Supplemental Material
The structure of this supplemental material is arranged as follows: Section 1 describes the
Coastal and Estuarine Storm Tide (CEST) model; Section 2 presents the process of refining the
model grid; Section 3 presents the algorithm for updating the water depths and Manning
coefficients of grid cells; Section 4 presents the linear addition by expansion inundation
algorithm; Section 5 shows computed peak storm surge heights (PSSHs) for 0, 0.6, and 1.05 m
SLRs using CEST and PSSHs derived using the linear addition by expansion method under
current and elevated sea levels; Section 6 examines the flooded heights, area, and volumes for
four representative regions; Section 7 analyzes the effects of inundation estimation methods on
exposed population and property.
1 The CEST model
The CEST model is a finite difference model developed by Zhang et al. (2008) to simulate storm
surge flooding induced by hurricanes. The CEST model is forced by winds, atmospheric
pressure drops, and astronomical tides or a time series of water levels at open boundaries. The
depth-averaged, two-dimensional CEST model operating over orthogonal curvilinear grids was
used to simulate storm surges in this study. In order to improve the computation efficiency and
stability of the model, a semi-implicit scheme is employed to produce a discrete form of the
control equations. Only the water pressure gradient and bottom friction items are solved
implicitly and the remaining terms are treated explicitly. The CEST model uses a mass-balanced
algorithm based on accumulated water volume to simulate wetting-drying processes (Zhang et al.,
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2008). The effect of the variation of land cover on the wind field and storm surge flow is
included by CEST through an adjustment factor in the calculation of the wind stress and an
empirical relationship for estimating Manning bottom friction coefficients (Zhang et al., 2012).
The model can also run on conformal grids such as those used by SLOSH, without modification
of the numerical algorithms. The comparison of modeled storm surges from SLOSH and CEST
and field measurements for historical hurricanes demonstrated that the CEST improved surge
simulations (Zhang et al., 2008). The inputs and outputs of the CEST model are in NetCDF
format (http://www.unidata.ucar.edu/software/netcdf/). A set of tools in MATLAB
(www.mathworks.com) have been developed to convert input files created in ArcGIS
(www.esri.com) into NetCDF files and to convert output NetCDF files into ArcGIS shapefiles
for displaying and analyzing simulated surges.
2 Refining the SLOSH basin
The resolution of the original SLOSH grid for the Miami Basin is about 0.6-0.7 km along the
coastal area. This resolution is too coarse to resolve many linear features such as navigation
channels, rivers, and barrier islands that are critical to model storm surges in Biscayne Bay and
adjacent areas (Fig. S1). The SLOSH model introduces subgrid features such as barriers and one
dimensional flow to incorporate the effects of linear features on storm surges, but the
representation of the linear features is not accurate due to a coarse resolution. Additionally, the
utilization of a coarse grid smoothes out local changes of topography that are important for
quantifying the inundation extent in a low relief area. In order to improve the representation of
linear features in the model domain, a refined grid was generated by reducing the cell size of the
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original SLOSH grid by a factor of four (Fig. S1). The elevations of the ocean cells in the model
basin were calculated by interpolating the elevations of original SLOSH cells, while the
elevations of the land cells were updated using the light detection and ranging (LiDAR) data
collected by the Florida Division of Emergency Management in 2007
(http://www.floridadisaster.org/gis/lidar/). The shapes of barrier islands at Miami Beach and
navigation channels next to Dodge Island are clearly resolved in the refined grid, making it
unnecessary to utilize subgrid features such as barriers and canals to represent many linear
features with widths less than cell sizes of the original SLOSH grid.
The refined grid also allows better representation of the complex river and canal systems in
South Florida (Fig. S1). This was achieved by first creating a shapefile in ArcGIS
(www.esri.com) for the edges of flow cells by intersecting canal and stream polygons with the
cell edges of the model grid. Then, the width of a river or canal on a flow cell edge was
calculated and assigned into the associated attribute table of the shapefile for flow cell edges.
Finally, automatically generated cell edges for rivers and canals were edited in ArcGIS to
remove redundant edges or add new edges to maintain the connection of flow cells. The effects
of flood control gates can also be included into the simulation by adding the gate elevations to
the edges of flow cells.
3 Algorithm 1: updating the water depths and Manning coefficients of grid cells
Given topographic elevations of all model cells and the magnitude of SLR.
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(1) Create a set of indicators for grid cells. If the topographic elevation of a grid cell is lower
than the elevated sea level, the indicator for the cell is set to be 1 (which represents a wet cell).
Otherwise, the indicator is 0 (which represents a dry cell).
(2) Find ocean and inundated land cells by the elevated sea level through examining the
connection of a wet grid cell with its neighbors and label the connected cells with a patch
indicator (e.g., 1) until no connected wet cells can be found. The number of the neighboring
cells of a grid cell is usually set to be either 4 or 8, which is often employed in the digital image
processing (Wilson and Ritter, 2001).
(3) Increase the value of the patch indicator by one (e.g., 2) and repeat Step 2 until all wet cells
are labeled with patch indicators.
The largest labeled patch represents the ocean and inundated land area by the elevated still water
level in the model domain. The water depths of the grid cells in this area were updated by
adding the SLR magnitude to the original water depths. The Manning coefficients were set up to
be equal to the value for the ocean bottom. The remaining labeled patches represent low-lying
land areas separated from the ocean by high elevation barriers. The water depths and Manning
coefficients for the grid cells in those patches remain unchanged.
4 Algorithm 2: estimating inundation using the linear addition by expansion method
Given base case PSSHs for all model grid cells with a missing flag value (e.g., -9999) for the
cells that are not inundated by current storm surges, topographic elevations of all grid cells, and
the magnitude of SLR.
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(1) Find an inundation set of wet cells that consist of the ocean and the inundated land area by
base case storm surges using Algorithm 1. Add the SLR magnitude to PSSHs of the cells in the
inundation set.
(2) Create a set of indicators, which represent wet cells with values of 1 and dry cells with values
of 0, respectively, for all grid cells in the first iteration. Find dry boundary cells between the
inundated and dry land areas by searching all dry cells based on the indicator value of a grid cell
and indicator values of its neighboring cells. If the sum of the indicator values of a dry cell and
its neighbors is larger than zero and less than or equal to the number of neighbor cells, the grid
cell is a dry boundary cell, otherwise, it is a regular dry cell.
(3) Expand the set of inundation cells by changing dry boundary cells into wet cells. Whether a
dry boundary cell becomes wet by surge inundation under an elevated sea level is determined by:
H
n  nT
1 n
 Hi
n i 1
H  D  dT
(1)
where H is the PSSH of the dry boundary cell estimated by averaging PSSHs (Hi) of its n
neighboring wet cells. D is the topographic elevation of the dry boundary cell. Parameter nT is
the minimum number of neighboring wet cells of the dry boundary cell and dT is the minimum
water depth for inundation. Set the indicators for the wet cells converted from dry boundary
cells to be 1.
(4) Repeat steps (2)-(3) until no dry boundary cells can be added into the inundation set.
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This method removes the jump in PSSHs between the area flooded by base case surges and the
inland area inundated by an elevated sea level. However, if the threshold value nT is small (e.g.
=1), the inundation extent will be largely exaggerated because the ocean water can flow to any
low-lying inland cells that only have a narrow connection to the cells in the inundation set.
Connection experiments show that a reasonable inundation result can be achieved by using the 4way-connected neighbors of a grid cell, and setting nT to be 2 and dT to be zero.
5 Storm surges modeled by CEST and derived by the linear addition by expansion method
Fig. S2 shows that computed PSSHs for 0, 0.6 and 1.05 m SLRs using the CEST model. Fig. S3
shows the PSSHs computed using the linear addition by expansion method along four profiles.
In comparison of these PSSHs with the PSSHs from the simple linear addition method (Fig. 2),
the linear addition by expansion method successfully eliminates abrupt changes in PSSHs for
elevated sea levels. The overall pattern of PSSHs from the linear addition by expansion method
is similar to that for PSSHs from simple linear addition method.
6 Flooded heights, areas, and volumes for four representative regions
Analysis of PSSH changes along profiles and inundation maps shows that the magnitudes of the
nonlinear interaction between storm surges and SLR vary spatially. In order to examine the
spatial differences in a regional scale, four regions in the study area including the open water
next to Biscayne Bay, Biscayne Bay, the mainland by the Bay, and the barrier island including
Miami Beach (Fig. S4) were selected to further compare the effects of SLR on storm surges.
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The three indices including flooded volume (V), flooded area (A), and average PSSHs ( h ) were
computed for each region.
N
V   hi ai
i 1
N
A   ai
i 1
h
V
A
(2)
where hi is the PSSH at a grid cell referenced to NAVD 88 and ai is the area of the grid cell.
Similar to the definition of Rego et al. (2008), the flooded volume for a land area does not
represent the volume of the inundation water, instead it includes both the volume of inundation
water and the volume of the land above NAVD 88.
Fig. S5 shows that the flooded volumes for Biscayne Bay and the open ocean outside Biscayne
Bay increase linearly as sea level rises. The flooded volumes generated using numerical
simulations are slightly lower than those generated using the simple linear addition and the linear
addition by expansion methods. Since the flooded areas of these two sites do not change
between the current and elevated sea levels, smaller flooded volumes from numerical simulations
indicate that the average PSSHs reduce slightly as sea level rises. The reason for this reduction
is that the PSSHs are inversely related to the water depth (Mousavi et al., 2011).
The flooded volumes for the mainland by Biscayne Bay from numerical simulations exhibit an
almost linear trend as sea level rises. However, the trend deviates remarkably away from the
flooded volumes from the simple linear addition and the linear addition by expansion methods.
The linear addition by expansion method produces higher flooded volumes than those from the
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simple linear addition method. The changes in flooded areas from numerical simulations exhibit
a weak fast-slow-fast pattern (Fig. S6). This pattern matches with the distribution of land areas
versus elevations (Fig. S7a), which indicates that the land area above a given elevation has a fastslow-fast change pattern for elevations less than 3 m. The flooded areas from numerical
simulations are 16-30% larger on average than those from two linear addition methods.
Comparison of the flooded areas from the simple linear addition and the linear addition by
expansion methods shows that these two methods estimate similar inundation areas with the
values from the linear addition by expansion method slightly larger in the initial SLR stage and
the values from the simple linear addition method slightly larger in the subsequent SLR stage.
However, the average PSSHs from the linear addition by expansion method are larger than those
from the simple linear addition method in most stages. The average PSSHs from numerical
simulations are 22-24% higher on average than those from the simple linear addition and linear
addition by expansion methods, indicating a nonlinear interaction between storm surges and SLR.
The flooded volumes from numerical simulations for the barrier island including Miami Beach
exhibit a strong nonlinear increase trend (Fig. S8). The flooded volumes from the linear addition
by expansion method better approximate the flooded volumes from numerical simulations than
do those from the simple linear addition method. The flooded areas for the barrier island
including Miami Beach show a nonlinear pattern with slow inundation in the initial stage and
rapid inundation in the later stage (Fig. S9), while the average PSSHs have a near-linear trend.
This occurs because the land area hypsometric curve of the barrier island changes little during
the initial rise of the elevation and rapidly as the elevation exceeds 0.6 m (Fig. S7b). The
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flooded areas with SLR magnitudes less than 0.6 m are small and the flooded areas increase
rapidly as the SLR magnitudes exceed 0.6 m.
7 Effects of inundation estimation methods on exposed population and property
Large differences in inundated areas and magnitudes occur when numerical simulation and linear
addition methods are employed to estimate surge flooding in the mainland area by Biscayne Bay
and the barrier island including Miami Beach as sea level rises. These differences can cause a
large deviation in estimation of exposed population and property to storm surge flooding in the
future. The exposed population properties for various scenarios were calculated based on the
centroids of the 2010 census block, the 2007 property parcels, and surge inundation polygons
using the method developed by Zhang (2011). Fig. S10a shows accelerations in increases of
exposed population derived using the simple linear addition, the linear addition by expansion,
and numerical simulation methods as sea level rises. The population exposed to storm surge
flooding are about 70,000, 80,000, 100,000 with the 0.3 m SLR for three methods, respectively,
while the exposed population with the 1.05 m SLR reach 90,000, 140,000, and 210,000,
respectively. The differences in exposed population from these three methods increase as the
magnitude of SLR becomes larger.
The population exposed to storm surge flooding for a given SLR scenario is determined by the
size of the inundation area and the spatial distribution of the population versus elevation. The
inundated areas versus SLR magnitudes (Fig. S6) from hydrodynamic simulations exhibit a
slight deceleration trend, but the exposed population versus SLR magnitudes shows an
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acceleration trend. This occurs because the majority of the population in the mainland by
southern Biscayne Bay is located within the area with elevations 0.3 m higher than NAVD88,
indicating another layer of nonlinear interaction between the population and inundated areas.
Note that the difference between inundated areas from the simple linear addition and the linear
addition by expansion methods is relatively small, as shown in Figure S6. However, the exposed
population from these two methods are considerably different (Fig. S10a). A careful
examination of the inundation polygons from these two methods indicates that the simple linear
addition method produces more inundation in the southern portion of the mainland area where
the elevation is lower. By contrast, the linear addition by expansion method produces less
inundation area over the same portion because the conversion of a dry boundary cell into a wet
one in expansion process requires that there are at least two wet neighbor cells of the dry
boundary cell, which reduces the inundation extent. Also, in this portion, most areas are
occupied by marsh and there are few people living there. The linear addition by expansion
method produced more inundation areas in the northern portion of the mainland where the
elevation is higher and population density is larger. Therefore, the exposed population from the
simple linear addition method and that from the linear addition by expansion method are
remarkably different from each other even though there is a small difference in total inundated
areas from both methods.
The exposed property versus SLR magnitudes in the mainland area exhibit patterns similar to the
patterns for population, with the values from the linear addition by expansion being closer to the
values from the numerical simulation method (Fig. S10b), indicating the nonlinear interaction
between spatial distribution of the inundation areas and exposed property. The exposed
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population and property for the barrier island including Miami Beach exhibit even faster
acceleration in increase trends (Fig. S11). The exposed population and property from the linear
addition by expansion method is close to that from the numerical simulation method, while the
exposed population and property from the simple linear addition method is considerably different
from those from these two methods. The major reason for this phenomenon is that the
inundation extents from the linear addition by expansion method approximate the flooded extents
from numerical simulations better (Fig. S9).
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References
Mousavi ME, Irish JL, Frey AE, Olivera F, Edge BL (2011) Global warming and hurricanes: the
potential impact of hurricane intensification and sea level rise on coastal flooding. Climatic
change 104:575-597.
Rego JL, Li C (2008) On the importance of the forward speed of hurricanes in storm surge
forecasting: a numerical study. Geophysical Research Letters 36:1-5.
Wilson J, Ritter G (2001) Handbook of Computer Vision–Algorithms in Image Algebra. CRC
Press, p. 417.
Zhang K (2011) Analysis of non-linear inundation from sea-level rise using LIDAR data: a case
study for South Florida. Climatic change 106:537-565.
Zhang K, Liu H, Li Y, Xu H, Shen J, Rhome J, Smith III TJ (2012) The role of mangroves in
attenuating storm surges. Estuarine, Coastal, and Shelf Science 102-103:11-23.
Zhang K, Xiao C, Shen J (2008) Comparison of the CEST and SLOSH models for storm surge
flooding. Journal of Coastal Research 24:489-499.
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Figure Captions
Fig. S1 The cells of the refined model grid covering Dodge Island, Miami Beach, and Miami
River. The channel lines represent the cell edges where the water depths are adjusted based on
channel widths to allow the water pass through the edges. The refined grid was generated by
reducing the cell size of the original SLOSH grid by a factor of four.
Fig. S2 The computed PSSHs caused by Hurricane Andrew with (a) the current sea level, (b) 0.6
m SLR, and (c) 1.05 m SLR. The PSSHs are referenced to NAVD 88.
Fig S3 The computed PSSHs for the current sea level (green), 0.6 m SLR (blue), and 1.05 m
SLR (red) along four profiles. The solid circle represents the PSSHs computed by the CEST
model, while the empty square represents the PSSHs derived by the linear addition by expansion
method.
Fig S4 Locations of Biscayne Bay, the mainland by the bay, the open ocean next to Biscayne
Bay, and the barrier island including Miami Beach.
Fig S5 The flooded volumes for Biscayne Bay, the mainland area by Biscayne Bay (Biscayne
Inland), and the open ocean outside Biscayne Bay (Ocean Outside Biscayne). The line with
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solid circles represents the flooded volumes from numerical simulations. The line with empty
squares represents the flooded volumes derived by the simple linear addition method. The dotted
line with empty diamonds represents the flooded volumes derived by the linear addition by
expansion method.
Fig S6 The flooded areas (blue) and average PSSHs (purple) for the mainland by Biscayne Bay.
The solid line with circles represents the flooded areas and average PSSHs from numerical
simulations. The dashed line with squares represents the flooded areas and PSSHs derived by
the simple linear addition method. The dotted line with diamonds represents the flooded areas
and average PSSHs derived by the linear addition by expansion method.
Fig S7 The histograms (purple line) of land areas over elevations and hypsometric curves (red
line with plus symbols) (a) for the land areas of the mainland by Biscayne Bay and (b) for the
barrier island including Miami Beach. The left Y axis is for land area, while the right Y axis is
for cumulative land area.
Fig. S8 The flooded volumes for the barrier island including Miami Beach. The solid line with
circles represents the flooded volumes from numerical simulations. The dashed line with squares
represents the flooded volumes derived by the simple linear addition method. The dotted line
with empty diamonds represents the flooded volumes derived by the linear addition by expansion
method.
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Fig. S9 The flooded areas (blue) and average PSSHs (purple) for the barrier island including
Miami Beach. The solid line with circles represents the flooded areas and average PSSHs from
numerical simulations. The dashed line with squares represents the flooded areas and PSSHs
derived by the simple linear addition method. The dotted line with diamonds represents the
flooded areas and average PSSHs derived by the linear addition by expansion method.
Fig. S10 (a) The inundated population and (b) property for the mainland by Biscayne Bay. The
solid line with circles represents the population and property affected by storm surges from
numerical simulations. The dashed line with circles represents the population and property
affected by the surge flood derived by the simple linear method. The dotted line with circles
represents the population and property affected by the surge flood derived by the linear addition
by expansion method.
Fig. S11 (a) The inundated population and (b) property for the barrier island including Miami
Beach.
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