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illuminating inferences can be made from this projection; for example, it suggests that regardless of
whether sea levels rise along the low or high trajectory, that between the years 2035 and 2045, mean sea
level exceedances will enter a phase of exponential growth. Under the high projection, it indicates that
circa 2050, mean sea level will be continuously above portions of the coastal ridge wherein one would
expect marine conditions to have displaced freshwater influences. If the low projection is realized,
then this transition is expected near 2070.
Such exceedance projections may therefore find utility in the identification of tipping points
where the transition to an exponential increase in saltwater inundation can be expected, as well as
demarcation of a time horizon upon which a fundamental transformation of the coastal environment
to submarine conditions will prevail.
Figure 11. Projected evolution of water level exceedances at Little Madeira Bay under the low and
high sea level rise scenarios. Mean water is the daily mean water level over the three-year period from
January 2014–December 2016.
3.3. Trends
Empirical mode decomposition of the water level and salinity data shown in Figures 3 and 4
provides a residual signal representing the time-varying trend after all oscillating modes are removed
as shown in Figure 12. Regarding salinity, Murray Key and Buoy Key in western Florida Bay exchange
waters with the Gulf of Mexico, as well as fresh water runoff from the coastal Everglades, but are
predominantly marine ecosystems. Seawater has a nominal salinity of 35 ppt, and we find that mean
Murray Key salinity has risen by 2.8 ppt from 32.7 in 1994 to 35.5 ppt in 2016, with values at Buoy Key
rising by 6.2 ppt from 30.6–36.8 ppt over the same period indicating that both stations are currently
experiencing higher mean salinity and lower freshwater mixing than was common 20 years ago. Little
Madeira Bay in the eastern coastal region is more influenced by freshwater runoff from the Everglades
and agricultural lands with its mean salinity increasing by 3.2 ppt from 22.4 ppt in 1994 to 25.7 ppt
in 2016.
Mean water levels are found to have increased in Florida Bay and the southern reaches of
Taylor Slough as shown in Figure 12. In Florida Bay, water levels at Buoy Key and Little Madeira
J. Mar. Sci. Eng. 2017, 5, 31 14 of 26
Bay have risen from 27.7 cm NGVD29 in 1994 to 32.7 cm in 2016, an increase of 5.0 cm, with similar
increases over the period observed at the Taylor Slough stations TR and E1462
.
Figure 12. Nonlinear trends of water level and salinity at hydrographic stations in Florida Bay and
Taylor Slough.
3.4. Marsh to Ocean Transformation
As described above, the MOI is designed to represent the relative similarity of a time series
spatially intermediate with respect to two reference time series representing oceanic and marsh
hydrology. Specifically, the relative similitude of water levels over the last three years at Little Madeira
Bay (LM) and within Taylor Slough at stations TR and E146, with respect to the oceanic reference
station of Buoy Key (BK) and marsh reference at station Taylor Slough Hilton (TSH), are shown in
Table 5. MOI values of −0.21 at Little Madeira Bay (LM), 0.02 at Taylor River (TR) and 0.34 in Taylor
Slough (E146) suggest that recent water levels at Little Madeira Bay follow the dynamics observed at
Buoy Key more closely than those of Taylor Slough (TSH), while levels at E146 are more similar to
TSH dynamics.
Table 5. Marsh-to-Ocean Index (MOI) values over the period 1 January 2014–31 December 2016
at stations LM, TR and E146 relative to the ocean-dominated station at Buoy Key (BK) and the
marsh-dominated station at TSH.
Station ω1 ω2 ω3 Ω µ1 µ2 µ3 M MOI
LM 0.00 0.62 0.00 0.62 0.00 0.00 0.00 0.00 −0.21
TR 0.46 0.38 0.00 0.84 0.32 0.58 0.00 0.90 0.02
E146 0.26 0.00 0.00 0.26 0.41 0.85 0.00 1.26 0.34
To assess changes in behavior over time, we apply the MOI to the three intermediate stations LM,
TR and E146 over a one-year moving window advanced in 10-day increments, as shown in Figure 13.
Also shown in Figure 13 is the monthly accumulation of streamflow measured at the confluence of
the Taylor River and Little Madeira Bay. This flow represents a fraction of total flow as freshwater
into Little Madeira Bay, but is representative of the annual hydrologic cycle driving marsh hydrology.
2
Ignoring the nonlinear nature of these trends, one might consider a linear mean water level rise of
5 cm/21 years = 2.4 mm/year, a result coincident with linear estimates of mean sea level rise over the 20th Century;
however, examination of the BK data found an increase over the last decade of 4.0 cm, suggesting a recent rate of 4 mm/year,
a value somewhat larger than current global estimates of 3.4 mm/year (https://sealevel.nasa.gov/) and an illustration of
difficulties in applying linear metrics to nonlinear processes.
J. Mar. Sci. Eng. 2017, 5, 31 15 of 26
For example, the large flow in 2005 associated with hurricanes Katrina and Wilma resulted in an
increase in MOI at Little Madeira Bay from negative to positive values. Overall, it is difficult to discern
patterns in the MOI dynamics, although it does appear that since 2012, MOI has remained largely
positive at the Taylor River (TR) and Taylor Slough (E146) stations.
Figure 13. (a) Monthly stream flow at the terminus of Taylor River; (b) Marsh-to-Ocean Index (MOI) in
Little Madeira Bay (LM) over a one year-long moving window advanced in 10-day increments; (c) MOI
at the Taylor River (TR) station; (d) MOI at the E146 station in Taylor Slough.
Since the effects of environmental and hydrologic perturbations on the biomes, landscapes and
ecosystems are cumulative, it makes sense to view the cumulative behavior of the time-varying MOI.
In Figure 14, we plot the time integral of the MOI shown in Figure 13, that is: R T
0 MOI(t) dt, where T
is a specific day past the data origin of 1 June 1994. This integrated view of the dynamics suggests
varying responses at the three stations. At Little Madeira Bay along the coastal interface between
Florida Bay and the confluence of Taylor Slough, the MOI exhibits an increasing oceanic influence from
1994–2004 followed by a stable, but still negative MOI over the 2004–2013 period punctuated by the
2005 freshwater event. At the Taylor River station a stable, near-zero MOI from 1994–2000 transitioned
to a steady decline from 2000–2012, followed by an increasing trend. At station E146 in Taylor Slough,
the cumulative MOI has been steadily increasing since 1994.
Our interpretation of these results is that northern Florida Bay has been transitioning away from
a freshwater marsh estuarine environment towards a marine environment over the last two decades.
While this transition appears to be essentially continuous in Little Madeira Bay since 1994, at the lower
reach of Taylor Slough (TR), hydrologic cycles appear to be transforming from marsh-dominated
dynamics to ocean-dominated since 2000. These shifts in hydrologic cycles are consistent with
increasing mean sea level (Figure 12) and the onset of accelerated water level exceedances as sea
level rises (Figure 10). In the middle-reaches of Taylor Slough represented by station E146, there
were periods of negative MOI during 2003 and 2006 (Figure 13) reflected in a stasis of the integrated
MOI over this period (Figure 14), but the overall assessment is that there is no evidence of emerging
ocean-dominated hydrologic cycles.
J. Mar. Sci. Eng. 2017, 5, 31 16 of 26
Figure 14. Integral over time of the Marsh-to-Ocean Index (MOI) at: (a) Little Madeira Bay (LM);
(b) Taylor River (TR); and (c) Taylor Slough (E146).
4. Discussion
South Florida is ranked ninth globally among urban areas with human populations exposed to sea
level rise impacts and first in terms of exposed assets [28]. South Florida is equally rich in natural assets
with national parks circumscribing the southern peninsula protecting vital freshwater ecosystems that
sustain both natural and human biomes. The exceedingly flat topography and low elevations provide
ideal conditions for the expansion of marine bays and estuaries into existent freshwater marshes, civil
infrastructure and human habitats, issues recognized by regional governments planning for future sea

illuminating inferences can be made from this projection; for example, it suggests that regardless of

whether sea levels rise along the low or high trajectory, that between the years 2035 and 2045, mean sea

level exceedances will enter a phase of exponential growth. Under the high projection, it indicates that

circa 2050, mean sea level will be continuously above portions of the coastal ridge wherein one would

expect marine conditions to have displaced freshwater influences. If the low projection is realized,

then this transition is expected near 2070.

Such exceedance projections may therefore find utility in the identification of tipping points

where the transition to an exponential increase in saltwater inundation can be expected, as well as

demarcation of a time horizon upon which a fundamental transformation of the coastal environment

to submarine conditions will prevail.

Figure 11. Projected evolution of water level exceedances at Little Madeira Bay under the low and

high sea level rise scenarios. Mean water is the daily mean water level over the three-year period from

January 2014–December 2016.

3.3. Trends

Empirical mode decomposition of the water level and salinity data shown in Figures 3 and 4

provides a residual signal representing the time-varying trend after all oscillating modes are removed

as shown in Figure 12. Regarding salinity, Murray Key and Buoy Key in western Florida Bay exchange

waters with the Gulf of Mexico, as well as fresh water runoff from the coastal Everglades, but are

predominantly marine ecosystems. Seawater has a nominal salinity of 35 ppt, and we find that mean

Murray Key salinity has risen by 2.8 ppt from 32.7 in 1994 to 35.5 ppt in 2016, with values at Buoy Key

rising by 6.2 ppt from 30.6–36.8 ppt over the same period indicating that both stations are currently

experiencing higher mean salinity and lower freshwater mixing than was common 20 years ago. Little

Madeira Bay in the eastern coastal region is more influenced by freshwater runoff from the Everglades

and agricultural lands with its mean salinity increasing by 3.2 ppt from 22.4 ppt in 1994 to 25.7 ppt

in 2016.

Mean water levels are found to have increased in Florida Bay and the southern reaches of

Taylor Slough as shown in Figure 12. In Florida Bay, water levels at Buoy Key and Little Madeira

J. Mar. Sci. Eng. 2017, 5, 31 14 of 26

Bay have risen from 27.7 cm NGVD29 in 1994 to 32.7 cm in 2016, an increase of 5.0 cm, with similar

increases over the period observed at the Taylor Slough stations TR and E1462

.

Figure 12. Nonlinear trends of water level and salinity at hydrographic stations in Florida Bay and

Taylor Slough.

3.4. Marsh to Ocean Transformation

As described above, the MOI is designed to represent the relative similarity of a time series

spatially intermediate with respect to two reference time series representing oceanic and marsh

hydrology. Specifically, the relative similitude of water levels over the last three years at Little Madeira

Bay (LM) and within Taylor Slough at stations TR and E146, with respect to the oceanic reference

station of Buoy Key (BK) and marsh reference at station Taylor Slough Hilton (TSH), are shown in

Table 5. MOI values of −0.21 at Little Madeira Bay (LM), 0.02 at Taylor River (TR) and 0.34 in Taylor

Slough (E146) suggest that recent water levels at Little Madeira Bay follow the dynamics observed at

Buoy Key more closely than those of Taylor Slough (TSH), while levels at E146 are more similar to

TSH dynamics.

Table 5. Marsh-to-Ocean Index (MOI) values over the period 1 January 2014–31 December 2016

at stations LM, TR and E146 relative to the ocean-dominated station at Buoy Key (BK) and the

marsh-dominated station at TSH.

Station ω1 ω2 ω3 Ω µ1 µ2 µ3 M MOI

LM 0.00 0.62 0.00 0.62 0.00 0.00 0.00 0.00 −0.21

TR 0.46 0.38 0.00 0.84 0.32 0.58 0.00 0.90 0.02

E146 0.26 0.00 0.00 0.26 0.41 0.85 0.00 1.26 0.34

To assess changes in behavior over time, we apply the MOI to the three intermediate stations LM,

TR and E146 over a one-year moving window advanced in 10-day increments, as shown in Figure 13.

Also shown in Figure 13 is the monthly accumulation of streamflow measured at the confluence of

the Taylor River and Little Madeira Bay. This flow represents a fraction of total flow as freshwater

into Little Madeira Bay, but is representative of the annual hydrologic cycle driving marsh hydrology.

2

Ignoring the nonlinear nature of these trends, one might consider a linear mean water level rise of

5 cm/21 years = 2.4 mm/year, a result coincident with linear estimates of mean sea level rise over the 20th Century;

however, examination of the BK data found an increase over the last decade of 4.0 cm, suggesting a recent rate of 4 mm/year,

a value somewhat larger than current global estimates of 3.4 mm/year (https://sealevel.nasa.gov/) and an illustration of

difficulties in applying linear metrics to nonlinear processes.

J. Mar. Sci. Eng. 2017, 5, 31 15 of 26

For example, the large flow in 2005 associated with hurricanes Katrina and Wilma resulted in an

increase in MOI at Little Madeira Bay from negative to positive values. Overall, it is difficult to discern

patterns in the MOI dynamics, although it does appear that since 2012, MOI has remained largely

positive at the Taylor River (TR) and Taylor Slough (E146) stations.

Figure 13. (a) Monthly stream flow at the terminus of Taylor River; (b) Marsh-to-Ocean Index (MOI) in

Little Madeira Bay (LM) over a one year-long moving window advanced in 10-day increments; (c) MOI

at the Taylor River (TR) station; (d) MOI at the E146 station in Taylor Slough.

Since the effects of environmental and hydrologic perturbations on the biomes, landscapes and

ecosystems are cumulative, it makes sense to view the cumulative behavior of the time-varying MOI.

In Figure 14, we plot the time integral of the MOI shown in Figure 13, that is: R T

0 MOI(t) dt, where T

is a specific day past the data origin of 1 June 1994. This integrated view of the dynamics suggests

varying responses at the three stations. At Little Madeira Bay along the coastal interface between

Florida Bay and the confluence of Taylor Slough, the MOI exhibits an increasing oceanic influence from

1994–2004 followed by a stable, but still negative MOI over the 2004–2013 period punctuated by the

2005 freshwater event. At the Taylor River station a stable, near-zero MOI from 1994–2000 transitioned

to a steady decline from 2000–2012, followed by an increasing trend. At station E146 in Taylor Slough,

the cumulative MOI has been steadily increasing since 1994.

Our interpretation of these results is that northern Florida Bay has been transitioning away from

a freshwater marsh estuarine environment towards a marine environment over the last two decades.

While this transition appears to be essentially continuous in Little Madeira Bay since 1994, at the lower

reach of Taylor Slough (TR), hydrologic cycles appear to be transforming from marsh-dominated

dynamics to ocean-dominated since 2000. These shifts in hydrologic cycles are consistent with

increasing mean sea level (Figure 12) and the onset of accelerated water level exceedances as sea

level rises (Figure 10). In the middle-reaches of Taylor Slough represented by station E146, there

were periods of negative MOI during 2003 and 2006 (Figure 13) reflected in a stasis of the integrated

MOI over this period (Figure 14), but the overall assessment is that there is no evidence of emerging

ocean-dominated hydrologic cycles.

J. Mar. Sci. Eng. 2017, 5, 31 16 of 26

Figure 14. Integral over time of the Marsh-to-Ocean Index (MOI) at: (a) Little Madeira Bay (LM);

(b) Taylor River (TR); and (c) Taylor Slough (E146).

4. Discussion

South Florida is ranked ninth globally among urban areas with human populations exposed to sea

level rise impacts and first in terms of exposed assets [28]. South Florida is equally rich in natural assets

with national parks circumscribing the southern peninsula protecting vital freshwater ecosystems that

sustain both natural and human biomes. The exceedingly flat topography and low elevations provide

ideal conditions for the expansion of marine bays and estuaries into existent freshwater marshes, civil

infrastructure and human habitats, issues recognized by regional governments planning for future sea