMs decrease from the univariate pattern scaling approach to the two-layer pattern scaling approach by 35% in RCP4.5 and by 33% in RCP8.5 (Table 3).
Figure 3: widehat{{zos}} predicted by univariate pattern scaling and two-layer pattern scaling at the grid cell (a) over Western Pacific (14.5˚N, 127˚E) and (b) over the North Atlantic (40˚N, 73˚W) for the five models in the three scenarios. The zos simulated by corresponding GCMs is shown by scatters in which colors indicate years. Root mean square errors between the widehat{{zos}} and zos determined over the entire simulating period for each GCM are shown in parentheses of legend (units: m).
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Figure 3: widehat{{zos}} predicted by univariate pattern scaling and two-layer pattern scaling at the grid cell (a) over Western Pacific (14.5˚N, 127˚E) and (b) over the North Atlantic (40˚N, 73˚W) for the five models in the three scenarios. The zos simulated by corresponding GCMs is shown by scatters in which colors indicate years. Root mean square errors between the widehat{{zos}} and zos determined over the entire simulating period for each GCM are shown in parentheses of legend (units: m).
At the North Atlantic grid cell, the relationship between DSL and GSAT also displays non-linear features for all the five models, especially in low- and moderate-emission scenarios (Figure 3b). These non-linear features, which may arise from the delayed response of deep branch of AMOC, cannot be captured by univariate pattern scaling but are captured to a large extent by the two-layer pattern scaling (lines in Figure 3). The value of the two-layer approach is highlighted by the clear non-linearity of the DSL response when viewed as a function of GSAT anomaly. Compare to the univariate approach, the RMSE between the DSL simulated by GCMs and the DSL predicted by the two-layer pattern scaling is smaller, with a reduction of 19%, 16%, and 13% for RCP2.6, RCP4.5, and RCP8.5, respectively. The method of two-layer pattern scaling generally has a better performance in emulating the DSL from the corresponding GCM than the univariate pattern scaling, as the two-layer pattern scaling includes one more predictor than univariate pattern scaling, allowing it to capture the delayed adjustment of DSL. The delayed adjustment of DSL due to the deep-ocean warming is important for the DSL projections, as different areas present different features that may reveal the regional variation in deep-ocean circulation (Held et al., 2010).
Projections of DSL
The procedure described in Section 2.4 allows us to produce a 1000-member probabilistic ensemble of DSL projections not only for the three CMIP5 scenarios: RCP2.6, RCP4.5, and RCP8.5, but also for any other scenarios with an emission pathway between these three scenarios. We demonstrate this capability using SSP3-7.0, a CMIP6 scenario that has forcing intermediate between RCP4.5 and RCP8.5 (O’Neill et al., 2016) and is closer than either to no-policy reference scenarios from most integrated assessment models (Riahi et al., 2017). The emission pathway of SSP3-7.0 used to drive the FaIR-2LM is taken from the Reduced Complexity Model Intercomparison Project (Nicholls et al., 2020).
The five projections using parameters calibrated to the five GCMs respectively are within the 66% range of the 1000-member ensemble for both surface and deep-ocean temperature in the three RCPs (Figure 4). By 2300, the median estimates (66% range) of the surface temperature relative the period of 1986-2005 are 0.5˚C (0.2-1.0˚C) for RCP2.6, 2.2˚C (1.2-3.6˚C) for RCP4.5, 7.4˚C (4.5-11.7˚C for RCP8.5, and 5.3˚C (3.2-8.6˚C) for SSP3-7.0.
Based on the projections of temperature pairs, we also produced projections of GMTSLR for the four scenarios (Figure 4). The spread of GMTSLR ensemble encapsulates the GMTSLR time series from the 5 GCMs (Figure 4). During the period of 2081-2100, the median estimates (66% range) of the GMTSLR relative the period of 1986-2005 are 0.12 (0.07-0.18) m for RCP2.6, 0.16 (0.10-0.24) m for RCP4.5, 0.19 (0.12-0.27) m for SSP3-7.0, and 0.24 (0.15-0.34) m for RCP8.5. This compares to Oppenheimer et al. (2019)’s projected median estimates (66% ranges) of 0.14 (0.10-0.18) m for RCP2.6, 0.19 (0.14-0.23) m for RCP4.5, and 0.27 (0.21-0.33) m for RCP8.5. By 2300, the median estimates (66% range) of GMTSLR relative to the period of 1986-2005 are 0.20 (0.12-0.33) m for RCP2.6, 0.43 (0.25-0.68) m for RCP4.5, 0.85 (0.50-1.33) m for SSP3-7.0, and 1.15 (0.69-1.76) m for RCP8.5. As climate warms, the projections of DSL changes increase along with the increase in GMTSLR. In the five GCMs, although the contributions of DSL changes to the local sterodynamic sea level (DSL+GMTSLR; Gregory et al., 2019) changes are small at some locations (i.e., regions marked by the light and dark gray shadings in Figure S11), in others the ratio of DSL change with respect to the GMTSLR changes are fairly significant. For instance, DSL changes at some regions (e.g., Arctic, North Atlantic, and Southern Ocean) are greater than 50% of the GMTSLR during the period of 2271-2290 (identified by yellow contours in Figure S11).
Figure 4: Ensemble projections of CO_2 concentrations (first row), GSAT (second row), deep-ocean temperature (third row), and GMTSLR (fourth row) changes relative to the baseline period 1986-2005 under the four scenarios. Shadings represents the 66% range, dark blue lines the median of probabilistic ensemble projections. The projection calibrated to the five GCMs in the three RCP scenarios are shown on top of the shadings (orange lines).
Compared with the GSAT and GMTSLR spread in 2300 estimated by M. D. Palmer et al. (2018), the FaIR.2LM projections have a slightly lower median for all the three RCPs. The 66% range of both surface temperature and GMTSLR estimated by FaIR-2LM is comparable to the 90% range of that estimated by M. D. Palmer et al. (2018) because we adopt a distribution of lambda based on the AR5 assessment of equilibrium climate sensitivity (Collins et al., 2012), which is broader than the 90% range estimated by the CMIP5 multi-model ensemble emulated by M. D. Palmer et al. (2018).
Comparing the DSL projections between the period of 2081-2100 and the period of 2271-2290 (Figure 5), the median estimate is lower and the 66% range of uncertainty is narrower at the end of 21st century than that at the end of 23rd century in moderate-to high-emission scenarios (RCP4.5, SSP3-7.0 and RCP8.5). But in RCP2.6, the median estimate and 66% uncertainty range are comparable in magnitude between these two periods. In both periods, the median DSL anomaly projections across the four scenarios share many similar features (Figure 5). Over the Arctic region, a weak increase in DSL is observed over the Chukchi Sea and the Beaufort Sea in RCP2.6. In the higher emission scenarios, the increase in DSL extends to the whole Arctic basin with intensified amplitudes. The changes in DSL over the North Atlantic are dominated by a negative anomaly under RCP2.6, and display positive anomalies over much of the North Atlantic under RCP8.5 and SSP3-7.0. The ensemble spread of the 5th-95th range of DSL projections are relatively large over the Southern Ocean, Arctic and Subpolar Atlantic than other areas. The large uncertainties over these areas, consistent with previous literatures (M. D. Palmer et al., 2020; Perrette et al., 2013; Yin, 2012), may be interpreted by the diverse characteristics simulated by GCMs that do not explicitly resolve non-linear mesoscale processes of the ocean current over these areas (van Westen et al., 2020).
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Comparing the DSL projections between the period of 2081-2100 and the period of 2271-2290 (Figure 5), the median estimate is lower and the 66% range of uncertainty is narrower at the end of 21st century than that at the end of 23rd century in moderate-to high-emission scenarios (RCP4.5, SSP3-7.0 and RCP8.5). But in RCP2.6, the median estimate and 66% uncertainty range are comparable in magnitude between these two periods. In both periods, the median DSL anomaly projections across the four scenarios share many similar features (Figure 5). Over the Arctic region, a weak increase in DSL is observed over the Chukchi Sea and the Beaufort Sea in RCP2.6. In the higher emission scenarios, the increase in DSL extends to the whole Arctic basin with intensified amplitudes. The changes in DSL over the North Atlantic are dominated by a negative anomaly under RCP2.6, and display positive anomalies over much of the North Atlantic under RCP8.5 and SSP3-7.0. The ensemble spread of the 5th-95th range of DSL projections are relatively large over the Southern Ocean, Arctic and Subpolar Atlantic than other areas. The large uncertainties over these areas, consistent with previous literatures (M. D. Palmer et al., 2020; Perrette et al., 2013; Yin, 2012), may be interpreted by the diverse characteristics simulated by GCMs that do not explicitly resolve non-linear mesoscale processes of the ocean current over these areas (van Westen et al., 2020).
Figure 5: Projection of DSL changes at median estimation (first column) and range of 17th-83rd percentile averaged over the period of 2081-2100 in four scenarios (a) relative to the baseline period 1986-2005. (b) is the same with (a) except for the period of 2271-2290. Units are m.
At the illustrative grid point near Philippines over western Pacific (Figure 6a), the 66% range of the probabilistic ensemble encapsulates DSL projections from 2 of the 5 GCMs in the three RCPs, while the 90% range of the probabilistic ensemble contains DSL projections from all the 5 GCMs in the three RCPs, except for HadGEM2-ES in RCP2.6. At the grid point near NYC, the projected DSL changes estimated by the probabilistic ensemble exhibits a fat tail, with a median projection in RCP 8.5 of 0.13 m and a 95th percentile projection of 0.8 m by the end of 23rd century. By contrast, RCP 2.6 exhibits a much narrower range, with a median of 0 m and a 95th percentile of 0.08 m. The 66% range of the projected DSL uncertainties encapsulates 2 of 5 GCM projections. The 90% range of the probabilistic ensemble only encapsulates the DSL projections from three over five GCMs in RCP2.6 and RCP4.5, but encapsulates the DSL projections from all five GCMs in RCP8.5. The emulator fails to capture multidecadal variability in DSL, a limitation which would be expected because the emulator is constructed based on the pattern scaling approach.
Figure 6: Ensemble projections of DSL changes relative to the baseline period 1986-2005 at the grid cells near Philippines over the western Pacific (upper panel) and near NYC over the North Atlantic (lower panel) for the four scenarios: RCP2.6, RCP4.5, SSP3-7.0, and RCP8.5. Shadings represent the projections produced by the two-layer emulator, with light and dark shadings indicating the 90% and 66% range, respectively, and dark blue lines the median of probabilistic ensemble projections. The black lines represent the projections produced by the univariate emulator, with the dashed and solid lines indicating the 90% and 66% range, respectively. The projection of DSL changes smoothed by 20-years running average in the five GCMs are shown on top of the shadings (colored lines). Units: m.
To compare with the DSL projections derived from two-layer pattern scaling, we also produced the DSL projections based on univariate pattern scaling following the same procedure (Figures S12 and S14). The median and 17th-83rd range of DSL projections derived from univariate pattern scaling are similar in patterns (Figure S12). However, differences of both median and spreads of the DSL projections between univariate and two-layer pattern scaling vary across regions, especially over high latitudes in high-emission scenarios (Figure S13). Specifically, compared to the univariate emulator, the median of DSL projected by the two-layer emulator is lower over the Pacific and Indian Ocean, and higher over Arctic, Atlantic and Southern Ocean in the period of 2081-2100, but the opposite in the period of 2271-2290. In addition, the 17th-83rd range of the DSL projected by the two-layer emulator is wider than that by the univariate emulator over the Arctic. The area-weighted increases in DSL spread over the Arctic are 0.02 m in RCP2.6, 0.03 m in RCP4.5, and 0.04 m in RCP8.5 during 2081-2100, and are 0.006 m in RCP2.6, 0.008 m in RCP4.5, 0.009 m in RCP8.5 during 2271-2290. For the grid cell near Philippines, despite the shift in median, the distributions of DSL projections derived from univariate pattern scaling exhibit a different shape from that derived from two-layer pattern scaling (Figure 6). In 2290, the 90% range of DSL projection from the univariate emulator is close to that from the two-layer emulator, slightly narrower by 0.03 m for RCP2.6, 0.02 m for RCP4.5, and 0.01 m for SSP3-7.0 and RCP8.5. The two-layer pattern scaling leads to not only a shift of the distribution but also a different shape of the distribution of the DSL projections, compared to that derived from univariate pattern scaling. There are more DSL projections simulated by GCMs encapsulated within the 90% range of the probabilistic ensemble of DSL projections derived from two-layer pattern scaling than that by the univariate pattern scaling (Figure 6). For the grid cell near the NYC, the shape of DSL distributions derived from univariate pattern scaling is similar to that derived from two-layer pattern scaling, except the spread of the DSL projections derived from univariate pattern scaling is slightly narrower than that derived from the two-layer pattern scaling, with the 90% range of DSL projection in 2290 narrower by 0.03 m for RCP2.6, 0.01 m for RCP4.5, and 0.03 m for SSP3-7.0 and RCP8.5 (Figure 6). The greatest difference is in RCP 2.6, where the difference in the 90% range is by far the largest compared to the overall range.
Table 2: The Averaged RMSE Between the DSL Simulated by GCMs and the DSL Predicted by Univariate/Two-Layer Pattern Scaling Across Five Models. Note: The averaged RMSEs and the reduction of RMSE from univariate pattern scaling approach to two-layer pattern scaling are calculated for the three RCP scenarios, respectively.
Discussion and Conclusions
We have developed a probabilistic ensemble of DSL projections through 2300 using a novel two-layer emulator. Replacing the climate module in the FaIR simple climate model with a two-layer energy-balance model, we developed FaIR-2LM, which produces projections of global average temperature in the well-mixed upper layer (T) for rapid responses to radiative forcing, and in the deep ocean layer (T_0) for delayed responses. Calibrated by the parameters for each GCMs, the GSAT (Figure S2) and GMTSLR (Figure S3) emulated by FaIR-2LM generally follow that from the corresponding GCM, with RMSE <0.43 K for GSAT and <0.05 m for GMTSLR. A two-layer pattern scaling based on surface and deep-ocean temperature is used to project DSL. During the period 2271-2290, for instance, the DSL predicted by the two-layer pattern scaling are closer to the DSL simulated by the corresponding GCM than that predicted by the univariate pattern scaling (Figure 2). At two selected grid cells (near the coast of Philippines and NYC), the time evolution of DSL projections predicted by the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, comparing with that predicted by the univariate technique (Figure 3).
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Table 2: The Averaged RMSE Between the DSL Simulated by GCMs and the DSL Predicted by Univariate/Two-Layer Pattern Scaling Across Five Models. Note: The averaged RMSEs and the reduction of RMSE from univariate pattern scaling approach to two-layer pattern scaling are calculated for the three RCP scenarios, respectively.
Discussion and Conclusions
We have developed a probabilistic ensemble of DSL projections through 2300 using a novel two-layer emulator. Replacing the climate module in the FaIR simple climate model with a two-layer energy-balance model, we developed FaIR-2LM, which produces projections of global average temperature in the well-mixed upper layer (T) for rapid responses to radiative forcing, and in the deep ocean layer (T_0) for delayed responses. Calibrated by the parameters for each GCMs, the GSAT (Figure S2) and GMTSLR (Figure S3) emulated by FaIR-2LM generally follow that from the corresponding GCM, with RMSE <0.43 K for GSAT and <0.05 m for GMTSLR. A two-layer pattern scaling based on surface and deep-ocean temperature is used to project DSL. During the period 2271-2290, for instance, the DSL predicted by the two-layer pattern scaling are closer to the DSL simulated by the corresponding GCM than that predicted by the univariate pattern scaling (Figure 2). At two selected grid cells (near the coast of Philippines and NYC), the time evolution of DSL projections predicted by the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, comparing with that predicted by the univariate technique (Figure 3).
Table 3: Comparison of the Distributions of GSAT Anomaly (Relative to 1986-2005) Projected by FaIR-2LM With the Distributions of Global-Mean Surface Temperature Assessed by AR5 (Collins et al., 2013) in RCP 2.6, RCP4.5, SSP3-7.0 and RCP 8.5 (the 2nd and 3rd Columns, units: ˚C). Note: Means are given without parentheses; likely range (for AR5) and 17th-83rd percentile range (for FaIR-2LM) are given in parentheses. The fourth column is similar with previous columns except for the GMTSLR projected by FAIR-2LM (Units: m).
By perturbating the key parameters, FaIR-2LM allows emulation of projected global-mean surface and deep-ocean temperature pairs and GMTSLR for emissions scenarios (e.g., SSP3-7.0; Figures 4 and 5) beyond those run by the GCMs to which it is calibrated. Compared with the likely ranges assessed by AR5 in the RCP 2.6, 4.5 and 8.5, the FaIR-2LM performs well in emulating the GSAT spread (Table 2 and Figure S5). By 2300, the ensembles of GSAT and GMTSLR estimated by FaIR-2LM have a slightly lower median and a slightly wider 90% range than the estimations by M. D. Palmer et al. (2018), likely because we use the uncertainty of ECS from AR5, which has a larger range than that estimated by CMIP5 multi-model ensemble.
We produce probabilistic ensembles of DSL projections for four different emissions scenarios. Characteristics of median DSL projections during 2271-2290 include increases in DSL along most of the coast around the Pacific and Indian Oceans and a decrease in DSL over the Southern Ocean in all four scenarios, as well as increased DSL over the Arctic and along the North Atlantic Current in moderate to high emissions scenarios (Figure 5). The 66% range (17th-83rd percentile) of uncertainties are small over the middle and low latitudes, and are relatively large over the Southern Ocean, Arctic and North Atlantic, where the simulations of GCMs are diverse due to the challenges of capturing the complex physical processes, such as deep water formation in the subpolar Atlantic, the Antarctic circumpolar current, and ice-albedo feedback in polar regions (Flato et al., 2013; Landerer et al., 2014; Wang et al., 2014). The ensemble of DSL projections also allows us to examine the trajectories of the DSL projections and their uncertainties at specific locations (Figure 6). At selected locations in the North Atlantic and Western Pacific, the 90% range of DSL spread generally encapsulates the time series of DSL changes relative to the baseline period from the 5 GCMs.
The two-layer emulator provides a useful tool to explore the uncertainty of DSL projections over multiple centuries with computational resources that are much less than a GCM requires. It can be calibrated to match assessments of key values like the equilibrium climate sensitivity, and allows the flexibility of simulating forcing conditions intermediate between the RCPs as the patterns are common for different scenarios. However, we should note that the errors between the DSL predicted by two-layer emulator and DSL simulated by the corresponding GCMs are small in middle and low latitudes but relatively large in high latitudes (e.g., the Southern Ocean, Arctic, and subpolar Atlantic). In addition, the two-layer emulator cannot explicitly resolve the non-linear mesoscale effects of the ocean current due to the coarse resolutions of the CMIP5 GCMs that the two-layer pattern scaling relies on. Comparing with the predicted DSL derived from univariate approach, the improvement of using the two-layer approach on predicting DSL has a similar magnitude with the uncertainty of DSL projections over the middle and low latitudes in RCP2.6 and RCP4.5 scenarios during the period of 2271-2290. But the improvement is limited comparing to the uncertainty of DSL projections in RCP8.5. As the non-linear responses of DSL are more obvious in the RCP2.6 and RCP4.5 than in RCP8.5, the notable improvement of using the two-layer approach over the middle- and low-latitudes in the RCP2.6 and RCP4.5 highlight the advantage on improving the DSL projections in these two scenarios.
Loss of land ice (e.g., Greenland Ice Sheet and Antarctic Ice Sheet) is an important contributor not only to GMSL but also to RSL. Glacio-isostatic adjustment (GIA) caused by changes in ice sheet mass loading induces local vertical land motion and associated changes in local sea level. Mass loss of an ice sheet also reduces the gravitational attraction that pulls sea water toward it, causing water to migrate away with a distinct spatial pattern, or “fingerprint”, of sea level change to the global ocean (Mitrovica et al., 2009). Freshwater flux from a melting ice sheet may drastically alter the salinity profile of the near-by ocean, bringing about complex feedbacks involving near-surface ocean stratification, sea ice formation, and corresponding changes in surface temperature, winds, and ocean currents (Bronselaer et al., 2018; Sadai et al., 2020) - each process could have its impact in RSL. Among these factors, only freshwater flux from the ice sheet can significantly affect both global climate and DSL (e.g., Golledge et al., 2019). Despite the importance of polar ice sheets, their contributions to DSL are not included in the current generation coupled climate models. Our study, relying on outputs from climate models participating the CMIP5 project, thus cannot take into account the effects of evolving ice sheets on DSL. In more comprehensive analyses, the effect of land-ice loss should be considered.
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References
Bilbao, R. A. F., Gregory, J. M., & Bouttes, N. (2015). Analysis of the regional pattern of sea level change due to ocean dynamics and density change for 1993–2099 in observations and CMIP5 AOGCMs. Climate Dynamics, 45, 2647-2666. https://doi.org/10.1007/s00382-015-2499-z
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Caesar, L., Rahmstorf, S., Robinson, A., Feulner, G., & Saba, V. (2018). Observed fingerprint of a weakening Atlantic Ocean overturning circulation. Nature, 556, 191–196. https://doi.org/10.1038/s41586-018-0006-5
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Church et al. (2013)
Title:
Evaluating the ability of process based models to project sea-level change
Key Points:
Evaluation of CMIP5 and other process-based models using observations
Process-based models, when properly calibrated, can reproduce a significant portion of the observed sea-level rise.
Ocean thermal expansion and glacier melting are the two dominant contributors to sea-level rise
The models’ ability to reproduce observed sea-level rise has improved significantly, increasing confidence in their projections for the 21st century.
Keywords:
sea level, climate change, projections
Corresponding author:
John A. Church
Citation:
Church, J. A., Monselesan, D., Gregory, J. M., & Marzeion, B. (2013). Evaluating the ability of process based models to project sea-level change. Environmental Research Letters, 8(1), 014051. doi:10.1088/1748-9326/8/1/014051
URL:
https://iopscience.iop.org/article/10.1088/1748-9326/8/1/014051
Abstract
We evaluate the ability of process based models to reproduce observed global mean sea-level change. When the models are forced by changes in natural and anthropogenic radiative forcing of the climate system and anthropogenic changes in land-water storage, the average of the modelled sea-level change for the periods 1900–2010, 1961–2010 and 1990–2010 is about 80%, 85% and 90% of the observed rise. The modelled rate of rise is over 1 mm yr−1 prior to 1950, decreases to less than 0.5 mm yr−1 in the 1960s, and increases to 3 mm yr−1 by 2000. When observed regional climate changes are used to drive a glacier model and an allowance is included for an ongoing adjustment of the ice sheets, the modelled sea-level rise is about 2 mm yr−1 prior to 1950, similar to the observations. The model results encompass the observed rise and the model average is within 20% of the observations, about 10% when the observed ice sheet contributions since 1993 are added, increasing confidence in future projections for the 21st century. The increased rate of rise since 1990 is not part of a natural cycle but a direct response to increased radiative forcing (both anthropogenic and natural), which will continue to grow with ongoing greenhouse gas emissions.
Introduction
A complete understanding of 20th century sea-level rise has been lacking, with the observed rise over recent decades being larger than projections in the Intergovernmental Panel on Climate Change (IPCC) Third (TAR, Church et al 2001) and Fourth Assessment Reports (AR4, Hegerl et al 2007). As a result, sea-level projections for the 21st century and beyond have been controversial. The omission of ‘rapid’ dynamic ice sheet contributions from the AR4 projections, because of the lack of a published basis for estimating them, compounded this problem. Rahmstorf et al (2007) argued that the observed sea-level rise since 1990 was at or above the upper limit of the TAR projections, and Rahmstorf et al (2012a) argued that both the TAR and AR4 projections were biased low. However, using an improved understanding of the impact of volcanic eruptions on sea level, Church et al (2011a) described the comparison slightly differently, finding that while the observed rise was in the upper quartile of the AR4 projections there was no inconsistency between observations and projections from 1990. Semi-empirical models (SEMs; Rahmstorf 2007, Horton et al 2008, Vermeer and Rahmstorf 2009, Grinsted et al 2010, Jevrejeva et al 2010, 2011, Rahmstorf et al 2012b) have been proposed as an alternative way to estimate future sea-level rise.
Using observations of 20th century temperatures, Bittermann et al (2013) [B13] compared SEM forecasts of 20th century sea-level rise to the observations. They concluded that, when both tide-gauge reconstructions of global mean sea-level and paleo sea-level data were used to estimate the parameters of their SEMs, their forecasts for 1900–2000 (range of 13–30 cm) were in agreement with the observations (14–26 cm). For the period 1961–2003, they also found that when the SEM was trained using the Church and White (2011) [CW11] estimates of GMSL and paleo data up to 1960, the predicted rate of 2.0 mm yr−1 (range of 1.9–2.3 mm yr−1) agreed with the observations within the uncertainties. However, using the Jevrejeva et al (2008) estimate of GMSL, with or without the paleo data, resulted in sea-level projections that were biased high by up to 70%. B13 challenged the sea-level process model community to test their projections for the same period.
Here we evaluate the ability of process based models (the basis of 21st century projections) to simulate 20th century global averaged sea-level rise. These process based models are dependent on our physical understanding of the climate system built up over many years. Modelling sea level requires simulations of oceanic and atmospheric global and regional temperatures. In contrast to the SEMs, the process based models are forced by greenhouse gas concentrations and simulate temperature changes, rather than using observed temperature or radiative forcing changes as input, and they are not trained with observed sea levels and are therefore not sensitive to uncertainties in them. This study builds upon recent progress in understanding the 20th century sea-level budget (Church et al 2011b, Moore et al 2011, Gregory et al 2013a) but focuses clearly on model results and their ability to project sea-level change. We compare individual contributions to sea level calculated with the World Climate Research Programme Coupled Model Intercomparison Project Phase 5 (CMIP5) model results with observations (section 2) and compare the sum of these terms to the observed sea-level rise since 1900, 1961 and 1990, as in B13. We discuss the possibility that some fraction of 20th century sea-level change is possibly due to internally generated variability that is unlikely to be simulated in phase and amplitude by the models (section 3). We also discuss the implications of the results for the observed increase in the rate of rise and for future projection of 21st century sea-level rise (section 4).
Sea-level response to historical radiative forcing and anthropogenic intervention in the water cycle
Ocean thermal expansion
Ocean thermal expansion (figure 1(a)) is available for 25 atmosphere–ocean general circulation models (AOGCMs) participating in the CMIP5 experiment. The simulations used here have been forced with the best estimates of historical radiative forcings up to 2005 and then radiative forcing from the RCP4.5 scenario (Moss et al 2010, Taylor et al 2012) until 2010. However, the preindustrial spin-up and the control simulation for these models assumed zero volcanic forcing and thus the sudden imposition of the negative volcanic forcing in the historical simulations from 1850 results in a negative bias in the estimated ocean thermal expansion (Gregory 2010). To overcome this bias, we have added 0.1 mm yr−1 (±0.05 mm yr−1) ocean thermal expansion to the model results (Gregory 2010, Gregory et al 2013b). We compare the model results to the observational estimates based on the analysis of Domingues et al (2008), updated to 2012 for the upper 700 m, the Levitus et al (2012) analysis from 700 to 2000 m, and a linear trend from 1992 to 2011 for the ocean below 2000 m (Purkey and Johnson 2010). From 1970, when the amount of observational data increases significantly, the models and the observations are not significantly different and the observations are near the centre of the model simulated range.
Figure 1: Comparisons of modelled and observed (a) ocean thermal expansion (observations in blue), (b) glacier contributions, (c) changes in terrestrial storage (the sum of aquifer depletion and reservoir storage) and (d) and the rate of change (10 year centred average) for the terms in (a) to (c). Individual model simulations are shown by grey lines with the model average shown in black (thermal expansion) and purple (glaciers). The estimated glacier contributions estimated by Cogley (2009, green), Leclercq et al (2011, red) and using the model of Marzeion et al (2012, dark blue) forced by observed climate are also shown in (b). All curves in (a) and (b) are normalized over the period 1980–1999 and the colours in (d) are matched to earlier panels.
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Figure 1: Comparisons of modelled and observed (a) ocean thermal expansion (observations in blue), (b) glacier contributions, (c) changes in terrestrial storage (the sum of aquifer depletion and reservoir storage) and (d) and the rate of change (10 year centred average) for the terms in (a) to (c). Individual model simulations are shown by grey lines with the model average shown in black (thermal expansion) and purple (glaciers). The estimated glacier contributions estimated by Cogley (2009, green), Leclercq et al (2011, red) and using the model of Marzeion et al (2012, dark blue) forced by observed climate are also shown in (b). All curves in (a) and (b) are normalized over the period 1980–1999 and the colours in (d) are matched to earlier panels.
Modelled thermal expansion (figures 1(a), (d)) falls slightly following the volcanic eruption of Santa Maria in 1902. The rate of expansion is then relatively constant up until the eruption of Mt Agung in 1963 when there is a significant fall in sea level. There are similar falls in sea level following the eruptions of El Chichon in 1982 and Mt Pinatubo in 1991. The increase in sulfur dioxide emissions by more than a factor of two from 1950 to 1975 (Smith et al 2011) results in an increasingly negative aerosol forcing that partially offsets the increasing greenhouse gas concentrations leading to a slower rate of warming (and thermal expansion) after 1960 (Church et al 2011b). Over the 20th century, there is a clear increase in the rate of rise with the fastest rate occurring from 1993. This latter increase is a result of increasing greenhouse gas concentrations, recovery from impacts of the Mt Pinatubo eruption (Gregory et al 2006, Gleckler et al 2006, Church et al 2005, Domingues et al 2008, Gregory et al 2013a) and falling sulfur dioxide emissions from 1975 to 2000 (Smith et al 2011).
Glacier contributions
Marzeion et al (2012) use an (offline) glacier model forced by regional surface temperatures and precipitation from AOGCM CMIP5 climate simulations to estimate glacier contributions for the 20th century (figures 1(b), (d), grey and purple lines). Their model is calibrated using individual glacier mass balance observations also used by Cogley (2009), such that the Marzeion et al (2012) results are neither strictly independent from the Cogley (2009) results, nor from observations. However, the dependency is very weak, since only about 0.1% of all the world’s glaciers are included in these observations (substantially less in terms of surface area and ice volume, and with a mean time series length of only 15 years). Two different validation methods in Marzeion et al (2012) show that the model is able to reconstruct observed glacier changes independent of the observations, such that the combined contribution of all the glaciers to sea level is in fact only weakly dependent on the observations of individual glacier contributions. From 1950, the model results (15 available models) used by Marzeion et al are not significantly different from the observed estimated changes in glacier mass of Cogley (2009) and the estimates based on glacier length from Leclercq et al (2011). The Marzeion et al modelled rate of rise is almost constant during the first half of the century up until 1960 but larger than the Leclercq et al estimate (that also relies on Cogley), then smaller until the 1990s (figure 1(d)), after which it increases. Loss of glacier area at low altitudes combined with the stabilization of temperatures for the 1950–1975 period could have contributed to this slowing of the rate of glacier contribution.
Greenland and Antarctic contributions
The contributions of the Greenland and Antarctic Ice Sheets for the 20th century are poorly determined. Observational estimates for 1993–2011 (Shepherd et al 2012) indicate a net contribution of about 11 mm, about two thirds of this from Greenland. Models of surface mass balance (using AOGCM results) for Greenland agree with the increased surface mass loss over the last two decades but indicate little impact on sea level over previous decades, and with divergent results for the first half of the 20th century. (See Gregory et al (2013a) for a full discussion.) Recent model results for four major Greenland outlet glaciers (Helheim, Jakobshavn, Petermann and Kangerdlugssuaq) forced by changes in ocean temperatures (Nick et al 2009, and personal communication) indicate a contribution of order 0.6 mm yr−1 for 2000–10, consistent with the observational estimates. However, we are unaware of any completed model simulations of the Greenland Ice Sheet contribution for the 20th century using the new generation of ice sheet models.
For Antarctica, Levermann et al (2012) have recently completed an ice sheet model simulation for the 20th century using ocean temperatures on the shelf near Antarctica and atmosphere–ice exchange from the CMIP5 AOGCMs, with an allowance for a delay of the warming to penetrate underneath the ice shelves. The 20th century contribution is only 4 mm, mostly since 1990, similar to recent observational estimates (Shepherd et al 2012).
These results indicate significant progress in modelling ice sheet response to climate and ocean forcing. However, as they are as yet incomplete, we have not included these new model results here. Instead, we include estimates of these terms in section 3 and discuss the implications in section 4.
Land-water storage
Internally generated climate variability influences the amount of water stored as soil moisture and in lakes, rivers and reservoirs. On short timescales, the rate of change in the storage can be several millimetres leading to rapid rates of sea-level change (Boening et al 2012). However, over decadal timescales the net contribution is small (Ngo-Duc et al 2005) and hence for the comparison we ignore this contribution.
There are also direct human related interventions in the hydrological cycle that impact the amount of water stored on land. This occurs principally through the building of reservoirs (Chao et al 2008, Lettenmaier and Milly 2009) and the depletion of groundwater (Konikow 2011, Wada et al 2012). For reservoir storage, we use the estimates of Chao et al with no allowance for seepage (as in Gregory et al 2013a). We assume that the reservoirs are on average 85% full (with a range of 70–100%). For groundwater depletion, we average the observational estimates of Konikow (2011) and model results of Wada et al (2012). Over the first half of the 20th century, both of these terms are small (figure 1(c)). After 1950, the significant increase in the rate of dam building leads to negative contribution to sea-level change. From the 1980s, a slowing in the rate of dam building and an increase in the rate of groundwater depletion leads to a small positive contribution to sea-level rise (figures 1(c) and (d)).
Observed and modelled sea-level change 1900–2012
We compare the sum of the ocean thermal expansion, glacier and estimated land-water contributions (available for 13 models) with observational estimates of global mean sea level of CW11 and Ray and Douglas (2011) [RD]; figure 2. Both estimates are similar over the 20th century (RD has a slightly larger trend), with a broad maximum in the rate of rise from 1930 to 1950, a minimum about 1960 and then a rising trend to the end of the records. Both series have a minimum in the rate of rise in the 1920s and a maximum in the 1970s, but it is unclear if these two features are robust or an indication of the inadequacy of the available sea-level data.
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There are also direct human related interventions in the hydrological cycle that impact the amount of water stored on land. This occurs principally through the building of reservoirs (Chao et al 2008, Lettenmaier and Milly 2009) and the depletion of groundwater (Konikow 2011, Wada et al 2012). For reservoir storage, we use the estimates of Chao et al with no allowance for seepage (as in Gregory et al 2013a). We assume that the reservoirs are on average 85% full (with a range of 70–100%). For groundwater depletion, we average the observational estimates of Konikow (2011) and model results of Wada et al (2012). Over the first half of the 20th century, both of these terms are small (figure 1(c)). After 1950, the significant increase in the rate of dam building leads to negative contribution to sea-level change. From the 1980s, a slowing in the rate of dam building and an increase in the rate of groundwater depletion leads to a small positive contribution to sea-level rise (figures 1(c) and (d)).
Observed and modelled sea-level change 1900–2012
We compare the sum of the ocean thermal expansion, glacier and estimated land-water contributions (available for 13 models) with observational estimates of global mean sea level of CW11 and Ray and Douglas (2011) [RD]; figure 2. Both estimates are similar over the 20th century (RD has a slightly larger trend), with a broad maximum in the rate of rise from 1930 to 1950, a minimum about 1960 and then a rising trend to the end of the records. Both series have a minimum in the rate of rise in the 1920s and a maximum in the 1970s, but it is unclear if these two features are robust or an indication of the inadequacy of the available sea-level data.
The sum of the modelled ocean thermal expansion, glacier, and terrestrial storage contributions from 1900 to 2010 (figure 2(a)) ranges from 110 mm to almost 200 mm with a model average of 153 mm. The spread of models encompasses the GMSL estimate of CW11 but is slightly less than RD. The average of the model results explains about 80% of the observed rise. The average modelled rate of sea-level rise (figure 2(b)) is more than 1 mm yr−1 prior to 1950, as a result of early 20th century warming and thermal expansion and increased glacier melting, but is somewhat less than the observed rate over 1930–50. The average modelled rate of rise decreases to less than 0.5 mm yr−1 in the 1960s before increasing again to reach a maximum of 3 mm yr−1 in 2000, about double the 20th century average and substantially greater than the modelled rate of rise in the first half of the 20th century. The slower rate of rise from 1950 to 1980 is likely a result of the impact of volcanic eruptions, the increase in tropospheric aerosol loading (emissions peak in the 1970s) on the modelled ocean thermal expansion and glacier melting contributions, a loss of glacier area following early 20th century melting and an increase in the rate of reservoir storage.
Figure 2: The sum of the modelled contributions from ocean thermal expansion, increased glacier melting and changes in land-water storage. The light grey lines are individual models with the black line the model mean. The 20th estimates of global mean sea level are indicated by the blue (CW11) and green (RD) lines with the shading indicating the uncertainty estimates (two standard deviations). The satellite altimeter data since 1993 is shown in red. The adjusted model mean (dashed black line) is the model mean after an allowance for the impact of natural variability on glacier contributions and a potential long-term ice sheet contribution are included. The results are given (a) for the period 1900–2010, (b) the rates of sea-level change for the same period, (c) for 1961–2010, and (d) for 1990–2010. The dotted black line is after inclusion of the Shepherd et al (2012) ice sheet observational estimates but excluding the peripheral glacier contribution (to avoid double counting). The red dot is the average rate from the altimeter record.
For the period since 1961 (figure 2(c)), the modelled rise ranges from about 50 to 110 mm and encompasses the observed rise of close to 90 mm, with the model average rise of 75 mm explaining about 85% of the observed rise. Since 1990 (the start of the projections for the TAR and the AR4; figure 2(d)), the modelled sea-level rise ranges from 30 to 65 mm and encompasses the observed rise of about 55 mm, with the average model rise of 51 mm explaining over 90% of the observed rise. The model average rate over 1993–2010 of 3 mm yr−1 is almost equal to the rate of 3.2 ± 0.4 mm yr−1 observed with satellite altimeters (with both rates being very linear). The increased rate of the modelled rise from 1980 to 2000, and particularly after 1993, is a result of continued increases in greenhouse gas concentrations, the recovery of the climate system from the series of volcanic eruptions (particularly Mt Pinatubo in 1993), decreasing sulfur dioxide emissions from 1975 to 2000 and increasing land-water contributions.
Other effects on sea-level change
There are at least two potential additional contributions to 20th century sea-level change. Firstly, the ice sheets are often assumed to have been in a state of approximate mass balance, hence making zero net contribution to sea level before the major increase in greenhouse gas emissions of the 20th century. However, the long response time of the Antarctic and (to a lesser extent) Greenland ice sheets means that there may be a small ongoing contribution to sea-level change due to climate change in previous centuries or millennia (Huybrechts et al 2011). An ongoing contribution of 0.0–0.2 mm yr−1 was considered in the sea-level budget studies of Gregory et al (2013a) and Church et al (2011b). Here we have added a 0.1 mm yr−1 contribution to the above modelled estimates (10 mm over the 20th century).
Secondly, there may be contributions related to internally generated variability on decadal timescales (Delworth and Knutson 2000). Marzeion et al (2012) have also computed glacier mass changes using observed rather than simulated temperature change (figure 1(b), blue line). An additional contribution of about 20 mm is estimated to occur between 1920 and 1960, with the largest additional contribution in the 1930s (the difference between the blue and purple lines in figure 1(b)). While the Leclercq et al (2011) estimates from measurements of glacier length indicate a smaller overall contribution during the 20th century, they also give a greater rate of mass contribution from 1920 to 1940 than for earlier and later periods. These additional early 20th century contributions are a result of a regional warming over Greenland during this period (Chylek et al 2004).
When these two terms are added to the AOGCM results, the sea-level rise over the 20th century (figure 2(a), dashed line) is 176 mm, which is over 90% of the observed GMSL estimate, and both observed time series lie within the model spread (the individual model results have not been replotted after the addition of these terms). The modelled rate of rise in the first half of the 20th century is now closer to the observed rate and the observed rate lies within the spread of the model rates through nearly all of the century, although the timing of the faster rate of rise occurs slightly earlier in the model results than in the observations. There is little change to the simulations from the additional terms for the periods since 1961 and 1990 and the average model results for these periods remain within 20% of the observed rise (figures 2(c), (d)). The observational estimates (Shepherd et al 2012) indicate a small 20th century ice sheet contribution that would further close the gap between the observed and modelled sea-level rise to about 10% or better, as depicted by the dotted lines in figure 2.
Discussion
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Secondly, there may be contributions related to internally generated variability on decadal timescales (Delworth and Knutson 2000). Marzeion et al (2012) have also computed glacier mass changes using observed rather than simulated temperature change (figure 1(b), blue line). An additional contribution of about 20 mm is estimated to occur between 1920 and 1960, with the largest additional contribution in the 1930s (the difference between the blue and purple lines in figure 1(b)). While the Leclercq et al (2011) estimates from measurements of glacier length indicate a smaller overall contribution during the 20th century, they also give a greater rate of mass contribution from 1920 to 1940 than for earlier and later periods. These additional early 20th century contributions are a result of a regional warming over Greenland during this period (Chylek et al 2004).
When these two terms are added to the AOGCM results, the sea-level rise over the 20th century (figure 2(a), dashed line) is 176 mm, which is over 90% of the observed GMSL estimate, and both observed time series lie within the model spread (the individual model results have not been replotted after the addition of these terms). The modelled rate of rise in the first half of the 20th century is now closer to the observed rate and the observed rate lies within the spread of the model rates through nearly all of the century, although the timing of the faster rate of rise occurs slightly earlier in the model results than in the observations. There is little change to the simulations from the additional terms for the periods since 1961 and 1990 and the average model results for these periods remain within 20% of the observed rise (figures 2(c), (d)). The observational estimates (Shepherd et al 2012) indicate a small 20th century ice sheet contribution that would further close the gap between the observed and modelled sea-level rise to about 10% or better, as depicted by the dotted lines in figure 2.
Discussion
Ocean thermal expansion and the increased melting of glaciers are the two dominant contributions to 20th century sea-level rise in the simulations, with a smaller contribution from changes in land-water storage. Each of these components has its own unique temporal dependence. The model results indicate that most of the variation in the thermal expansion and glacier contributions to global mean sea level is a response to radiative forcing of the climate system from changes in concentrations of greenhouse gases, stratospheric volcanic aerosol and tropospheric anthropogenic aerosol. Observations in the latter half of the 20th century provide strong support for and confidence in the model simulations of these components. However, since parameters in the glacier model are estimated from observations in the latter half of the 20th century, the evaluation of the glacier models is not a fully independent test of their skill.
Not all 20th century sea-level rise is necessarily externally forced. There is evidence for an enhanced glacier contribution in the first half of the 20th century (Marzeion et al 2012, Leclercq et al 2011). Since climate models can simulate early 20th century global averaged temperature well (Stott et al 2000), the difference between the two glacier estimates may be partly related to regional climate changes (rather than global averaged temperatures), although natural variability impacts both regional and global averaged temperatures (Delworth and Knutson 2000). The extent to which internally generated climate variability can lead to enhanced sea-level rise deserves further investigation. If the apparent impact during the first half of the 20th century was repeated in the future, it would increase projections for the 21st century by the order of 20 mm. However this additional sea-level rise will enter the calibrations of SEMs that use global averaged temperatures (or radiative forcing) and thus will impact the SEM projections.
The range of the model simulations over the three periods, and particularly since 1961 and 1990, encompasses the observed sea-level rise with the model mean within 20% (about 10% since 1990) of the observed rise. Experience with multi-model ensembles is that they generally outperform individual models (Weigel et al 2008, 2010), but specific results are not available for sea level. The agreement of observations with the model mean represents a significant improvement since the IPCC TAR (Church et al 2001) and AR4 (Hegerl et al 2007) and is a reason for increased confidence in the next generation of global mean sea-level projections. This agreement also means that it should now be possible to attribute 20th century sea-level rise to the various climate forcings. Reasons for the improvement include allowance for the omission of volcanic forcing in the spin-up of the AOGCMs, more complete representation of the radiative forcing driving the AOGCMs, a larger initial glacier mass (Arendt et al 2012) and more complete observations of glacier mass loss (Cogley 2009). Also, the Marzeion et al glacier model is able to reconstruct observed glacier changes independent of the observations and is an important part of the improved representation of 20th century sea-level rise.
Significant challenges remain. It is likely that the model spread does not cover the full range of possibilities because of systematic uncertainties that are common to many models. Hence, the model spread found here (about 40% of the observed rise for the 20th century and more than 50% since 1961) may underestimate the full uncertainty, particularly as it was not possible to include models of the ice sheet components. The observational estimates of ice sheet contributions since 1993 further close the gap between the observed and modelled sea-level rise to 10% or better. This evaluation is also incomplete as the ice sheet contributions to date are only a small fraction for the potential longer-term contributions. Careful comparison of the new generation of ice sheet simulations with observations is required to critically evaluate them.
Chambers et al (2012) argue there is an apparent 60 year cycle in the observed sea-level record. Similar variability is present in the forced simulations of the first half of the 20th century but is enhanced when the additional glacier contributions are included in the sum of terms. For the latter half of the 20th century, the observed minimum in the rate of sea-level rise in the 1960s (a deceleration from 1940 to 1970) and the subsequent increase in rate to about twice the 20th century average at the end of the record is present in the forced sea-level estimates. This increase is principally in response to increasing greenhouse gas concentrations and a combination of changing volcanic forcing and tropospheric aerosol loading, leading to a larger ocean thermal expansion and increased glacier melting. There is an additional contribution of less than 20% from anthropogenic interference in the hydrological cycle (figures 1(c) and (d)). Thus, the observed increased rate of rise since 1990 is not part of a natural cycle but a direct response to increased radiative forcing (both anthropogenic and natural) of the climate system. This radiative forcing will continue to increase with ongoing greenhouse gas emissions. The simulation of the observed 20th century sea-level rise and its variability within the uncertainties is a reason for increased confidence in projections of 21st century sea-level rise in future projections.
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Church and White (2011)
Title:
Sea-Level Rise from the Late 19th to the Early 21st Century
Keywords:
Sea level, Climate change, Satellite altimeter, Tide gauge
Corresponding author:
Church
Citation:
Church, J. A. & White, N. J. (2011). Sea-Level Rise from the Late 19th to the Early 21st Century. Surveys in Geophysics, 32, 585–602.
URL:
https://link.springer.com/article/10.1007/s10712-011-9119-1
Abstract
We estimate the rise in global average sea level from satellite altimeter data for 1993Ð2009 and from coastal and island sea-level measurements from 1880 to 2009. For 1993-2009 and after correcting for glacial isostatic adjustment, the estimated rate of rise is 3.2 ± 0.4 mm year$^{-1}$ from the satellite data and 2.8 ± 0.8 mm year$^{-1}$ from the in situ data. The global average sea-level rise from 1880 to 2009 is about 210 mm. The linear trend from 1900 to 2009 is 1.7 ± 0.2 mm year$^{-1}$ and since 1961 is 1.9 ± 0.4 mm year$^{-1}$. There is considerable variability in the rate of rise during the twentieth century but there has been a statistically significant acceleration since 1880 and 1900 of 0.009 ± 0.003 mm year$^{-2}$ and 0.009 ± 0.004 mm year$^{-2}$, respectively. Since the start of the altimeter record in 1993, global average sea level rose at a rate near the upper end of the sea level projections of the Intergovernmental Panel on Climate ChangeÕs Third and Fourth Assessment Reports. However, the reconstruction indicates there was little net change in sea level from 1990 to 1993, most likely as a result of the volcanic eruption of Mount Pinatubo in 1991.
Introduction
Rising sea levels have important direct impacts on coastal and island regions where a substantial percentage of the world’s population lives (Anthoff et al. 2006). Sea levels are rising now and are expected to continue rising for centuries, even if greenhouse gas emissions are curbed and their atmospheric concentrations stabilized. Rising ocean heat content (and hence ocean thermal expansion) is an important element of climate change and sea-level rise. The remaining contributions to sea-level rise come principally from the melting of land ice: glaciers and ice caps (which include the small glaciers and ice caps fringing the major ice sheets) and the major ice sheets of Antarctica and Greenland, with additional contributions from changes in the storage of water on (or in) land. (See Church et al. 2010 for a summary of issues). Correctly estimating historical sea-level rise and representing global ocean heat uptake in climate models are both critical to projecting future climate change and its consequences. The largest uncertainty in projections of sea-level rise up to 2100 is the uncertainty in global mean sea level (GMSL) and thus improving estimates of GMSL rise (as well as regional variations in sea level) remains a high priority.
Since late 1992, high quality satellite altimeters (TOPEX/Poseidon, Jason-1, and OSTM/Jason-2) have provided near global measurements of sea level from which sea-level rise can be estimated. However, this altimeter record is still short (less than 20 years) and there is a need to know how sea level has varied over multi-decadal and longer time scales. Quantifying changes in the rate of sea-level rise and knowing the reasons for such changes are critical to improving our understanding of twentieth century sea-level rise and improving our projections of sea-level change for the twenty first century and beyond.
For the period prior to the altimeter record, estimates of sea-level change are dependent on a sparsely distributed network of coastal and island tide-gauge measurements (Wood.worth and Player 2003). Even today, there are many gaps in the global network of coastal and island sea-level measurements and the network was sparser early in the twentieth century and in the nineteenth century. Many previous studies have used the individual sea-level records (corrected for vertical land motion) to estimate the local rate of sea-level rise (as a linear trend; e.g. Douglas 1991) and some studies attempted to detect an acceleration in the local rate of sea-level rise (Woodworth 1990; Woodworth et al. 2009; Douglas 1992). However, these individual records have considerable interannual and decadal var.iability and thus long records are required to get accurate estimates of the local trends in sea level (Douglas 2001). These authors assumed that these long-term trends are either representative of the global averaged rise or a number of records have been averaged, in some cases regionally and then globally, to estimate the global average rate of rise. However, the modern satellite record has made it clear that sea level is a dynamic quantity and it does not rise uniformly around the globe.
Sea level at any location contains the inßuences of local and regional meteorological effects (including storm surges), modes of climate variability (for example the El Nino-Southern Oscillation) and long-term trends (from both the ocean surface and land move.ments), including the impact of anthropogenic climate change. As the altimeter record has clearly demonstrated, GMSL has much less short term variability (more than an order of magnitude) than sea level at individual locations because while the volume of the oceans is nearly constant the distribution changes with time. While the variability at individual locations can be minimised by low pass filtering, there remains significant energy at yearly to decadal periods that may be either positively or negatively correlated between stations, thus confounding estimates of GMSL rise when few records are available.
To date, there have been two approaches to determining time series of GMSL from coastal and island tide gauges. The first and most straight forward approach averages the sea-level records (corrected for land motion) from individual locations. When there are only a small number of locations with continuous records, this approach is relatively straight forward, although care must be taken to remove data inhomogeneities. When more gauges are used, the records usually have different lengths and starting times. It is then necessary to average the rates of rise over some time step and integrate the results to get the sea-level change. Holgate and Woodworth (2004) used this approach and Jevrejeva et al. (2006) used a virtual station method of averaging neighbouring station sea-level changes in several regions and then averaging to get the global mean sea-level change. No attempt was made to interpolate between the locations of observations and thus to estimate deep ocean sea level. Thus these are essentially estimates of coastal sea-level change. However, note that White et al. (2005) argued that over longer periods the rates of coastal and global rise are similar.
The second approach uses spatial functions which represent the large-scale patterns of variability to interpolate between the widely distributed coastal and island sea-level observations and thus to estimate global sea level (as distinct from coastal sea level). This technique was first developed by Chambers et al. (2002) for interannual sea-level variability and extended by Church et al. (2004) to examine sea-level trends. The Church et al. approach uses the Reduced Space Optimal Interpolation technique (Kaplan et al. 2000) developed for estimating changes in sea-surface temperature and atmospheric pressure. The spatial functions used are the empirical orthogonal functions (EOFs) of sea-level variability estimated from the satellite altimeter data set from TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite data, which now cover the period from January 1993 into 2011. We use data from January 1993 through December 2009 in this paper.
Here, we update previous estimates of GMSL rise for the period of the instrumental record using a longer (17 years) altimeter data set and an expanded in situ sea-level observational data set extending back to 1860. We use the Reduced Space Optimal Interpolation technique to quantify the rate of sea-level rise and the changes in the rate since 1880.
Methods and Data
In Situ Sea-Level Data
We use monthly sea-level data downloaded from the Permanent Service for Mean Sea Level (PSMSL; Woodworth and Player 2003) web site (http://www.psmsl.org) in August 2010. Careful selection and editing criteria, as given by Church et al. (2004) were used. The list of stations used in the reconstruction is available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html. Tide gauge records are assigned to the nearest locations (with good satellite altimeter data) on the 1˚-by-1˚ grid of the satellite altimeter based EOFs. Where more than one record is assigned to a single grid point they are averaged. Changes in height from 1 month to the next are stored for use in the reconstruction.
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The second approach uses spatial functions which represent the large-scale patterns of variability to interpolate between the widely distributed coastal and island sea-level observations and thus to estimate global sea level (as distinct from coastal sea level). This technique was first developed by Chambers et al. (2002) for interannual sea-level variability and extended by Church et al. (2004) to examine sea-level trends. The Church et al. approach uses the Reduced Space Optimal Interpolation technique (Kaplan et al. 2000) developed for estimating changes in sea-surface temperature and atmospheric pressure. The spatial functions used are the empirical orthogonal functions (EOFs) of sea-level variability estimated from the satellite altimeter data set from TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite data, which now cover the period from January 1993 into 2011. We use data from January 1993 through December 2009 in this paper.
Here, we update previous estimates of GMSL rise for the period of the instrumental record using a longer (17 years) altimeter data set and an expanded in situ sea-level observational data set extending back to 1860. We use the Reduced Space Optimal Interpolation technique to quantify the rate of sea-level rise and the changes in the rate since 1880.
Methods and Data
In Situ Sea-Level Data
We use monthly sea-level data downloaded from the Permanent Service for Mean Sea Level (PSMSL; Woodworth and Player 2003) web site (http://www.psmsl.org) in August 2010. Careful selection and editing criteria, as given by Church et al. (2004) were used. The list of stations used in the reconstruction is available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html. Tide gauge records are assigned to the nearest locations (with good satellite altimeter data) on the 1˚-by-1˚ grid of the satellite altimeter based EOFs. Where more than one record is assigned to a single grid point they are averaged. Changes in height from 1 month to the next are stored for use in the reconstruction.
The number of locations with sea-level data available for the reconstruction is larger than in our earlier 2004 (Church et al. 2004) and 2006 (Church and White 2006) studies, particularly prior to 1900 (Figure 1). In the 1860s there are only 7-14 locations available, all north of 30˚N. In the 1870s, there is one record available South of 30˚N but still none in the southern hemisphere and it is only in the second half of the 1880s (Fort Denison, Sydney, Australia starts in January 1886) that the first southern hemisphere record becomes available. While we attempted the reconstruction back to 1860, the results showed greater sensitivity to details of the method prior to the 1880s when the first southern hemisphere record is available (see below for further discussion). As a result, while we show the reconstruction back to 1860, we restricted the subsequent analysis (computation of trends, etc.) to after 1880. The number of locations with data available increases to 38 in 1900 (from 71 individual gauges), including several in the southern hemisphere, to about 85 locations in 1940 (from 130 individual gauges but with still less than 10 in the southern hemisphere), and to about 190 in 1960 (from about 305 individual gauges with about 50 locations in the southern hemisphere). The number of locations peaks in May 1985 at 235 (from 399 individual gauges, with slightly less than one-third in the ocean-dominated southern hemisphere; Figure 1). The largest gaps are in the Southern Ocean, the South Atlantic Ocean and around Africa (Figure 1f). Through the 1990s there are at least 200 locations available from between 370 and 400 gauges. For the last few years there are fewer records available because of the unavoidable delay in the transmission by national authorities of monthly and annual mean information to the PSMSL. In December 2009, there are 135 locations available from 250 gauges.
Figure 1: The number and distribution of sea-level records available for the reconstruction. (a) The number of locations for the globe and the northern and southern hemispheres. (b-f) indicate the distribution of gauges in the 1880s, 1910s, 1930s, 1960s and 1990s. The locations indicated have at least 60 months of data in the decade and the number of records are indicated in brackets.
Sea-level measurements are affected by vertical land motion. Corrections for local land motion can come from long-term geological observations of the rate of relative local sea-level change (assuming the relative sea-level change on these longer times scales is from land motions rather than changing ocean volume), or from models of glacial isostatic adjustment, or more recently from direct measurements of land motion with respect to the centre of the Earth using Global Positioning System (GPS) observations. Here, the ongoing response of the Earth to changes in surface loading following the last glacial maximum were removed from the tide-gauge records using the same estimate of glacial isostatic adjustment (GIA; Davis and Mitrovica 1996; Milne et al. 2001) as in our earlier study (Church et al. 2004).
We completed the analysis with and without correction of the sea-level records for atmospheric pressure variations (the “inverse barometer” effect). The HadSLP2 global reconstructed atmospheric pressure data set (Allan and Ansell 2006) was used for this correction.
We tested the impact of correcting the tide-gauge measurements for terrestrial loading and gravitational changes resulting from dam storage (Fiedler and Conrad 2010). For the large number of tide gauges used in the period of major dam building after 1950 (mostly over 200), the impact on global mean sea level is only about 0.05 mm year^{-1} (smaller than the 0.2 mm year^{-1} quoted by Fiedler and Conrad, which is for a different less globally-distributed set of gauges). Tests of similar corrections for changes in the mass stored in glaciers and ice caps, and the Greenland and Antarctic Ice Sheets show that these effects have an even smaller impact on GMSL.
Satellite Altimeter Data Processing Techniques
The TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite altimeter missions measure sea surface height (SSH) relative to the centre of mass of the Earth along the satellite ground track. A number of instrumental and geophysical corrections must be applied. Every 10 days (one cycle) virtually global coverage of the worldÕs ocean, between 66˚N and S, is achieved. Our gridded data set as used here goes to 65˚N and S.
Our satellite altimeter data processing mostly follows the procedures, and uses the edits and tests, recommended by the providers of the satellite altimeter data sets, and are similar to those described in Leuliette et al. (2004). The documents for the three missions used are Benada (1997) for TOPEX/Poseidon, Aviso (2003) for Jason-1 and CNES (2009) for OSTM/Jason-2.
Orbits from the most recent versions of the Geophysical Data Records (GDR Þles; MGDR-B for TOPEX/Poseidon, GDR-C for Jason-1 and GDR-T for OSTM/Jason-2) are used. GDR corrections from the same Þles for tides, wet troposphere, dry troposphere, ionosphere, sea-state bias (SSB), inverse barometer correction (when required) and the mean sea surface are applied in accordance with these manuals, except for some TOPEX/ Poseidon corrections: firstly, the TOPEX/Poseidon wet troposphere correction has been corrected for drift in one of the brightness temperature channels (Ruf 2002) and offsets related to the yaw state of the satellite (Brown et al. 2002). Secondly, the inverse barometer correction (when used) has been recalculated using time-variable global-mean over-ocean atmospheric pressure, an improvement on the GDR-supplied correction which assumes a constant global-mean over-ocean atmospheric pressure. This approach makes the correction used for TOPEX/Poseidon consistent with the Jason-1 and OSTM/Jason-2 processing.
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Satellite Altimeter Data Processing Techniques
The TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite altimeter missions measure sea surface height (SSH) relative to the centre of mass of the Earth along the satellite ground track. A number of instrumental and geophysical corrections must be applied. Every 10 days (one cycle) virtually global coverage of the worldÕs ocean, between 66˚N and S, is achieved. Our gridded data set as used here goes to 65˚N and S.
Our satellite altimeter data processing mostly follows the procedures, and uses the edits and tests, recommended by the providers of the satellite altimeter data sets, and are similar to those described in Leuliette et al. (2004). The documents for the three missions used are Benada (1997) for TOPEX/Poseidon, Aviso (2003) for Jason-1 and CNES (2009) for OSTM/Jason-2.
Orbits from the most recent versions of the Geophysical Data Records (GDR Þles; MGDR-B for TOPEX/Poseidon, GDR-C for Jason-1 and GDR-T for OSTM/Jason-2) are used. GDR corrections from the same Þles for tides, wet troposphere, dry troposphere, ionosphere, sea-state bias (SSB), inverse barometer correction (when required) and the mean sea surface are applied in accordance with these manuals, except for some TOPEX/ Poseidon corrections: firstly, the TOPEX/Poseidon wet troposphere correction has been corrected for drift in one of the brightness temperature channels (Ruf 2002) and offsets related to the yaw state of the satellite (Brown et al. 2002). Secondly, the inverse barometer correction (when used) has been recalculated using time-variable global-mean over-ocean atmospheric pressure, an improvement on the GDR-supplied correction which assumes a constant global-mean over-ocean atmospheric pressure. This approach makes the correction used for TOPEX/Poseidon consistent with the Jason-1 and OSTM/Jason-2 processing.
Calibrations of the TOPEX/Poseidon data against tide gauges have been performed by Gary Mitchum and colleagues (see, e.g., Nerem and Mitchum 2001). Here and in earlier publications, we have used the calibrations up to the end of 2001 (close to the end of the TOPEX/Poseidon mission). One of the problems these calibrations address is the changeover to the redundant “side B” altimeter electronics in February 1999 (at the end of cycle 235) due to degradation of the ÔÔside AÕÕ altimeter electronics which had been in use since the start of the mission. An alternative processing approach to address the side A to side B discontinuity is to use the separate Chambers et al. (2003) SSB models for TOPEX sides A and B without any use of the Poseidon data, as this correction does not address the substantial drift in the Poseidon SSH measurements, especially later in the mission. No tide-gauge calibrations are applied to Jason-1 or OSTM/Jason-2 data. The altimeter data sets as used here are available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html.
The Analysis Approach
The full details of our approach to estimating historical sea level were reported in Church et al. (2004). Briefly, the reconstructed sea level H^r(x, y, t) is represented as
H^r(x, y, t) = U^r(x, y) alpha(t) + epsilon
where U^r(x, y) is a matrix of the leading empirical orthogonal functions (EOFs) calculated from monthly satellite altimeter data mapped (using a Gaussian filter with a length scale of 300 km applied over a square with sides of 800 km) to a one degree by one degree grid for the ice free oceans between 65ûS and 65ûN, epsilon is the uncertainty, x and y are latitude and longitude and t is time. This matrix is augmented by an additional “mode” that is constant in space and used to represent any global average sea-level rise. In the reduced space optimal interpolation, the amplitude of the constant mode and these EOFs are calculated by minimising the cost function
S(alpha) = (K U^r alpha - H^0)^T M^{-1} (K U^r alpha - H^0) + alpha^T Lambda alpha
This cost function minimises the difference between the reconstructed sea levels and the observed coastal and island sea levels H^0, allowing for a weighting related to the observational uncertainties, omitted EOFs and also down-weights higher order EOFs. K is a sampling operator equal to 1 when there is observed sea-level data available and 0 otherwise, Lambda is the diagonal matrix of the eigenvalues of the covariance matrix of the altimeter data and M is the error covariance matrix given by
M = R + KU’ Lambda’ U’^{T}K^T
where R is the matrix of the covariance of the instrumental errors (assumed diagonal here) and the primes indicate the higher order EOFs not included in the reconstruction.
The EOFs are constructed from the covariances of the altimeter sea-level data after removal of the mean. Any overall increase in sea level as a result of ocean thermal expansion or the addition of mass to the ocean is difficult to represent by a finite number of EOFs. We therefore include an additional “mode” which is constant in space to represent this change in GMSL.
Because the sea-level measurements are not related to a common datum, we actually work with the change in sea level between time steps and then integrate over time to get the solution. The least squares solution provides an estimate of the amplitude of the leading EOFs, global average sea-level and error estimates.
Christiansen et al. (2010) tested the robustness of various reconstruction techniques, including an approach similar to that developed by Church et al. (2004) using thermosteric sea level calculated from climate model results. They used an ensemble of model results (derived by randomising the phase of the principal components of the model sea level, see Christiansen et al. (2010) for details). For a method similar to that used here (including the additional “constant” mode and for a 20 year period for determining the EOFs), the trend in the ensemble mean reconstruction was within a few percent of the true value when 200 gauges were available (with about a 10% variation for the inter.quartile range of individual estimates, decreasing to about 5% when a 50 year period for determining the EOFs was available). When only 40 gauges were used, the ensemble mean trend was biased low by a little under 10% (with an interquartile range of about 15%). They further showed that the reconstructions tend to overestimate the interannual variability and that a longer period for determining the EOFs is important in increasing the correlation between the reconstructed and model year to year variability. Reconstructions that do not use the constant mode perform poorly compared to those that do. These results are similar to our own tests with climate model simulations, with the reconstruction tending to have a slightly smaller trend. Christiansen et al. also found a simple mean of the tide gauges reproduces the trend with little bias in the ensemble mean and about a 10% variation in the interquartile range. However, the simple mean has larger interannual variations and correlates less well with the model interannual variability.
The GMSL estimates are not sensitive to the number of EOFs (over the range 4Ð20 plus the constant mode) used in the reconstruction, although the average correlation between the observed and reconstructed signal increases and the residual variance decreases when a larger number of EOFs is used. For the long periods considered here and with only a small number of records available at the start of the reconstruction period, we used only four EOFs which explain 45% of the variance, after removal of the trend.
Computation of EOFs
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Christiansen et al. (2010) tested the robustness of various reconstruction techniques, including an approach similar to that developed by Church et al. (2004) using thermosteric sea level calculated from climate model results. They used an ensemble of model results (derived by randomising the phase of the principal components of the model sea level, see Christiansen et al. (2010) for details). For a method similar to that used here (including the additional “constant” mode and for a 20 year period for determining the EOFs), the trend in the ensemble mean reconstruction was within a few percent of the true value when 200 gauges were available (with about a 10% variation for the inter.quartile range of individual estimates, decreasing to about 5% when a 50 year period for determining the EOFs was available). When only 40 gauges were used, the ensemble mean trend was biased low by a little under 10% (with an interquartile range of about 15%). They further showed that the reconstructions tend to overestimate the interannual variability and that a longer period for determining the EOFs is important in increasing the correlation between the reconstructed and model year to year variability. Reconstructions that do not use the constant mode perform poorly compared to those that do. These results are similar to our own tests with climate model simulations, with the reconstruction tending to have a slightly smaller trend. Christiansen et al. also found a simple mean of the tide gauges reproduces the trend with little bias in the ensemble mean and about a 10% variation in the interquartile range. However, the simple mean has larger interannual variations and correlates less well with the model interannual variability.
The GMSL estimates are not sensitive to the number of EOFs (over the range 4Ð20 plus the constant mode) used in the reconstruction, although the average correlation between the observed and reconstructed signal increases and the residual variance decreases when a larger number of EOFs is used. For the long periods considered here and with only a small number of records available at the start of the reconstruction period, we used only four EOFs which explain 45% of the variance, after removal of the trend.
Computation of EOFs
For each altimeter mission the along-track data described above are smoothed onto a 1˚-by-1˚-by-1 month grid for the permanently ice-free ocean from 65˚S to 65˚N. The smoothing uses an e-folding length of 300 km and covers 90% of the global oceans. The three data sets are combined by matching means at each grid point (rather than just the global average) over the common periods between TOPEX/Poseidon and Jason-1 and between Jason-1 and OSTM/Jason-2. This is an attempt to overcome the problem of different geographically correlated errors in the missions, for example due to different sea-state bias corrections. The overlap between TOPEX/Poseidon and Jason-1 was from 15-January-2002 to 21-August-2002 (T/P cycles 344-365, J-1 cycles 1-22) or, effectively, February to July 2002 in our monthly data sets. The overlap between Jason-1 and OSTM/ Jason-2 was from 12-July-2008 to 26-January-2009 (J-1 cycles 240-259 and J-2 cycles 1-20) or, effectively, August to December 2008 in our monthly data sets.
Separate versions of the altimeter data sets with and without the inverse barometer correction and with and without the seasonal signal are produced, as follows:
Only whole years (in this case 17 years) are used.
Grid points with gaps in the time series (e.g. due to seasonal sea ice) are ignored.
The data are area (cos(latitude)) weighted.
The global-mean trend is removed.
The GIA correction appropriate for this data is applied (Mark Tamisiea, NOC Liverpool, private communication).
In the original (Church et al. 2004; Church and White 2006) reconstructions, the EOFs were defined with the 9 and 12 years (respectively) of TOPEX/Poseidon and Jason-1 satellite altimeter data available at those times. There are now 17 years of monthly satellite altimeter data available, almost twice as long as the original series. This longer time series should be able to better represent the variability and result in an improved reconstruction of global average sea level, as found by Christiansen et al. (2010). After removing the global average trend and the seasonal (annual plus semi-annual) signal, the first four EOFs account for 29, 8, 5 and 4% of the variance (Figure 2). If the seasonal signal is not removed, the first four EOFs account for 24, 18, 14 and 4% of the variance. These EOFs characterise the large-scale interannual variability, particularly that associated with the El Nino-Southern Oscillation phenomenon, and for the case where the seasonal signal has not been removed, also include the seasonal north/south oscillation of sea level.
Figure 2: The EOFs used in the sea-level construction. The four EOFs on the left include the seasonal signal and represent a combination of the seasonal signal and interannual variability. The corresponding four EOFs on the right are after the seasonal signal has been removed from the altimeter data. The EOFs are dimensionless and of unit length.
Sensitivity of the Results
To complete the reconstruction, we need to specify two parameters: the instrumental error covariance matrix R and the relative weighting of the “constant” mode to the EOFs. Church and White (2006) used the first differences between sets of nearby sea-level records to compute an average error estimate of the first differences of 50 mm and assumed errors were independent of and between locations (i.e. the error covariance matrix was diagonal). When the seasonal signal was removed, tests indicated the residual variance increased when a smaller error estimate was used but was not sensitive to the selection of larger values. Similarly, the residual variance increased when the weighting of the ÔÔconstantÕÕ mode was less than 1.5 times the first EOF but was not sensitive to larger values. The computed trends for the 1880Ð2009 increased slightly (0.06 mm year -1 or about 4%) when the relative weighting was increased by 33% from 1.5 to 2.0 or the error estimate was decreased by 40% to 30 mm. Prior to 1880 when there were less than 15 locations available and none in the southern hemisphere, there was considerably greater sensitivity to the parameter choice than for the rest of the record and hence we focus on results after 1880. When the seasonal signal was retained in the solution, a larger error estimate of 70 mm was appropriate. This solution also had a larger residual variance and a slightly greater sensitivity in the trend to the parameter choice and hence we focus on the solution with the seasonal signal removed, as in our earlier studies.
As a further test of the effectiveness of the EOFs to represent the interannual variability in GMSL, we computed EOFs using shorter periods of 9 and 12 years, similar to our earlier analyses (Church et al. 2004; Church and White 2006). The resulting estimates are well within the uncertainties.
The atmospheric pressure correction makes essentially no difference to the GMSL time series for the computations with the seasonal signal removed and no difference to the computations including the seasonal signal after about 1940. However, prior to 1940, the correction does make a significant difference to the GMSL calculated with the seasonal signal included. These results suggests some problem with the atmospheric correction prior to 1940 and as a result we decided not to include this correction in the results. This issue seems to be related to the HadSLP2 data set not resolving the annual cycle and, possibly, the spatial patterns well for the Southern Hemisphere south of 30 S for the 1920s and 1930s, presumably because of sparse and changing patterns of input data at this time and in this region. This is being investigated further.
Results
We present results for two periods: from 1880 to 2009 and the satellite altimeter period from January 1993 to December 2009. The latter is only a partial test of the reconstruction technique because the EOFs used were actually determined for this period.
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As a further test of the effectiveness of the EOFs to represent the interannual variability in GMSL, we computed EOFs using shorter periods of 9 and 12 years, similar to our earlier analyses (Church et al. 2004; Church and White 2006). The resulting estimates are well within the uncertainties.
The atmospheric pressure correction makes essentially no difference to the GMSL time series for the computations with the seasonal signal removed and no difference to the computations including the seasonal signal after about 1940. However, prior to 1940, the correction does make a significant difference to the GMSL calculated with the seasonal signal included. These results suggests some problem with the atmospheric correction prior to 1940 and as a result we decided not to include this correction in the results. This issue seems to be related to the HadSLP2 data set not resolving the annual cycle and, possibly, the spatial patterns well for the Southern Hemisphere south of 30 S for the 1920s and 1930s, presumably because of sparse and changing patterns of input data at this time and in this region. This is being investigated further.
Results
We present results for two periods: from 1880 to 2009 and the satellite altimeter period from January 1993 to December 2009. The latter is only a partial test of the reconstruction technique because the EOFs used were actually determined for this period.
The reconstructed and satellite estimates of GMSL have somewhat different error sources. The two largest uncertainties for the reconstructed sea level are the incomplete global coverage of sea-level measurements (particularly in the southern hemisphere), and uncertainties in land motions used to correct the sea-level records. The former contributes directly to the formal uncertainty estimates that are calculated on the basis that the sea-level records are independent. In estimating uncertainties on linear trends and accelerations, we recognise the series are autocorrelated and the number of effective degrees of freedom is only a quarter of the number of years of data. Previous tests using various GIA models suggest an additional uncertainty in trends of about ±0.1 mm year^{-1} (Church et al. 2004) that should be added in quadrature to the uncertainty in the trend estimate from the time series (but not for estimates of the acceleration in the rate of rise). The annual time series of GMSL and the estimated uncertainty estimates are available at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html.
1993-2009
The global mean sea level can be computed cycle-by-cycle (every 10 days) directly from the along track satellite data or from the mapped (monthly) satellite data. After averaging the cycle-by-cycle data set over 3 cycles these two estimates for the Jason-1 mission (February 2002 to January 2009; Figure 3) are very similar; the differences have a standard deviation of 1.0 mm. The trends are different by only 0.2 mm year^{-1}, with the trend from the gridded data set being higher numerically, but not statistically different from the trend from the along-track data set.
Figure 3: Comparison of the satellite-altimeter estimates of GMSL from the along-track data (including all ocean areas where valid data are available) and the mapped data (for a fixed grid) for the duration of the Jason-1 altimeter mission.
The reconstructed and altimeter GMSL both increase from 1993 to the end of the record (Figure 4). The larger year-to-year variability of the reconstructed signal (compared with the altimeter record) of ~4-5 mm is less than the one standard deviation uncertainty estimates of about ±7 mm. For almost all of the record, the reconstruction is within the one standard deviation uncertainty estimate of the altimeter record. The uncertainty of the reconstruction increases slightly in the last couple of years because of the smaller number of tide gauge records available through the PSMSL.
Figure 4: Global average sea level from 1990 to 2009 as estimated from the coastal and island sea-level data (blue with one standard deviation uncertainty estimates) and as estimated from the satellite altimeter data from 1993 (red). The satellite and the in situ yearly averaged estimates have the same value in 1993 and the in situ data are zeroed in 1990. The dashed vertical lines indicate the transition from TOPEX Side A to TOPEX Side B, and the commencement of the Jason-1 and OSTM/Jason-2 records.
After correcting for the GIA, the linear trend from the altimeter data from January 1993 to December 2009 is 3.2 ± 0.4 mm year^{-1} (note the GIA values appropriate for correcting the altimeter data are different to that necessary for the in situ data). The uncertainty range (1 standard deviation) comes from fitting a linear trend to the data using uncertainties on the annual averages of 5 mm and is consistent with an updated error budget of altimeter sea-level trend uncertainties (Ablain et al. 2009). They estimate the largest uncertainties are related to the wet tropospheric (atmospheric water vapour) correction, the bias uncertainty of successive missions, orbit uncertainty and the sea-state bias correction. These total to about 0.4 mm year -1, similar to our uncertainty estimate. The reconstructed global average sea-level change over the same period is almost the same as for the altimeter data. However, as a result of different interannual variability, the trend of 2.8 ± 0.8 mm year^{-1} is smaller but not significantly different to the altimeter estimate after correction for glacial isostatic adjustment.
1880-2009
The GMSL time series (Figure 5) are not significantly different from our earlier 2006 result (Church and White 2006). The total GMSL rise (Figure 5) from January 1880 to December 2009 is about 210 mm over the 130 years. The trend over this period, not weighted by the uncertainty estimates, is 1.5 mm year^{-1} (1.6 mm year^{-1} when weighted by the uncertainty estimates). Although the period starts 10 years later in 1880 (rather than 1870), the total rise (Figure 5) is larger than our 2006 estimate of 195 mm mostly because the series extends 8 years longer to 2009 (compared with 2001).
Figure 5: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue). The one standard deviation uncertainty estimates plotted about the low passed sea level are indicated by the shading. The Church and White (2006) estimates for 1870-2001 are shown by the red solid line and dashed magenta lines for the 1 standard deviation errors. The series are set to have the same average value over 1960-1990 and the new reconstruction is set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.
The interannual variability is mostly less than the one standard deviation uncertainty estimates, which range from ~25 mm in 1880 to a minimum of ~6 mm in 1988 (as shown in Figure 5, where the yearly GMSL time series is plotted over the envelope of smoothed (±3 year boxcar) 1 standard deviation limits). However, there are a number of features which are comparable to/larger than the uncertainty estimates. Firstly, there is a clear increase in the trend from the first to the second half of the record; the linear trend from 1880 to 1935 is 1.1 ± 0.7 mm year^{-1} and from 1936 to the end of the record the trend is 1.8 ± 0.3 mm year^{-1}. The period of relatively rapid sea-level rise commencing in the 1930s ceases abruptly in about 1962 after which there is a fall in sea level of over 10 mm over 5 years. Starting in the late 1960s, sea level rises at a rate of almost 2.4 mm year^{-1} for 15 years from 1967 and at a rate of 2.8 ± 0.8 mm year^{-1} from 1993 to the end of the record. There are brief interruptions in the rise in the mid 1980s and the early 1990s.
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Figure 5: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue). The one standard deviation uncertainty estimates plotted about the low passed sea level are indicated by the shading. The Church and White (2006) estimates for 1870-2001 are shown by the red solid line and dashed magenta lines for the 1 standard deviation errors. The series are set to have the same average value over 1960-1990 and the new reconstruction is set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.
The interannual variability is mostly less than the one standard deviation uncertainty estimates, which range from ~25 mm in 1880 to a minimum of ~6 mm in 1988 (as shown in Figure 5, where the yearly GMSL time series is plotted over the envelope of smoothed (±3 year boxcar) 1 standard deviation limits). However, there are a number of features which are comparable to/larger than the uncertainty estimates. Firstly, there is a clear increase in the trend from the first to the second half of the record; the linear trend from 1880 to 1935 is 1.1 ± 0.7 mm year^{-1} and from 1936 to the end of the record the trend is 1.8 ± 0.3 mm year^{-1}. The period of relatively rapid sea-level rise commencing in the 1930s ceases abruptly in about 1962 after which there is a fall in sea level of over 10 mm over 5 years. Starting in the late 1960s, sea level rises at a rate of almost 2.4 mm year^{-1} for 15 years from 1967 and at a rate of 2.8 ± 0.8 mm year^{-1} from 1993 to the end of the record. There are brief interruptions in the rise in the mid 1980s and the early 1990s.
The linear trend from 1900 to 2009 is 1.7 ± 0.2 mm year^{-1} and from 1961 to 2009 is 1.9 ± 0.4 mm year^{-1}. However, there are significant departures from a linear trend. We estimate an acceleration in GMSL by fitting a quadratic to the time series, taking account of the time variable uncertainty estimates. From 1880 to 2009, the acceleration (twice the quadratic coefficient) is 0.009 ± 0.003 mm year^{-2} (one standard deviation). This estimate is slightly less than but not significantly different from the (one standard deviation) estimate of Church and White (2006) of 0.013 ± 0.003 mm year^{-2}, but still significantly different from zero at the 95% level. From 1900 to 2009, the acceleration is also 0.009 ± 0.004 mm year^{-2}. If the variable uncertainty estimates are ignored the equivalent accelerations are 0.010 and 0.012 mm year^{-2}.
Discussion
There are other recent estimates of changes in GMSL for this period widely available (Jevrejeva et al. 2006; Holgate and Woodworth, 2004; Fig. 6). They all agree approximately with our updated GMSL time series and the longer of these estimates (Jevrejeva et al. 2006) also has an acceleration in the 1930s and a pause in the rise commencing in the 1960s. These changes are also present in a number of individual sea-level records (Woodworth et al. 2009). However, note that the interannual variability in the Jevrejeva et al. series is unrealistically large in the early part of the record and larger than their uncertainty estimates. The Jevrejeva et al. estimate of sea level prior to 1850 (Jevrejeva et al. 2008) indicates an acceleration in the rate of rise commencing at the end of the eighteenth century. Note that their pre-1850 estimate uses only three-sea level records. We do not attempt to extend our construction back prior to 1860. If instead of the recon.struction technique, we employed a straight average of tide gauges, the overall trend back to 1910 is very similar but there is larger interannual variability (Figure 6). Prior to 1910, the variability is even larger (consistent with the results of Christiansen et al. (2010), with unrealistic decadal trends of ±10 mm year^{-1}.
One source of error is the poor corrections for land motion. Bouin and Wooppelmann (2010) used GPS time series for correcting tide-gauge records for land motion from all sources and estimated a global average sea-level rise of 1.8 mm year^{-1} for the twentieth century, consistent with the present results and early studies (e.g. Douglas 1991). These GPS series are just now beginning to be long enough to provide useful constraints on land motion from all sources (not just GIA).
A significant non-climatic influence on sea level is the storage of water in dams and the depletion of ground water from aquifers, some of which makes it into the ocean. Chao et al. (2008) estimated that about 30 mm of sea-level equivalent is now stored in man-made dams and the surrounding soils; most of this storage occurred since the 1950s. Globally, the rate of dam entrapment has slowed significantly in the last decade or two. The depletion of ground water (Konikow et al. personal communication; Church et al. in preparation) offsets perhaps a third of this terrestrial storage over the last two decades and the rate of depletion has accelerated over the last two decades.
Figure 6: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue) compared with estimates of Jevrejeva et al. (2006, brown), Holgate and Woodworth (2004, red) and from a simple average of the gauges (yellow). All series are set to have the same average value over 1960-1990 and the reconstructions are set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.
We remove this direct (non-climate) anthropogenic change in terrestrial water storage (both dam storage and aquifer depletion) from our observations to focus on the sea-level change related to climatic influences. The resulting time series (Figure 7) shows a slightly faster rate of sea-level rise since about 1960 and a slightly larger acceleration for the periods since 1880 and 1900. Terrestrial storage contributed to the sea level fall in the 1960s but does not fully explain it. The volcanic eruptions of Mt Agung in 1963, El Chichon in 1982 and Mt Pinatubo in 1991 probably contribute to the small sea level falls in the few years following these eruptions (Church et al. 2005; Gregory et al. 2006; Domingues et al. 2008) but it has not yet been possible to quantitatively explain the mid 1960s fall in sea level (Church et al. in preparation).
Figure 7: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (grey) and after correcting for the changes in terrestrial storage associated with the building of dams and the deletion of aquifers (blue). Note these series are virtually identical before 1950.
The acceleration in the rate of sea-level rise since 1880 is in qualitative agreement with the few available long (mostly northern hemisphere) sea-level records and longer term estimates of sea level from geological (e.g. salt-marsh) data (for example Donnelly et al. 2004; Gehrels et al. 2006). These data mostly indicate an acceleration at the end of the nineteenth or start of the twentieth century (see Woodworth et al. 2011, this volume, for a summary and references).
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Figure 6: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue) compared with estimates of Jevrejeva et al. (2006, brown), Holgate and Woodworth (2004, red) and from a simple average of the gauges (yellow). All series are set to have the same average value over 1960-1990 and the reconstructions are set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.
We remove this direct (non-climate) anthropogenic change in terrestrial water storage (both dam storage and aquifer depletion) from our observations to focus on the sea-level change related to climatic influences. The resulting time series (Figure 7) shows a slightly faster rate of sea-level rise since about 1960 and a slightly larger acceleration for the periods since 1880 and 1900. Terrestrial storage contributed to the sea level fall in the 1960s but does not fully explain it. The volcanic eruptions of Mt Agung in 1963, El Chichon in 1982 and Mt Pinatubo in 1991 probably contribute to the small sea level falls in the few years following these eruptions (Church et al. 2005; Gregory et al. 2006; Domingues et al. 2008) but it has not yet been possible to quantitatively explain the mid 1960s fall in sea level (Church et al. in preparation).
Figure 7: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (grey) and after correcting for the changes in terrestrial storage associated with the building of dams and the deletion of aquifers (blue). Note these series are virtually identical before 1950.
The acceleration in the rate of sea-level rise since 1880 is in qualitative agreement with the few available long (mostly northern hemisphere) sea-level records and longer term estimates of sea level from geological (e.g. salt-marsh) data (for example Donnelly et al. 2004; Gehrels et al. 2006). These data mostly indicate an acceleration at the end of the nineteenth or start of the twentieth century (see Woodworth et al. 2011, this volume, for a summary and references).
In addition to the overall increase in the rate of sea-level rise, there is also considerable variability in the rate. Using the yearly average data, we computed trends for successive 16 year periods (close to the length of the altimeter data set) from 1880 to the present (Figure 8). We find maxima in the rates of sea-level rise of over 2 mm year^{-1} in the 1940s and 1970s and nearly 3 mm year^{-1} in the 1990s (Figure 8). As in earlier studies (using 10 and 20 year windows; Church and White 2006; Church et al. 2008), the most recent rate of rise over these short 16 year windows is at the upper end of a histogram of trends but is not statistically higher than the peaks during the 1940s and 1970s. Consistent with the findings of Christiansen et al. (2010), our computed variability in the rates of rise are almost a factor of two less than those where an average of tide gauges (Holgate and Woodworth 2004; Holgate 2007) is used to estimate GMSL. The rate of sea-level rise since 1970 has now been quantitatively explained (Church et al. in preparation) by a gradual increase in ocean thermal expansion, with fluctuations at least partly related to volcanic eruptions, and an increasing cryospheric contribution. The contribution from glaciers and ice caps (Cogley 2009), and the Greenland Ice Sheet (Rignot et al. 2008, 2011) both increased in the 1990s. There are also recent indications of an increasing contribution from the West Antarctic Ice Sheet (Rignot et al. 2011). The larger rate of rise in the 1940s may be related to larger glacier and ice-cap contributions (Oerlemanns et al. 2007) and higher temperatures over Greenland resulting in larger sea-level contributions at that time.
Figure 8: Linear trends in sea level over successive 16 year periods for the yearly averaged reconstructed sea-level data. The trend from the satellite altimeter data are shown at the end of the time series.
The rate of sea-level rise as measured both by the satellite altimeter record and the in situ reconstruction of about 3 mm year^{-1} since 1993 is near the upper end of the sea-level projections for both the Intergovernmental Panel on Climate Change’s Third (Church et al. 2001) and Fourth (Meehl et al. 2007 - see also Hunter 2010) Assessment Reports. However, note that the in situ data also indicates that there was little net change in GMSL from 1990 to 1993, most likely as a result of the volcanic eruption of Mount Pinatubo in 1991 (Domingues et al. 2008; Church et al. in preparation).
Significant progress has been made during the last decade in estimating and understanding historical sea-level rise. However, much remains to be done. Of particular importance is the maintenance and continuation of the observing network and associated infrastructure such as the PSMSL archive. The in situ sea-level data set continues to provide a very valuable contribution to our understanding of late nineteenth, twentieth and early twenty first century sea-level rise. Data archaeology and paleo observations to extend the spatial and temporal coverage of in situ sea-level observations need to be vigorously pursued. Modern GPS measurements at tide-gauge locations, which are now beginning to provide valuable information on vertical land motion (e.g., Bouin and Woppelmann 2010) should be continued and expanded. This applies in particular to the use of in situ data to monitor the accuracy of satellite altimeter measurement systems. Increasing the number and geographical distribution of these GPS observations is a priority. Of course a major priority is maintaining a continuous record of high-quality satellite-altimeter observations of the oceans and continuing to improve the International Terrestrial Reference Frame and maintaining and expanding the associated geodetic networks. These improved observations need to be combined with more elegant analysis of the observations, including, for example, considering changes in the gravitational field associated with evolving mass distributions on the Earth and using observations of sea-level rise, ocean thermal expansion and changes in the cryosphere in combined solutions.
Acknowledgments:
This paper is a contribution to the Commonwealth Scientific Industrial Research Organization (CSIRO) Climate Change Research Program. J. A. C. and N. J. W. were partly funded by the Australian Climate Change Science Program. NASA & CNES provided the satellite altimeter data, PSMSL the tide-gauge data.
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References
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Couldrey et al. (2021)
Title:
What causes the spread of model projections of ocean dynamic sea-level change in response to greenhouse gas forcing?
Key Points:
Ocean model diversity in AOGCMs is a key source of uncertainty in sea-level projections under greenhouse gas forcing.
Increased air-sea heat flux sets the broad pattern of dynamic sea-level change; wind stress and freshwater flux have localized effects.
Nonlinear dynamic sea-level responses occur with simultaneous flux perturbations, especially in the Arctic and North Atlantic
Keywords:
sea-level rise, ocean heat uptake, climate change, climate modeling, ocean model diversity, air-sea flux perturbations, FAFMIP
Corresponding author:
Matthew P. Couldrey
Citation:
Couldrey, M. P., Gregory, J. M., Dias, F. B., Dobrohotoff, P., Domingues, C. M., Garuba, O., et al. (2021). What causes the spread of model projections of ocean dynamic sea-level change in response to greenhouse gas forcing? Climate Dynamics, 56(1–2), 155–187. doi:10.1007/s00382-020-05471-4
URL:
https://link.springer.com/article/10.1007/s00382-020-05471-4
Abstract
Sea levels of different atmosphere–ocean general circulation models (AOGCMs) respond to climate change forcing in different ways, representing a crucial uncertainty in climate change research. We isolate the role of the ocean dynamics in setting the spatial pattern of dynamic sea-level (ζ) change by forcing several AOGCMs with prescribed identical heat, momentum (wind) and freshwater flux perturbations. This method produces a ζ projection spread comparable in magnitude to the spread that results from greenhouse gas forcing, indicating that the differences in ocean model formulation are the cause, rather than diversity in surface flux change. The heat flux change drives most of the global pattern of ζ change, while the momentum and water flux changes cause locally confined features. North Atlantic heat uptake causes large temperature and salinity driven density changes, altering local ocean transport and ζ. The spread between AOGCMs here is caused largely by differences in their regional transport adjustment, which redistributes heat that was already in the ocean prior to perturbation. The geographic details of the ζ change in the North Atlantic are diverse across models, but the underlying dynamic change is similar. In contrast, the heat absorbed by the Southern Ocean does not strongly alter the vertically coherent circulation. The Arctic ζ change is dissimilar across models, owing to differences in passive heat uptake and circulation change. Only the Arctic is strongly affected by nonlinear interactions between the three air-sea flux changes, and these are model specific.
Introduction
Sea-level rise presently is and will continue to be an important consequence of anthropogenically forced climate change. Global mean thermosteric sea-level rise, due to thermal expansion of a warming ocean, accounts for 30–55% of the global mean sea-level rise (GMSLR) projected for the years 2081–2100 (Church et al. 2013). The remainder results mostly from ocean mass gain due to melting land ice (glaciers and ice sheets). Regional sea-level changes are much more complicated, involving ocean and climate dynamics as well as solid-Earth processes, typically not included in coupled climate models. The latter can make up 50% or more of regional sea-level change pattern by the end of the 21st Century (Slangen et al. 2012; Stammer et al. 2013).
As part of the Coupled Model Intercomparison Project (CMIP), atmosphere–ocean general circulation models (AOGCMs) simulate anthropogenic sea-level change related to changes in climate dynamics by starting from a near-equilibrium (i.e. well spun-up) preindustrial control state (piControl) and running forward with time-varying forcing agents (greenhouse gases, anthropogenic aerosol, etc.). In these models, ocean dynamic sea level, ζ, is defined at each location and time as
ζ = η − η̅ (1)
where η is the local sea-surface height relative to a surface on which the geopotential has a uniform constant value, and η̅ is its global mean over the ocean area. η is termed ‘sterodynamic sea level’ according to recent terminology conventions (Gregory et al. 2019). By definition, the global mean of ζ is zero, but locally it is not zero due to ocean circulation and horizontal density gradients. Using CMIP terminology, ζ is the variable ‘zos’ (Griffies et al. 2016). The sterodynamic sea-level change (Δη) that an individual location experiences may differ substantially from the global mean thermosteric sea-level rise (GMSLR, Δ𝜂−), because of changes in ocean circulation and density. This present work focuses on the spatial pattern in ocean dynamic sea-level change
∆ζ(x,y,t) = Δ𝜂(𝑥,𝑦,𝑡) − ∆η̅(𝑡),(2)
projected to occur over the coming century due to anthropogenic greenhouse gas forced climate change. Accordingly, Δζ is calculated from CMIP output as the difference between the ‘zos’ fields in a forcing experiment relative to a control state (see Sects. 2.2 and 2.3 for details). In results from AOGCMs from CMIP’s fifth phase (CMIP5), the spatial standard deviation of the multi-model mean Δζ projected under scenario RCP4.5 by 2081–2100 is 0.06 m, which is 30% of the multi-model mean GMSLR due to thermal expansion (Gregory et al. 2016). Thus, in some locations, Δη is more than twice its global mean, because of ocean dynamic sea-level change. Moreover, different AOGCMs predict diverse spatial patterns and magnitudes of sea-level change (Slangen et al. 2014). The global mean of the inter-model standard deviation of Δζ in the same projections is also about 0.06 m; in other words, the systematic uncertainty in predicting the pattern of dynamic sea-level change is of first order, being about the same magnitude as the pattern itself (see also Fig. 3). It is this spread among AOGCMs that we seek to investigate: one of the largest uncertainties affecting regional impacts of anthropogenic sea-level and climate change this century and beyond.
Part of the spread among AOGCMs comes from their different representations of forcing agents, especially anthropogenic aerosol (Melet and Meyssignac 2015). The idealized scenario of increasing the concentration of CO2 by 1% per year, called ‘1pctCO2’ is simpler to interpret than more complex experiments with differing time profiles of numerous types of climate forcing (Eyring et al. 2016). After seven decades, 1pctCO2 reaches a similar magnitude of radiative forcing to RCP 4.5 by the end of the twenty-first century.
Developing a more complete understanding of the climate response to idealized 1pctCO2 forcing provides insight into how we expect the climate to respond to moderate greenhouse gas and aerosol emissions by the end of this century. However, even when AOGCMs are forced with this simple, idealized setup, they produce a range of climate response, primarily because of their differing climate sensitivities (i.e. the degree of surface warming that results per radioactive forcing). Differences in the representation of cloud feedback mechanisms in atmosphere models accounts for the greatest uncertainty in climate sensitivity (Ceppi et al. 2017). The control climate, which is different for each model, also contributes to the spread (Bouttes and Gregory 2014), e.g. via the strength of the ice coverage and water vapour feedbacks (Hu et al. 2017), and sea-surface temperature (SST) biases (He and Soden 2016). These and other factors affect the spatial patterns and magnitudes of the air-sea fluxes of heat, freshwater, and momentum, which are the drivers of Δζ. Unpacking the influence of oceanic processes from atmospheric processes is therefore difficult in experiments like 1pctCO2.
Previous work has investigated how the diversity in the changes of air-sea fluxes of heat, freshwater and momentum contribute to the spread in projections of sea-level change. A typical approach is to force a single model with ensembles of boundary conditions like SST (Huber and Zanna 2017) or air-sea flux change (Bouttes and Gregory 2014) to mimic the spread of fully coupled simulations. These studies find that forcing individual models with a variety of boundary conditions produces a large spread of ocean responses, in terms of sea-level change (Bouttes and Gregory 2014), ocean heat uptake (OHU) and circulation change (Huber and Zanna 2017). While these studies demonstrate that models are sensitive to surface fluxes, the uncertainty that results from the diversity of ocean model structure in coupled models has not yet been assessed.
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Developing a more complete understanding of the climate response to idealized 1pctCO2 forcing provides insight into how we expect the climate to respond to moderate greenhouse gas and aerosol emissions by the end of this century. However, even when AOGCMs are forced with this simple, idealized setup, they produce a range of climate response, primarily because of their differing climate sensitivities (i.e. the degree of surface warming that results per radioactive forcing). Differences in the representation of cloud feedback mechanisms in atmosphere models accounts for the greatest uncertainty in climate sensitivity (Ceppi et al. 2017). The control climate, which is different for each model, also contributes to the spread (Bouttes and Gregory 2014), e.g. via the strength of the ice coverage and water vapour feedbacks (Hu et al. 2017), and sea-surface temperature (SST) biases (He and Soden 2016). These and other factors affect the spatial patterns and magnitudes of the air-sea fluxes of heat, freshwater, and momentum, which are the drivers of Δζ. Unpacking the influence of oceanic processes from atmospheric processes is therefore difficult in experiments like 1pctCO2.
Previous work has investigated how the diversity in the changes of air-sea fluxes of heat, freshwater and momentum contribute to the spread in projections of sea-level change. A typical approach is to force a single model with ensembles of boundary conditions like SST (Huber and Zanna 2017) or air-sea flux change (Bouttes and Gregory 2014) to mimic the spread of fully coupled simulations. These studies find that forcing individual models with a variety of boundary conditions produces a large spread of ocean responses, in terms of sea-level change (Bouttes and Gregory 2014), ocean heat uptake (OHU) and circulation change (Huber and Zanna 2017). While these studies demonstrate that models are sensitive to surface fluxes, the uncertainty that results from the diversity of ocean model structure in coupled models has not yet been assessed.
The change of the Atlantic Meridional Overturning Circulation (AMOC) strength in response to climate change is model specific, and is believed to be a key factor setting the pattern of North Atlantic sea-level change (Yin et al. 2009; Hawkes 2013; Bouttes et al. 2014). Globally, ocean heat uptake has been related to the degree of AMOC weakening (Xie and Vallis 2012; Rugenstein et al. 2013; Kostov et al. 2014). However, more recently, the correlation between OHU and AMOC strength was shown to arise because both are affected by mesoscale eddy transfer (Saenko et al. 2018), where OHU is more intense and deep reaching with decreasing mesoscale eddy transfer. The ocean components of most CMIP5 and CMIP6 models are not able to resolve mesoscale eddies, so their effects are parameterized in different ways across models. It is therefore plausible that the differing representations of mesoscale and other unresolved phenomena are likely to contribute to the spread of sea-level projections among AOGCMs, through their influence on seawater properties (e.g. temperature, salinity and density) and ocean transports of heat and salt.
The Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) outlines a protocol for forcing different AOGCMs with perturbations to their air-sea fluxes—heat, freshwater, and momentum—to systematically explore the oceanic response to CO2-forced climate change (Gregory et al. 2016). The key goal of FAFMIP is to replicate the oceanic response to 1pctCO2 forcing, while excluding the model spread due to changes in air-sea fluxes. Initial FAFMIP results have highlighted the importance of the heat flux perturbation in setting much of the global pattern of Δζ, and that both the wind stress and heat flux perturbations set the Southern Ocean dipole (Gregory et al. 2016).
Building on previous findings, we present in this study: (1) new sea-level results based on AOGCM simulations forced with simultaneous rather than separate flux perturbations, (2) an intercomparison of the roles of temperature and salinity-driven density changes, and (3) further examination of the decomposition of ocean heat content (OHC) changes due to changes in temperature and transport. Our study also includes new CMIP6 simulations and paves the way for possible forthcoming FAFMIP analyses.
This paper is structured as follows: an explanation of the configuration of model experiments and analysis methods is given in Sect. 2. In Sect. 3.1, the sea-level responses to FAFMIP and 1pctCO2 forcing are compared, followed by a comparison of the 1pctCO2 sea-level response from CMIP5 and CMIP6 in Sect. 3.2. The response of AOGCMs to individually applied surface flux perturbations (heat, freshwater and momentum) is assessed in Sect. 3.3, while nonlinear interactions between these flux perturbations are described in Sect. 3.4. A decomposition of ocean heat uptake based on a subset of the AOGCMs is presented in Sect. 3.5. Results are discussed in Sect. 4 and the conclusions are laid out in Sect. 5. An appendix with further notes on the decomposition of ocean heat uptake is included in “Appendix”.
Methods
Perturbation of air-sea fluxes
The FAFMIP protocol presents a method that mimics the effect of 1pctCO2 forcing on the ocean but applies identical perturbations to each model (Gregory et al. 2016). The perturbations are the multi model mean changes in the air-sea fluxes of heat, freshwater, and momentum from 1pctCO2 simulations averaged over the 61st-80th years of forcing relative to the piControl state. This period covers the time where CO2 concentration reaches double its preindustrial values (at year 70). The suite of CMIP5 AOGCMs available at the time to derive the required surface flux perturbations for the FAFMIP protocol comprises 13 members; CNRM-CM5, CSIRO-Mk3-6-0, CanESM2, GFDL-ESM2G, HadGEM2-ES, MIROC-ESM, MIROC5, MPI-ESM-LR, MPI-ESM-MR, MPI-ESM-P, MRI-CGCM3, NorESM1-ME, and NorESM1-M. It was decided that all perturbations should be derived from a common set of models to allow for consistent comparison of model-mean sea-level change and the associated spread (Gregory et al. 2016). Further details about FAFMIP and the protocol, including the perturbation files can be found at https://www.fafmip.org.
Time-dependent CO2 and other forcing causes a varying magnitude of sea-level change, while the spatial pattern is relatively time-invariant (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). This phenomenon of ‘pattern scaling’ means that time-dependent forcing is not necessary for our investigation of the spatial structure. Therefore, in the interest of simplicity the FAFMIP flux perturbations are applied as a constant forcing for the full 70 years of each experiment, with no time-variation except for the annual cycle.
Experiments
FAFMIP perturbations to the fluxes of heat, water and momentum (Fig. 1) were applied in five different experiments, as listed below. All perturbations were applied at the air-sea interface in direct contact with seawater surface, such that sea ice is not directly affected. However, there will be indirect effects on sea ice due to the redistribution of heat and freshwater in response to all the perturbations. The heat and freshwater fluxes are defined positive downward into the ocean, and the momentum flux perturbations are positive eastward and northward. FAFMIP experiments were run by nine modelling groups using 13 AOGCMs (Table 1).
Fig. 1: Annual means of downward flux perturbations applied in FAFMIP experiments at the ocean surface for heat, water, eastward momentum, and northward momentum, a–d respectively. Perturbations are the multi model mean surface flux anomalies from simulations forced with 1% per year rising CO2 concentrations averaged over years 61–80
Table 1 Key features of the main AOGCMs studied, where dashes in Ocean horizontal resolution indicate a spatially varying resolution
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Time-dependent CO2 and other forcing causes a varying magnitude of sea-level change, while the spatial pattern is relatively time-invariant (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). This phenomenon of ‘pattern scaling’ means that time-dependent forcing is not necessary for our investigation of the spatial structure. Therefore, in the interest of simplicity the FAFMIP flux perturbations are applied as a constant forcing for the full 70 years of each experiment, with no time-variation except for the annual cycle.
Experiments
FAFMIP perturbations to the fluxes of heat, water and momentum (Fig. 1) were applied in five different experiments, as listed below. All perturbations were applied at the air-sea interface in direct contact with seawater surface, such that sea ice is not directly affected. However, there will be indirect effects on sea ice due to the redistribution of heat and freshwater in response to all the perturbations. The heat and freshwater fluxes are defined positive downward into the ocean, and the momentum flux perturbations are positive eastward and northward. FAFMIP experiments were run by nine modelling groups using 13 AOGCMs (Table 1).
Fig. 1: Annual means of downward flux perturbations applied in FAFMIP experiments at the ocean surface for heat, water, eastward momentum, and northward momentum, a–d respectively. Perturbations are the multi model mean surface flux anomalies from simulations forced with 1% per year rising CO2 concentrations averaged over years 61–80
Table 1 Key features of the main AOGCMs studied, where dashes in Ocean horizontal resolution indicate a spatially varying resolution
Experiment 1 In FAF-passiveheat, the heat flux perturbation (Fig. 1a) is applied to a ‘passive added temperature’ tracer, Ta. FAF-passiveheat is a control (similar to piControl), since its climate is not perturbed and experiences only internal variability while the extra tracer allows for the passive uptake of the heat perturbation to be quantified. Ta is initially set to 0 everywhere and the forcing, F, is applied at the surface like a heat flux (none of it penetrates below the surface, like shortwave radiation does). It is transported within the ocean via the same schemes that each model uses to advect and diffuse temperature, T, without affecting the evolution of the ocean state at all because it is passive. Since the perturbation has positive and negative values locally, Ta can be positive and negative. While the input of the passive added heat tracer via the prescribed surface heat flux is identical across models, the geographic patterns of its distribution in the ocean will differ across models, depending on each model’s preindustrial circulation and parameterized tracer transports. The FAF-passiveheat experiment makes it possible to consistently compare the unperturbed tracer uptake across models, which is necessary for a decomposition of the heat uptake in each model when forced with transient climate change (Sect. 2.4).
Experiment 2 In FAF-heat, the heat flux perturbation F is applied as a forcing to ocean temperature, T. (Note that we call it a “forcing” because it is an external perturbation to the climate system, but it is not a radiative forcing, such as is given by CO2 increase.) The perturbation is strongly positive in the North Atlantic and in the Southern Ocean (Fig. 1a). Relative to annual mean climatological heat fluxes, the perturbation reduces the North Atlantic (north of the equator) basin-mean upward heat flux by about 50% (the precise amount varies between models). In the Southern Ocean south of 45° S, the perturbation is roughly 160% of the climatological flux and of opposite sign, switching the basin into a region of net ocean heat uptake. To avoid the atmosphere’s tendency to eliminate the SST anomaly through an opposing air-sea flux, a further passive tracer is used, called the redistributed temperature tracer, Tr which is initialized to equal T at the start and is transported within the ocean in the just the same ways as T but is not forced by the surface heat flux perturbation. The atmosphere is decoupled from the SST of T, and instead sees the surface field of Tr (Fig. 2). The result is that the perturbation gets added to the ocean, where it accumulates and modifies seawater density, and changes ocean transport, but the atmosphere does not absorb any of the added heat and is only modified by changes to surface Tr that arise indirectly through the changing ocean circulation. In FAF-heat, fields of Tr and T quickly diverge from each other by a value approximately equal to Ta. Sub-grid scale schemes (e.g. boundary layer schemes; neutral diffusion; parameterized eddy advection) have nonlinear effects on the transport of temperature that we ignore, meaning that T is assumed equal to Tr + Ta (Gregory et al. 2016). In FAF-passiveheat, Tr (if introduced and treated in the same way) would be identical to T, because no forcing is applied to T. By comparing the distribution of Ta in FAF-heat (whose circulation changes) against FAF-passiveheat (whose circulation follows the steady state) it is possible to identify regions where the changing circulation stores added heat ‘actively’ (i.e. unlike a passive tracer).
Fig. 2: Treatment of surface heat flux perturbation in FAF-heat and FAF-all, redrawn from (Gregory et al. 2016). Q is the net surface heat from the atmosphere and sea ice into the ocean and F is the flux perturbation. The SST used to calculate the surface heat flux to atmosphere and sea ice is coupled to a redistributed temperature tracer Tr, which does not feel F
Experiment 3 The water flux perturbation is derived from the CMIP5 ‘wfo’ diagnostic, which is the sum of precipitation, evaporation, river inflow and water fluxes between floating ice and seawater. There is no perturbation applied over land. The freshwater flux perturbation applied in FAF-water has a very small global annual average, and mainly redistributes freshwater (Fig. 1b). The perturbation is broadly consistent with the “wet gets wetter, dry gets drier” pattern (Held and Soden 2006), reinforcing evaporation in the mid latitudes (by about 10%), and adding freshwater elsewhere (also about 10% reinforcement): namely the equatorial Pacific, the Southern Ocean, the Arctic Ocean, and the high latitude North Pacific and North Atlantic.
Experiment 4 The surface momentum perturbation applied in FAF-stress is mainly characterized by a reinforcement and southward shift of the Southern Ocean westerlies (Fig. 1c). Between 45° and 65° S, the perturbation strengthens the westerlies by about 10%. The perturbation has smaller effects on the zonal and meridional downward momentum fluxes in the mid latitudes (Fig. 1c, d). The perturbation is added to the momentum balance of the ocean surface, such that it does not directly affect sub-grid scale parameterization schemes (e.g. planetary boundary closures) that depend on wind stress or ice stress.
Experiment 5 All three perturbations are applied together in the FAF-all experiment. This experiment serves two purposes: to assess how well the perturbations mimic the effect of CO2 forcing as in 1pctCO2, and to determine the extent to which the perturbations counteract or amplify each other’s effects on sea level when applied simultaneously. If the flux perturbations interact with each other when applied together in FAF-all, then the FAF-all sea-level response will not equal the sum of the sea-level responses to the individual perturbations. This aspect of the FAFMIP design was not tested by Gregory et al. (2016), since no results for FAF-all were available at the time from the five pre-CMIP6 models analysed.
Calculation of change due to perturbations
∆ζ can be derived from CMIP output as the difference in the ‘zos’ field from a forced experiment relative to the ‘zos’ field in an unforced control state. Although ‘zos’ is usually defined to have a zero global area mean (Griffies et al. 2016), for some models it was necessary to subtract the nonzero area mean. This study is focused on the regional sea-level changes expected by the end of the twenty-first century. Because exponentially increasing CO2 concentration, such as in 1pctCO2, gives a radiative forcing which increases linearly in time, and the FAFMIP perturbations correspond to 1pctCO2 forcing at year 70, 70 years of time invariant FAFMIP forcing integrates to approximately the same as a 100-year time integral of 1pctCO2 forcing. ∆ζ is therefore calculated from the final decade (years 61–70) of the perturbation experiments (FAF-stress, -water etc.), and from years 91–100 of 1pctCO2 experiments for comparison. This approach means the amplitudes of ∆ζ will be approximately similar, but in any case, the spatial pattern of ∆ζ is the object of interest in this study.
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Experiment 5 All three perturbations are applied together in the FAF-all experiment. This experiment serves two purposes: to assess how well the perturbations mimic the effect of CO2 forcing as in 1pctCO2, and to determine the extent to which the perturbations counteract or amplify each other’s effects on sea level when applied simultaneously. If the flux perturbations interact with each other when applied together in FAF-all, then the FAF-all sea-level response will not equal the sum of the sea-level responses to the individual perturbations. This aspect of the FAFMIP design was not tested by Gregory et al. (2016), since no results for FAF-all were available at the time from the five pre-CMIP6 models analysed.
Calculation of change due to perturbations
∆ζ can be derived from CMIP output as the difference in the ‘zos’ field from a forced experiment relative to the ‘zos’ field in an unforced control state. Although ‘zos’ is usually defined to have a zero global area mean (Griffies et al. 2016), for some models it was necessary to subtract the nonzero area mean. This study is focused on the regional sea-level changes expected by the end of the twenty-first century. Because exponentially increasing CO2 concentration, such as in 1pctCO2, gives a radiative forcing which increases linearly in time, and the FAFMIP perturbations correspond to 1pctCO2 forcing at year 70, 70 years of time invariant FAFMIP forcing integrates to approximately the same as a 100-year time integral of 1pctCO2 forcing. ∆ζ is therefore calculated from the final decade (years 61–70) of the perturbation experiments (FAF-stress, -water etc.), and from years 91–100 of 1pctCO2 experiments for comparison. This approach means the amplitudes of ∆ζ will be approximately similar, but in any case, the spatial pattern of ∆ζ is the object of interest in this study.
Decadal fields of ζ are calculated to reduce (but cannot not totally eliminate) the effect of unforced interannual variability, reflecting our interest in understanding the climate response to forcing by the end of this century. A change (i.e. ∆ζ) is deemed significant for our purposes if its magnitude is more than twice the decadal standard deviation (a 95% interval for a normal distribution) of variability determined at that location in the relevant control simulation (i.e. piControl for 1pctCO2 and FAF-passiveheat for all other experiments). Decadal mean fields of ζ are calculated for each decade of control simulation, and the threshold for significance is taken to be double the standard deviation across the decadal averages. Insignificant ∆ζ features (within ± 2 standard deviations) are set to 0 for plotting purposes.
The steric sea-level responses to each perturbation can be decomposed into the thermosteric (∆ζT) and halosteric (∆ζS) components:
Δ𝜁𝑇=∫𝜂𝐻(𝛼Δ𝑇Δ𝑧)−𝑙𝜃, (3)
Δ𝜁𝑆=−∫𝜂𝐻𝛽Δ𝑆Δ𝑧. (4)
The thermosteric sea-level change (resulting from temperature change), ∆ζT (3), is the depth integral (from the surface, η, to the full ocean depth, H, with a layer thickness Δz) of the change in temperature (∆T, °C) multiplied by the seawater thermal expansion coefficient (α, °C−1) with the global mean thermosteric sea-level change, 𝑙𝜃, removed. We focus on the thermosteric component with its global mean removed to because the spatial pattern of change is the quantity of interest for this study, not the global mean change. The temperature change is the difference in potential temperature from the forced experiment relative to the control (FAF-passiveheat) averaged over the final decade. A similar Eq. (4) can be constructed for the halosteric component of sea-level change, using the change in salinity (S) and the haline contraction coefficient of seawater (β, dimensionless). Since saline water of a given mass has a smaller volume than the same mass of freshwater, a minus sign converts contraction to expansion, which is more readily comparable with ∆ζ and ∆ζT. The halosteric change typically has a near-zero global mean because total ocean salinity changes are small, making only a very small or negligible contribution to the global mean sea-level change (Gregory et al. 2019). α and β were calculated using the mean temperature, salinity and pressure fields of the final decade of the control simulation using standard nonlinear equations of state (McDougall and Barker 2011).
A sensitivity test (not shown) found that the calculation of ∆ζT and ∆ζS is not strongly affected by the choice of decade used to derive α and β; the effect of the temperature and salinity changes on α and β are small and it is the spatial patterns of Δ𝑇 and Δ𝑆 that set ∆ζT and ∆ζS. Note that the dynamic sea-level change will differ from the steric change (the sum of ∆ζT and ∆ζS) in locations where there is a large barotropic redistribution of density such as the subpolar North Atlantic and the Arctic (Lowe and Gregory 2006; Yin et al. 2010). The dynamic and steric sea-level changes will also differ in locations such as shelf seas, where the change in mass loading of the full water column (a non-steric effect) can be large (Landerer et al. 2007; Yin et al. 2010).
We quantify the part of dynamic sea-level change that is non-steric, Δ𝜁𝑁, as
Δ𝜁𝑁=Δ𝜁−Δ𝜁𝑇−Δ𝜁𝑆.(5)
In plots of Δ𝜁𝑁, we subtract the area mean to reveal the spatial pattern of non-steric sea-level change, since spatial anomalies are the quantity of interest for this work. According to recent terminology conventions (Gregory et al. 2019), Δ𝜁 is related to other components of sea-level change through
Δ𝜁=Δ𝐵+Δ𝑅𝑚+Δ𝜁𝑇+Δ𝜁𝑆−ΔΓ−𝑙𝑏,(6)
where Δ𝐵 is the change due to the inverse barometer effect, Δ𝑅𝑚 is the manometric sea-level change (due to change in ocean mass per unit area), ΔΓ is the change due gravitational, rotational and deformational (GRD) effects from the redistribution of mass over the surface of the planet, 𝑙𝑏 is the barystatic change (due to addition of water to the ocean, mostly from land ice). The difference between the dynamic sea-level change and the steric change in the real world is
Δ𝜁−Δ𝜁𝑇−Δ𝜁𝑆=Δ𝜁𝑁=Δ𝐵+Δ𝑅𝑚−ΔΓ−𝑙𝑏.(7)
However, in the AOGCMs considered in this study (Table 1) ΔΓ and 𝑙𝑏 are zero because these processes are not represented. Δ𝐵 is not readily quantifiable from these models, but is assumed to be small and average to near zero over long time periods since it is of most relevance on meteorological rather than climate timescales (Ponte 2006; Gregory et al. 2019). Therefore, maps of Δ𝜁𝑁 relative to its global area mean in these models reveals the spatial pattern of Δ𝑅𝑚, the manometric sea-level change. This sea-level component is broadly analogous to the ‘barotropic component’ of sea-level change discussed in previous literature, although they are calculated differently (e.g. see Lowe and Gregory 2006).
Decomposition of ocean heat content change
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In plots of Δ𝜁𝑁, we subtract the area mean to reveal the spatial pattern of non-steric sea-level change, since spatial anomalies are the quantity of interest for this work. According to recent terminology conventions (Gregory et al. 2019), Δ𝜁 is related to other components of sea-level change through
Δ𝜁=Δ𝐵+Δ𝑅𝑚+Δ𝜁𝑇+Δ𝜁𝑆−ΔΓ−𝑙𝑏,(6)
where Δ𝐵 is the change due to the inverse barometer effect, Δ𝑅𝑚 is the manometric sea-level change (due to change in ocean mass per unit area), ΔΓ is the change due gravitational, rotational and deformational (GRD) effects from the redistribution of mass over the surface of the planet, 𝑙𝑏 is the barystatic change (due to addition of water to the ocean, mostly from land ice). The difference between the dynamic sea-level change and the steric change in the real world is
Δ𝜁−Δ𝜁𝑇−Δ𝜁𝑆=Δ𝜁𝑁=Δ𝐵+Δ𝑅𝑚−ΔΓ−𝑙𝑏.(7)
However, in the AOGCMs considered in this study (Table 1) ΔΓ and 𝑙𝑏 are zero because these processes are not represented. Δ𝐵 is not readily quantifiable from these models, but is assumed to be small and average to near zero over long time periods since it is of most relevance on meteorological rather than climate timescales (Ponte 2006; Gregory et al. 2019). Therefore, maps of Δ𝜁𝑁 relative to its global area mean in these models reveals the spatial pattern of Δ𝑅𝑚, the manometric sea-level change. This sea-level component is broadly analogous to the ‘barotropic component’ of sea-level change discussed in previous literature, although they are calculated differently (e.g. see Lowe and Gregory 2006).
Decomposition of ocean heat content change
We can decompose OHC change into components due to changes in ocean temperature and in transport. Following Gregory et al. (2016), we let Φ represent the transport operator that encompasses all processes that affect heat transport, including resolved and parameterized advection, diffusion, and convection. That is, Φ(𝑇)=−∇∙(𝑢𝑢𝑇+𝑃𝑃), the convergence of temperature due to the three dimensional resolved velocity field 𝑢𝑢 and parameterized subgrid-scale tracer transport processes 𝑃𝑃. In Φ(𝑇) parentheses around 𝑇 indicates the action of ocean tracer transport on the temperature within the parentheses. At steady state, the ocean has an unperturbed temperature, 𝑇−, and an unperturbed three-dimensional transport, Φ−, where overlines indicate a long time average over the control run. The convergence of unperturbed temperature transport, Φ−(𝑇−), is zero in the steady state, except at the surface where it balances the surface heat flux.
Forced climate change modifies the surface fluxes. It alters the ocean temperature by an amount T′, relative to the unperturbed state by the addition of heat, and the transport by Φ′ through changing both the wind driven and density driven transports. As a result, the convergence Φ(𝑇) of heat is modified as well and is no longer zero. Hence, interior temperature changes according to
∂𝑇′∂𝑡=[Φ− + Φ′](T− + 𝑇′) = Φ−(𝑇′)+Φ′(T−) + Φ′(𝑇′), (8)
where [Φ−+Φ′](𝑇−+𝑇′) is symbolically the action of both the unperturbed and perturbed transport acting on the unperturbed and perturbed temperature. Note also that Φ−(𝑇−)=0.
Thus we distinguish three different causes of temperature change that arise from the convergence of: Φ−(𝑇′), transport of the added heat by the unperturbed transport processes; Φ′(𝑇−), changes in the ocean transport redistributing unperturbed heat; and Φ′(𝑇′), perturbation in the transport that redistributes the added heat (8).
If the oceans absorbed the added heat from anthropogenic climate change like a passive tracer that does not affect ocean circulation or other transport processes, then OHU would be driven entirely by the first term, Φ−(𝑇′). This term is therefore the “passive uptake of added heat”. In reality, the ocean circulation and subgrid scale processes are affected by temperature change and other surface flux changes, so the other terms play a part. The second term is a pure redistribution, whose global volume integral is small (but not precisely zero because 𝑇− can be fluxed to the atmosphere). The final term is of second order in perturbation quantities, but it is not always negligible.
Consider the following illustrative situation in a convective zone of the Labrador Sea, where climate change causes increased heat flux into the ocean, and the ocean temperature gets warmer at around 250 m depth. Positive Φ−(𝑇′) describes the change in temperature that results from the unperturbed circulation and subgrid processes that passively transport the additional heat downwards. However, these transport processes are weakened by the input of 𝑇′ because the air-sea heat input strengthens stratification and weakens downward heat transport by convection. The weakened downward transport carries less additional heat than in the passive case; and Φ′(𝑇′) is weakly negative because Φ′ is negative. Finally, weakened downward transport means that less heat from lower latitudes gets brought northward and downward, causing strongly negative Φ′(𝑇−).
FAFMIP experiments and diagnostics allow for the three contributions to the change in the convergence of heat to be distinguished. We can express the change in ocean heat content (∆h, Jm−2) due to each contribution by converting the appropriate temperature (T) field using a reference heat capacity for seawater (cp0 = 4000 J kg−1 K−1), a reference density (ρ0 = 1026 kg m−3) and the ocean grid cell vertical thickness (Δz, m). Differencing particular experiments and temperature fields (T, Ta, or Tr) yields different components of OHC change. Further notes on the time evolution of Tr, Ta and T, describing how different temperature change terms are grouped in the decomposition are included in the “Appendix”.
The OHC change due all three convergences of temperature in (8), Δh, is
Δℎ=Δ𝑇𝑐𝑝0𝜌0Δ𝑧, (9)
where ∆T, is the difference of the model’s temperature field (T) between the final decades of FAF-heat and FAF-passiveheat (9). In FAF-heat, the heat flux changes the transport processes (Φ′ ≠ 0) and the temperature (𝑇′ ≠ 0) and, thus there is a change in heat content due to all three types of temperature convergence.
The OHC change due to passive uptake of additional heat, Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)] is
Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)]=𝑇⎯⎯⎯⎯𝑎𝑐𝑝0𝜌0Δ𝑧, (10)
where the notation Δℎ[…] symbolically represents the change in OHC due to the convergence of temperature enclosed by the square brackets. Since passive temperature is initially 0, its decadal mean change by the end of simulation is simply 𝑇−𝑎, the time mean Ta from FAF-passiveheat for the years 61–70.
The OHC change due to the redistribution of unperturbed temperature, Δℎ[Φ′(𝑇⎯⎯⎯⎯)] is
Δℎ[Φ′(𝑇⎯⎯⎯⎯)]=Δ𝑇𝑟𝑐𝑝0𝜌0Δ𝑧, (11)
where ∆Tr is the difference between FAF-heat redistributed temperature, Tr, and FAF-passiveheat T, averaged over the final decade.
The OHC change due to the perturbation in the transport redistributing the added heat, Δℎ[Φ′(𝑇′)] is
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The OHC change due all three convergences of temperature in (8), Δh, is
Δℎ=Δ𝑇𝑐𝑝0𝜌0Δ𝑧, (9)
where ∆T, is the difference of the model’s temperature field (T) between the final decades of FAF-heat and FAF-passiveheat (9). In FAF-heat, the heat flux changes the transport processes (Φ′ ≠ 0) and the temperature (𝑇′ ≠ 0) and, thus there is a change in heat content due to all three types of temperature convergence.
The OHC change due to passive uptake of additional heat, Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)] is
Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)]=𝑇⎯⎯⎯⎯𝑎𝑐𝑝0𝜌0Δ𝑧, (10)
where the notation Δℎ[…] symbolically represents the change in OHC due to the convergence of temperature enclosed by the square brackets. Since passive temperature is initially 0, its decadal mean change by the end of simulation is simply 𝑇−𝑎, the time mean Ta from FAF-passiveheat for the years 61–70.
The OHC change due to the redistribution of unperturbed temperature, Δℎ[Φ′(𝑇⎯⎯⎯⎯)] is
Δℎ[Φ′(𝑇⎯⎯⎯⎯)]=Δ𝑇𝑟𝑐𝑝0𝜌0Δ𝑧, (11)
where ∆Tr is the difference between FAF-heat redistributed temperature, Tr, and FAF-passiveheat T, averaged over the final decade.
The OHC change due to the perturbation in the transport redistributing the added heat, Δℎ[Φ′(𝑇′)] is
Δℎ[Φ′(𝑇′)]=Δ𝑇𝑎𝑐𝑝0𝜌0Δ𝑧, (12)
where Δ𝑇𝑎 is the difference of Ta between FAF-heat and FAF-passiveheat (12).
Models analysed
Different suites of models are analysed in different parts of this work, subject to the availability of output fields. The first analysis required sea-surface height above geoid, ζ, ocean temperature, and seawater salinity, available from 13 FAFMIP AOGCMs (Table 1), although less than the full set of output for all experiments was available for CESM2, GISS-E2-R-CC and MIROC6. The ocean heat budget decomposition in Sect. 3.5 required 3-D fields of redistributed and added temperature, available for ten FAFMIP models (the exceptions being CESM2, GISS-E2-R-CC and MIROC6). A comparison of the sea-level response to 1pctCO2 forcing was also performed for a suite of 19 CMIP5 models and 16 CMIP6 models listed in Table 2. The ‘zos’ fields of MIROC5, CAMS-CSM1-0 and GISS-E2-1-G required correction for the inverse barometer effect due to sea ice loading, following (Griffies et al. 2016).
Table 2: List of models from CMIP5 and CMIP6 that appear in Fig. 4
From the 13 models that have performed FAFMIP experiments, five are from the CMIP5 era, seven from CMIP6, and one (HadCM3) is pre-CMIP5. All ocean model components of models feature similar horizontal resolution (roughly 1-by-1 degree of latitude), and so unresolved features such as mesoscale eddies are parameterized. Even the finest of these ocean grids (MPI-ESM1-2-HR, about 0.4-by-0.4 degrees of latitude) is ‘eddy-permitting’ and not ‘eddy-resolving’, as it can resolve some large ocean eddies, but it still employs an eddy flux parameterization to represent unresolved mesoscale and sub-mesoscale processes. While horizontal resolution is broadly similar across models, details such as the vertical grids or refined resolution near the equator are model-specific.
Results
FAF-all versus 1pctCO2
This section explores the diversity in Δζ in FAF-all versus 1pctCO2, to demonstrate the extent to which patterns of Δζ are generated by ocean processes rather than by the patterns and magnitude of all fluxes.
The spatial pattern of the sea-level response to all flux perturbations applied simultaneously (FAF-all, Fig. 3a) is similar to the pattern that results from 1pctCO2 forcing (Fig. 3c). The agreement between responses to 1pctCO2 and FAF-all forcing is an intended feature of the experimental design and shows that the mean pattern of CO2-forced sea-level change can be reproduced when the models are forced instead with perturbations to their surface fluxes. The spatial standard deviation of ∆ζ is a useful scalar that summarizes the magnitude (or heterogeneity) of the spatial pattern of dynamic sea-level change. The spatial standard deviation of ∆ζ is 0.082 m for FAF-all; larger than 0.059 m for 1pctCO2, indicating a stronger spatial pattern in FAF-all.
Fig. 3: Ocean dynamic sea-level response Δζ to greenhouse gas forcing in 1pctCO2 runs (above) and FAF-all runs (below) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Mean across models (above) and standard deviation across models (below)
The three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive Δζ north of 55° S and negative Δζ at higher latitudes, (2) the meridional dipole of positive Δζ in the northern North Atlantic against weakly negative Δζ in the southern North Atlantic, and (3) positive Δζ in the Arctic.
The large positive Δζ in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the “North Atlantic redistribution feedback”, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore “sees” a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.
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The three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive Δζ north of 55° S and negative Δζ at higher latitudes, (2) the meridional dipole of positive Δζ in the northern North Atlantic against weakly negative Δζ in the southern North Atlantic, and (3) positive Δζ in the Arctic.
The large positive Δζ in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the “North Atlantic redistribution feedback”, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore “sees” a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.
When the different AOGCMs are forced with identical surface flux perturbations in FAF-all, the spread in sea-level response (Fig. 3d) is similar to the spread that results from 1pctCO2 forcing (Fig. 3b). The largest spread of sea-level change among the 11 models (measured as the standard deviation across models) is focused on the same three regions in FAF-all as in 1pctCO2—the Arctic, the Southern Ocean, and the North Atlantic—and is of similar magnitude. The area mean of inter-model standard deviation is 0.045 m in 1pctCO2, and 0.046 m in FAF-all. This evidence indicates that much of the spread in projections of the dynamic sea-level response to climate forcing arises due to differences in ocean model formulation, rather than in the surface flux forcing from the diverse atmosphere models. This conclusion is different from that of Huber and Zanna (2017), who found that the parametric uncertainty of a given model is too small to explain the spread of ocean responses to climate change. The dynamic sea-level responses of the individual AOGCMs to FAF-all forcing are included in the “Appendix” (Fig. 13 in “Appendix”).
Sea-level response to 1% per year CO2 forcing in CMIP5 and CMIP6
There is strong similarity between the sea-level responses to 1pctCO2 forcing from the much larger CMIP5/6 ensembles (Fig. 4a, c) and the sea-level responses to our smaller suite of FAFMIP models (Fig. 3), especially in the North Atlantic, Arctic, and Southern oceans. This similarity indicates that the FAFMIP-participant models form a representative subset of the wider CMIP5 and CMIP6 ensembles. It also suggests that the findings of FAFMIP are likely to be applicable to a wider range of models than the 13 FAFMIP models analysed here.
Fig. 4: Multi model mean projections of ∆ζ (left) from 1pctCO2 forcing experiments averaged over years 91–100 for 19 CMIP5 models (a), 16 CMIP6 models (c). Standard deviation of the model spread (right). Models used are described in Table 2
The 1pctCO2 response in the two different CMIP eras is similar (Fig. 4a, c), in agreement with recent findings (Lyu et al. 2020). The similarity of responses of models from the different eras indicates that models from across the eras may be analysed together as one ensemble, rather than separately. The current generation of AOGCMs show diverse sea-level responses in the Arctic, Southern Ocean, North Atlantic and North Pacific (Fig. 4d), much like the previous generation (Fig. 4b), indicating a continuing need to focus on these regions.
The CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1°-by-1° of latitude, with a refinement to 1/3° at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.
Ocean response to perturbations in individual fluxes
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The CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1°-by-1° of latitude, with a refinement to 1/3° at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.
Ocean response to perturbations in individual fluxes
Comparison of the multi model mean ∆ζ from FAF-all with the sea-level response to individual perturbations allows us to determine which features result from changes to each flux. The spatial pattern of sea-level change from the heat flux forcing (Fig. 5c) most closely matches the response to all perturbations simultaneously applied (Fig. 3c). For FAF-heat, the spatial standard deviation is 0.080 m, which is close to that of FAF-all (0.082 m). The spatial standard deviation is 0.021 m for FAF-stress and 0.018 m for FAF-water. This indicates that the heat flux contributes the most to the sea-level change in FAF-all and 1pctCO2, in agreement with previous work (Bouttes and Gregory 2014; Gregory et al. 2016). The wind stress perturbation causes part of the pattern of ∆ζ, but its influence is mostly confined to the Southern Ocean (Fig. 5a). There, strengthened and poleward-shifted westerlies steepen the meridional sea-level gradient across the ACC (Frankcombe et al. 2013). The freshwater perturbation contributes the least sea-level change of the three perturbations, but it sets part of the spatial pattern of ∆ζ in the Southern and Arctic Oceans (Fig. 5e). Recall that the three key locations for which models show diverse predictions of ∆ζ in 1pctCO2 and FAF-all were the Arctic, the eastern subpolar North Atlantic and the Southern Ocean south of Australia and New Zealand (Fig. 3c, d). There is coincident diversity in the FAF-heat responses (Fig. 5d), which suggests that spread in FAF-all is due primarily to the heat flux perturbation. The dynamic sea-level responses of each AOGCM to each individually applied flux perturbation are shown in the “Appendix” (Fig. 13–16).
Fig. 5: Maps of multi model ensemble mean ocean dynamic sea-level response to individually-applied flux perturbations (left) and standard deviation across 13 AOGCMs (right) for the wind stress (FAF-stress, top), heat flux (FAF-heat, middle), and water flux (FAF-water, bottom) experiments. AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0
Wind stress
The wind stress perturbation creates a gradient of ∆ζ across the Southern Ocean (Fig. 5a). The intensified Southern Ocean westerlies drive a northward positive meridional ∆ζ gradient with a zonal mean of 0.05–0.025 m from 75° to 35° S. South of 60° S, ∆ζ diverges depending on the model (Fig. 5b). The models disagree on whether the wind stress perturbation causes negative or weakly positive depth integrated OHC change south of 60° S (Fig. 6g), which is not yet well understood but merits further investigation. The wind stress perturbation tends to weakly warm the surface ocean, cool the shallow subsurface and warm the deeper ocean (Fig. 6d, j). Part of the discrepancy between models occurs because although this area-integrated picture is qualitatively common to models, the depth at which each OHC change inflection occurs is model-specific. In agreement with Gregory et al. (2016), while the local OHC change due to the wind stress perturbation can be large (Fig. 6a, g, j) its global integral is small; two orders of magnitude smaller than the heat flux perturbation (not shown). Other work finds that the Southern Ocean OHC response to wind stress change is sensitive to the location of the zero wind stress curl, which may be a source of some of the spread reported here (Stewart and Hogg 2019).
Fig. 6: Multi model ensemble mean integrated ocean heat content (OHC) change for FAF-stress (left), FAF-heat (middle), FAF-water (right) for 12 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Depth integrated OHC change (a–c), area integrated OHC change (d–f), zonally and depth integrated OHC change (g–i), zonally integrated OHC change (j–l). Dashed lines in d–i indicate ± 2 standard deviations of ensemble spread. 1 GJ = 109 J, 1 ZJ = 1021 J, 1 EJ = 1018 J
The maps of ∆ζT, ∆ζS and ∆ζN show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55° and 30° S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced ∆ζT change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative ∆ζ (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).
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The maps of ∆ζT, ∆ζS and ∆ζN show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55° and 30° S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced ∆ζT change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative ∆ζ (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).
Fig. 7: Multi model ensemble mean dynamic sea-level response to momentum flux forcing (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM-GC31-LL, MIROC6, MPI-ESM1-2-HR, MPI-ESM-LR and MRI-ESM2-0. Multi model mean momentum flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
In some models, but not all, the wind stress perturbation drives sea-level change in the Arctic East Siberian Sea and northwestern Atlantic (Fig. 5b). GISS-E2-R-CC predicts widespread, large positive ∆ζ in the Arctic, while CanESM5, MPI-ESM1-2-HR and HadCM3 predict a gradient of ∆ζ that is negative at the pole and increases southwards (Fig. 14). HadGEM3-GC31-LL shows positive ∆ζ at the pole. The other models predict near zero ∆ζ in the Arctic. The spread in the North Atlantic is due to the responses of HadGEM2-ES, MPI-ESM-LR, MPI-ESM1-2-HR and GFDL-ESM2M, which predict weakly positive ∆ζT and ∆ζS here, while the other models show ∆ζ ≈ 0 (Fig. 14).
Heat flux
The heat flux perturbation drives the most change in sea level, both in terms of magnitude and area of effect (Fig. 5c). The perturbation causes positive OHC change over most of the ocean area (Fig. 6b) in the upper 1000 m (Fig. 6e, k). Note that even though the heat flux perturbation adds large amounts of heat to the global ocean, it is possible for the net OHC change in some locations to be weakly negative; either because of negative values of the perturbation flux or via the redistribution of heat by changing ocean transport. The models agree that the largest OHC change occurs in south of 30° S, and the changes elsewhere are more model dependent (Fig. 6h). In the upper 300 m, the ensemble spread of the area integrated OHC change is on the order of half the mean change (Fig. 6e). This spread indicates that the strength of the mechanisms by which heat is transported away from the surface is different among models. The largest values of ∆ζ are in the North Atlantic. The most intense perturbation to the heat flux per unit area is directed here. As described earlier in Sect. 3.1, the North Atlantic redistribution feedback means that the magnitude of North Atlantic sea-level response is greater in FAF-heat and FAF-all than in 1pctCO2 experiments.
In general, the pattern of ∆ζ is similar across most models, and the magnitude of the change varies between models (Fig. 5). The fact that the hotspots of inter-model spread (Fig. 5d) are coincident with most of the strongest ∆ζ features reflects this. The multi-model mean map of ∆ζ (Fig. 5c) therefore reflects a pattern that is very similar to each individual model’s response, rather than the mean of several very different patterns. Most models show the maximum ∆ζ between 45° and 65° N in the western North Atlantic (Fig. 15). All models predict the Atlantic dipole of positive ∆ζ north of 45° N and weakly negative ∆ζ near Cape Hatteras in the western basin around 35° N. The weak dynamic sea-level drop occurs at the center of the subtropical gyre, consistent with the decline of the dynamic sea-level gradient across the Gulf Stream. In the eastern basin off the west Saharan-African coast most models predict a “tropical arm” of positive ∆ζ that diminishes westward (Fig. 5c), which is weak in HadGEM2-ES and absent in GFDL-ESM2M (which shows near zero ∆ζ, Fig. 15e, h). Most models predict a small region of negative ∆ζ north of Iceland. MPI-ESM-LR and MRI-ESM2-0 instead predict positive ∆ζ north of Iceland and negative/neutral ∆ζ to the south of Iceland (Fig. 15k, m). HadGEM2-ES and MPI-ESM1-2-HR exhibit regions of negative/neutral ∆ζ both south and north of Iceland (Fig. 15h, l).
The steric sea-level rise in the Atlantic subpolar gyre, north of 45° N, is due predominantly to positive ∆ζS (i.e. freshening), opposed by weaker negative ∆ζT (Fig. 8c). North of 45° N, there is positive ∆ζS and weaker negative ∆ζT,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of ∆ζ, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).
Fig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
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The steric sea-level rise in the Atlantic subpolar gyre, north of 45° N, is due predominantly to positive ∆ζS (i.e. freshening), opposed by weaker negative ∆ζT (Fig. 8c). North of 45° N, there is positive ∆ζS and weaker negative ∆ζT,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of ∆ζ, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).
Fig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
The thermosteric and halosteric effects change sign south of 45° N and the thermal effect dominates, but they compensate more closely, and so ∆ζ is smaller than further north. The 45° N latitude line coincides with the divide between the North Atlantic subpolar and subtropical gyres formed by the northern boundary of the North Atlantic Current. The opposing changes either side of the divide are consistent with a change in the inter-gyre exchange of heat and salt: a warmer and saltier subtropical gyre and a cooler and fresher subpolar gyre. Further south, most models predict positive ∆ζ in the eastern basin off the West African coast (Fig. 8a). There is also considerable inter-model spread in the thermosteric and halosteric contributions (Fig. 8d, f). Interestingly, five models predict a mixture of thermo- and halosteric contributions (ACCESS-CM2, CanESM2, CanESM5, HadGEM3-GC31-LL, MPI-ESM1-2-HR), four models predict the tropical arm as being purely halosteric (HadCM3, MIROC6, MPI-ESM-LR and MRI-ESM2-0), one model predicts a purely thermosteric effect (HadGEM2-ES), and one model shows no positive ∆ζ feature here at all (GFDL-ESM2M) (not shown).
In the North Pacific, all models respond to the heat flux perturbation with a North–South dipole in ∆ζ that changes sign around 35° N (Fig. 8c). This meridional dipole has the opposite sign to that of the North Atlantic. In the western basin, the pattern is essentially the same across models, and its extent eastward is model dependent (Fig. 15). The dipole is mostly thermosteric (Fig. 8c), owing to a stronger accumulation of heat per unit area north of 35° N in the region east of Newfoundland than further south (Fig. 6b). This is sea-level change is consistent with a steepening of the across-current sea-level slope, and an intensification of the Kuroshio western boundary current (Chen et al. 2019).
The lower latitudes of the Arctic around the East Siberian and Beaufort Seas show positive ∆ζ in response to the heat flux perturbation, while ∆ζ is negative at higher latitudes. The only exception to this is HadCM3 (Fig. 15), which predicts strongly negative ∆ζ everywhere in the Arctic, contributing strongly to the large inter-model spread there (Fig. 8b). The Arctic shows a strong non-steric component of ∆ζ (Fig. 8g), corresponding to a shift of mass from the highest latitudes onto the shelves. The patterns of Arctic sea-level change in 1pctCO2 and FAF-all are very similar (Fig. 3), suggesting that the coupling of sea ice to redistributed temperature rather than regular temperature in FAFMIP experiments (Sect. 2.2) does not introduce unintended effects on ocean transport. Nevertheless, the diverse representations of sea ice in AOGCMs generally remains a key source of uncertainty in the projection of future polar climate change (Meredith et al. 2019).
The Southern Ocean sea-level change in response to heat flux forcing is smallest at the highest latitudes (negative ∆ζ), changing sign to positive ∆ζ between 40° and 55° S (Fig. 8a). All models predict a maximum of ∆ζ off the South African coast that extends eastward. The spatial pattern of negative ∆ζ across much of the Southern Ocean is predicted by all models. CanESM2, HadGEM3-GC31-LL, MPI-ESM-LR and GFDL-ESM2M (and to a lesser extent, HadCM3 and ACCESS-CM2) show positive ∆ζ in the sector between 130° and 160° E, south of Australia and New Zealand (not shown). This inter-model variation is also identifiable in the spread of sea-level responses in FAF-all (Fig. 3d) and is thermosteric (Fig. 8d).
The Southern Ocean Δζ zonal gradient in FAF-heat is the result of both thermosteric and halosteric effects (Fig. 8a, c, e). Gregory et al. (2016) pointed out that the gradient of Δζ across the Southern Ocean arises primarily because more heat accumulates in the mid latitudes (around 45° S) than further south (Fig. 9a). However, if sea-level change were simply proportional to OHU, then Δζ would show a prominent maximum at 45° S and decline until 25° S. Instead, Δζ increases northward to about 45° S, with only a slight decline further North (Fig. 9b, solid black line). The waters further North are warmer and therefore have greater thermal expansivity, which, in addition to the convergence of heat between 30–45° S, creates a thermosteric maximum around 40° S (Fig. 9b, red dotted line). However, at the same latitude, the changing salinity causes a halosteric effect that opposes the thermosteric effect and the meridional gradient of Δζ plateaus, instead of peaking at 40° S and declining to the north (Fig. 9b, cyan dashed line). Note that the deviation between the steric sea-level change (Fig. 9b, cyan dashed line) and the dynamic change (Fig. 9b, solid black line) north of 40° N indicates a considerable barotropic component of the change due to the redistribution of ocean mass (Lowe and Gregory 2006; Yin et al. 2010; Bouttes and Gregory 2014 and Fig. 8g).
Fig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing Δζ (black solid line), the thermosteric component ΔζT (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0
Freshwater flux
Interestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).
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Fig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing Δζ (black solid line), the thermosteric component ΔζT (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0
Freshwater flux
Interestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).
Fig. 10: Multi model ensemble mean dynamic sea-level response to freshwater flux perturbation (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Multi model mean freshwater flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
The locations where the models disagree on the sea-level response to freshwater forcing are not always coincident with the locations of largest sea-level change (Fig. 10a, b), particularly in the North Atlantic and the Arctic. This indicates that different models predict different features (Fig. 16), rather than all models responding with similar patterns of different magnitude. The models predict diverse patterns of sea-level change in the subpolar North Atlantic (Fig. 10b) because they disagree on the eastward extent of the sea-level change (Fig. 16). Presumably, simulated North Atlantic currents have differing sensitivities to freshwater forcing.
The sea-level changes closest to the Antarctic coast are predicted with some agreement across models (Fig. 10b). The inter-model spread around 50°–60° S south of Australia arises due to different thermosteric responses to freshwater forcing (Fig. 10d). A poleward contraction of the ACC here would explain the positive Δζ (Fig. 10a) but the inter model spread suggests that not all models predict this (Figs. 10b, 16a, b, d, f, h, j).
In the Arctic, the freshwater forcing is widespread and positive, due to a mixture of increased river runoff and precipitation. This causes freshening, which in turn causes halosteric sea-level rise (Fig. 10e). However, the models disagree on the spatial extent of the halosteric sea-level rise (Fig. 10f).
Linearity of sea-level responses to flux perturbations
Here we explore how sea level responds to flux perturbations applied individually versus simultaneously. If the sea-level response to all perturbations is linear, then the sum of the responses when the perturbations are applied individually Δζsum,
Δ𝜁𝑠𝑢𝑚=Δ𝜁𝑤𝑖𝑛𝑑+Δ𝜁ℎ𝑒𝑎𝑡+Δ𝜁𝑤𝑎𝑡𝑒𝑟, (13)
should equal the response when the fluxes are applied together, Δζall. The differences between Δζsum and Δζall represent the nonlinear sea-level response to simultaneous flux forcing and is explored for 11 AOGCMs (Table 1, excluding CESM2 and GISS-E2-CC). The significance of nonlinear features is tested against the variability of the seven decades of FAF-passiveheat, calculated as the standard deviation of seven decadal averages, which we assume is representative of the internally generated variability in the other experiments as well. The quantity Δζsum − Δζall is calculated using four independent simulations (FAF-heat, -stress, -water, -all), each with its own unforced variability. The difference Δζsum − Δζall can therefore be affected by the unforced variability of four different simulations, so the standard deviation of the difference is twice the standard deviation of unforced decadal variability (from FAF-passiveheat). For a Δζsum − Δζall feature to be judged significant at the 5% level, it must be larger than four times the unforced standard deviation. Locations where Δζsum − Δζall is not significant are set to 0 for each model, before being averaged in Fig. 11 to reveal only significant differences. The features removed through this process are small in spatial extent and magnitude, and are particular to each model (not shown). The flux perturbations show significant nonlinear interaction in the Arctic and subpolar North Atlantic (Fig. 11a). Across the Arctic, Δζsum − Δζall is negative, meaning most models predict a stronger dynamic sea-level change in FAF-all than the individual flux perturbation experiments suggest.
Fig. 11: Multi model ensemble mean nonlinear sea-level response to flux perturbations (a) and standard deviation (b) across 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0
For most of the global ocean, Δζsum − Δζall is small and therefore Δζsum approximates the patterns of Δζall. However, small values of multi-model mean Δζsum − Δζall are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, Δζwind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model’s results is necessary to explore this.
In the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the Δζsum − Δζall dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.
HadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.
Decomposition of ocean heat uptake
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For most of the global ocean, Δζsum − Δζall is small and therefore Δζsum approximates the patterns of Δζall. However, small values of multi-model mean Δζsum − Δζall are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, Δζwind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model’s results is necessary to explore this.
In the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the Δζsum − Δζall dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.
HadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.
Decomposition of ocean heat uptake
As shown above, ocean dynamic sea-level change is largely thermosteric, and reflects changes in OHC. Here, we decompose the OHC change (see Sect. 2.4 and “Appendix” for details) of ten AOGCMs (Table 1, excluding CESM2, GISS-E2-R-CC, MIROC6) into contributions from changes in ocean transports and the uptake of the imposed perturbation. Most of the heat added to the oceans in FAF-heat is stored in the Southern Ocean, between 30° S and 60°S (Figs. 6h, 12a), particularly in the Indo–Pacific sectors. The North Atlantic shows the highest rate of heat uptake per unit area, but the small total area of the basin means its contribution the global total OHU is smaller than that of the much larger Southern Ocean (Fig. 6h). The Arctic also shows moderate rates of heat storage per unit area (Fig. 12a), but this basin stores less heat than other latitudes because of its small total area (Fig. 6h).
Fig. 12: Decomposition of depth-integrated ocean heat uptake in ten AOGCMs (ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0) in FAF-heat, left panels show the multi-model ensemble mean and right panels show the standard deviation across models for the total ocean heat uptake mean (a) and spread (b). Components of heat uptake (c, e, g) are shown as a percentage of the total (a). Passive uptake of added heat, Δh[Φ−(T′)], mean (c) and spread (d). Pure redistribution of unperturbed heat, Δh[Φ′(T−)] mean (e) and spread (f). Redistribution of added heat by the perturbed transport, Δh[Φ′(T′)], mean (g) and spread (h)
In the Southern Ocean, passive heat uptake in the Southern Ocean (Fig. 12c) is close to 100% of the total heat uptake (Fig. 12a). The OHC change due to the perturbed transport (Fig. 12e, g) is much smaller than the total passive uptake, but is locally important and strongly negative near the Ross and Weddell gyres. Further, there is relatively little spread of Δℎ[Φ−(𝑇′)] across models (Fig. 12d). This means that these AOGCMs agree that heat uptake by the Southern Ocean is mostly passive, in agreement with recent findings (Bronselaer and Zanna 2020). The perturbed transport has secondary influence on heat uptake in the Southern Ocean. Both Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇−)] are important components in the Indian sector (Fig. 12c, e), and the spread here is not due to passive uptake (Fig. 12d). South of Australia and New Zealand, where the total OHC change differs across models (Fig. 12b) the spread comes from Δℎ[Φ′(𝑇−)] (Fig. 12f), which could suggest a model-dependent reduction of upwelling.
OHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative Δℎ[Φ′(𝑇−)] and Δℎ[Φ′(𝑇′)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with Δℎ[Φ′(𝑇′)] and Δℎ[Φ−(𝑇′)] also playing smaller roles.
Moderate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇′)] are strongly positive while Δℎ[Φ′(𝑇−)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of Δℎ[Φ′(𝑇−)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive Δℎ[Φ′(𝑇′)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.
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OHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative Δℎ[Φ′(𝑇−)] and Δℎ[Φ′(𝑇′)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with Δℎ[Φ′(𝑇′)] and Δℎ[Φ−(𝑇′)] also playing smaller roles.
Moderate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇′)] are strongly positive while Δℎ[Φ′(𝑇−)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of Δℎ[Φ′(𝑇−)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive Δℎ[Φ′(𝑇′)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.
The equatorial Atlantic shows moderate area-weighted OHU (Fig. 12a). The equatorial Atlantic OHU is mostly driven byΔℎ[Φ′(𝑇−)], (Fig. 12e) and passive heat storage is important in the west, (Fig. 12c). The local heat flux perturbation is near zero (Fig. 1a) and so the heat content change here is mostly a consequence of Φ′, rather than T′. These results echo previous work, which also identify an important role of active transport change in the low latitudes (e.g. Garuba and Klinger 2018). This is one of the few locations where the redistribution of unperturbed heat has a large positive depth integral. Elsewhere in the tropics, although Δℎ[Φ′(𝑇−)] is a large component, the total heat storage per area is smaller (Fig. 12a). In the western basin, Δℎ[Φ′(𝑇′)] is weakly negative, in contrast with the eastern. This could be consistent with a weakened poleward transport of heat causing an accumulation of unperturbed and added heat, and a coincident reduced westward equatorial transport of added heat. Reduced upwelling of unperturbed temperature as a part of the weakened poleward transport of unperturbed heat could explain the accumulation of Δℎ[Φ′(𝑇−)] here. Changes in the subtropical and subpolar gyre circulation (and the exchange of heat between them) as suggested by previous authors could also play a role that has not yet been explored. A complete explanation is currently lacking but warranted (Boeira Dias et al. 2020).
Discussion
Diversity of sea-level response to common air-sea flux perturbation
The largest and most widespread features of dynamic sea-level change in response to 1pctCO2 forcing have been shown to result mostly from the change in air-sea heat flux. Further, the inter-model uncertainty of the pattern of Δζ results from model-specific ocean transport responses to standardized air-sea flux changes, rather than diversity in the flux changes themselves. For the most part, the spread in response to heat flux perturbation relates to different models responding with a similar pattern of sea-level change, whose magnitude differs across models. The North Atlantic hosts a large diversity of Δζ across models, but although the geographic pattern is different across models, the sea-level changes have similar dynamical origins. We find that the North Atlantic inter-model variance is mostly due to the redistribution of preindustrial heat being different in each model, probably in turn due to the spread in predicted weakening of the AMOC. The spread of Δζ also has smaller contributions from uptake of added heat by both the perturbed and unperturbed transport. Part of the spread of North Atlantic sea-level change arises because added heat penetrates into the deep ocean in deep convection sites that are geographically different among models (Bouttes et al. 2014), but this reason is found to be secondary in our analysis. Other authors pointed out that ocean heat uptake is sensitive to model-specific factors such as SST biases (He and Soden 2016), mesoscale eddy transfer (Exarchou et al. 2015; Saenko et al. 2018), stratification (Huber and Zanna 2017) and the isopycnal diffusion scheme (Exarchou et al. 2015). These factors may explain why the models that we have examined show similar horizontal patterns of heat uptake with differing magnitudes even though these models are forced with identical heat inputs.
Previous work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system’s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component’s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.
Role of individual and simultaneous flux perturbations causing key regional sea-level changes
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Previous work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system’s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component’s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.
Role of individual and simultaneous flux perturbations causing key regional sea-level changes
One of the key features of the sea-level response to heat flux forcing was the contrast in meridional dipoles in the North Pacific and North Atlantic (Gregory et al. 2016). In the North Atlantic, the meridional dipole is positive to the north, while in the North Pacific, it is positive to the south. The opposite dipoles are consistent with recent work investigating why the Kuroshio current is predicted to strengthen in AOGCM simulations of climate change, whereas the Gulf Stream weakens (Chen et al. 2019). Those authors described how the air-sea heat flux that results from a warming climate causes stronger warming to the east of the Kuroshio than to the west, steepening the across-current density slope. In the North Atlantic, the heat flux change causes a reduction of northward salinity transport that freshens the high latitudes, reducing the across-current slope and weakening the current. This is consistent with the dynamic sea-level changes that result from FAF-heat. The thermosteric change tends to steepen the across-current slope of the Gulf Stream, but this is counteracted by the larger opposing effect of haline contraction. Our results show that the intensity and pattern of Kuroshio strengthening is similar across models, but the change in the North Atlantic is more uncertain across models (Fig. 12f). The Gulf Stream dipole, unlike the Kuroshio dipole, is likely to be affected by the AMOC weakening, and so will be different for each model. Further, Bouttes and Gregory (2014) reported that the sea-level change in the western North Pacific was caused by both the wind stress and heat flux perturbations. In our ensemble, not every model’s Kuroshio and extension regions were sensitive to wind forcing.
The water flux perturbation shows the smallest changes of all three perturbations when applied alone, but it nevertheless has important local effects in parts of the Southern Ocean, Arctic and subpolar North Atlantic. However, the importance of the water flux change may be underestimated by considering experiments in which only one flux is varied because of nonlinear interactions between flux perturbations. Other work has described how the sea-level responses to individually applied flux perturbations combine approximately linearly (Bouttes and Gregory 2014), which we also find is true to first order. However, we have identified that the nonlinear interaction between the three forcings is model dependent, which cannot be understood from a multi-model mean perspective. Models such as GFDL-ESM2M and MRI-ESM2-0 show strong nonlinear amplification of the sea-level response in the North Atlantic when all fluxes are perturbed simultaneously. Further, other work has shown that perturbing freshwater fluxes increases the uptake of heat by the subpolar Atlantic (Garuba and Klinger 2018).
The Southern and Arctic Oceans host many local features of dynamic sea-level change that are model specific. Coupled models (including the ones analysed here) show markedly different sea-ice extents and sensitivities to forcing (Turner et al. 2013). It seems likely that at least some of the model spread in projections of ∆ζ stems from the fact that sea-ice thermodynamics are model specific. The Weddell Gyre and its heat budget are thought to be sensitive to regional wind forcing (Jullion et al. 2010; Saenko et al. 2015). The spread of ∆ζ and ∆ζT in response to FAF-stress in the western Weddell Gyre indicates that some models show a significant thermosteric response to intensified westerlies. Inter-model differences in Arctic dynamic sea-level change and heat uptake have very different mechanisms for each model. The diversity of Arctic climate responses forcing is not necessarily limited to the representation of the oceans, but perhaps also poor representation of ice albedo and cloud feedbacks (Karlsson and Svensson 2013), biases in the unperturbed state (Franzke et al. 2017) or other factors that have not been explored.
The east Atlantic “tropical arm” of positive ∆ζ in response to heat flux forcing is halosteric, but is not predicted by all models. The analysis of ocean heat content therefore yields little information about the cause of the feature. The feature bears strong resemblance to the tropical arm SST anomalies characteristic of the Atlantic Multidecadal Variability (Yuan et al. 2016), however, our ∆ζ feature is the result of 70 years of integration of step forcing rather than variability, and is a vertical integral signal rather than purely SST. Nevertheless, the similarity between that pattern of variability and the forced response we present suggests common driving mechanisms may be responsible. In the context of the AMV, the tropical arm is thought to arise in response to midlatitude warm SST anomalies that weaken the tropical trade winds, which reduce low cloud and dust loading, thereby warming tropical SST (Yuan et al. 2016). Observations and some models show that the tropical SST arm coincides with freshening in the upper 50 m (Kavvada et al. 2013), which is consistent with the positive ∆ζS response to FAF-heat. The origin of the freshening in our simulations is not known, and the roles of input from the subpolar Atlantic, the Mediterranean or elsewhere are not ruled out. Whether this is driven by the atmospheric response to forcing, the thermohaline circulation or a mixture of effects is not clear, but merits further investigation.
Caveats, unmodeled processes and further outlook
FAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.
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Caveats, unmodeled processes and further outlook
FAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.
Previous work investigating ‘pattern scaling’ has shown that the spatial structure of sea-level change remains similar across a range of magnitudes of forcing (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). The spatial patterns of change and the underlying drivers presented here are therefore likely to be qualitatively applicable to greenhouse gas-forced experiments. Nevertheless, the sensitivity of the ocean response to different heat inputs into the North Atlantic is an open area of research, and will be further investigated in future work. Additional FAFMIP experiments, which apply heat inputs like those presented here, except with differing magnitudes in the North Atlantic, are already underway, and will be presented in future work.
FAFMIP experiments do not account for the input of freshwater by the melting of the Greenland and Antarctic ice sheets. Over the North Atlantic area (50°–70° N, 70° W–30° E), the freshwater perturbation integrates to a freshwater input of 0.007 Sv (1 Sv = 106 m3 s−1). This is comparable in magnitude to the input of 0.006 Sv (0.00065 m year−1 or 0.01625 m of global mean sea-level rise) of meltwater from the Greenland Ice Sheet (GIS) over 1993–2018 (Frederikse et al. 2020), albeit applied for a much longer duration. Recent projections (Oppenheimer et al. 2019) of the GIS contribution to global mean sea-level rise by the year 2100 relative to 2000 across the full range of emissions scenarios are 0.063 to 0.119 m (0.00063–0.00119 m year−1), which corresponds to a freshwater input of about 0.007–0.013 Sv. This rough comparison suggests that the rate of addition of meltwater from the GIS alone is 1–1.8 times stronger than the local water flux perturbation in the North Atlantic. The water flux perturbation in the Southern Ocean (south of 45° S) integrates to 0.115 Sv. The Antarctic Ice Sheet (AIS) loss contribution to recent historical global mean sea-level rise is smaller than that of the GIS, at 0.00032 m year−1 or 0.008 m over 1993–2018, approximately 0.003 Sv (Frederikse et al. 2020). The AIS, unlike the GIS, is dominated by marine melting (Paolo et al. 2015; Wouters et al. 2015), a coupled atmosphere-ice sheet-ocean process that cannot yet be fully interactively represented in climate models (Oppenheimer et al. 2019). As such, projections of the AIS contribution to future global mean sea level remain highly uncertain, although recent estimates of the AIS have an across-scenario range of 0.040–0.120 m by the year 2100 relative to 2000 (Oppenheimer et al. 2019), equivalent to 0.0004–0.0012 m year−2 or 0.004–0.013 Sv. The AIS contributions are therefore on the order of 0.03–0.1 times the perturbation imposed over the Southern Ocean. The water flux perturbation studied here was sufficient to produce features of regional sea-level change 0.05–0.1 m greater than the global mean in the Northwestern Atlantic and the coastal Southern Ocean. The missing GIS and AIS meltwater contributions (which are locally of a similar order to the freshwater perturbation that we imposed) could plausibly enhance the local freshwater-forced sea-level changes by an amount the order of 0.01–0.1 m, especially in the northwestern Atlantic. Note that this rough estimate of unmodeled meltwater contributions is not intended as a quantitative account, but instead serves to highlight a need for experiments that include these effects (Nowicki et al. 2016).
Gravitational, rotational and deformational (GRD) processes associated with ice mass loss to the oceans, which typically impose a negative feedback on sea-level rise by elevating retreating glaciers away from marine heat, are also not accounted for in this study. However, the magnitude of these effects is too small to reduce the rate of AIS melting over the twenty-first century sea-level rise, and become more important after the year 2250 (Larour et al. 2019; Oppenheimer et al. 2019). More generally though, GRD processes are vital in the determination of local relative sea-level change through the 21st Century and beyond (Mitrovica et al. 2011; Oppenheimer et al. 2019). The complex interaction between atmosphere–ocean-ice sheet-GRD processes makes it difficult to speculate about the net effects of all processes, and highlights a need to interactively simulate all such elements of the system.
Echoing findings from the previous generation of coupled atmosphere–ocean climate models, the regions showing the largest dynamic sea-level changes at the end of the twenty-first century also show the largest inter-model uncertainty (Church et al. 2013, Figs., 3, 4). Regions with both large projected changes and large uncertainty are the northwestern Atlantic, the Arctic, parts of the Southern Ocean and the northwest Pacific. This uncertainty highlights an ongoing need to better understand the reasons for diverse predictions of ocean transport change in these regions. This inter-model spread cannot presently be readily reduced by excluding models, since it is not trivial to determine the relative robustness of each AOGCM projection. Accordingly, the upper and lower limits of future sea-level scenarios should be constructed with the consideration that the dynamic sea level in these regions could be larger or smaller than the multi-model ensemble mean suggests. There is an increasing understanding that the diversity of cloud feedbacks is an important cause of the variations of climate sensitivity across different AOGCMs (Zelinka et al. 2020). Establishing realistic representations of cloud feedbacks in AOGCMs is therefore a key step to reduce the spread future climate and sea-level projections. Regarding ocean components, Lyu et al. (2020) have recently attributed the spread of sea-level projections to biases in model mean states, and so the reduction of such biases remains an important goal for climate projection.
Conclusions
This work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:
Most of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.
The increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.
The main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.
The sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.
The Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.
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Conclusions
This work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:
Most of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.
The increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.
The main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.
The sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.
The Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.
The flux perturbations create nonlinear dynamic sea-level responses when applied simultaneously, especially in the Arctic and the North Atlantic, but the details are different across models.
FAFMIP simulations provide new avenues to probe the sea-level response to greenhouse gas forcing, and ocean heat-content change generally. The results presented here represent a step highlighting where AOGCMs give diverse predictions of sea-level change because of their different ocean models. Many details of local processes that cause the sea-level changes described here remain to be fully explored. We have highlighted that a key source of spread of AOGCM predictions of sea-level change in the North Atlantic is because the change of local transport is highly model dependent; subsequent work should uncover what characteristics of ocean models cause this. AOGCMs give diverse predictions about Arctic heat uptake, owing to the interaction between passive and active heat uptake processes that call for more detailed examination. Further process-based analysis of FAFMIP simulations will shed new light on the key areas of uncertainty highlighted here.
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Kopp et al. (2014)
Title:
Probabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites
Key Points:
Rates of local sea-level rise differs from rate of global sea-level rise
Differences arise from land motion, ocean dynamics, and Antarctic mass balance
Local sea-level rise can dramatically increase flood probabilities
Corresponding author:
Robert E. Kopp
Citation:
Kopp, R. E., R. M. Horton, C. M. Little, J. X. Mitrovica, M. Oppenheimer, D. J. Rasmussen, B. H. Strauss, and C. Tebaldi (2014), Probabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites, Earth’s Future, 2, 383 – 406, doi:10.1002/2014EF000239.
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2014EF000239
Abstract
Sea-level rise due to both climate change and non-climatic factors threatens coastal settlements, infrastructure, and ecosystems. Projections of mean global sea-level (GSL) rise provide insufficient information to plan adaptive responses; local decisions require local projections that accommodate different risk tolerances and time frames and that can be linked to storm surge projections. Here we present a global set of local sea-level (LSL) projections to inform decisions on timescales ranging from the coming decades through the 22nd century. We provide complete probability distributions, informed by a combination of expert community assessment, expert elicitation, and process modeling. Between the years 2000 and 2100, we project a very likely (90% probability) GSL rise of 0.5 to 1.2 m under representative concentration pathway (RCP) 8.5, 0.4 to 0.9 m under RCP 4.5, and 0.3 to 0.8 m under RCP 2.6. Site-to-site differences in LSL projections are due to varying non-climatic background uplift or subsidence, oceanographic effects, and spatially variable responses of the geoid and the lithosphere to shrinking land ice. The Antarctic ice sheet (AIS) constitutes a growing share of variance in GSL and LSL projections. In the global average and at many locations, it is the dominant source of variance in late 21st century projections, though at some sites oceanographic processes contribute the largest share throughout the century. LSL rise dramatically reshapes flood risk, greatly increasing the expected number of “1-in-10” and “1-in-100” year events.
Introduction
Sea-level rise figures prominently among the consequences of climate change. It impacts settlements and ecosystems both through permanent inundation of the lowest-lying areas and by increasing the frequency and/or severity of storm surge over a much larger region. In Miami-Dade County, Florida, for example, a uniform 90-cm sea-level rise would permanently inundate the residences of about 5% of the county’s population, about the same fraction currently threatened by the storm tide of a 1-in-100 year flood event [Tebaldi et al., 2012]. A 1-in-100 year flood on top of such a sea-level rise would, assuming geographically uniform flooding, expose an additional 35% of the population (Climate Central, Surging Seas, 2013, retrieved from SurgingSeas.org, updated November 2013).
The future rate of mean global sea-level (GSL) rise will be controlled primarily by the thermal expansion of ocean water and by mass loss from glaciers, ice caps, and ice sheets [Church et al., 2013]. Changes in land water storage, through groundwater depletion and reservoir impoundment, may have influenced twentieth-century sea-level change [Gregory et al., 2013] but are expected to be relatively minor contributors compared to other factors in the current century [Church et al., 2013].
Local sea-level (LSL) change can differ significantly from GSL rise [Milne et al., 2009; Stammer et al., 2013], so for adaptation planning and risk management, localized assessments are critical. The spatial variability of LSL change arises from: (1) non-uniform changes in ocean dynamics, heat content, and salinity [Levermann et al., 2005; Yin et al., 2009], (2) perturbations in the Earth’s gravitational field and crustal height (together known as static-equilibrium effects) associated with the redistribution of mass between the cryosphere and the ocean [Kopp et al., 2010; Mitrovica et al., 2011], (3) glacial isostatic adjustment (GIA) [Farrell and Clark, 1976], and (4) vertical land motion due to tectonics, local groundwater, and hydrocarbon withdrawal, and natural sediment compaction and transport [e.g., Miller et al., 2013].
Most past assessments of LSL change have focused on specific regions, such as the Netherlands [Katsman et al., 2011], the U.S. Pacific coast [National Research Council, 2012], New York City [Horton et al., 2011; New York City Panel on Climate Change, 2013], and New Jersey [Miller et al., 2013]. Slangen et al. [2012], Slangen et al. [2014], Perrette et al. [2013], and Church et al. [2013] [AR5] have produced global projections of LSL using Coupled Model Intercomparsion Project (CMIP) projections [Taylor et al., 2012] for thermal expansion and ocean dynamics, along with estimates of net land ice changes, their associated static-equilibrium effects and GIA.
Here we expand upon past efforts to project LSL globally. First, we present a complete probability distribution. This is critical for planning purposes; the likely (67% probability) ranges presented in AR5 and many other previous efforts provide no information about the highest 17% of outcomes, which may well be key to risk management. Second, we indicatively extend our projections to 2200, in order to inform both decision-making regarding long-term infrastructure investment decisions and their longer term land use consequences, and also greenhouse gas mitigation decisions in the context of long-term sea-level rise commitments [Levermann et al., 2013]. Finally, using a Gaussian process model [Kopp, 2013] of historical tide-gauge data [Holgate et al., 2013], we include probabilistic estimates of local non-climatic factors.
We first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.
Methods
LSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.
Figure 1: Logical flow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.
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We first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.
Methods
LSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.
Figure 1: Logical flow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.
We construct separate projections for three representative concentration pathways (RCPs): RCP 2.6, RCP 4.5, and RCP 8.5 [Meinshausen et al., 2011], which correspond respectively to likely global mean temperature increases in 2081 – 2100 of 1.9-2.3˚C, 2.0-3.6˚C, and 3.2-5.4˚C above 1850-1900 levels [Intergovernmental Panel on Climate Change, 2013]. We do not consider RCP 6.0, as 21st-century sea-level rise projections for this pathway are nearly identical to those for RCP 4.5, and few CMIP Phase 5 (CMIP5) model runs for RCP 6.0 extend beyond 2100 [Taylor et al., 2012]. The RCPs do not represent socioeconomic scenarios but can be compared to emissions in no-policy socioeconomic projections such as the Shared Socioeconomic Pathways (SSPs) [O’Neill et al., 2014]. Radiative forcing in RCP 6.0 in the second half of the century is comparable to that in the lowest emissions SSP (SSP 1), while RCP 8.5 is above four of the SSPs but below the highest-emission SSP [Riahi, 2013]. Thus, RCP 8.5 can be viewed as corresponding to high-end business-as-usual emissions and RCP 4.5 as a moderate mitigation policy scenario. RCP 2.6 requires net-negative global emissions in the last quarter of the 21st century, implying a combination of intensive greenhouse gas mitigation and at least modest active carbon dioxide removal.
Ice Sheets
Our projections of 21st-century changes in mass balance of GIS and the Antarctic ice sheet (AIS) are generated by combining the projections of AR5 and the expert elicitation of Bamber and Aspinall [2013] [BA13]. AR5 is used to characterize median and likely ranges of sea-level change, while BA13 is used to calibrate the shape of the tails (Supporting Information Figure S1 and Table S1).
Figure S1: Exceedance probabilities for GIS (left) and AIS (right) mass loss between 2000 and 2100 in RCP 8.5, in meters equivalent sea level. Green curves are derived from Bamber and Aspinall [2013], blue curves from the median and likely range of AR5, and red curves are a hybrid based on the green curves but shifted and scaled to match the median and likely range of AR5.
Table S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)
cm
GIS
AIS
50
17-83
5-95
0.5-99.5
99.9
50
17-83
5-95
0.5-99.5
99.9
Default
14
8-25
5-39
3-70
<95
4
-8-15
-11-33
-14-91
<155
AR5
14
8-25
5-39
3-68
<95
4
-8-15
-16-23
-26-35
<40
BA
14
10-21
9-29
7-48
<65
14
2-41
-2-84
-4-220
<375
Alt. Corr.
14
8-25
5-39
3-70
<95
4
-8-15
-12-33
-14-85
<185
AR5 separately assesses AIS and GIS mass balance changes driven by SMB and ice sheet dynamics. For ice sheet dynamics, AR5 determined that there was insufficient knowledge to differentiate between RCP 2.6 and 4.5 (and 8.5 for AIS). Projections of total ice sheet mass loss – given as a likely cumulative sea-level rise contribution – are thus partially scenario-independent. BA13 probed more deeply into the tail of ice sheet mass loss projections, inquiring into the 5th-95th percentile ranges of GIS, EAIS, and WAIS. However, BA13 does not differentiate between SMB and ice sheet dynamics or between RCPs.
We reconcile the projections as described in the Supporting Information. For AIS, the reconciled RCP 8.5 projections (median/likely/very likely [90% probability] of 4/−8 to 15/−11 to 33 cm) are significantly reduced in range relative to BA13 (median/likely/very likely of 13/2 to 41/−2 to 83 cm); for GIS, the reconciled projections are almost identical to those based directly on AR5 and have a likely range (8 – 25 cm) close to the very likely range estimated from BA13 (9-29 cm) (Supporting Information Table S1).
Ice sheet mass balance changes do not cause globally uniform sea-level rise. To account for the differing patterns of static-equilibrium sea-level rise caused by land ice mass loss, we apply sea-level fingerprints, calculated after Mitrovica et al. [2011] (Supporting Information Figure S2). These fingerprints assume mass loss from each ice sheet is uniform; in most regions, the error introduced by this assumption is minimal [Mitrovica et al., 2011].
Figure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.
Glacier and Ice Caps
For each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).
The projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.
Oceanographic Processes
Projections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.
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Figure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.
Glacier and Ice Caps
For each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).
The projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.
Oceanographic Processes
Projections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.
Figure S3: CMIP5 thermal expansion projections (left) and after smoothing and drift correction (right). Black = GSL curve of Church and White [2011]. Dashed = mean/max/min of GSL with glacier and ice cap projections removed.
Figure S4: Map of (top) median and (middle) width of likely range of ocean dynamic contribution to sea-level rise between 2000 and 2100 for RCP 8.5 (not including the contribution of global mean thermal expansion). (Bottom) Number of model projections retained at each site in RCP 8.5.
Table S2: CMIP5 models used for thermal expansion and oceanographic processes
The horizontal resolution of the CMIP5 ocean models is ~1 degree. In these coarse-resolution models, sea level at the coast may differ from the open ocean due to local biases driven by unresolved processes (e.g., coastal currents) and bathymetry [Holt et al., 2009] or via the influence of small-scale processes (e.g., eddies) on larger-scale steric and dynamic changes [Penduff et al., 2010, 2011]. Although there is some evidence that climate-forced trends in sea level are not sensitive to resolution [Penduff et al., 2011; Suzuki et al., 2005], higher-resolution coastal modeling is required to determine whether the probabilities estimated at the GCM grid scale are significantly changed by sub-grid processes.
GCM projections exhibit a range of late nineteenth-century sea-level behavior largely attributable to model drift. Uncorrected GCM-based estimates of the rate of mean global sea-level change from 1861 to 1900 range from −0.4 to +1.1 mm/yr. To correct for global-mean model drift, we apply a linear correction term to each model. The linear correction adjusts the rate of GSL rise over 1861-1900 to match a rate of thermal expansion estimated by removing the multi-model average of GIC mass loss from Marzeion et al. [2012] from the GSL curve of Church and White [2011]. After correction, the rate of thermal expansion over 1861–1900 is 0.3 ± 0.9 (2σ) mm/yr (Supporting Information Figure S3).
Consistent with AR5’s judgment that the 5th-95th percentile of CMIP5 output represents a likely (67% probability) range for global mean thermal expansion, we multiply the standard deviation of the t-distribution for oceanographic processes by 1.7.
Land Water Storage
Following the approach of Rahmstorf et al. [2012], we estimate GSL change due to changes in water storage on land based upon the relationship between such changes and population (Supporting Information Figure S5). For changes in reservoir storage, we use the historical cumulative impoundment estimate of Chao et al. [2008]. We assume that reservoir construction is a sigmoidal function of population:
\[I = a \times \mathrm{erf}\left(\frac{{P(t) - b}}{{c}}\right) + I_0\]
where I is impoundment expressed in mm equivalent sea level (esl), P(t) is world population as a function of time, and the remaining variables are constants. The results imply a maximum additional impoundment of 6 mm (esl) on top of the current 30 mm; based on the discrepancy between the “nominal” and “actual” impoundment estimated by Chao et al. [2008], we conservatively allow a 2σ error in this estimate of ±50 %.
For the rate of groundwater depletion, we fit the estimates of Wada et al. [2012] and Konikow [2011] as linear functions of population, forced through the origin. The estimate of Wada et al. [2012] is based on fluxes estimated from a global hydrological model of groundwater recharge and a global database of groundwater abstraction, while that of Konikow [2011] uses a range of approaches depending on the data available for each aquifer. We take the mean and standard deviation of the two slopes estimated (0.06 ± 0.02 mm/yr/billion people) and allow an additional 2 error of ±50%, a level based upon the errors estimated by the authors of the two impoundment studies. In our main calculation, we do not include the water resource assessment model-based estimate of Pokhrel et al. [2012], which is about a factor of three higher than the other two estimates; we include this estimate in a sensitivity case.
We employ population projections derived from United Nations Department of Economics and Social Affairs [2014]. We treat population as distributed following a triangular distribution, with the median, minimum, and maximum values corresponding to the middle, low, and high U.N. scenarios (10.9, 6.8, and 16.6 billion people in 2100, respectively). For scenarios in which population declines, we allow some reduction in impoundment, but do not allow impoundment to decrease below its year 2000 level.
Glacial Isostatic Adjustment, Tectonics, and Other Non-Climatic Local Effects
GIA, tectonics, and other non-climatic local effects that can be approximated as linear trends over the twentieth century are assumed to continue unchanged in the 21st and 22nd centuries. This is a good assumption for GIA, but imperfect for other processes. Tectonic processes can operate unsteadily, and a linear trend estimated from the historical record may be inaccurate. LSL rise related to fluid withdrawal is subject to engineering, resource depletion, market factors and policy controls, and might either increase or decrease in the future relative to historical levels. In addition, the trend estimates can encompass slow ocean dynamic changes that are close to constant over the historical record but could change in the future. Nonetheless, for a global analysis, assuming the continuation of observed historical changes offers the best currently feasible approach.
We estimate historical rates using a spatiotemporal Gaussian process model akin to that employed by Kopp [2013]. Sea level as recorded in the tide-gauge records (Permanent Service for Mean Sea Level, Tide-gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014) is represented as the sum of three Gaussian processes: (1) a globally uniform process, (2) a regionally varying, temporally linear process, and (3) a regionally varying, temporally autocorrelated non-linear process. We allow for spatial non-stationarity in the Gaussian process prior by optimizing the hyperparameters separately for each of 15 regions (Supporting Information Table S4 and Figure S6). The posterior estimate of the second (linear) process at each site is used for forward projections. Mathematical details are provided in the Supporting Information.
Table S4: Optimized model hyperparameters by region
Figure S6: Tide gauge sites and regions used in background rate calculation.
Post-2100 Projections
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Glacial Isostatic Adjustment, Tectonics, and Other Non-Climatic Local Effects
GIA, tectonics, and other non-climatic local effects that can be approximated as linear trends over the twentieth century are assumed to continue unchanged in the 21st and 22nd centuries. This is a good assumption for GIA, but imperfect for other processes. Tectonic processes can operate unsteadily, and a linear trend estimated from the historical record may be inaccurate. LSL rise related to fluid withdrawal is subject to engineering, resource depletion, market factors and policy controls, and might either increase or decrease in the future relative to historical levels. In addition, the trend estimates can encompass slow ocean dynamic changes that are close to constant over the historical record but could change in the future. Nonetheless, for a global analysis, assuming the continuation of observed historical changes offers the best currently feasible approach.
We estimate historical rates using a spatiotemporal Gaussian process model akin to that employed by Kopp [2013]. Sea level as recorded in the tide-gauge records (Permanent Service for Mean Sea Level, Tide-gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014) is represented as the sum of three Gaussian processes: (1) a globally uniform process, (2) a regionally varying, temporally linear process, and (3) a regionally varying, temporally autocorrelated non-linear process. We allow for spatial non-stationarity in the Gaussian process prior by optimizing the hyperparameters separately for each of 15 regions (Supporting Information Table S4 and Figure S6). The posterior estimate of the second (linear) process at each site is used for forward projections. Mathematical details are provided in the Supporting Information.
Table S4: Optimized model hyperparameters by region
Figure S6: Tide gauge sites and regions used in background rate calculation.
Post-2100 Projections
Indicative post-2100 projections are developed according to the methods described in the previous sections. For ice sheet mass balance, we continue the constant 21st century acceleration. For non-climatic factors that are approximated as linear in the 21st century, we continue the constant 21st century rate. For land water storage, we extend the population projections using the 22nd century growth rates of United Nations Department of Economics and Social Affairs [2004] and use the same relationships of impoundment and groundwater depletion to population as in the 21st century (Supporting Information Figure S5). The number of GCM-based model results for GIC and oceanographic processes drops significantly beyond 2100 (Supporting Information Table S2), leading in these terms to a modest discontinuity and a reduction in variance in these terms at the start of the 22nd century (Supporting Information Figure S7). Acknowledging the limitations of these assumptions, we present post-2100 projections in tables rounded to the nearest decimeter.
Flood Probabilities
To examine the implications of our projections for coastal flooding, we combine Latin hypercube samples from the sea-level distribution for an illustrative subset of sites with maximum-likelihood generalized Pareto distributions (GPDs) estimated from observed storm tides after Tebaldi et al. [2012], updated to use the full historic record of hourly water levels available at each location. Hourly data for non-U.S. sites are from the University of Hawaii Sea Level Center (retrieved from uhslc.soest.hawaii.edu, May 2014). The estimated GPDs do not take into account any future changes in storm frequency, intensity, or track [e.g., Knutson et al., 2010], so projected future flood probabilities should be viewed primarily as an illustration.
Using the maximum-likelihood GPDs, we compute return levels corresponding to a set of representative return periods (e.g., the 1-in-10 or 1-in-100 year flood events). For each decade of each realization of LSL change, we then add the projected sea-level change and re-estimate a GPD. The result for each realization is a trajectory of probabilities over time for each of the original return levels. For example, for the 10-year event, the initial probability at 2000 is 10% per year and increases over time as sea-level rises. Cumulatively summing each decade’s expectation through the century, we compute the expected number of the original events by 2100. Under stationary sea levels, there would be one expected 1-in-100 year event and ten expected 1-in-10 year events between 2001 and 2100.
Sea-Level Projections
Mean Global Sea-Level Projections
The cumulative 21st century GSL contribution of each component is shown in Figure 2 (for RCP 8.5) and in Table 1 and Supporting Information Figure S7 (for all RCPs). In the 21st century, thermal expansion and GIC provide the largest contributions to the median outcome and have narrower uncertainty ranges than the ice sheet contributions. AIS has the broadest uncertainty range, extending from a small negative contribution to sea level (presumably due to warming-induced increased snow accumulation) to a large positive contribution (requiring a substantial and/or widespread dynamic change).
Figure 2: Projections of cumulative contributions of (a) the Greenland ice sheet, (b) the Antarctic ice sheet, (c) thermal expansion, and (d) glaciers to sea-level rise in RCP 8.5. Heavy = median, light = 67% range, dashed = 5th – 95th percentile; dotted = 0.5th-99.5th percentiles.
Table 1: GSL Projections. TE: Thermal expansion, LWS: Land water storage, H14: Horton et al. [2014], J12: Jevrejeva et al. [2012], S12: Schaeffer et al. [2012]. All values are cm above 2000 CE baseline except for AR5, which is above a 1986–2005 baseline.
RCP 8.5
RCP 4.5
RCP 2.6
cm
50
17-83
5-95
0.5-99.5
99.9
50
17-83
5-95
0.5-99.5
99.9
50
17-83
5-95
0.5-99.5
99.9
2100 - Components
GIC
18
14-21
11-24
7-29
<30
13
10-17
7-19
3-23
<25
12
9-15
7-17
3-20
<25
GIS
14
8-25
5-39
3-70
<95
9
4-15
2-23
0-40
<55
6
4-12
3-17
2-31
<45
AIS
4
-8 to 15
-11 to 33
-14 to 91
<155
5
-5 to 16
-9 to 33
-11 to 88
<150
6
-4 to 17
-8 to 35
-10 to 93
<155
TE
37
28-46
22-52
12-62
<65
26
18-34
13-40
4-48
<55
19
13-26
8-31
1-38
<40
LWS
5
3-7
2-8
-0 to 11
<11
5
3-7
2-8
-0 to 11
<11
5
3-7
2-8
-0 to 11
<11
Total
79
62-100
52-121
39-176
<245
59
45-77
36-93
24-147
<215
50
37-65
29-82
19-141
<210
Projections by year
2030
14
12-17
11-18
8-21
<25
14
12-16
10-18
8-20
<20
14
12-16
10-18
8-20
<20
2050
29
24-34
21-38
16-49
<60
26
21-31
18-35
14-44
<55
25
21-29
18-33
14-43
<55
2100
79
62-100
52-121
39-176
<245
59
45-77
36-93
24-147
<215
50
37-65
29-82
19-141
<210
2150
130
100-180
80-230
60-370
<540
90
60-130
40-170
20-310
<480
70
50-110
30-150
20-290
<460
2200
200
130-280
100-370
60-630
<950
130
70-200
40-270
10-520
<830
100
50-160
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4
-8 to 15
-11 to 33
-14 to 91
<155
5
-5 to 16
-9 to 33
-11 to 88
<150
6
-4 to 17
-8 to 35
-10 to 93
<155
TE
37
28-46
22-52
12-62
<65
26
18-34
13-40
4-48
<55
19
13-26
8-31
1-38
<40
LWS
5
3-7
2-8
-0 to 11
<11
5
3-7
2-8
-0 to 11
<11
5
3-7
2-8
-0 to 11
<11
Total
79
62-100
52-121
39-176
<245
59
45-77
36-93
24-147
<215
50
37-65
29-82
19-141
<210
Projections by year
2030
14
12-17
11-18
8-21
<25
14
12-16
10-18
8-20
<20
14
12-16
10-18
8-20
<20
2050
29
24-34
21-38
16-49
<60
26
21-31
18-35
14-44
<55
25
21-29
18-33
14-43
<55
2100
79
62-100
52-121
39-176
<245
59
45-77
36-93
24-147
<215
50
37-65
29-82
19-141
<210
2150
130
100-180
80-230
60-370
<540
90
60-130
40-170
20-310
<480
70
50-110
30-150
20-290
<460
2200
200
130-280
100-370
60-630
<950
130
70-200
40-270
10-520
<830
100
50-160
30-240
10-500
<810
Other projections for 2100
AR5
73
53–97
52
35–70
43
28–60
H14
70–120
50–150
40–60
25-70
J12
110
81–165
75
52–110
57
36–83
S12
90
64–121
75
52–96
Figure S7: Projections of (a) Greenland ice sheet, (b) Antarctic ice sheet, (c) thermal expansion, and (d) glacier contributions to sea-level rise in RCP 8.5 (red), RCP 4.5 (blue) and RCP 2.6 (green). Heavy = median, dashed = 67% range.
Adding samples from the component distributions together indicates a likely GSL rise (Figure 3 and Table 1) in RCP 8.5 of 0.6 – 1.0 m by 2100, with a very likely range of 0.5 – 1.2 m and a virtually certain (99% probability) range of 0.4 – 1.8 m. The right-skewed “fat tail” of the projections arises from the ice sheet components. Even in the low-emissions RCP 2.6 pathway, sea-level rise by 2100 very likely exceeds the 32 cm that would be projected from a simple linear continuation of the 1993 – 2009 rate [Church and White, 2011].
Figure 3: Projections of GSL rise for the three RCPs. Heavy = median, dashed = 5th – 95th percentile, dotted = 0.5th – 99.5th percentiles.
Through the middle of the current century, GSL rise is nearly indistinguishable between the three forcing pathways (Figure 3 and Table 1). Only in the second half of the century do differences of >6 cm begin to emerge in either the median or the tails of the projections. By 2100, median projections reach 0.8 m for RCP 8.5, 0.6 m for RCP 4.5 and 0.5 m for RCP 2.6. By 2200, upper tail outcomes are clearly higher in the high-forcing pathway, yet there remains significant overlap in the ranges of all three pathways, with likely GSL rise by 2200 of 1.3 – 2.8 m in RCP 8.5 and 0.5 – 1.6 m in RCP 2.6. The overlap between RCPs is due in significant part to the large and scenario-independent uncertainty of AIS dynamics, even as the thermal expansion, GIC and, to a lesser extent, GIS contributions begin to differentiate (Supporting Information Figure S7).
The importance of different components to the GSL uncertainty varies with time. While in 2020 about two-thirds of the total variance in GSL is due to uncertainty in projections of thermal expansion, by 2050 in RCP 8.5 changes in ice sheet volume are responsible for more than half the variance and changes in thermal expansion for only about one-third. By 2100, AIS alone is responsible for half the variance, with an additional 30% due to GIS uncertainty and only 15% due to uncertainty in thermal expansion (Figure 4). Because the uncertainty in AIS mass loss is largely scenario-independent, its dominant contribution to variance holds across RCPs; indeed, it is even more dominant in lower emissions pathways where the contributions from other sources are smaller and more strongly constrained (Supporting Information Figure S8).
Figure 4: Sources of variance in raw (a, c) and fractional terms (b, d), globally (a – b) and at New York City (c – d) in RCP 8.5. AIS: Antarctic ice sheet, GIS: Greenland ice sheet, TE: thermal expansion, Ocean: oceanographic processes, GIC: glaciers and ice caps, LWS: land water storage, Bkgd: local background effects.
Figure S8: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 2.6.
Comparison With Other Global Projections
By construction, our likely projections of GSL in 2100 are close to those of AR5 (Table 1), though differ slightly (e.g., in RCP 8.5 in 2100, 0.6 – 1.0 m vs. AR5’s 0.5 – 1.0 m) due to: (1) the drift correction to a possibly non-zero (0.3 ± 0.9 mm/yr) background thermal expansion, (2) the use of Marzeion et al. [2012] for GIC, and (3) the use of a year 2000 as opposed to 1985 – 2005 baseline. AR5 projections of GSL rise are lower than those from other sources, such as semi-empirical models [Rahmstorf , 2007; Schaeffer et al., 2012; Vermeer and Rahmstorf , 2009] and expert surveys [Horton et al., 2014]. However, AR5 only projects likely ranges; higher magnitudes of ice loss are implied if less likely outcomes are considered [Little et al., 2013a].
By using plausible information to complement the AR5 analysis, we project a very likely GSL rise in 2100 of 0.4 – 0.9 m for RCP 4.5, which compares to the 90% probability semi-empirical projections of 0.5 – 1.1 m [Jevrejeva et al., 2012] and 0.6 – 1.2 m [Schaeffer et al., 2012]. The widths of the semi-empirical very likely ranges are similar to those of our projections, with the entire distribution shifted to higher values. The 95th percentiles of these two semi-empirical projections resemble the 98th and 99th percentiles of our projection, respectively.
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Figure S8: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 2.6.
Comparison With Other Global Projections
By construction, our likely projections of GSL in 2100 are close to those of AR5 (Table 1), though differ slightly (e.g., in RCP 8.5 in 2100, 0.6 – 1.0 m vs. AR5’s 0.5 – 1.0 m) due to: (1) the drift correction to a possibly non-zero (0.3 ± 0.9 mm/yr) background thermal expansion, (2) the use of Marzeion et al. [2012] for GIC, and (3) the use of a year 2000 as opposed to 1985 – 2005 baseline. AR5 projections of GSL rise are lower than those from other sources, such as semi-empirical models [Rahmstorf , 2007; Schaeffer et al., 2012; Vermeer and Rahmstorf , 2009] and expert surveys [Horton et al., 2014]. However, AR5 only projects likely ranges; higher magnitudes of ice loss are implied if less likely outcomes are considered [Little et al., 2013a].
By using plausible information to complement the AR5 analysis, we project a very likely GSL rise in 2100 of 0.4 – 0.9 m for RCP 4.5, which compares to the 90% probability semi-empirical projections of 0.5 – 1.1 m [Jevrejeva et al., 2012] and 0.6 – 1.2 m [Schaeffer et al., 2012]. The widths of the semi-empirical very likely ranges are similar to those of our projections, with the entire distribution shifted to higher values. The 95th percentiles of these two semi-empirical projections resemble the 98th and 99th percentiles of our projection, respectively.
Horton et al. [2014] conducted a survey of 90 experts with a substantial published record in sea-level research. Their survey found likely/very likely sea-level rise by 2100 of 0.7 – 1.2/0.5 – 1.5 m under RCP 8.5 and 0.4 – 0.6/0.3 – 0.7 m under RCP 2.6. Our projections for RCP 2.6 are similar to those of the surveyed experts, with a slightly fatter upper tail, while the experts’ responses for RCP 8.5 are considerably fatter-tailed than our projections. The surveyed experts’ 83rd and 95th percentiles correspond to our 95th and 99th percentiles, respectively. Although Horton et al. [2014] did not probe the reasons why their surveyed experts different from AR5, we suggest it may be related to expectations about the behavior of Antarctica. As noted previously, high-end estimates of Antarctic mass loss from the expert elicitation of BA13 are higher than would be expected from the likely range of AR5 projections; our reconciled ice sheet projections significantly lower this contribution. (See also the sensitivity tests in section 4 for comparison.)
Our 99.9th percentile estimate for 2100 under RCP 8.5, 2.5 m, is consistent with other estimates of the maximum physically possible rate of sea-level rise in the 21st century [e.g., Miller et al., 2013]. It is higher than the 2.0 m estimate of Pfeffer et al. [2008], which corresponds to our 99.7th percentile. Comparing the individual contribution to Pfeffer et al.’s high-end projection shows that their projected GIC mass loss (55 cm) exceeds our highest projected value (32 cm), while their projections of GIS and AIS mass loss (53 and 62 cm, respectively) correspond to our 98th and 99th percentiles. Their projection of thermal expansion (30 cm) includes no uncertainty and corresponds to our 22nd percentile [cf., Sriver et al., 2012]. They do not include changes in sea-level rise resulting from changes in land water storage. As noted previously, the tail of the sea-level rise projections is dominated by the uncertainty in AIS mass loss, which is lower in Pfeffer et al. [2008] than in either our projections or BA13.
Local Sea-Level Projections: Patterns
Figure 5 displays the median LSL projections for RCP 8.5 in 2100 and the projection uncertainty, as reflected by the difference between the 17th and 83rd percentile levels. In Figure 6, we illustrate the relationship between LSL and GSL using three indices: (1) the median value of R, which we define as the ratio of LSL change driven by land ice and oceanographic components to GSL change driven by those same components (Figure 6a), (2) the uncertainty in R, reflected in Figure 6b by the difference between its 17th and 83rd percentile levels, and (3) the magnitude and uncertainty of background, non-climatic LSL change (Figure 6c). For sites where R is close to 1 and exhibits little uncertainty, GSL projections with adjustment for local land motion provide a reasonable estimate of LSL; for other sites, more detailed projections, such as those in this article, are necessary.
Figure 5: (a) Median projection and (b) width of likely range of local sea-level rise (m) in 2100 under RCP 8.5.
Figure 6: (a) Median ratio R of climatically driven LSL change to climatically driven GSL exchange (i.e., excluding land water storage and local land motion) in RCP 8.5 in 2100; (b) width of the 17th – 83rd percentile range of R; (c) mean estimates of background rate of sea-level rise due to GIA, tectonics, and other local factors (mm/yr). Open circles in bottom indicate sites where 2 $sigma$ range spans zero.
The median value of R (Figure 6a) is within 5 % of unity at about a quarter of tide-gauge sites, with higher values in much of Oceania, the Indian Ocean, and southern Africa resulting from the static-equilibrium effects of land ice mass loss. R generally declines toward higher latitudes due to static-equilibrium effects, but with values elevated in northeastern North America and to a lesser extent the North and Baltic Seas by oceanographic processes. This pattern — with sea-level rise dampened near land ice and enhanced far from it and in the northwestern North Atlantic — resembles that found by previous studies [Kopp et al., 2010; Perrette et al., 2013; Slangen et al., 2012, 2014]. Uncertainty in R (Figure 6b) is also relatively small (likely range width of < 30 %) in the inhabited southern hemisphere and low-latitude northern hemisphere, with the range increasing northwards due to both the sensitivity of static-equilibrium effects to the particular distribution of shrinking land ice reservoirs and — especially in northeastern North America, the Baltic Sea, and the Russian Arctic — uncertainty in oceanographic processes (Supporting Information Figure S4).
Added on top of the climatically driven factors reflected in R are the global effects of land water storage (not shown in Figure 6) and the effects of local land motion (Figure 6c). Moderately high rates of land subsidence can be associated with GIA, as in the northeastern United States (e.g., 1.3 ± 0.2 mm/yr at New York City), while more extreme rates generally include contributions from fluid withdrawal, delta processes, and/or tectonics. Subsidence driven by fluid withdrawal and delta processes is high at sites such as Bangkok, Thailand (background rate of 11.9 ± 1.1 mm/yr at the Fort Phracula Chomklao tide gauge), Grand Isle, Louisiana (7.2 ± 0.5 mm/yr), Manila, the Philippines (background rate of 4.9 ± 0.6 mm/yr), and Kolkata, India (5.1 ± 1.0 mm/yr). Episodic tectonic factors play an important role in both subsidence and uplift in Japan, where average background rates can range from − 5.2 ± 0.7 mm/yr at Onahama to 18.0 ± 1.6 mm/yr at Toba. At high latitudes, GIA-related uplift gives rise to high background rates of sea-level fall, as can be seen in places like Juneau, Alaska, (− 14.9 ± 0.5 mm/yr), and Ratan, Sweden (− 9.3 ± 0.2 mm/yr). While some previous global projections have used physical models to incorporate GIA [e.g., Slangen et al., 2012, 2014], the current projections are to our knowledge the first to employ observationally based rates.
Local Sea-Level Projections: Examples
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Added on top of the climatically driven factors reflected in R are the global effects of land water storage (not shown in Figure 6) and the effects of local land motion (Figure 6c). Moderately high rates of land subsidence can be associated with GIA, as in the northeastern United States (e.g., 1.3 ± 0.2 mm/yr at New York City), while more extreme rates generally include contributions from fluid withdrawal, delta processes, and/or tectonics. Subsidence driven by fluid withdrawal and delta processes is high at sites such as Bangkok, Thailand (background rate of 11.9 ± 1.1 mm/yr at the Fort Phracula Chomklao tide gauge), Grand Isle, Louisiana (7.2 ± 0.5 mm/yr), Manila, the Philippines (background rate of 4.9 ± 0.6 mm/yr), and Kolkata, India (5.1 ± 1.0 mm/yr). Episodic tectonic factors play an important role in both subsidence and uplift in Japan, where average background rates can range from − 5.2 ± 0.7 mm/yr at Onahama to 18.0 ± 1.6 mm/yr at Toba. At high latitudes, GIA-related uplift gives rise to high background rates of sea-level fall, as can be seen in places like Juneau, Alaska, (− 14.9 ± 0.5 mm/yr), and Ratan, Sweden (− 9.3 ± 0.2 mm/yr). While some previous global projections have used physical models to incorporate GIA [e.g., Slangen et al., 2012, 2014], the current projections are to our knowledge the first to employ observationally based rates.
Local Sea-Level Projections: Examples
To illustrate the importance of local factors for sea-level rise projections, we consider several sites along the coasts of the United States where different factors dominate LSL change (Tables 2 and 3). While we focus on projections for RCP 8.5 as a way of highlighting the differences between GSL and LSL, similar considerations apply to other RCPs, which are shown in the tables.
Table 2: LSL Projections for New York, NY, USA (Bkgd: 1.31 ± 0.18 mm/yr), Sewell’s Point, VA, USA (Bkgd: 2.45 ± 0.29 mm/yr), Key West, FL, USA (Bkgd: 0.46 ± 0.41 mm/yy), Galveston, TX, USA (Bkgd: 4.56 ± 0.27 mm/yr), San Francisco, CA, USA (Bkgd: − 0.08 ± 0.18 mm/yr), Juneau, AK, USA (Bkgd: − 14.91 ± 0.53 mm/yr), Honolulu, HI, USA (Bkgd: − 0.20 ± 0.39 mm/yr), Cuxhaven, Germany (Bkgd: 1.00 ± 0.17 mm/yr), Stockholm, Sweden (Bkgd: − 5.01 ± 0.12 mm/yr), Kushimoto, Japan (Bkgd: 1.46 ± 0.80 mm/yr), Valparaiso, Chile (Bkgd: − 2.47 ± 0.79 mm/yr) in RCP 8.5, RCP 4.5 and RCP 2.6 emission scenarios.
Table 3: Components of LSL rise in 2100 for New York, NY, USA, Sewell’s Point, VA, USA, Key West, FL, USA, Galveston, TX, USA, San Francisco, CA, USA, Juneau, AK, USA, Honolulu, HI, USA, Cuxhaven, Germany, Stockholm, Sweden, Kushimoto, Japan, Valparaiso, Chile in RCP 8.5, RCP 4.5 and RCP 2.6 emission scenarios.
New York City experiences greater-than-global sea-level rise under almost all plausible projections, with a likely range of 0.7 – 1.3 m by 2100 under RCP 8.5. Three factors enhance sea-level rise at New York. First, due to its location on the subsiding peripheral bulge of the former Laurentide Ice Sheet, the site experiences GIA-related sea-level rise of 1.3 ± 0.2 mm/yr. Second, the rotational effects of WAIS mass loss increase
the region’s sea-level response to WAIS mass loss by about 20% [Mitrovica et al., 2009]. Third, as noted
in earlier papers [Kopp et al., 2010; Yin et al., 2009; Yin and Goddard, 2013], changes in the Gulf Stream may result in dynamic sea-level rise in the mid-Atlantic United States. This enhancement can be seen by examining the difference between oceanographic sea-level rise at New York and the global average, which has a median of 14 cm and a likely range of −6 to +35 cm. These three effects are partially counteracted by the ∼55 % reduction in the sea-level response due to GIS mass loss, associated with the gravitationally induced migration of water away from of this relatively proximal ice mass. Indeed, the climatic factors that amplify and reduce LSL rise relative to GSL rise are nearly balanced in the median projection (R = 1.03, with a likely range of 0.73 – 1.30), with GIA effects pushing local rise to levels that exceed the global rise.
Sewell’s Point in Norfolk, VA, is projected to experience higher-than-global mean sea-level rise due to the same factors as New York City: subsidence due to GIA, enhanced influence of WAIS mass loss, and exposure to changes in the Gulf Stream. Being located farther south along the U.S. East Coast, Norfolk experiences somewhat smaller ocean dynamic changes (median and likely ocean dynamic sea-level rise increment of 9 cm and −8 to 26 cm) but greater sea-level rise due to GIS mass loss (experiencing about ∼45 % less sea-level rise than the global mean). Its R value (1.00, likely range of 0.75 – 1.22) is similar to New York City. However, whereas New York City sits upon bedrock, Norfolk is located on the soft sediments of the Coastal Plain [Miller et al., 2013]. As a consequence, it is exposed to sea-level rise due to both natural sediment compaction and compaction caused by groundwater withdrawal, which increases the background non-climatic rate of sea-level rise to 2.5 ± 0.3 mm/yr. Accordingly, the likely range of LSL rise for RCP 8.5 in 2100 is 0.8 – 1.3 m.
Sea-level rise at Key West, Florida, is closer to the global mean, with a likely range in RCP 8.5 by 2100 of 0.6 – 1.1 m (median R = 1.00, likely range of 0.83 – 1.15, background rise of 0.5 ± 0.4 mm/yr). By contrast, the deltaic western Gulf of Mexico coastline experiences some of the fastest rates of sea-level rise in the world as a result of groundwater withdrawal and hydrocarbon production [Kolker et al., 2011; White and Tremblay, 1995]. At Galveston, Texas, a background subsidence rate of 4.6 ± 0.3 mm/yr drives a likely range of sea-level rise by 2100 in RCP 8.5 of 1.0 – 1.5 m. Because the uncertainty in subsidence rate is small relative to other sources of uncertainty, this causes a shift in the range rather than a broadening of overall uncertainty, as occurs at New York City (reflected in a likely R of 0.78 – 1.13, which is narrower than at New York City).
The Pacific Coast of the contiguous United States is subject to considerable short length-scale sea-level rise variability due to tectonics, as can be seen by comparing the background non-climatic rate of sea-level rise at Los Angeles (− 1.1 ± 0.3 mm/yr) and nearby Santa Monica (− 0.6 ± 0.3 mm/yr). In general, sea-level rise on this coast is close to the global average, with a likely range in 2100 under RCP 8.5 at San Francisco of 0.6 – 1.0 m (median R = 0.96, likely 0.84 – 1.08, background rate of − 0.1 ± 0.2 mm/yr). The slightly lower-than-global projection is a result of smaller Greenland and GIC contributions due to proximity to these land ice reservoirs, though counterbalanced by enhanced sea-level rise from AIS mass loss. Ocean dynamic factors are projected to play a minimal role.
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Sea-level rise at Key West, Florida, is closer to the global mean, with a likely range in RCP 8.5 by 2100 of 0.6 – 1.1 m (median R = 1.00, likely range of 0.83 – 1.15, background rise of 0.5 ± 0.4 mm/yr). By contrast, the deltaic western Gulf of Mexico coastline experiences some of the fastest rates of sea-level rise in the world as a result of groundwater withdrawal and hydrocarbon production [Kolker et al., 2011; White and Tremblay, 1995]. At Galveston, Texas, a background subsidence rate of 4.6 ± 0.3 mm/yr drives a likely range of sea-level rise by 2100 in RCP 8.5 of 1.0 – 1.5 m. Because the uncertainty in subsidence rate is small relative to other sources of uncertainty, this causes a shift in the range rather than a broadening of overall uncertainty, as occurs at New York City (reflected in a likely R of 0.78 – 1.13, which is narrower than at New York City).
The Pacific Coast of the contiguous United States is subject to considerable short length-scale sea-level rise variability due to tectonics, as can be seen by comparing the background non-climatic rate of sea-level rise at Los Angeles (− 1.1 ± 0.3 mm/yr) and nearby Santa Monica (− 0.6 ± 0.3 mm/yr). In general, sea-level rise on this coast is close to the global average, with a likely range in 2100 under RCP 8.5 at San Francisco of 0.6 – 1.0 m (median R = 0.96, likely 0.84 – 1.08, background rate of − 0.1 ± 0.2 mm/yr). The slightly lower-than-global projection is a result of smaller Greenland and GIC contributions due to proximity to these land ice reservoirs, though counterbalanced by enhanced sea-level rise from AIS mass loss. Ocean dynamic factors are projected to play a minimal role.
Farther north, the proximity of historic and modern glaciers controls LSL projections. At Juneau, predicted sea-level rise is dominated by a glacio-isostatic sea-level fall of 14.9 ± 0.5 mm/yr, interpreted as resulting primarily from the ongoing response to post-Little Ice Age glacial mass loss, with a secondary contribution from post-Last Glacial Maximum GIA [Larsen et al., 2005]. Moreover, shrinking glaciers in Alaska and western Canada cause about 2.4 mm of LSL fall at Juneau for every mm of global sea-level rise, which reduces the overall magnitude of sea-level rise caused by projected glacial mass loss (median R = 0.71, likely 0.59 – 0.83). As a consequence, under RCP 8.5 Juneau is likely to experience a sea level fall of 0.7 – 1.1 m by 2100.
Hawai‘i and other central Pacific islands experience significantly greater-than-average sea-level rise resulting from land ice mass loss (20% enhancement for GIS, EAIS, and the median combination of shrinking glaciers, and 30% for WAIS, giving rise to median R = 1.13 and likely 0.98 – 1.26). The likely range of sea-level rise at Honolulu, Hawai‘i, is slightly higher than the global mean (0.6 – 1.1 m in 2100 under RCP 8.5, with a background rate of − 0.2 ± 0.4 mm/yr). The amplification relative to the global mean is more apparent in the tail of the projections, where ice sheet mass loss contributions constitute a larger proportion of the sea-level rise. As a consequence, the tail of sea-level rise is fatter at Hawai‘i than globally, with a 95th percentile in RCP 8.5 of 1.4 m (compared to GSL of 1.2 m) and a 99.5th percentile of 2.1 m (compared to GSL of 1.8 m).
A similar range of behaviors is seen outside the United States. At Cuxhaven, on the German North Sea coast, a slightly higher-than-global likely range of 0.6 – 1.1 m arises from a background subsidence rate of 1.0 ± 0.2 mm/yr. Because of its relative proximity to Greenland, Cuxhaven is less exposed to climatically driven sea-level rise than average (median R = 0.89, likely 0.62 – 1.15); unlike sites in eastern North America that are similarly close to Greenland, it does not experience a countervailing oceanographic sea-level rise. The city of Stockholm, Sweden, like Juneau, is experiencing a strong GIA-related uplift of −5.0 ± 0.1 mm/yr, leading to a likely sea-level rise of −0.4 to +0.8 m. Being farther from a large, actively shrinking glacier, however, Stockholm is in the median more exposed than Juneau to climatically driven sea-level change (median R = 0.83, likely 0.41 – 1.20).
Like Honolulu, the town of Kushimoto, in Wakayama Prefacture, Japan, is in the far-field of the major ice sheets and most major glaciers. It is also exposed to a likely ocean dynamic sea-level rise of −5 to +18 cm in 2100. Together, these factors lead to a median R = 1.14, likely 0.98 – 1.28. Kushimoto also is experiencing tectonic subsidence, leading to a likely sea-level rise in 2100 of 0.8 – 1.3 m.
The city of Valparaiso, on the Chilean Pacific coast, is experiencing tectonic uplift of 2.5 ± 0.8 and exposed to a likely ocean dynamic sea-level fall of −2 to 9 cm. Although it experiences about 30% less-than-global sea-level rise due to WAIS mass loss, it experiences a larger-than-average response to GIS, EAIS, and most glaciers; accordingly its overall sensitivity to sea-level rise is close to the global average (median R = 0.99, likely 0.90 – 1.08). All these factors together yield a likely 2100 sea-level rise 0.4 – 0.8 m.
Variance and Sensitivity Assessment
As shown in the previous section, LSL rise is controlled by different factors — both climatic and non-climatic — at different locations and intervals over the next two centuries. The analysis also reveals that the adopted risk tolerance (choice of exceedance probability) influences the importance of different components. Median outcomes will vary regionally, driven strongly by varying levels of subsidence and, in certain regions, oceanographic processes. High-end (low-probability) outcomes are driven, globally and in most locations, by uncertainty in the ice sheet contribution, with the Antarctic signal becoming dominant in the highest end of the tail, particularly later in the century (Figure 4 and Supporting Information Figures S8 and S9). This contribution varies less by location.
Figure S9: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 8.5.
To test the robustness of our results, we examine three alternate assumptions regarding ice sheet mass loss and two alternative assumptions regarding the robustness of GCM projections (Supporting Information Tables S1 and S3):
AR: using a lognormal fit to the AR5 median and likely ranges of ice sheet mass balance (GIS almost unchanged from reconciled projections; for AIS, very likely range of −15 to 23 cm in RCP 8.5 by 2100)
BA: using a lognormal fit to the BA13 median and very likely projections of ice sheet mass balance (GIS: median 14 cm and very likely 9 – 29 cm; AIS: median 14 cm, very likely −2 to 83 cm)
Alt. Corr.: assuming positive correlations of 0.7 between WAIS and GIS and a negative correlation of −0.2 between EAIS and the other two ice sheets, following the main projections of Bamber and Aspinall [2013]
High GCM Confidence: assuming the very likely ranges estimated by the GCMs for oceanographic changes are very likely rather than likely ranges.
Reduced degrees of freedom (DOF): Assuming the GCMs collectively provide only six independent estimates of GIC and oceanographic change, due to non-independence of models.
Higher groundwater depletion (GWD): The ratio of groundwater depletion to population is treated as a triangular distribution, with the minimum, median, and maximum estimated respectively from Konikow [2011], Wada et al. [2012] and Pokhrel et al. [2012].
Table S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)
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Figure S9: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 8.5.
To test the robustness of our results, we examine three alternate assumptions regarding ice sheet mass loss and two alternative assumptions regarding the robustness of GCM projections (Supporting Information Tables S1 and S3):
AR: using a lognormal fit to the AR5 median and likely ranges of ice sheet mass balance (GIS almost unchanged from reconciled projections; for AIS, very likely range of −15 to 23 cm in RCP 8.5 by 2100)
BA: using a lognormal fit to the BA13 median and very likely projections of ice sheet mass balance (GIS: median 14 cm and very likely 9 – 29 cm; AIS: median 14 cm, very likely −2 to 83 cm)
Alt. Corr.: assuming positive correlations of 0.7 between WAIS and GIS and a negative correlation of −0.2 between EAIS and the other two ice sheets, following the main projections of Bamber and Aspinall [2013]
High GCM Confidence: assuming the very likely ranges estimated by the GCMs for oceanographic changes are very likely rather than likely ranges.
Reduced degrees of freedom (DOF): Assuming the GCMs collectively provide only six independent estimates of GIC and oceanographic change, due to non-independence of models.
Higher groundwater depletion (GWD): The ratio of groundwater depletion to population is treated as a triangular distribution, with the minimum, median, and maximum estimated respectively from Konikow [2011], Wada et al. [2012] and Pokhrel et al. [2012].
Table S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)
Table S3: Sensitivity tests (cm, RCP 8.5 in 2100) for GSL and LSL in set of locations.
At a global level and at most locations, the two alternative characterizations of ice sheet mass changes have the largest effects, with the median sea-level rise under RCP 8.5 in 2100 varying between 79 cm under default assumptions and case AR and 91 cm under case BA. The effect is larger in the tails, with 99.5th percentile projections of 140 cm under AR, 176 cm under default assumptions, 187 cm under Alt. Corr., and 300 cm under BA. Varying the confidence in GCMs, by contrast, has little global effect. Although the per-capita rate of groundwater depletion estimated from Pokhrel et al. [2012] is about three times that of the Wada et al. [2012], the overall effect of the Higher GWD assumption is small due to the magnitude of other uncertainties; this case experiences 3 cm extra GSL rise at the 5th percentile, 4 cm at the median, and 6 cm at the 99.5th percentile.
While all LSL projections are sensitive to assumptions about ice sheet behavior, some are sensitive to assumptions about confidence in GCM output. Due to the wide range of projections in the CMIP5 ensemble at New York City [Yin, 2012], the 99.5th percentile projections are 212 cm under default assumptions, 205 cm under High GCM Confidence, and 232 cm under Reduced DOF. Even at New York City, however, GCM uncertainty remains secondary to ice sheet uncertainty; the 99.5th percentile is 178 cm under AR, 212 cm under Alt. Corr., and 359 cm under BA. Moreover, the significance of GCM uncertainty can be quite small: at the sites discussed above, the difference between the 99.5th percentiles of the High GCM Confidence and Reduced DOF cases under RCP 8.5 in 2100 is 27 cm at New York, 19 cm at Sewell’s Point, 12 cm at Cuxhaven, 9 cm at Galveston, and 6 cm or less at Honolulu, Juneau, Key West, Kushimoto, San Francisco, and Valparaiso. A large difference (55 cm) at Stockholm may reflect differences between GCMs in the representation of the semi-closed Baltic Sea.
These sensitivity analyses are not exhaustive. There remains a need for improved ice sheet models to allow robust projections of the ice sheet component without heavy reliance upon expert elicitation. However, the development of such models is hindered by the limited consensus on the magnitude of positive and negative feedbacks on ice loss, such as those involving (a) temperature and snow albedo [Picard et al., 2012], (b) forest fires and snow albedo [Keegan et al., 2014], (c) snowfall and ice sheet discharge [Winkelmann et al., 2012], (d) grounding line retreat [Joughin et al., 2014; Rignot et al., 2014; Schoof , 2007],(e) static-equilibrium sea-level and grounding line retreat [Gomez et al., 2010, 2012, 2013], (f ) meltwater, ocean temperature, sea ice, and snowfall [Bintanja et al., 2013], and (g) ice-cliff collapse [Bassis and Walker, 2012; Pollard and DeConto, 2013]. The wide range of projections and underlying uncertainties in continental-scale model projections pose challenges for interpreting the likelihood of their results [Bindschadler et al., 2013]. It is possible, however, that incomplete information could be better integrated in a probabilistic framework [Little et al., 2013a, 2013b].
Furthermore, structural errors in models of other sea level components remain probable. These errors (e.g., a systematic bias caused by a missing process and/or feedback) may have a large impact on tails. Here, we do not attempt to perform a systematic analysis. However, we believe that this framework may be used to effectively allow for these possibilities to be considered. The subjective judgment applied in formulating these distributions is explicit and may be revisited over time.
Implications for Coastal Flooding
Since our projections provide full probability distributions, they can be combined with extreme value distributions to estimate the expected number of years in which flooding exceeds a given elevation, integrated over a given interval of time. Note that this is different from the expected number of flood events in a single year; the question here is not, “what is the probability of a flood of at least height X, given the projected sea-level change in 2050?” but, “in how many years between 2000 and 2050 do we expect floods of at least height X, given the projected pathway of sea level change?” Table 4 shows the expected number of years under each RCP with current “1-in-10 year” (10% probability per year) and “1-in-100 year” (1% probability per year) flood events for a selection of sites over 2001 – 2030, 2001 – 2050, and 2001 – 2100. Figure 7 shows the expected fraction of years with at least one event at the New York City, Key West, Cuxhaven, and Kushimoto tide gauges for a range of heights and the same periods of time under RCP 8.5; additional tide gauges and RCPs are shown in Supporting Information Figure S10.
Table 4: Expected number of years with flood events of a given height under different RCPs. Heights for U.S. sites are with respect to the local mean higher high water datum for the 1983–2001 epoch. Heights for non-U.S. sites are with respect to the local mean sea level datum for the 1983–2001 epoch.
Figure 7: Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (black) and RCP 8.5 over 2001 – 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.
Figure S10. Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (solid black), RCP 2.6 (dot-dashed), RCP 4.5 (dashed) and RCP 8.5 (solid), over 2001 to 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.
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Table 4: Expected number of years with flood events of a given height under different RCPs. Heights for U.S. sites are with respect to the local mean higher high water datum for the 1983–2001 epoch. Heights for non-U.S. sites are with respect to the local mean sea level datum for the 1983–2001 epoch.
Figure 7: Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (black) and RCP 8.5 over 2001 – 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.
Figure S10. Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (solid black), RCP 2.6 (dot-dashed), RCP 4.5 (dashed) and RCP 8.5 (solid), over 2001 to 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.
At seven of the nine sites considered (New York, Sewell’s Point, Key West, Galveston, San Francisco, Kushimoto, and Valparaiso, though not Cuxhaven or Stockholm), the expected number of years with current 1-in-10 year flood events, integrated over the 21st century, is under all RCPs at least five times larger than the 10 that would be predicted without sea-level rise. At the same seven sites, the expected number of years in the 21st century with current 1-in-100 year flood events is at least four times higher under RCP 2.6 and at least 8 times higher under RCP 8.5 than the 1 that would be expected without sea-level rise.
The increase in expected flood events is influenced both by the magnitude of projected LSL rise and by the range of past flood events. The latter is reflected in the difference between the 1-in-10 year and 1-in-100 year flood elevations, which will be larger at tide gauges that have experienced more extreme flood events. New York City and Cuxhaven are projected to experience fairly high sea-level rise (likely 0.7 to 1.3 m and 0.6 to 1.1 m by 2100 under RCP 8.5, respectively) but have also historically experienced large flood events, with the 1-in-100 year flood level about 70 cm higher than the 1-in-10 year flood level. Under RCP 8.5, these two sites respectively expect nine and four 1-in-100 year floods over the 21st century — the same as would be expected for 1-in-11 year and 1-in-25 year events without sea-level rise.
Stockholm has experienced fairly few large flood events, with the 1-in-100 year flood level only about 20 cm higher than the 1-in-10 year flood level, but also has a low projected sea-level rise (likely –0.2 to 0.5 m). As a consequence, it also expects nine 1-in-100 year floods over the 21st century under RCP 8.5. Key West, by contrast, has a projected sea-level rise similar to Cuxhaven but has not experienced as many large flood events. The 1-in-100 year flood level there is only about 23 cm higher than the 1-in-10 year flood level. Accordingly, it is expected to experience 48 years over the 21st century with a 1-in-100 year flood event, about the same as would be expected for a 1-in-2 year event without sea-level rise
The most extreme case among the nine sites considered is Kushimoto, which both has a large projected sea-level rise (likely 0.8 – 1.3 m by 2100) and has experienced few large flood events, with the 1-in-100 year flood level just 10 cm higher than the 1-in-10 year flood level. Over the course of the 21st century, under all RCPs, Kushimoto is expected to experience more than 60 years with flooding exceeding the current 1-in-100 year flood level.
Sea-level rise allowances [Hunter et al., 2013] quantify the amount by which a structure needs to be raised so that its current flood probability remains unchanged. For example, the U.S. National Flood Insurance Program’s Special Flood Hazard Areas are defined as areas with a 1% per year flood probability [National Flood Insurance Program, 2013]. A corresponding sea-level rise allowance would indicate the height above the current 1-in-100 year flood zone that would maintain an average 1% per year flood probability over the period of interest. Note that, because the allowance is with respect to flood risk integrated over time, its magnitude is less than that of the sea-level change expected by the end of the period of interest. At New York City, a project with a 2001–2030 lifetime, such as a house with a 30-year mortgage, would need to be elevated by 17 cm above the no-sea-level-rise 1-in-100 year flood zone to maintain a 1% per year flood probability. An infrastructure project with a 2001–2050 lifetime would need to be raised 26 cm, while a project with a 2001–2100 life time would need to be elevated by 52–69 cm, depending on the emissions trajectory (Figure 7).
Cautions
In addition to highlighting the sensitivities and research needs noted in section 4, we raise several cautions in interpreting our projections.
First, in the near-term, internal variability in sea-level rise [e.g., Bromirski et al., 2011] makes estimation of precise timing of LSL change difficult. Most sites experience interannual variability with a 2 sigma ($sigma$) range of about 4 – 10 cm [Hay et al., 2013; Kopp et al., 2010]. At the illustrative sites we consider, the difference between the 17th and 83rd percentile projections exceeds the decimeter level between 2030 and 2050. Until this threshold is reached, year-to-year variability will be comparable to the uncertainty in projections.
Second, as previously noted, historically estimated background rates of local, non-climatic processes may not continue unchanged. For example, while we project 72 ± 5 cm of 21st century sea-level rise due to non-climatic factors at Grand Isle, Louisiana, changes in fluid withdrawal could reduce the projection [Blum and Roberts, 2012].
Third, our background rate estimates are the result of an algorithm applied to a global database of tide-gauge data, with different sites having been subjected to different degrees of quality control. Some tide-gauge sites may have experienced datum shifts or other local sources of errors not identified by the analysis. We recommend that users of projections for practical applications in specific regions scrutinize local tide-gauge records for such effects.
Fourth, our flood probability estimates should be viewed indicatively. They are based on hourly tide-gauge records that may be of insufficient length to capture accurately the statistics of rare flood events. They do not account for projected changes in tropical or extratropical cyclone climatology, such as the expectation that Category 4 and 5 hurricanes may become more frequent in the North Atlantic [e.g., Bender et al., 2010] and perhaps globally [Emanuel, 2013]. They are developed for specific tide-gauge locations where flood risk is likely indicative of, but not identical to, risk for the wider vicinity, due to variation in local topography and hydrodynamics. Nonetheless, they do highlight the inadequacy of flood risk assessments based on historic flood probabilities for guiding long-term decisions in the face of ongoing sea-level rise.
Conclusions
Assessments of climate change risk, whether in the context of evaluation of economic costs or the planning of resilient coastal communities and ecosystem reserves, require projections of sea-level changes that characterize not just likely sea-level changes but also tail risk. Moreover, these projections must estimate sea-level change at specific locations, not just at the global mean. They must also cover a range of timescales relevant for planning purposes, from the 30-year time scale of a typical U.S. mortgage, to the > 50 year lifetime of long-lived infrastructure projects, to the > 1 century lifetime of the development effects of infrastructure investments. In this article, we synthesize several lines of information, including model projections, formal expert elicitation, and expert assessment as embodied in the Intergovernmental Panel on Climate Change’s Fifth Assessment Report, to generate projections that fulfill all three desiderata.
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Third, our background rate estimates are the result of an algorithm applied to a global database of tide-gauge data, with different sites having been subjected to different degrees of quality control. Some tide-gauge sites may have experienced datum shifts or other local sources of errors not identified by the analysis. We recommend that users of projections for practical applications in specific regions scrutinize local tide-gauge records for such effects.
Fourth, our flood probability estimates should be viewed indicatively. They are based on hourly tide-gauge records that may be of insufficient length to capture accurately the statistics of rare flood events. They do not account for projected changes in tropical or extratropical cyclone climatology, such as the expectation that Category 4 and 5 hurricanes may become more frequent in the North Atlantic [e.g., Bender et al., 2010] and perhaps globally [Emanuel, 2013]. They are developed for specific tide-gauge locations where flood risk is likely indicative of, but not identical to, risk for the wider vicinity, due to variation in local topography and hydrodynamics. Nonetheless, they do highlight the inadequacy of flood risk assessments based on historic flood probabilities for guiding long-term decisions in the face of ongoing sea-level rise.
Conclusions
Assessments of climate change risk, whether in the context of evaluation of economic costs or the planning of resilient coastal communities and ecosystem reserves, require projections of sea-level changes that characterize not just likely sea-level changes but also tail risk. Moreover, these projections must estimate sea-level change at specific locations, not just at the global mean. They must also cover a range of timescales relevant for planning purposes, from the 30-year time scale of a typical U.S. mortgage, to the > 50 year lifetime of long-lived infrastructure projects, to the > 1 century lifetime of the development effects of infrastructure investments. In this article, we synthesize several lines of information, including model projections, formal expert elicitation, and expert assessment as embodied in the Intergovernmental Panel on Climate Change’s Fifth Assessment Report, to generate projections that fulfill all three desiderata.
Under RCP 8.5, we project a very likely mean global sea-level rise of 0.5 – 1.2 m by 2100 and 1.0 – 3.7 m by 2200, which under the strong emissions mitigation of RCP 2.6 is lowered to 0.3 – 0.8 m by 2100 and 0.3 – 2.4 m by 2200. Local sea-level rise projections differ from the global mean due to differing background rates of non-climatic sea-level change, spatially variable responses to different land ice reservoirs due to static-equilibrium effects, and spatially variable ocean steric and dynamic changes. Static-equilibrium effects lead to a tendency for greater-than-global sea-level rise in the central and western Pacific Ocean. Mid-latitude and high-latitude sites in North America and Europe are generally less exposed to climatically driven sea-level change, with the exception of northeastern North America, which has potential for a high oceanographic sea-level contribution. At most sites, by the end of the century, uncertainty is due primarily to uncertainty in AIS mass loss, though oceanographic uncertainty is also a major term at sites where oceanographic processes may make a significant contribution to sea-level rise.
Probabilistic projections of future local sea-level rise pathways can be combined with statistical or hydrodynamic flood projections to estimate flood probabilities that more accurately assess the risks relevant to structures and populations. Projected sea-level rise can dramatically change estimated risks; at the Battery in New York City, for example, we project over the 21st century an expected nine years with “1-in-100 year”’ flood events under RCP 8.5 and four under RCP 2.6. Such projections, especially if improved or augmented by more detailed storm and flood models that include factors such as changes in tropical and extratropical cyclone climatology and by hydrodynamic models of overland flooding, can guide insurance, land use planning, and other forms of coastal climate change risk management.
Supplementary methods
Ice sheet mass loss
To reconcile the AR5 and BA13 projections of ice sheet mass loss, we first fit log-normal distributions to the rates of ice mass change in 2100 for AR5 and BA13. Assuming linear increases in ice loss rates from the levels of 2000–2011 [Shepherd et al., 2012], we calculate a distribution of cumulative ice sheet mass loss at each time point. We then shift the BA13-derived projections by a constant, so that their medians agree with those of the AR5-derived projections. Since BA13 separates WAIS and EAIS while AR5 does not, we approximate the median ‘AR5’ WAIS contribution by scaling the AR5 median AIS estimate by the ratio of the median BA13 WAIS projection to the median BA13 AIS projection. Finally, we apply a multiplier to the difference from the median so that the derived distribution matches the 67% probability AR5 range. We use separate multipliers for outcomes above and below the median projections. For example, for RCP 8.5 in 2100, we decrease the RCP 8.5 projections for AIS by 10 cm (from 14 cm to 4 cm), then multiply positive deviations from the median by 0.4 and negative deviations by 1.0. We use the same scale factors for WAIS and for total AIS. The resulting distributions are shown in Table S1 and Figure S1.
Glacier and ice caps
We project mass loss for seventeen glacier and ice cap source regions: Alaska, Western Canada and the United States, Ellesmere Island, Ban Island, the Greenland periphery, Iceland, Svalbard, Scandinavia, Kamchatka, Novaya Zemlya, the Alps, the Caucasus, the northern Himalayas, the southern Himalayas, the low latitude Andes, Patagonia, and New Zealand. (Following AR5, Antarctic peripheral glaciers and ice caps are included in the calculation of AIS mass loss.)
Oceanographic processes
The ‘zostoga’ or (for the GFDL models) ‘zosga’ variables were used for GSL, while for LSL the global term was added to the local dynamic sea level anomaly, given by the difference between ‘zos’ and the global mean of ‘zos’.
To account for identifiable problems with specific models (for example, the way some models, such as MIROC-ESM, handle inland seas), we remove on a site-by-site basis projections that have an amplitude in 2100 more than ten times the median local amplitude. In cases where the standard deviation of projections in 2100 (after removal of the extreme outliers identified by the median amplitude) is greater than 20 cm, we also remove models that deviate from the mean by more than three standard deviations. Finally, to account for discrepancies in the accounting of sea surface height where there is sea ice coverage, we exclude MIROC and GISS models at latitudes greater than 50 degrees. Figure S4 shows the median and likely range of the projected ocean dynamic contribution to RCP 8.5 in 2100 (excluding the effects of global mean thermal expansion), as well as the number of models contributing to the assessment at each site after the removal of outliers.
Gaussian process model for tide gauge data
The Gaussian process prior for sea level has a mean given by the GIA projections of the ICE-5G VM2-90 model [Peltier , 2004] and a covariance given by the covariance function $k(r_1,t_1,r_2,t_2)$. The covariance is the sum of three terms: one representing GSL change ($k_{global}$), one representing linear local and regional sea-level changes ($k_{linear}$), and one representing non-linear local and regional sea-level changes ($k_{nonlin}$). The covariance function is given by
$$ k(r_1,t_1,r_2,t_2) = k_{global}(t_1,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{nonlin}(r_1,t_1,r_2,t_2) $$ (S1)
$$ k_{global}(t_1,t_2) = theta^2_1 t_1 t_2 + theta^2_2 C(| t_2-t_1 | /theta_3,theta_4) $$ (S2)
$$ k_{linear}(r_1,t_1,r_2,t_2) = theta^2_5 t_1 t_2 times (theta_7 delta_{r1,r2} + (1 - theta_7) times D(alpha(r_1, r_2)/theta_6)) + delta_{r1,r2} theta^2_Delta $$ (S3)
$$ k_{nonlin}(r_1,t_1,r_2,t_2) = theta^2_8 C( | t_2 - t_1 | /theta_9,theta_{10}) times (theta_{11}delta_{r1,r2} + (1 - theta_{11}) times D(alpha(r_1, r_2)/theta_{12})) $$ (S4)
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Gaussian process model for tide gauge data
The Gaussian process prior for sea level has a mean given by the GIA projections of the ICE-5G VM2-90 model [Peltier , 2004] and a covariance given by the covariance function $k(r_1,t_1,r_2,t_2)$. The covariance is the sum of three terms: one representing GSL change ($k_{global}$), one representing linear local and regional sea-level changes ($k_{linear}$), and one representing non-linear local and regional sea-level changes ($k_{nonlin}$). The covariance function is given by
$$ k(r_1,t_1,r_2,t_2) = k_{global}(t_1,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{nonlin}(r_1,t_1,r_2,t_2) $$ (S1)
$$ k_{global}(t_1,t_2) = theta^2_1 t_1 t_2 + theta^2_2 C(| t_2-t_1 | /theta_3,theta_4) $$ (S2)
$$ k_{linear}(r_1,t_1,r_2,t_2) = theta^2_5 t_1 t_2 times (theta_7 delta_{r1,r2} + (1 - theta_7) times D(alpha(r_1, r_2)/theta_6)) + delta_{r1,r2} theta^2_Delta $$ (S3)
$$ k_{nonlin}(r_1,t_1,r_2,t_2) = theta^2_8 C( | t_2 - t_1 | /theta_9,theta_{10}) times (theta_{11}delta_{r1,r2} + (1 - theta_{11}) times D(alpha(r_1, r_2)/theta_{12})) $$ (S4)
$$ theta_Delta = 50 sqrt{theta^2_1 + theta^2_5} $$ (S5)
$$ C(r,v) = frac{2^{1-v}}{Gamma(v)} (sqrt{2v}r)^v K_v (sqrt{2v}r) $$ (S6)
$$ D(r) = (1 + sqrt{5}r + 5r^2 / 3) times exp{(-sqrt{5}r)} $$ (S7)
where $theta_i$ are hyperparameters, $C$ is a Matérn covariance function with smoothness parameter $v$, $Gamma$ is the gamma function, $K_v$ is a modified Bessel function of the second kind, $D$ is a twice-differentiable Matérn covariance function with smoothness parameter $v = 5/2$, $delta_{i,j}$ is the Kroneker delta function (equal to 1 if $i = j$ and 0 otherwise), and $alpha(r_1,r_2)$ is the angular distance between points $r_1$ and $r_2$ [Rasmussen and Williams, 2006]. The product terms $(t_1t_2)$ represent linear deviations from the prior mean; the times $t_i$ are measured with respect to the year 2005 CE.
The hyperparameters reflect prior estimates of: the amplitude of the rate of linear GSL change ($theta_1$), the amplitude of non-linear GSL change ($theta_2$), the timescale of non-linear GSL change ($theta_3$), the smoothness of non-linear GSL change ($theta_4$), the amplitude of the rate of linear LSL change ($theta_5$), the spatial scale of regionally-coherent linear LSL change ($theta_6$), the fraction of linear LSL change that is not regionally coherent ($theta_7 in [0, 1]$), the amplitude of non-linear LSL change ($theta_8$), the timescale of non-linear LSL change ($theta_9$), the smoothness of non-linear LSL change ($theta_{10}$), the fraction of non-linear LSL change that is not regionally coherent ($theta_{11} in [0, 1]$), the spatial scale of regionally-coherent non-linear LSL change ($theta_{12}$), and the amplitude of datum offsets between tide gauges ($theta_{Delta}$).
The regions for hyperparameter tuning (Table S4, Figure S6) are defined using the coastlines defined by the Permanent Service for Mean Sea Level (PSMSL) [Holgate et al., 2013] (Permanent Service for Mean Sea Level, Tide gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014). There is limited overlap between regions; for prediction in areas where regions overlap, the prediction from the region with more data is used.
For each region, we first optimize the hyperparameters of $k_{global}$ to maximize the likelihood of the GSL curve of Church and White [2011]. Then, we optimize the hyperparameters through a four step process: first optimizing assuming no spatial correlation ($theta_7,theta_{11} = 1$), then optimizing the spatial correlation of the background linear term, then re-optimizing assuming no spatial correlation in the non-linear terms ($theta_{11} = 1$), then finally optimizing the spatial correlation of the Matérn terms. For the hyperparameter optimization, we only consider the longest half of all tide gauges in a region provided that there are more than five tide gauges in the region; otherwise (as occurs in the Antarctic and Iceland/Svalbard regions), we include any tide gauge with a record length of at least 15 years.
Within each region, we estimate the regional and local linear rates using the optimized model for that region, applied to the tide gauge data from the region and the GSL curve of Church and White [2011]. We then fit the regional field of linear rates with a Gaussian process having mean 0 and covariance function
$$ theta_5^2 t_1 t_2 times (theta_7^2 D (alpha(r_1,r_2)/theta_6^{prime}) + (1 - theta_7)^2 D (alpha(r_1,r_2)/theta_6)) $$,
optimizing $theta_6^{prime}$ under the constraint that $theta_6^{prime} < theta_6$. This additional step allows for spatial continuity in rates at a finer length scale than $theta_6$. Optimized hyperparameters are listed in Table S4.
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