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Ocean Engineering
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Analysis of the coastal Mississippi storm surge hazard
A.W. Niedoroda a,, D.T. Resio b, G.R. Toro c, D. Divoky d, H.S. Das e, C.W. Reed a
a
URS Corporation, 1625 Summit Lake Drive, Suite 200, Tallahassee, FL 32317, USA
US Army Corps of Engineers, ERDC-CHL, 3909 Halls Ferry Rd., Vicksburg, MS 39180, USA
Risk Engineering Inc. – William Lettis and Associates, 3 Farmers Row, Acton, MA 01720, USA
d
Watershed Concepts – AECOM Water, 2835 Brandywine Road, Suite 102, Atlanta, GA 30341, USA
e
Department of Civil & Environmental Engineering, Jackson State University, 1440 J. R. Lynch St., Jackson, MS 39217, USA
b
c
a r t i c l e in fo
abstract
Article history:
Received 25 November 2008
Accepted 26 August 2009
Following the extreme flooding caused by Hurricane Katrina, the Federal Emergency Management
Agency (FEMA) commissioned a study to update the Mississippi coastal flood hazard maps. The project
included development and application of new methods incorporating the most recent advances in
numerical modeling of storms and coastal hydrodynamics, analysis of the storm climatology, and flood
hazard evaluation. This paper discusses the methods that were used and how they were applied to the
coast of the State of Mississippi.
& 2009 Elsevier Ltd. All rights reserved.
Keywords:
Hurricane storm surge
Coastal flood hazard
Surge modeling
1. Introduction
In 2004, the Federal Emergency Management Agency (FEMA)
initiated a program to update the flood insurance rate maps for
the State of Mississippi. Soon after, Hurricane Katrina devastated
the State and refocused the study in several ways. Both Katrina
and Hurricane Rita contributed important new data regarding the
local climatology; high quality observations of flood elevations
were obtained throughout the region, and major erosion changes
were experienced on the coastal islands. Owing to the widespread property destruction, there was an urgent need to establish
accurate new maps expeditiously to assist the recovery efforts.
Hurricanes Katrina and Rita also galvanized related efforts for
coastal Louisiana. FEMA assigned the task of restudying the
Mississippi coastal areas to a team led by the URS Corporation, and
directed it to work closely with related efforts of the US Army Corps
of Engineers (Corps) already underway in the region. The project
teams worked closely together sharing data and methodology.
knowledge of the local climatology combined with numerical
hydrodynamic models capable of accurately simulating hurricane
storm surges throughout the coastal zone. A variety of simulation
approaches have been used in coastal flood studies; for this work,
a newly developed and highly efficient version of the Joint
Probability Method (JPM) was used.
In addition to a hydrodynamic model of the region, the
approach requires an understanding of the regional storm
climatology in order to define the characteristic storms to be
modeled. This is a challenging task owing to infrequent and
sporadic occurrence of large hurricanes and to the localized
nature of their peak surge effects.
2.2. Project components
The study consisted of seven major steps, as follows:
Characterization of the local hurricane climatology from the
historical record.
2. Approach
2.1. Basis of analysis
The paucity of gage data and the spatial variability of coastal
storm surge defeat attempts to base flood statistics on a
straightforward analysis of historical flood measurements. Accordingly, it is necessary to perform simulation studies using
Selection of a simulation set of synthetic storms and their rates
of occurrence.
Development of a detailed hydrodynamic model faithfully
representing the region.
Numerical simulation of the wind and pressure fields of the
synthetic storms and the resulting storm surges.
Estimation of the additional flood contributions associated
with wind waves and astronomic tide.
Determination of elevation–frequency curves at a dense network of points throughout the region.
Corresponding author. Tel.: + 1850 402 6349; fax: + 1850 402 6489.
E-mail address: [email protected] (A.W. Niedoroda).
Mapping of the coastal flood zones according to FEMA
standards.
0029-8018/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.oceaneng.2009.08.019
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2.3. Data sources
The major sources of storm data were: the National Oceanic
and Atmospheric Administration (NOAA) Atlantic basin hurricane
database (HURricane DATabase or HURDAT), NOAA Technical
Report NWS 38, Hurricane Climatology for the Atlantic and Gulf
Coasts of the United States (Ho et al., 1987), NOAA Technical
Memo NWS TPC-4 (Blake et al., 2006), NOAA Technical Memo
NWS TPC-1 (Hebert et al., 1996), and the National Hurricane
Center Tropical Cyclone reports for individual storms. Other
sources included: NOAA and US Air Force hurricane hunter
aircraft measurements, NHRD HWind analyses, NOAA buoy and
C-MAN stations, composite NWS radar imagery, Doppler radar PBL
flow velocity estimates, NOAA GOES visual, infrared, and water
vapor imagery, NCEP model wind fields, QUIKSCAT scatterometer
winds, and TOPEX altimeter winds and waves.
Additional information was obtained for Hurricanes Camille
and Betsy. This included the USACE Mobile District Hurricane
Camille Report (May 1970), the reports by Hamilton and Steere
(1969) and Oceanweather Inc. (2007), and the papers by Goudeau
and Conner (1968), Frank (1970), and Simpson et al. (1979).
2.4. The suite of numerical models
A number of models were required to simulate the governing
mechanisms. A Planetary Boundary Layer Model (PBL Model
TC-96) was employed to simulate the translating wind and
pressure fields of hurricanes. This model is described in Thompson
and Cardone (1996). Its input meteorological parameters include
the hurricane’s track, forward speed, radius of maximum wind,
barometric pressure distribution from the hurricane center to the
periphery, and the ambient pressure system through which the
hurricane is moving.
The Wave Action Model (WAM-Uniwave 3G) with a 10 km grid
size was used for deep-water waves. Extensive validation studies
have been previously performed for this model using measurements from notable historic storms including Audrey, 1957;
Bertha, 1957; Carla, 1961; Camille, 1969; Edith, 1971; Frederic,
1979; Danny, 1985; Juan, 1985 (Reece and Cardone, 1982); Lili,
2002 (Cardone et al., 2004); and Ivan, 2004 (Leverette et al.,
2005).
The SWAN model (ver. 40.51) described in Rogers et al. (2002)
was implemented with 72 directional bins and 26 frequency bins.
An offshore grid with 2.5 km grid spacing provided an interface
between the WAM grid and nine overlapping detailed nearshore
grids with 160 m grid elements extending from Alabama to
Louisiana. This model was forced by the PBL Model winds and
included outer boundary wave conditions from the WAM model
and the offshore SWAN model.
The ADCIRC hydrodynamic model (ver46.52.03) described in
Westerink and Luettich (1991) was used for simulations of the
storm surges. The model domain extended from an inland limit at
approximately the 9 m elevation contour, across the Gulf of
Mexico and Caribbean Sea to an open boundary in the midAtlantic. The grid had 900,450 nodes with elements ranging in
size between 80 m in areas of significant variation in the
topography and 2 km in the offshore areas near the coast, and
with a maximum size of about 45 km in the distant Atlantic. The
model is forced by the PBL wind and pressure fields. The model
input parameters are described in the ADCIRC Web site (http://
adcirc.org/documentv46/fort_13.hmtl.and/fort_15hmtl). For this
grid, the model required between 7 and 17 wall clock hours on
a large parallel CPU cluster to simulate an individual storm.
The PBL model was extensively tested and verified through
comparisons with recent storms including Hurricane Katrina
(2005). The WAM and SWAN models, used in combination, were
tested and verified against buoy observations taken offshore of
Mississippi during Hurricanes Georges (1998) and Katrina (2005).
More discussion of these models and the methods used to include
wave setup in the modeling can be found in Niedoroda et al.
(2008). The whole model framework including the ADCIRC
hydrodynamic model used in conjunction with these hurricane
and waves models was verified against measured coastal high
water marks taken after Hurricanes Betsy (1965) and Camille
(1969). The agreement between measurements and modeled
maximum surge heights was deemed acceptable. However, to
account for uncertainty arising from the differences between real
and modeled hurricane wind fields and the uncertainty introduced by the lack of skill of the overall modeling approach,
additional error terms were added to the representation of the
JPM integral, as described later in this paper (see discussion of the
random terms e3 and e4 in the Statistical Analysis Section).
Appropriate alternative methods and assumptions were developed and tested using the NOAA Sea, Lake, and Overland Surge
from Hurricanes (SLOSH) Model as a highly efficient diagnostic
tool (requiring only about two minutes per simulation, vs. many
hours with the primary ADCIRC model). SLOSH includes both
hurricane and storm surge simulations, adequately capturing the
major features of the surge; it does not, however, include the
additional effects of storm waves. NOAA provided a model grid
that is centered on Bay St. Louis including the coastal land areas
that are subject to storm surge flooding. This model was not used
in the detailed analyses. Instead, it was used for relative
comparisons to efficiently explore the sensitivity to changes in
synthetic storm selections and sufficiency of the selected set of
simulations.
3. Hurricane climatology
3.1. Storm parameters
In the JPM approach, storms are characterized parametrically,
with the likelihood of a particular storm (a particular combination
of the parameters) being defined by the observed statistics of
those parameters. To keep the dimensionality of the climatological model and of the JPM analysis from becoming too large, three
classes of parameters were defined. The first and the most
important parameter class included the central pressure deficit,
storm radius, track azimuth, forward speed, and landfall position.
These five fundamental parameters were treated by systematic
variation over representative ranges of values. The second class
consisted of Holland’s B parameter for which a defined pattern of
variation suggested by north-central Gulf of Mexico observations
was imposed; for storms with radii exceeding 10 nm B is typically
seen to vary from about 1.0 to about 1.3 as the storm traverses the
final 90 miles before landfall (Resio, 2007).
The third class of storm parameters includes secondary factors
contributing to the surge, or to the variability of the surge, that are
not explicitly accounted for in the modeling. These include
random departures of real storms from the idealized PBL
behavior; random surge variations not captured by the hydrodynamic model; and the random contribution of astronomic tide.
A series of sensitivity tests were run using the SLOSH model to
assess the variation of computed surge levels versus variations in
the five major storm parameters. A set of 147 diagnostic points
were distributed along the coast, in coastal valleys and lowlands,
and across uplands, representing all major topographic features.
These tests showed that central pressure deficit, proximity to the
landfall point, and storm radius dominated the surge response,
with track azimuth and forward speed having less significance.
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3.2. Period of record
Based on considerations of data quality, the period of record
was taken to be the 67 year span from 1940 through 2006. The
HURDAT database includes some information back to 1851. Very
few of the older observations apply to offshore conditions; the
older pressures may be unreliable; and storm radius is entirely
absent. Aircraft reconnaissance of hurricanes began during World
War II and permitted systematic observations of storms throughout the Gulf of Mexico. Since the initiation of those hurricane
hunter flights, the quality of storm data has continued to improve
as satellites, ocean data buoys, Doppler radar, and other
measurement systems have been introduced.
3.3. Simplified project shoreline
A version of the simplified shoreline used in NWS 38 was
adopted as a reference for track characterization. This is a
smoothed curve ignoring many of the unimportant details of the
actual shoreline, the most significant departure being the
truncation of the Mississippi River birdfoot delta. By eliminating
this low-lying wetland feature (small compared to the size of the
storms), ambiguity in characterizing the landfall point is avoided;
the simplified project shoreline is shown in Fig. 1.
3.4. Storm sample
Because hurricanes, especially powerful ones, are rare events
with widely varying behaviors, it is difficult to characterize the
local population from the local sample. One wishes to accept data
from as wide an area as possible in order to enlarge the sample
and thereby minimize sample error. On the other hand, the
characteristics of the underlying storm population are known to
vary over space, so that data taken from a wider area may fail to
accurately represent conditions at the site. Balancing these
opposing factors is a critical task in determining the storm
sample.
30°40°
3
The Mississippi Coastal Flood Hazard Project adopted a method
originally introduced by Chouinard and Liu (1997), (also see
Chouinard, 1992) to determine the local storm rate (storms/km/
year) and the pressure deficit distribution. Input data were taken
from a regional zone centered at a Mississippi coastal reference
point (CREF in Fig. 1). The sample included storms making landfall
between 85 and 95 W during the period from 1940 and 2006,
totaling 33 events in all. The Chouinard method assigns a weight
to each storm according to its distance from the CREF using a
Gaussian kernel function, and determines the optimal kernel
width (see Toro, 2008 for a full discussion). The kernel half-width
determined for storm rate and central pressure determinations
was 200 km; for track azimuth, the kernel half-width was 301.
The overall analysis was divided into two parts in order to
obtain a preliminary estimate of the 1% annual chance flood levels
needed for urgent planning purposes. The stronger storms, with
pressure deficits exceeding 48 mb, were simulated first, while
weaker storms with pressure deficits between 31 and 48 mb
were considered in a second group; in what follows, these are
referred to as the greater and lesser storm sets, respectively. Of the
33 storms in the sample, 15 were in the greater storm set, which
was expected to dominate surge at the 1% annual chance level and
above.
3.5. Storm rate
The storm rate for the greater storms was found to be 2.88E-4
storms per kilometer per year; the rate for the lesser storms was
determined to be 2.57E-4 storms per kilometer per year. These can
be added to obtain a total rate of 5.45E-4 storms/km/year for all
storms in the region having a central pressure deficit of 31 mb or
more.
3.6. Track azimuth
The analysis showed that the storm path heading at landfall
could be well-described by a beta distribution for the greater
storms, and by a normal distribution for the lesser storms. The
mean path was directed about 10 and 121 west of north, for the
greater and the lesser storms, respectively. These distributions are
illustrated in Figs. 2 and 3.
NWSS8
3.7. Central pressure deficit
CREF
30°20°
The Chouinard method was also used to determine the
probability distribution of the central pressure deficit, based on
data from the sources identified earlier. Some inconsistencies in
the central pressures reported by various data sources were
resolved through a detailed storm-by-storm review. The Chouinard analysis showed that the distribution of pressure deficit
could be satisfactorily represented by a two-parameter Weibull
Distribution. The distributions for greater and lesser families are
shown in Figs. 4 and 5.
30°
29°40°
3.8. Pressure scale radius
29°20°
29°
-89°40°
-89°20°
-89°
-88°40°
Fig. 1. The simplified project shoreline.
-88°20°
Either the radius to maximum winds (Rmax) or the pressure
scale radius (Rp) can be used to represent hurricane size.; the
parameter Rp is used in this paper. It is the input to the PBL model
that controls the dimensional scaling of the radial pressure
distribution. For typical hurricane sizes, most wind models yield
nearly identical values for the two radii, and many authors do not
distinguish between them.
There is considerable uncertainty about the degree to which
storm size (the radius to maximum winds or the pressure scale
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Fig. 5. Probability distribution of DP for lesser storms.
Fig. 2. Directional rates and beta distribution of storm heading for the greater
storms (DP 448 mb).
landfall in the north-central Gulf of Mexico showed no apparent
relationship between these parameters. However, a larger sample
of (Rp, DP) pairs for these storms over the entire Gulf of Mexico
does indicate that the pressure scale radius is inversely correlated
with the pressure deficit, in accordance with common supposition
and physical arguments. The trend suggested by the larger Gulfwide sample was used to define the conditional distribution of
storm radius for the greater storms, given the pressure deficit; the
relationship is illustrated with Fig. 6.
However, this relationship tends to over predict the pressure
radius when extended to the lesser storms. Consequently, a
second representation of the relationship between the radius and
the pressure deficit was developed using data from 1950 to 2006
(Fig. 7). This provided agreement with the trend adopted for the
greater storms (which control 1% or 100 year conditions), and
provides more realistic radii for the lesser storms. The conditional
distributions of Rp|DP were represented as lognormal functions.
3.9. Forward speed
Fig. 3. Directional rates and normal distribution of storm heading for the lesser
storms (31 mbo DPr 48 mb).
The forward speed of the storms at the time of landfall was
determined from their recorded positions in the 6 hour intervals
bracketing shoreline crossing. The data for both the greater and
the lesser storms were well approximated by lognormal distributions. The distributions are illustrated in Figs. 8 and 9.
3.10. Storm tracks
A series of sensitivity tests were carried out with the full PBLWAM-SWAN-ADCIRC model suite to investigate the distance from
shore over which the surge develops. As a result of these tests, it
was concluded that the surge simulations should commence 312
days before landfall (in addition to a 3 day model spin-up time
needed to establish antecedent conditions such as freshwater
inflow). Because wave setup was to be resolved explicitly in the
hydrodynamic simulation of each storm (rather than being
treated as a separate add-on) the PBL-WAM modeling involved
whole Gulf simulations. Three families of curved tracks similar to
those developed for the Corps IPET and LaCPR studies were used;
the rationale for those is given in Resio (2007).
Fig. 4. Probability distribution of DP for greater storms. The empirical distribution
was derived from the data, using weights determined with the kernel function. The
16th and the 84th percentiles indicate the uncertainty in the CCCDF.
radius) and central pressure deficit are correlated. The data are
very sparse, and relationships may be confounded by secondary
factors. A review of data for the greater storms at the time of
3.2. Landfall
As expected, the storm surge is usually greatest in the vicinity
of the greatest winds, and occurs about one storm radius to the
right of the landfall point; the surge height usually diminishes
rapidly to either side of that point. Consequently, the model
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Fig. 6. Data and regression for Rp vs. DP for greater storms using all Gulf of Mexico data. (Different symbols are used for data obtained North or South of 29.51 latitude in an
effort to detect trends associated with proximity to land (which corresponds approximately to 30.31 latitude for Mississippi)).
Fig. 8. Distribution of forward velocity Vf at landfall for the greater storms. The
histogram indicates the observed values and the smooth curve indicates the
lognormal model fit.
Fig. 7. Data and regression for Rp (offshore) vs. DP (coast) for lesser and greater
storms using all Gulf of Mexico data. The whole Gulf percentile curves obtained
earlier for the greater storms (Fig. 6) are also shown.
simulations need to include a large number of synthetic storm
tracks to properly represent conditions across the entire length of
the Mississippi coast. A separate sensitivity study was conducted
using the SLOSH model to establish the optimum spacing between
these synthetic storms, balancing the need to obtain accurate
results and to minimize the number of very lengthy hydrodynamic simulations. This sensitivity analysis showed that the
perpendicular spacing of tracks should be approximately equal to
the radius to maximum winds. It also showed that the track layout
for a given radius should extend at least one storm radius to the
east of Mississippi, and three to the west, and confirmed the
desirability of randomly shifting the track pattern for each radius.
Fig. 9. Distribution of forward velocity Vf at landfall for the lesser storms. The
histogram indicates the observed values and the smooth curve indicates the
lognormal model fit.
The patterns of tracks for the greater and the lesser storms are
shown in Figs. 10 and 11, respectively. Note that the sharp curves
at the bottom of these tracks are an artifact of the plotting
software.
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where l is the mean annual rate of storms of interest for that site,
fX ðxÞ is the joint probability density function of the defining storm
parameters, and P½ZðxÞ 4 Z is the conditional probability that a
storm with the specific characteristics x will generate a flood
elevation in excess of Z (a Heaviside function in the absence of any
uncertainties). Although the right-hand side of Eq. (1) is a rate
with units of l, for small values it is a good numerical
approximation of the probability on the left.
In practice, this multiple integral is approximated by a
summation over a discrete set of storm–parameter values, as in
P½Zmaxð1 yrÞ 4 Z n
X
li P½Zðx i Þ 4 Z
ð2Þ
i¼1
where each term in the summation corresponds to one combination of storm parameters (i.e., one synthetic storm with annual
rate li). In its most direct form of implementation, the JPM
requires a very great number of such simulations to accurately
integrate over the multi-dimensional parameter space. Each
parameter must be represented by several values, and the number
of parameter combinations to be simulated quickly becomes
unwieldy. In order to reduce the computational burden while
maintaining accuracy, a method of optimally sampling (OS) the
parameter space was developed, and is discussed next. This JPM–
OS approach involves selecting combinations of storm parameters
and their weights in such a way as to minimize the number of
simulations needed to obtain a given accuracy. It has been found
possible to reduce the conventional JPM effort by about an order
of magnitude.
Fig. 10. Synthetic storm tracks of the greater storms.
4.2. Development of the JPM–OS method for the
Mississippi FEMA project
Fig. 11. Synthetic storm tracks of the lesser storms.
4. Method for statistical analysis
4.1. Choice of method
The adopted approach was based on the JPM method, which
has been widely used in coastal flood studies by NOAA (Myers,
1975; Ho and Myers, 1975), FEMA, and others for many years.
Other approaches were considered, including Monte Carlo (MC)
methods and the Empirical Simulation Technique (EST: Borgman
et al., 1992; Scheffner et al., 1993). Monte Carlo methods are
generally inefficient for determination of extremes, and so were
not pursued. An EST approach was initially considered, but JPM
was chosen after coordination with both the Corps and FEMA, and
after it was determined that a JPM implementation could be
optimized so as to match EST in computational efficiency, while
preserving JPM’s advantages in statistical stability.
In the JPM approach, the conditional probability that a storm
with parameters x will generate a flood elevation exceeding Z at a
particular point can be expressed as
Z Z
P½Zmaxð1 yrÞ 4 Z ¼ l ::: fX ðxÞP½ZðxÞ 4 Zdx
x
ð1Þ
The approach followed by the URS team used a Gaussian
process Bayesian quadrature scheme based on the work of Minka
(2000), combined with more traditional numerical integration
methods. This approach optimizes the selection of the set of storm
parameters x i i and associated weights pi (from which the rates
li = lpi are computed; see Toro et al., 2010a). Because the approach
makes a number of assumptions regarding the correlation
structure of Z(:) and because it requires some inputs based on
expert judgment (i.e., the correlation distances associated with
various storm parameters), a number of candidate JPM–OS
combinations (differing in the numbers of synthetic storms and
in the values for the correlation distances) were defined and
tested against ‘‘reference’’ results that could be considered exact.
The Reference Case was developed for the greater storms and
consisted of an extended JPM analysis involving 2967 storm
simulations; these were performed using the SLOSH model as a
diagnostic tool. The results for the 100 and 500 year surge levels at
147 coastal and inland stations were compared for similar SLOSH
simulations using the several candidate JPM–OS storm sets.
Candidate Set 6 (designated as JPM-OS 6) was found to closely
replicate the Reference Case while requiring only 156 storm
simulations, and was chosen for simulation using the full suite of
the detailed models. The storm parameters for the JPM–OS 6
simulation set of the greater storms are given in Table 1.
Subsequent simulations of the lesser storms were based on the
parameters shown in Table 2.
Each of the greater and the lesser synthetic storms was
replicated on a number of parallel tracks, as described earlier,
so that a spatially smooth response estimate would be achieved.
Figs. 10 and 11 show these tracks near landfall for the greater
(152) and the lesser storms (76), respectively (slight adjustments
of track positions reduced the greater set from 156 to 152 storms).
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Table 1
Parameters of the JPM–OS-6 scheme for the greater storms.
Reference storm ID
DP (mb; coast)
Rp (nmi; offshore)
Vf (m/s)
h (degrees)
Probability
Annual rate (for each track)
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
66.69
57.17
49.72
57.17
57.17
92.95
78.59
78.59
78.59
78.59
70.02
78.59
128.7
103.7
103.7
103.7
103.7
94.47
103.7
18.61
39.82
22.93
10.83
20.77
14.7
30.8
16.56
8.904
16.56
17.98
16.56
11.66
25.3
13.6
7.313
13.6
14.53
13.6
6.047
6.047
6.047
6.047
6.047
5.943
6.014
4.349
6.014
14.54
5.943
4.346
5.943
6.014
4.349
6.014
14.54
5.943
4.346
38.91
13.49
38.92
13.49
56.66
12.81
12.82
47.33
12.82
12.86
12.82
71.04
12.81
12.82
47.33
12.82
12.86
12.82
71.04
1.33E-01
1.20E-01
1.33E-01
1.20E-01
1.08E-01
3.42E-02
5.34E-02
4.20E-02
5.34E-02
3.49E-02
3.42E-02
4.20E-02
1.06E-02
1.65E-02
1.30E-02
1.65E-02
1.08E-02
1.06E-02
1.30E-02
1.32E-03
2.55E-03
1.63E-03
6.94E-04
1.19E-03
2.68E-04
8.77E-04
3.71E-04
2.54E-04
3.08E-04
3.28E-04
3.71E-04
6.58E-05
2.23E-04
9.44E-05
6.44E-05
7.83E-05
8.20E-05
9.43E-05
Table 2
Parameters of JPM–OS scheme for the lesser storms.
Reference storm ID
DP (mb; coast)
Rp (nmi; offshore)
Vf (m/s)
h (degrees)
Probability
Annual rate (for each track)
01
02
03
04
05
06
07
08
09
10
11
12
13
46.38
37.75
44.28
40.71
31.78
32.11
34.67
47.53
42.09
34.67
44.28
37.75
37.04
41.59
53.63
21.64
12.72
44.24
17.19
24.32
16.94
27.82
24.31
21.64
53.63
29.79
5.42
3.00
3.40
4.93
4.88
6.10
6.94
4.38
3.71
2.46
10.50
7.89
6.64
8.758
23.55
63.87
9.324
11.27
31.22
71.07
31.63
59.19
5.25
13.83
45.75
46.64
4.74E-02
2.93E-02
7.61E-02
1.76E-01
3.92E-02
9.30E-02
8.75E-02
6.26E-02
9.49E-02
8.75E-02
7.62E-02
2.93E-02
1.01E-01
9.37E-04
7.47E-04
7.83E-04
1.06E-03
8.25E-04
7.60E-04
1.01E-03
5.04E-04
1.25E-03
1.01E-03
7.83E-04
7.46E-04
1.44E-03
4.3. Inclusion of the secondary terms
As noted earlier, certain secondary factors were accounted for
using an approximate method. These factors included the
astronomic tide, which occurs with random phasing and amplitude but which is small in the Mississippi vicinity, and other
random factors associated with secondary complexities of storms
and surge response. The relationship given in Eq. (2) can be
expanded to include these factors by inclusion of the term e:
P½Zmaxð1 yrÞ 4 Z n
X
li P½Zðxi Þ þ e 4 Z
ð3Þ
i¼1
In this project, the random term e included four components,
all considered Gaussian with zero means.
number of points for Hurricanes Katrina, Betsy and Camille; its
standard deviation was found to be 0.23 m.
e4—represents variations in the surge due to a wide range of
departures in the real behavior of hurricane wind and pressure
fields that are not represented by the PBL model. This was
evaluated by comparing the results of surge modeling done
using hand-crafted ‘best winds’ with the findings for the same
storms as represented using the PBL model. A standard
deviation of 0.36 m was found.
These four components of e are taken to be independent, and so
can be combined into a single term having a standard deviation
given (with obvious notation) by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð4Þ
se ¼ s2e1 þ s2e2 þ s2e3 þ s2e4
e1—represents the astronomical tide level as a random function of
time. It was estimated from a two-month Biloxi tide prediction,
and was characterized by a standard deviation of 0.2 m.
e2—represents variations in the surge response caused by
random variations of the Holland B parameter that are not
represented in the adopted pattern of variation. This term was
estimated as described by Resio (2007), and is represented by a
standard deviation of 0.15 times the local surge elevation.
e3—represents random errors in the computed surge caused by
lack of skill of the numerical modeling. This was evaluated by
comparing values of computed and measured surge at a large
5. Hurricane surge simulations
5.1. Storm simulation work flow
Each of the 228 synthetic storms was simulated with the
model suite consisting of the PBL storm model, the WAM model
for waves in the deep Gulf, the SWAN model for nearshore waves,
and the ADCIRC hydrodynamic model for the computation of the
storm surge. Since each of these models was set up and operated
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Fig. 12. Histogram generated for a single geographic point based on surges and event probabilities.
on an independent grid, various interpolations were needed to
convert the output from one model to input for the next.
In order to account for the effects of wave radiation stress
(responsible for wave setup) in the ADCIRC surge computation, a
two-step procedure was adopted. First, ADCIRC simulations
without wave effects were run using a grid of reduced resolution
and coverage in order to obtain first-order estimates of the water
elevations needed for wave simulations (since wave behavior is
sensitive to depth). Using these first-order water level estimates,
the wave models (driven by the PBL determinations of the time
histories of the wind and pressure fields for each storm) were
exercised to determine wave generation and behavior, and the
resulting variation of the radiation stresses; the deep Gulf
simulations obtained with WAM were used to define boundary
conditions for the higher resolution nearshore SWAN grids, Then,
in the second step of the surge calculation, the SWAN estimates of
the radiation stresses were imposed during new ADCIRC simulations performed on the high-resolution surge grid.
Fig. 13. Example of redistribution of the accumulated rate within single bin to
account for secondary random processes.
6. Hurricane surge frequencies
The calculation of still water elevations for given return
intervals was made at each of nearly 7000 output points covering
the Mississippi coastal flood plain. At each point, the ADCIRC
model simulations provided 228 peak surge heights, each with an
associated rate of occurrence.
The 228 results at each point were processed to determine the
surge elevations associated with the recurrence intervals of
interest (the 10, 2, 1, and 0.2% annual chance elevations). At each
site, a histogram of accumulated storm rate was constructed,
consisting of 600 2-cm-wide elevation bins spanning the surge
range from 0 to 12 m (well-above the highest anticipated 0.2%
surge). These histograms are approximations of the surge height
density distributions, similar to the example shown in Fig. 12.
The effect of the secondary Gaussian term e was then
accounted for by redistributing the contents of these bins in a
Gaussian pattern over the neighboring bins; the width of the
Gaussian redistribution was determined by the standard deviation
associated with the bin (different from bin to bin since the
standard deviation of the B-related term was taken to be
proportional to the surge elevation). An example of this
redistribution is shown in Fig. 13 for the contents of a single
bin. The result after redistribution of all bins is illustrated in
Fig. 14. Because a Gaussian distribution has infinite tails, any small
probability mass lost by dispersal beyond the range of the
histogram was allocated to the end bins.
The modified histogram was then summed from the highest
bin down to the lowest, resulting in an estimate of the cumulative
Fig. 14. Histogram following the application of the Gaussian redistribution (blue
line).
surge distribution, as illustrated in Fig. 15. The surge height for any
return period can be interpolated from this curve. For example,
the 100 year surge elevation corresponds to a cumulative rate of
0.01 occurrences per year, and is estimated to be about 4.5 m for
the case illustrated in the figure. The same procedure yields the
10, 50, and 500 year levels, corresponding to cumulative rates of
0.10, 0.02, and 0.002 occurrences per year.
As a final step, the 2%, 1%, and 0.2% annual chance surge
levels were compared to the corresponding results obtained
by the Corps (using different methods) during its concurrent
Please cite this article as: Niedoroda, A.W., et al., Analysis of the coastal Mississippi storm surge hazard. Ocean Engineering (2009),
doi:10.1016/j.oceaneng.2009.08.019
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9
References
Fig. 15. Annual exceedance rate and determination of the 100 year surge.
MsCIP project. The studies compared acceptably well and were
combined so as to produce a single best estimate for the
Mississippi coast.
It is worth noting that the Corps’ work in Louisiana and
Mississippi was done with a substantially different approach to
the optimal sampling of parameters within the JPM scheme. The
Corps approach was based on construction of a higher-dimensional response surface relating surge to storm parameters, rather
than use of a quadrature scheme of the sort used here. The
response surface method requires about the same number of
storm simulations as used with the quadrature scheme. The two
methods have been carefully compared and found to give surge
estimates of comparable accuracy when evaluated against a
reference standard (see Toro et al., 2010b). The fact that these
two independent approaches succeed in producing nearly identical surge estimates, serves to validate both.
7. Wave heights and flood zone mapping
An additional flood hazard is associated with the waves that
ride atop the still water elevation determined above. This
additional wave crest elevation was determined using FEMA’s
WHAFIS 4.0 program, following the procedures outlined in FEMA’s
Guidelines and Specifications (FEMA, 2003, 2007).
Acknowledgments
The authors express their appreciation for the extensive
discussions and technical exchanges with other members of the
URS/FEMA and USACE teams, particularly the late Leon Borgman,
Vince Cardone, Robert Dean, Donald Slinn, Todd Walton, Joannes
Westerink, John Atkinson, Lyle Zevenbergen, Andrew Cox, David
Levinson, Stephen Baig, Ty Wamsley, Jane Smith, Norm Scheffner,
Peter Vickery, and Lynda Charles. The URS project team included
not only staff from its Tallahassee FL and Gaithersburg MD offices,
but also, as subcontractors, Watershed Concepts (AECOM Water),
Dewberry, Risk Engineering, Oceanweather Inc (OWI), and Ayres
Associates. Essential project support was provided by Dr. Shabbar
Saifee and Mr. Robert Lowe of FEMA. Special appreciation is
expressed to Richard Sanborn for his technical assistance and
documentation efforts, including preparation of this manuscript.
This work was sponsored by FEMA under Contract HSFEHQ-06-J0018. The opinions expressed here are not necessarily those of the
US Government or the sponsoring agency.
Blake, E.S., Jarrell, J.D., Rappaport, E.N., Landsea, C.W., 2006. The deadliest, costliest,
and most intense United States hurricanes of this century (and other
frequently requested hurricane facts). NOAA Technical Memorandum NWS
TPC-4.
Borgman, L.E, Miller, M., Butler, L., Reinhard, R., 1992. Empirical simulation of
future hurricane storm histories as a tool in engineering and economic
analysis. In: Proceedings of the Fifth Intnational Conference on Civil
Engineering in the Ocean, ASCE, College Station, TX, November.
Cardone, V.J., Cox, A.T., Lisaseter, K.A., Szasbo, D., 2004. Hindcast of winds, waves
and currents in Northern Gulf of Mexico in Hurricane Lili (2002). In:
Proceedings of the Offshore Technology Conference, OTC 16821.
Chouinard, L.E., 1992. A statistical method for regional design wave heights in the
Gulf of Mexico. In: Proceedings of the Offshore Technology Conference, OTC
6832, Houston, TX.
Chouinard, L.M., Liu, C., 1997. Model for recurrence rate of hurricanes in Gulf of
Mexico. Journal of Waterway, Port, Coastal and Ocean Engineering 123 (3),
113–119.
Federal Emergency Management Agency, 2003. Guidelines and Specifications for
Flood Hazard Mapping Partners, Appendix D: Guidance for Coastal Flooding
Analyses and Mapping. Washington, DC. /http://www.fema.gov/plan/prevent/
fhm/gs_arch.shtmS.
Federal Emergency Management Agency, 2007. Atlantic Ocean and Gulf of Mexico
Coastal Guidelines Update. Washington, DC. /http://www.fema.gov/library/
viewRecord.do?id=2458S.
Frank, N., 1970, Atlantic tropical systems of 1969, Monthly Weather Review.
pp. 307–314.
Goudeau, D.A., Conner, W.C., 1968. Storm surge over the Mississippi River
delta accompanying Hurricane Betsy, 1965. American Meteorological Society
96 (2).
Hamilton, R.C., Steere, D.B., 1969. Ocean Gathering Program Report No. 2 Covering
Hurricane Camille (17 August 1969), Baylor CO. Consulting Report, October 8,
1969, 27 pp.
Hebert, P.J., Jarrell, J.D., Mayfield, M., 1996. The deadliest, costliest, and most
intense United States hurricanes of this century (and other frequently
requested hurricane facts). NOAA Technical Memorandum NWS TPC-1.
Ho F.P., Myers V.A. 1975, Joint probabilitiy method of tide frequency analysis
applied to Appalachicola Bay and St. George Sound, Florida, NOAA Technical
Report WS.18, 43 p.
Ho, F.P., Su, J.C., Hanevich, K.L., Smith, R.J., Richards, F.P., 1987. Hurricane
climatology for the Atlantic and Gulf coasts of the United States. NOAA
Technical Report NWS 38, Silver Spring, MD, April.
Leverette, S., Bian, S., Taberner, D., Van-der-Linden, C., 2005. Matterhorn SeaStar
Hurricane Ivan response. Deep Ocean Technology, Brazil, November 2005.
Minka, T.P., 2000. Deriving quadrature rules from Gaussian processes. Technical
Report, Statistics Department, Carnegie Mellon University. Available on-line at
/http://research.microsoft.com/ minka/papers/minka-quadrature.ps.gzS.
Myers, V.A., 1975, Storm tide frequencies on the South Carolina coast, NOAA
Technical Report NWS-16, 79p.
Niedoroda, A.W., Das, H., Slinn, D., Dean, R., Weaver, R., Reed, C., Smith, J. 2008. The
role of wave set-up during extreme storms. In: Proceedings of the 31st
International Conference on Coastal Engineering, 1, 250–261.
Oceanweather Inc., 2007. Hindcast wind and wave forcing in support of URS FEMA
Mississippi coastal flood map update. Consulting Report.
Reece, A.M., Cardone, V.J., 1982. Test of wave hindcast model results against
measurements during four different meteorological systems. In: Proceedings
of the Offshore Technology Conference, OTC 4323.
Resio, D.T., 2007. White Paper on Estimating Hurricane Inundation Probabilities. US
Army Corps of Engineers Engineer Research and Development Center,
Vicksburg, MS.
Scheffner, N., Borgman, L., Mark, D., 1993. Empirical simulation technique
applications to a tropical storm surge frequency analysis of the coast of
Delaware. In: Proceedings of the Third International Conference on Estuarine
and Coastal Modeling.
Simpson, R.H., Sugg, A.L., Clark, G.B., Frank, N.L., Hope, J.R., Hebert, P.J., Kraft, R.L.,
Pelissier, J.M., 1979. The Atlantic Hurricane Season of 1969, Monthly Weather
Review, pp. 293–306.
Toro, G., Niedoroda, A.W., Divoky, D., Reed, C.W., 2010a, Quadrature-based
approach for the efficient calculation of surge hazard, Ocean Engineering, this
issue, doi:10.1016/j.oceaneng.2009.09.005.
Toro, G., Resio, D.T., Divoky, D., Niedoroda, A.W., Reed, C.W., 2010b, Efficient joint
probability methods for hurricane surge frequency analysis, Ocean Engineering, this issue, doi:10.1016/j.oceaneng.2009.09.004.
Toro, G., Resio, D.T., Divoky, D., Niedoroda, A.W., Reed, C.W., in press-b.
Efficient joint probability methods for hurricane surge frequency
analysis. Journal of Ocean Engineering, Special Edition, submitted for
publication.
Thompson, E.F., Cardone, V.J., 1996. Practical modeling of hurricane surface wind
fields. Journal of Waterway, Port, Coastal, and Ocean Engineering July/August,
195–205.
Westerink, J.J., Luettich, R.A., 1991. Tide and storm surge prediction in the Gulf of
Mexico using model ADCIRC-2D. Report to the US Army Engineer Waterways
Experiment Station, July 1991.
Please cite this article as: Niedoroda, A.W., et al., Analysis of the coastal Mississippi storm surge hazard. Ocean Engineering (2009),
doi:10.1016/j.oceaneng.2009.08.019