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patrickbdevaney
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mia9

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IMFMi
(2)
where IMFΩ represent ocean-dominated empirical basis functions, IMFM marsh-dominated basis
functions, L the IMF mode number of the lowest frequency mode or residual, H the mode number of
the highest frequency mode and ωi and µi fit coefficients determined by a nonlinear quasi-Newton
minimization of the variance of the difference between the weighted sum of the empirical basis
functions, W(t), and the target time series (low pass signal of station LM, TR or E146 shown in
Figure 5) [25].
The resultant coefficient vectors ω and µ are summed to produce an overall metric Ω = ∑ ωi
,
M = ∑ µi representing the ocean or marsh influence. For example, with N = 3 empirical basis
functions and using the Buoy Key (BK) time series as the target, all ωi equal 1 with the result Ω = 3,
M = 0, while if TSH is the target then Ω = 0, M = 3. To construct a relative metric denoted as the
Marsh-to-Ocean Index (MOI), we normalize the difference of the two influence metrics by the number
of basis functions N:
MOI =
M − Ω
N
(3)
so that a water level signal identical with that of Buoy Key (BK) would express MOI = −1, while a
station with a signal equivalent to the upper reach of Taylor Slough (TSH) would produce MOI = 1.
The MOI discriminates between ‘oceanic’ and ‘marsh’ water level variations based on the
assumption that variations in the designated ocean signal represent ocean forcing, and likewise for the
marsh signal. Implicitly, a storm surge elevating coastal water levels at the ocean station is characterized
as an ocean influence, while a runoff event from storm rainfall at the marsh station is attributed as a
marsh water level forcing. Here, we are interested in assessing long-term transformations in hydrologic
responses, basing MOI low-pass signals on intra-annual and longer cycles. The MOI methodology is
general such that inclusion of higher-frequency IMFs that resolve temporally-compact events should
J. Mar. Sci. Eng. 2017, 5, 31 9 of 26
be properly accounted for as originating from either the oceanic or marsh reference signals. The time
period over which the ocean and marsh basis functions are fit to the intermediate station can also be
varied to emphasize shorter-term events or longer-term processes.
3. Results
3.1. Inundation Maps for Mean Sea Level
Figures 7 and 8 present mean sea level inundation maps for the southern Florida peninsula and
Dry Tortugas. Blue shadings represent the extent of projected mean sea level inundation at the four
time horizons of 2025, 2050, 2075 and 2100. Grey areas indicate elevations higher than the expected
mean sea level at 2100. Note that the low and high projections do not share a common legend such that
the shade of blue corresponding to a specific land elevation is not shared between the low and high
projections; however, the time horizon at which mean sea level reaches an elevation does correspond
to the same shade of blue in both projections. Digital versions of the inundation maps are available in
the Supplementary Materials.
2100
2075
2050
2025
ENP
BNP
2015
2100
2075
2050
2025
ENP
BNP
2015
High (99th Percentile)
Low (50th Percentile)
Elevation NAVD88
cm
-14.8 (2015)
-8.1 (2025)
11.4 (2050)
35.8 (2075)
62.4 (2100)
>62.4
Bottom Types
Bank Top Suite
Major Canals
Major Roads
Elevation NAVD88
cm
-14.8 (2015)
-4.9 (2025)
26.2 (2050)
76.6 (2075)
146.2 (2100)
>146.2
Bottom Types
Bank Top Suite
Major Canals
Major Roads
Figure 7. Mean sea level elevation maps for South Florida including Everglades and Biscayne National
parks for the median (50th) and high (99th percentile) RCP 8.5 projections using current topography
and the NAVD88 datum. Tides and storm surges are not included in this projection.
J. Mar. Sci. Eng. 2017, 5, 31 10 of 26
Loggerhead Key
Low (50th Percentile)
Elevation NAVD88
cm
-14.8 (2015)
-4.9 (2025)
26.2 (2050)
76.6 (2075)
146.2 (2100)
>146.2
Elevation NAVD88
cm
-14.8 (2015)
-8.1 (2025)