The Estimation of Very-Low 

Probability Hurricane Storm 

Surges for Design and 

Licensing of Nuclear Power 

Plants in Coastal Areas

Office of Nuclear Regulatory Research

NUREG/CR-7134
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p 

The Estimation of Very-Low 

Probability Hurricane Storm 

Surges for Design and 

Licensing of Nuclear Power 

Plants in Coastal Areas

Manuscript Completed: May 2012

Date Published: October 2012

Prepared by

Donald T. Resio, Ty V. Wamsley, Mary A. Cialone, 

and T. Christopher Massey

U.S. Army Engineer Research and Development Center

Coastal and Hydraulics Laboratory

3909 Halls Ferry Road

Vicksburg, MS 39180 

John Randall, NRC Project Manager

NRC Job Code N6676

Office of Nuclear Regulatory Research

 

NUREG/CR-7134

iii

Abstract

Design criteria for nuclear power plants require, in part, that structures, systems, and 

components important to safety be designed to withstand the effects of natural phenomena, 

including floods, without loss of capability to perform their safety functions. The objective of this 

project is to provide the NRC with a technical basis for estimating probable maximum water 

levels due to storm surge from extreme events along the southern coast of the U.S. A review of 

the existing guidance was conducted and limitations in the technical basis for estimating storm 

surge identified. Required updates based on the most recent data available and state-of-thepractice analysis methods, tools, and models are recommended for NRC consideration. A 

deterministic-probabilistic approach for estimating very-low probability hurricane storm surges 

for design and licensing of nuclear power plants in coastal areas is developed. The proposed 

approach determines which factors affecting hurricane surges can be shown to have asymptotic 

upper limits and which factors should be treated within a context that allows for natural 

uncertainty in estimating an upper limit for surges at a specified site. The proposed approach is 

demonstrated through application at three nuclear plant sites. A screening method is also 

developed to determine if a prospective site is at risk of flooding from coastal storm surge. The 

proposed screening method includes criteria for proceeding or not proceeding to more detailed 

definitions of design-basis storm surges and explicitly considers local conditions and bathymetry 

that may affect water level estimates.

v

FOREWORD

This report documents work sponsored by the U.S. Nuclear Regulatory Commission (NRC) as 

part of the research project “Research to Develop Guidance on Probable Maximum Storm 

Surge Flood Estimates along the U.S. Southern Coast”. The objective of the project was to 

provide the NRC with modern, state-of-the-practice methods for hurricane storm-surge 

estimation. The methods described in this report represent significant advances that have been 

made in hurricane storm surge estimation since the relevant NRC guidance on design-basis 

flood estimation (Regulatory Guide 1.59, “Design Basis Floods for Nuclear Power Plants,”

Revision 2) was last updated in 1978. The work and recommendations presented in this report 

will be considered by the NRC as it updates Regulatory Guide 1.59.

This report provides example calculations to illustrate use of the state-of-the-practice technical 

basis for deriving low-probability storm surge estimates. The example calculations are 

performed for three locations near existing nuclear power plants. However, the report does not 

make detailed, site-specific comparisons between surge estimates used for licensing of the 

existing power plants at these locations and the example surge estimates derived using the 

proposed methods. It would not be appropriate to draw conclusions about the adequacy of 

flood protection for existing plants based on the example calculations in this report. It should be 

noted that, as part of the its overall response to the March 2011 Fukushima accident, the NRC 

has issued a request for information to all power reactor licensees and holders of construction

permits under 10 CFR Part 50 on March 12, 2012. The March 12, 2012 50.54(f) letter includes 

a request that respondents reevaluate flooding hazards at nuclear power plant sites using 

updated information and present-day regulatory guidance and methodologies. 

Richard Correia, Director

Division of Risk Analysis

Office of Nuclear Regulatory Research

vii

TABLE OF CONTENTS

Section Page 

ABSTRACT................................................................................................................................ iii

FOREWORD ..............................................................................................................................v

LIST OF FIGURES ....................................................................................................................ix

LIST OF TABLES..................................................................................................................... xiii

ABBREVIATIONS AND ACRONYMS .......................................................................................xv

1.0 INTRODUCTION.............................................................................................................1 

2.0 REVIEW OF EXISTING GUIDANCE...............................................................................3

2.1 Probable Maximum Hurricane Surge Estimate ..........................................................3

2.2 Meteorological Criteria for a Probable Maximum Hurricane .......................................6

2.3 Uncertainty ..............................................................................................................11

2.4 Recommendations for NRC Consideration ..............................................................11

3.0 DETERMINISTIC-PROBABLISTIC APPROACH FOR DERIVING LOWPROBABILITY HURRICANE SURGE LEVELS.............................................................13

3.1 Problems with a Strictly Deterministic Approach......................................................13

3.2 Problems with a Strictly Probabilistic Approach .......................................................13

3.3 Development of a Combined Deterministic-Probabilistic Approach..........................19

3.4 Upper Limit Storm Surge Estimation Procedure.......................................................23

3.5 Summary.................................................................................................................25

4.0 APPLICATION OF APPROACH....................................................................................27

4.1 Modeling System and Execution..............................................................................27

4.2 Estimate of Limiting Values for Very-Low Probability Surge Levels..........................39

4.3 Analyses of Surges at Two Sites in Florida..............................................................48

4.4 Analyses of 10-6 Storms...........................................................................................53

4.5 Summary.................................................................................................................60

5.0 SCREENING METHOD.................................................................................................61

5.1 Processes That Affect Storm Surge.........................................................................61

5.2 Requirements for a Screening Approach .................................................................62

5.3 Method for Development of Screening Map.............................................................63

5.4 Screening Criteria....................................................................................................75

5.5 Summary.................................................................................................................76

6.0 SUMMARY AND PMSS ESTIMATION PROCEDURES RECOMMENDED

FOR NRC CONSIDERATION ......................................................................................79

7.0 REFERENCES.............................................................................................................83

ix

LIST OF FIGURES

Figure Page

2-1 Storm tracks for maximum possible intensity storms. Brown lines are ADCIRC

sub-grid features or grid extents ......................................................................................5 

2-2 Envelope of maximum water level for all six storms.........................................................6 

2-3 Alongshore variation in PMH central pressure from NWS 23...........................................7

2-4 Minimum central pressure as a function of SST from Tonkin et al. (2000); Emanuel

Model (black dots joined by a solid line), Holland’s model (dashed line), and

observed intensities (open triangles joined by a solid line).............................................10 

2-5 Storm intensity as a function of SST under the eye with feedback due to relative 

humidity considered, from Schade (2000). Subscript a is ambient and subscript c

is center of storm...........................................................................................................10 

3-1 Comparison of surges estimated from Saffir-Simpson scale to actual measured

maximum surge values at coast for historical storms (from Irish and Resio, 2010) ........14

3-2 Comparison of surges estimated from Powell-Reinhold scale to actual measured

maximum surge values at coast for historical storms (from Irish and Resio, 2010) ........14

3-3 Comparison of surges estimated from simplified hydrodynamics based scale to

actual measured maximum surge values at coast for historical storms (from Irish

and Resio, 2010)...........................................................................................................15 

3-4 Numerically simulated (using ADCIRC) dimensionless alongshore surge

(ζ/ζpeak) distribution. Demonstrates the similarity in surge scaling for hurricanes 

of different sizes (Rp is an input value to the TC96 model that is equivalent to Rmax

for practical purposes) and intensities (cp is storm central pressure), where x’ is 

the deviation between a site and the landfall location divided by the radius to 

maximum winds (from Irish et al. 2008) .........................................................................20

3-5 Results from numerical ADCIRC simulations showing maximum surge values as a

function of storm size and storm intensity. The bold vertical line corresponds to 

a pressure differential of 133 mb ...................................................................................21 

3-6 Simulated peak surge as a function of hurricane track angle, measured counterclockwise from a due north approach. Plus or minus 10%, and 20% increases 

or decreases in value are marked by the dashed and dotted lines, respectively 

(from Irish et al., 2008) ..................................................................................................21

3-7 SLOSH results for a set of 44 points along the coast of Mississippi for storms of 

different central pressures .............................................................................................22

4-1 Project test site..............................................................................................................27

4-2 Storm tracks developed with the maximum wind speeds over the point of interest ........28

4-3 Schematic of hurricane modeling system ......................................................................29

4-4 ADCIRC (brown), TC96 PBL (red), and WAM (red) model domains ..............................31

4-5 ADCIRC mesh in project area, colors represent bathymetry and topography

and black lines are mesh elements................................................................................31

4-6 STWAVE grid ................................................................................................................32

4-7 Example of maximum wind speed contours generated by TC96 (Storm 027)................33

4-8 Example of minimum pressure field contours generated by TC96 (Storm 027)..............34

4-9 Example snapshot of the wind speed (color contoured) and wind direction at the

landfall output from TC96 (Storm 027)...........................................................................34
x

LIST OF FIGURES

(continued)

Figure Page

4-10 Example of maximum overall total significant wave height contours generated by

WAM (Storm 027)..........................................................................................................35

4-11 Example of maximum significant wave height generated by STWAVE (Storm 027).......36 

4-12 Example of envelope of maximum water level generated by ADCIRC...........................37

4-13 Lines drawn between pairs of ADCIRC simulations with different central pressures 

for various combinations of fixed storm track, storm size, and forward speed................38

4-14 Relationship between maximum velocity squared and pressure differential for the

TC96 PBL model...........................................................................................................39

4-15 Geographic area used in Tonkin et al. (2000) study.......................................................42

4-16 Variation of average August through October SST in Gulf of Mexico from 1940 

through 2006 (from Extended Reconstructed Sea Surface online repository)................43

4-17 Comparison of observed USACE HWMs for Hurricane Katrina and the simulation

using the PBL wind fields at the recorded USACE HWMs. Thin blue lines display a

1:1 correlation as well as 1.5 ft standard deviation on each side....................................45

4-18 ADCIRC mesh near the project area, marked with a red circle and x, for the Levy

County site in Florida.....................................................................................................49

4-19 ADCIRC mesh near the project area, marked with a red circle and x, for the Turkey

Point site in Florida........................................................................................................49

4-20 ADCIRC topography and bathymetry contours near the project area, marked with a

red circle and x, for the Levy County site in Florida........................................................50

4-21 ADCIRC topography and bathymetry contours near the project area, marked with a

black circle and x, for the Turkey Point site in Florida ....................................................50

4-22 Storm tracks, blue lines, for the Levy County site, shown with a red circle and x, in

Florida ...........................................................................................................................51

4-23 Storm tracks, blue lines, for the Turkey Point site, shown with a red circle and x, in

Florida ...........................................................................................................................52

4-24 Comparison of “risk-based” return periods for central pressures without uncertainty

considered (Cases 1 and 2) and with uncertainty considered (Cases 3 and 4) for the

Levy County site using data from 1940-2009. Case 4 represents the actual estimate

for the Levy County site.................................................................................................58

4-25 Comparison of “risk-based” return periods for central pressures without uncertainty

considered (Cases 1 and 2) and with uncertainty considered (Cases 3 and 4) for the

Turkey Point site using data from 1940-2009. Case 4 represents the actual estimate 

For the Turkey Point site ...............................................................................................59

5-1 Location of Matagorda, TX, Biloxi, MS, Levy County, FL, and Turkey Point, FL

regions with storm tracks for screening storm................................................................65

5-2 EC2001 finite element grid (from Mukai et al. 2002) ......................................................66

5-3 EC2001 composite bathymetry in meters relative to the geoid (from Mukai et al.

2002).............................................................................................................................67
xi

LIST OF FIGURES

(continued)

Figure Page

5-4 EC2001 mesh and bathymetry in the vicinity of Matagorda, TX.....................................68

5-5 Detailed mesh and bathymetry/topography in the vicinity of Matagorda, TX..................68

5-6 Matagorda peak surge elevations on the EC2001 mesh................................................69

5-7 Matagorda peak surge elevations on the detailed mesh ................................................69

5-8 Peak surge elevations on the detailed mesh in the vicinity of Matagorda, TX for a

storm with a central pressure of 870 mb, radius to maximum winds of 45 nm and a

forward velocity of 11 kt.................................................................................................70

5-9 Peak surges on detailed mesh plotted versus the peak surge for the screening

storm on the EC2001 mesh...........................................................................................71

5-10 Approximate upper and lower limits of the ratio of the wave contribution to water

levels at the coast (wave setup) to the total surge at the coast ......................................72

5-11 Topographic contours (elevations between 25 and 30 ft) in the vicinity of 

prospective site at Matagorda, TX .................................................................................76

xiii

LIST OF TABLES

Table Page

4-1 Storm parameter values used in Matagorda Bay simulations ........................................28

4-2 Surges produced by Matagorda Bay storms..................................................................37

4-3 Annual probabilities of a storm with a combination of size and intensity equal to or

greater than the storms simulated in this study..............................................................41

4-4 Storm parameters and surge for Levy County site.........................................................51

4-5 Storm parameters and surge for Turkey Point site.........................................................53

4-6 Storms included in analysis of extremes for Levy County site........................................54

4-7 Analysis of central pressures of hurricanes for selected return periods at the Levy

County site: Results are for a storm striking anywhere along a 240 nm stretch of

coast .............................................................................................................................55

4-8 Storms included in analysis of extremes for Turkey Point site .......................................58

4-9 Analysis of central pressures of hurricanes for selected return periods at the 

Turkey Point site: Results are for a storm striking anywhere along a 240 nm 

stretch of coast..............................................................................................................59

5-1 Screening storm parameters .........................................................................................65

5-2 Estimated wave setup ...................................................................................................73

xv

ABBREVIATIONS AND ACRONYMS

B Holland B parameter

cd coefficient of drag

G acceleration due to gravity; and

h water depth on the shelf

L shelf width

N’ effective number of years used to estimate the distribution parameters

N number of samples used to estimate the distribution parameters

Pn non-encounter probability of exceedance of the design value in n years

p seal level pressure at distance r from the storm center

p0 minimum pressure at the center of the hurricane

pw pressure at the storm periphery

R radius to maximum winds

Rmax distance from storm eye to maximum winds

r distance from the center of the storm

T return period

V wind speed

Vmax maximum wind speed

V10 wind speed 10 m above the mean water surface

x along coast spatial coordinate

vf forward velocity of the storm

x0 along coast location of landfall

Z ratio of spatial area covered to the spatial extent of a hurricane surge

∆p peripheral pressure minus central pressure

ε deviation in storm due to potential errors in estimate

ρ density of air

ρw density of water

Φi multiplicative functions of surge that depend on the specific

bathymetric/topographic setting of the specific point being investigated

σT rms error at return period

σ distribution standard deviation

σT’ rms error at return period, ˆ T TT ' / =

Tˆ average years between hurricanes

η water surface elevation

θf angle of storm heading

ADCIRC ADvanced CIRCulation model

FEMA Federal Emergency Management Agency

GEV Generalized Extreme Value

HURDAT HURricane DATabase

HWM High Water Mark

IPET Interagency Performance Evaluation Team

JPM Joint Probability Method

JPM-OS Joint Probability Method with Optimal Sampling

LaCPR Louisiana Coastal Protection and Restoration

MPI Maximum Possible Intensity

MsCIP Mississippi Coastal Improvements Program
xvi

ABBREVIATIONS AND ACRONYMS

(continued)

NOAA National Oceanic and Atmospheric Administration

NRC Nuclear Regulatory Commission

NWS National Weather Service

PBL Planetary Boundary Layer

PMS Probable Maximum Surge

PMSS Probable Maximum Storm Surge

PMH Probable Maximum Hurricane

SPH Standard Project Hurricane

SPMSS Screening Probable Maximum Storm Surge

SST Sea Surface Temperature

STWAVE STeady state WAVE model

USACE U.S. Army Corps of Engineers

WAM WAve Model
1

1.0 INTRODUCTION

Design criteria for nuclear power plants require, in part, that structures, systems, and 

components important to safety be designed to withstand the effects of natural phenomena, 

including floods, without loss of capability to perform their safety functions. These structures, 

systems and components must be designed such that appropriate consideration is given to the 

most severe of the natural phenomena that have been historically reported for the site and 

surrounding region, with sufficient margin for the limited accuracy and quantity of the historical 

data and the period of time in which the data have been collected. Design guidance specifically 

requires that the probable maximum flood be estimated. Applicants for nuclear reactor 

operating licenses must therefore demonstrate the ability of the proposed facilities to withstand 

the probable maximum flood, among other hazards. The demonstration is scrutinized by the 

Nuclear Regulatory Commission (NRC) internally and through a public review process.

The NRC staff is in need of a review of relevant data collected and used since the 1977 

publication of its Regulatory Guide 1.59, “Design Basis Floods for Nuclear Power Plants,” to 

estimate the probable maximum flood for appropriate locations. The NRC also needs to be able 

to specify acceptable methods for estimating design-basis floods that reflect changes in the 

state of the art flood estimation since 1977, especially for regions susceptible to severe storm 

events. The objective of this project is to provide the NRC with a technical basis for estimating 

probable maximum water levels due to storm surge from extreme storm events along the 

southern coast of the U.S. for consideration in evaluating flood protection for nuclear power 

plants.

For decades, the U.S. Army Corps of Engineers (USACE) has conducted storm surge and wave 

studies to support the design of flood control systems. The hurricanes of 2005 produced 

unparalleled wave and storm surge conditions that affected the entire southern coast of the U.S. 

from the panhandle of Florida to Texas, causing direct destruction to the immediate coast and 

its population centers. In response to this disaster, the USACE created the Interagency 

Performance Evaluation Task Force (IPET), a distinguished group of government, academic, 

and private sector scientists and engineers. USACE Coastal and Hydraulics Laboratory (CHL) 

team members conducted much of the technical work for IPET. IPET applied some of the most 

sophisticated capabilities available in civil engineering to understand what happened during 

Hurricane Katrina and why. The IPET purpose was not just to acquire new knowledge, but also 

to improve engineering practice and policies. Peer reviews have been conducted by the 

distinguished External Review Panel of the American Society of Civil Engineers, and the 

National Academy of Sciences. In addition, the Congress of the United States authorized the 

USACE to initiate two important and comprehensive planning efforts to address the impacts 

caused by the 2005 storms and to plan actions that would make the region more resilient and 

less susceptible to future risk from such disasters. The Louisiana Coastal Protection and 

Restoration (LaCPR) and Mississippi Coastal Improvements Program (MsCIP) efforts applied 

and further developed the technical approach and tools for estimating storm surge flood levels 

and waves established under IPET. These USACE studies, tools, and approaches were also 

extensively reviewed. 

The USACE interagency team of engineers and scientists, which also included members from 

academia and the private sector, developed an integrated modeling system to estimate storm 

surge inundation along the Gulf Coast. Through the work of IPET, the following requirements 

for accurate simulations were recognized: inclusion of numerically simulated wave set-up, use 

of detailed grids to capture high-resolution bathymetric effects, and the application of improved 
2

near-coast meteorological models for hurricane evolution and wind-field behavior. The 

modeling system can be applied to establish the coastal surge flood limits associated with 

statistical return periods.

 

One of the clear lessons from the Gulf of Mexico storms of 2005 was the need to develop a new 

method for estimating hurricane inundation probabilities. Previous methodologies suffered from 

a paucity of historical data; and an interagency research team led by USACE developed a 

modified Joint Probability Method (JPM), termed the JPM-OS (JPM with Optimal Sampling), 

since the underlying concept of this methodology is to provide a good estimate of the surges in 

as small a number of dimensions as possible. The approach attempts to minimize the issues 

related to the lack of quantity and quality historical hurricane data and the number of model 

simulations required by a typical JPM by improving methods used for interpolating between 

combinations of variables in different simulations. Previous methodologies for estimating flood 

levels also did not include many of the modeling advances that are now regarded as necessary 

for accurate simulations. The Federal Emergency Management Agency (FEMA) has adopted 

the modeling system and methodology and applied it in under USACE leadership in Louisiana, 

and is currently applying the methodology in Texas, North Carolina, the Great Lakes, and in the 

Chesapeake Bay area.

 

Section 2 documents a review of the existing guidance and identifies limitations in the technical 

basis for estimating storm surge. It provides recommendations for updating the technical basis 

based on the most recent data available and state-of-the-practice analysis methods, tools, and 

models. Section 3 presents a proposed deterministic-probabilistic approach for estimating 

very-low probability hurricane storm surges. The proposed approach determines which factors 

affecting hurricane surges can be shown to have asymptotic upper limits and which factors 

should be treated within a context that allows for natural uncertainty in estimating an upper limit 

for surges at a specified site. Section 4 documents the application of the proposed approach at 

three nuclear plant sites. The Matagorda Bay site served as a platform for developing the initial 

concepts for very low probability surges. Analyses of the upper limit for storm surges at two 

other sites in Florida were also examined. Section 5 introduces a screening method developed 

to determine if a prospective site is at risk of flooding from coastal storm surge. The proposed 

screening method includes criteria for proceeding or not proceeding to more detailed definitions 

of design-basis storm surges and explicitly considers local conditions and bathymetry that may 

affect water level estimates. Section 6 summarizes the procedures recommended, for NRC 

consideration, for estimating the probable maximum storm surge at a site. It should be noted 

that the approach presented herein is a methodology for estimating the flood hazard from 

coastal storm surges and wave setup only on the U.S. southern coast. River flows can also be 

included in the modeling of a system but other contributors to flooding such as precipitation and 

runoff from the watershed are not considered.
3

2.0 REVIEW OF EXISTING GUIDANCE

The purpose of this Section is to document a review of the National Oceanic and Atmospheric 

Administration (NOAA) Technical Report NWS 23, “Meteorological Criteria for Standard Project 

Hurricane and Probable Maximum Hurricane Windfields, Gulf and East Coasts of the United 

States” and the NRC Regulatory Guide 1.59, “Design Basis Floods for Nuclear Power Plants”. 

Both NWS Report 23 and Regulatory Guide 1.59 require updating. Based on the review of 

NWS Report 23, procedures for supplementing and or modifying the report are recommended 

that reflect data and analysis methods that have been developed since its publication in 1979. 

The review of Regulatory Guide 1.59 and its supporting documents focused on the storm surge 

section of the report “Probable Maximum Flood and Hurricane Surge Estimates,” which is cited 

in Regulatory Guide 1.59 and Appendix A of Regulatory Guide 1.59, “Determining Design-Basis 

Flooding at Power Reactor Sites”. The technical basis for estimating storm surge was reviewed 

and required updates recommended for NRC consideration.

2.1 Probable Maximum Hurricane Surge Estimate

Regulatory Guide 1.59 and its supporting documents provide a methodology for estimating the 

probable maximum surge (PMS) for open coast locations of the Atlantic and Gulf of Mexico. 

The PMS estimates are determined by use of the probable maximum hurricane (PMH) 

parameters applied as input to the Bathystrophic Storm Surge model developed in the early 

1970s (Bodine 1971; Pararas-Carayannis 1975). The PMH is a hypothetical hurricane having a 

combination of characteristics that give the highest sustained wind speed that can probably 

occur at a specified location. A review of the guidance on developing PMH characteristics and 

recommendations for modifying the guidance are presented in a subsequent section.

The Bathystrophic Storm Surge model applied in NRC guidance was originally developed by 

Bodine (1971). The model estimates the sea surface rise along the open ocean coast as a 

response to surface winds and pressures, as well as the Coriolis forces. Pararas-Carayannis 

(1975) describes the model as a quasi-two-dimensional numerical scheme, which is a steadystate integration of the wind stresses of the hurricane winds on the surface of the water from the 

edge of the continental shelf to the shore. The storm surge is computed along a single “traverse 

line” at a time over the continental shelf for a straight open-ocean coast by numerically 

integrating the two-dimensional hydrodynamic equations of motion and neglecting the continuity 

equation. Surge propagation along most coasts is heavily influenced by the surrounding 

bathymetry/topography. The one-dimensional nature of the Bathystrophic model does not allow 

the simulation of these effects. In addition, the “traverse line” is a straight line that must be 

oriented perpendicular to the sea bed contours. This orientation restriction is a problem for 

most realistic shorelines which have complex bed contours and it creates problems when 

placing a “traverse line” in relation to a storm that moves over the shelf with a large crossing 

angle. In some locations, storms with large crossing angles may produce the maximum surge 

values and this cannot be simulated with the Bathystrophic model. An important point is that 

this model is intended solely for use on open coasts and not for use on protected bays, 

estuaries, and inlets. Additional analysis must be performed to simulate the propagation of the 

surge into these areas, which are common along both the Atlantic and Gulf coasts. Existing 

technology now allows for the simulation of surge propagation in these areas as well as along 

the open coast in the same simulation.

The Bathystrophic model is limited by a number of initial conditions and assumptions. The 

assumptions made that have some of the greatest impact on the physics being modeled are: 
4

(1) there is no volume transport normal to the shore, (2) the onshore wind setup responds 

instantaneously to the onshore wind stress, (3) advection of momentum is negligible, and (4) the 

alongshore sea surface height and velocity is uniform. In addition, the barometric and 

astronomical tide effects are not accounted for directly within the discrete equations and the 

model is best suited for slow moving storms and not for fast moving storms where inertial effects 

become important. Because there is no volume transport normal to the shore, no inundation is 

allowed during the simulation. Instead a boundary condition is imposed at the coastline that 

basically represents an impermeable vertical wall. This is a physically unrealistic assumption 

that impacts the accuracy of the surge level and the velocity solutions.

 

In terms of the initial conditions, the model assumes a constant value for the initial water rise, or 

“forerunner” of the hurricane. The initial water level is an important contribution to the overall 

storm surge value and can be over 6 ft (Kennedy et al. 2011). This initial water level can be 

captured in modern simulations without specifying it as a constant. Another limiting factor is that 

wind and bottom frictional stresses are coupled in the Bathystrophic model and it does not allow 

for each to have an individual resolution.

In summary, the Bathystrophic Storm Surge model is extremely limited by restrictions and 

simplifications made in order to make the problem computationally tractable given the computer 

resources available in the early to mid 1970’s. The model assumptions and simplifications 

reduce the applicability and accuracy of the model. Because the surge is not allowed to 

propagate onshore, but instead piles up at the coastline, it does not allow for accurate 

representation of the inundation. The treatment of the surface and bottom frictional stresses are 

combined and do not allow for accurate spatially varying values. The model can only be applied 

on open-ocean coasts and does not allow for predictions at protected bays, inlets, and 

estuaries. Most alarming, yet not surprising, is the fact that the accuracy of the model can vary 

wildly. To this end, Pararas-Carayannis (1975) states that while the model can produce 

reasonable estimates of surge, there are times the surge estimate can be in error by a factor of 

two or more. Such a large potential error is not acceptable by today’s standards.

 

Many regions along the Atlantic and Gulf of Mexico coasts are extremely complex, 

characterized by bays, inlets, barrier islands, and wetlands. Modeling coastal surge in complex 

regions requires an accurate definition of the physical system and inclusion of all significant flow 

processes. Processes that affect storm surge inundation include atmospheric pressure, winds, 

air-sea momentum transfer, waves, river flows, tides, and friction. Numerical models now exist 

that can properly define the physical system and include an appropriate non-linear coupling of 

the relevant processes. A coupled system of wind, wave, and coastal circulation models has 

been developed and implemented for regions in both the Gulf of Mexico and the Atlantic. The 

system combines the TC96 Planetary Boundary Layer (PBL) model (Thompson and Cardone 

1996), the WAM offshore (Komen et al 1994) and STWAVE nearshore (Smith et al 2001, Smith 

2007) wave models, and the ADCIRC (Westerink et al. 2008; Bunya et al. 2009) basin to 

channel scale unstructured grid circulation model.

 

There are several advantages of this modern modeling system. First, because ADCIRC is 

based on an unstructured finite element formulation, it allows for accurate representation of the 

coastline and surrounding features. ADCIRC also solves the full depth-averaged set of 

equations that describe storm surge and includes the ability to inundate dry land, thereby better 

capturing the actual dynamics of the surge, not just the surge height. ADCIRC can therefore 

estimate the influence of surrounding bathymetry/topography on storm surge across the 

coastline, unlike the Bathystrophic Storm Surge model. ADCIRC also allows for separate 

spatially and temporarily varying treatments of surface and bottom stress. Furthermore, there 
5

are no restrictions on the orientation of the grid/mesh with respect to the coastline, the bed 

contours, or the storms track. Storms with large crossing angles across complex bathymetries 

are readily simulated. The ADCIRC model can also be coupled with wave models to include the 

impact of wave set up. The wave model outputs include estimates of hurricane generated wave 

heights and periods, which may be important in understanding the flood threat in some areas.

To illustrate the capability of existing modeling technology, six hypothetical storms with high 

surge potential and landfall points along the Mississippi coast were simulated. These six large 

surge potential storms made landfall at various points along the coast as shown in Figure 2-1. 

The storms were defined at their most intense point as having a minimum central pressure of 

880 mb, radius to maximum winds of 36 nm, and a forward speed of 11 kt. Peak water level 

envelopes from each of the six storm simulations were computed. The peak water level 

envelope is the maximum water level estimated at each node during the entire simulation. The 

six peak water level envelopes were then combined to compute the “peak of peaks”, which is 

considered the inundation limit along the entire Mississippi coastline (Figure 2-2).

Figure 2-1. Storm tracks for maximum possible intensity storms. Brown lines are 

ADCIRC sub-grid features or grid extents.

Figure 2-2 illustrates the spatial variability in the surge both along and across the coastline. 

Coastal features such as barrier islands, inlets, bays, and wetlands can significantly influence 

surge propagation as seen in Figure 2-2. The ADCIRC modeling system is able to capture the 

influence of these features, unlike the Bathystrophic model. The current guidance provided by 

Regulatory Guide 1.59 allows for interpolation along the coast between locations with computed 

PMS values. Figure 2-2 illustrates how this is unrealistic as there is significant variability in peak 

surge values due to the complex nature of surge propagation in many coastal regions.
6

Figure 2-2. Envelope of maximum water level for all six storms.

2.2 Meteorological Criteria for a Probable Maximum Hurricane 

In 1959, the USACE contracted the National Weather Service (NWS) to develop a hypothetical 

hurricane that could be used to design hurricane protection projects along the Gulf and Atlantic 

coasts of the United States. At that time the NWS, as part of its National Hurricane Research 

Project, set out to define “the most severe storm that is considered reasonably characteristic of 

a region.” A storm with such characteristics was termed the Standard Project Hurricane (SPH). 

This effort is described in U.S. Weather Bureau Report No. 33 (Graham and Nunn, 1959).

In 1979, the NWS (NWS Technical Report 23 authored by Schwerdt et al. in 1979, hereafter 

termed NWS 23) redefined the SPH as “a steady state hurricane having a severe combination 

of values of meteorological parameters that will give high sustained wind speeds reasonably 

characteristic of a given region,” removing the idea that the SPH pertained to the “most severe 

storm” for a particular area from the definition of the SPH. Since most of USACE projects are 

examined on an economic basis over a fixed interval of time, this re-definition of the SPH 

offered improved quantitative guidance for the relative costs and benefits of projects (given that 

the probability of an SPH is properly estimated) over the use of an absolute maximum value. In 

fact, NWS goes on to say that this revised “concept of the SPH has been developed for Gulf 

and Atlantic coasts as a bench mark against which to judge the hazards for a particular 

community”.

Also in NWS 23, the concept of a Probable Maximum Hurricane (PMH) was introduced as “a 

hypothetical steady-state hurricane having a combination of values of meteorological 
7

parameters that will give the highest sustained wind speed that can probably occur at a 

specified coastal location.” It is clear from this definition that the PMH was intended to be an 

event that was much rarer than the SPH; but it is not clear that an objective definition can be 

gleaned from what is written in NWS 23. For example, it is not clear exactly what is meant by 

the words “the highest wind speed that can probably occur.” In its executive summary, NWS 23 

states that the central pressure of the PMH “is simply the lowest sea-level pressure at the 

hurricane center.” It does not state the specific geographic area for this determination around 

U.S. coasts. Figure 2-3, taken from NWS 23, shows the estimated values of the central 

pressure for the PMH within the Gulf of Mexico, with values varying between about 887 mb at 

Port Isabel, Texas to about 891 in the vicinity of Apalachicola, Florida and then diminishing to 

about 885 at Ft Myers, Florida. All of these are values that are substantially lower than the 

lowest central pressure in the observations within the Gulf of Mexico available at that time, so it 

is hard to interpret the meaning of these values in an objective context. It is more likely that a 

considerable dose of “expert judgment” was utilized in estimating the central pressure for the 

PMH.

Figure 2-3. Alongshore variation in PMH central pressure from NWS 23.

The meteorological criteria for the Probable Maximum Hurricane (PMH) wind fields are 

developed in a general sense in NOAA Technical Report NWS 23. This is an excellent 

treatment of hurricanes, given the time frame in which that study was conducted; however, 

additional information from the many sources which were unavailable at the time of that study, 

along with data from many well-documented storms since the report was published in 1979, 

have shown some potentially important inconsistencies between the PMH derived in that study 

and our present understanding of the characteristics of intense hurricanes. In addition to the 

general guidelines for the PMH that appeared in NWS 23, which in many cases only specified 
8

acceptable ranges for parameters, there were some specific values of parameters that were 

selected for application to specific coastal sites in the Probable Maximum Surge (PMS) studies 

as a part of the U.S. Nuclear Regulatory Commission’s Regulatory Guide produced by its Office 

of Standards Development. Information from both the NWS 23 and Office of Standards 

Development sources are considered in this review.

The state of the art in 1979 was such that hurricane wind fields were estimated parametrically 

from a “vortex model” which was a function of 5 primary parameters: storm intensity (central 

pressure), storm size (radius to maximum winds), forward translation speed of the storm, 

direction of heading of the storm, and location of landfall. Holland (1980) showed that an 

additional factor (now termed the Holland “B” factor) was needed to properly specify winds and 

pressures within a hurricane. The radial pressure profile formula adopted in NWS 23 is given by

−   − =   −  

0

0

exp ,

w

p p R

pp r Equation 2-1

where

p is the seal level pressure at distance r from the storm center;

p0 is the minimum pressure at the center of the hurricane;

pw is the pressure at the storm periphery;

R is the radius to maximum winds; and

r is the distance from the center of the storm.

In the Holland B model of hurricane pressure field, this pressure profile is written as

  − =+ −     0 0 ( )exp , w B

A

pp p p

r Equation 2-2

where A and B are scaling parameters such that A=RB has units of meters. It can be shown that 

the form given in Equation 2-2 will be equivalent to that shown in Equation 2-1 only if B is equal 

to 1. Existing data shows that this is not the case. Instead, characteristic values of B vary from 

basin to basin, typically over a range of values from 0.8 to 2.5 (IPET 2009). The form for the 

maximum gradient wind based on Equation 2-1 is given as:

ρ

  = −−    

1/ 2

1/ 2

0

1 ( ), 2 g w

rf V pp

e Equation 2-3

where 

ρ is the density of air;

e is ~2.71828; and

f is the Coriolis parameter.

The form for the maximum gradient wind based on Equation 2-2 is given by:

ρ

    −   −     = + −

 

1/ 2

0 2 2 ( )exp

. 4 2

w B

g B

A AB p p

r r f rf V

r

 Equation 2-4
9

For values of B greater than 1, the maximum wind speeds predicted by Equation 2-4 can be 

substantially higher than those predicted by Equation 2-3, which can lead to a potential underconservative estimate in the PMH winds.

In modern surge prediction, the reduction of wind speeds from the gradient level to a fixed 10-

meter reference level is typically handled within a planetary boundary layer model or from 

empirical factors based on large sets of data. Such models, although in existence at the time 

that NWS 23 was written, were not widely used and data sets were very limited in the 1970s; 

consequently, the reduction factor used in NWS 23 is a simple empirical relationship given by

10 = 0.95 , V Vg Equation 2-5

where V10 is the wind speed 10 m above the mean water surface. The value of the empirical 

constant in Equation 2-5 can be shown to vary substantially depending on a number of 

dynamical factors; however, the 0.95 value in Equation 2-5 represents an upper limit for the 

range of values determined in planetary boundary model studies.

For a number of years now, the theoretical concept of a PMH has been replaced by a concept 

of the “Maximum Possible Intensity” (MPI) since this latter concept has theoretical underpinning

to support the empirical data. Figures 2-4 and 2-5 are from papers by Tonkin et al. (2000) and 

Schade (2000) and plot the relationship between storm intensity and sea surface temperatures 

(SST). These figures indicate that the probable lowest central pressure is approximately 880 

mb and possibly even a bit lower if SSTs within the Gulf of Mexico rise due to climate change. 

The dashed vertical line corresponds to the record high average August to September SST, 

which occurred in 1962. Since the lowest central pressure in the Gulf of Mexico according to 

NWS 23 is 885 mb, it is possible that the central pressures used in the PMH do not represent 

the reasonably expected worst storm case.

The radius to maximum winds specified in NWS 23 covers a relatively wide range (typically from 

about 5 nm to slightly over 20 nm in the Gulf of Mexico); however, the NRC publication on the 

PMS applies a specific value in its calculations. The values listed in that publication are in all 

cases somewhat higher than the limits described in NWS 23. As a typical example, the 

specified value for the PMS calculations at Biloxi is 30 nm, whereas the upper limit for the PMH 

in that area is about 23 nm. For hurricanes still offshore, this might be a relatively conservative 

value; however, Katrina at landfall in Mississippi had an estimated value of 33 nm for the radius 

to maximum winds (IPET 2007). Thus, the 30 nautical mile value does not appear to represent 

a realistic upper limit to the storm sizes in this area.

An important point raised in the last paragraph concerns the behavior of hurricanes as they 

approach the coast. In the 1970’s it was believed that hurricanes retained their strength until 

after making landfall and then began to substantially modify and weaken. Recent studies (e.g. 

IPET 2009) have shown that in the Gulf of Mexico the overall storm strength and the structure of 

the wind fields change significantly during the approach to the coast (IPET 2009). It is difficult to 

gage the impact of this difference on storm surges, since both storm intensity and storm 

structure affect the surge levels.

The range of values for storm translation speed and storm heading given in NWS 23 are 

consistent with values obtained in more recent studies. Also, since storm locations are

distributed in the PMS calculations according to some idea of maximum surges, this aspect of 

NWS 23 does not present any problems in its applications.
10

Figure 2-4. Minimum central pressure as a function of SST from Tonkin et al. (2000); 

Emanuel Model (black dots joined by a solid line), Holland’s model (dashed 

line), and observed intensities (open triangles joined by a solid line).

Figure 2-5. Storm intensity as a function of SST under the eye with feedback due to 

relative humidity considered, from Schade (2000). Subscript a is ambient and 

subscript c is center of storm.
11

Besides nagging issues with the objectivity of the PMH definition, other problems with the earlier 

work have arisen. For example, the use of “sustained wind speed” as the parameter of primary 

basis for the evaluation of the PMH characteristics has been superseded by the adoption of the 

Probable Maximum Storm Surge (PMSS) (U.S. Nuclear Regulatory Commission, 2007) as a 

project design basis. The degree of severity implicit within the PMH was also clarified 

somewhat in this report; however, the report mixes the PMH and the PMSS when it states that 

the “PMSS is the surge that results from a combination of meteorological parameters of a 

probable maximum hurricane (PMH).... and has virtually no probability of being exceeded in the 

region involved.” It is not clear how the PMH can be used in this context, unless the definition is 

altered from its purely sustained wind speed basis, since Irish et al. (2008) and Irish and Resio 

(2010) have clearly shown that storm size, in addition to maximum wind speed, is extremely 

important to the magnitude of the storm surges generated. Based on this evidence, it is logical 

to retain the term PMSS and to drop usage of the term PMH in future discussions of very 

extreme surges used for determining potential locations for critical infrastructure such as nuclear 

power plants.

2.3 Uncertainty

The range of uncertainty that is inherent in the storm wind fields and the resulting modeling 

representation of these wind fields must be considered. A considerable amount of uncertainty 

exists for the predictive models and the limiting estimates of the meteorological inputs to the 

predictive models. There are three main types of uncertainty with respect to understanding 

hurricane hazards along coasts. First, there is uncertainty that the actual sample of storms is 

representative of the “true” climatology today. Second, there is uncertainty in the events within 

future intervals of time, even if the “true” climatology is known exactly. And, third, there is 

uncertainty that some non-stationary process (sea level rise, subsidence, climate change, new 

development patterns, man-made alterations to the coasts, marsh degradation, etc.) will affect 

future hazards. The approach proposed in this report attempts to determine which factors 

affecting hurricane surges can be shown to have asymptotic upper limits and which factors must 

be treated within a context that allows for this natural uncertainty in estimating an upper limit for 

surges at a specified site.

2.4 Recommendations for NRC Consideration

The Bathystrophic Storm Surge model is extremely limited by restrictions and simplifications 

made in order to make the problem computationally tractable given the computer resources 

available in the early to mid 1970’s. The model assumptions and simplifications reduce the 

applicability and accuracy of the model. It is recommended that a modern coupled system of 

wind, wave, and coastal circulation models that properly define the physical system and include 

an appropriate non-linear coupling of the relevant processes be adopted. The USACE 

hurricane modeling system combines the TC96 PBL model for winds, the WAM offshore and 

STWAVE nearshore wave models, and the ADCIRC basin to channel scale unstructured grid 

circulation model. The modeling system is well validated and, in addition to being applied for 

USACE projects, has also been adopted by several Federal FEMA regional offices for flood 

mapping.

There are several assumptions in the PMH described in NWS 23 that are now known to be 

invalid. It is recommended that the PMH concept be updated in accordance with new 

theoretical concepts and data. Two particular changes should be to:
12

• Allow the MPI to attain a somewhat lower central pressure than the older values; and

• Estimate storm size as a conditional probability function of storm intensity in simulations. 

Also, the term PMSS should be retained and the usage of the term PMH dropped in future 

discussions of very extreme surges used for determining potential site locations for critical 

infrastructure such as nuclear power plants. Finally, it should be noted that it is also important 

to consider the range of uncertainty that is inherent in the storm wind fields, and the resulting 

modeling representation of these wind fields and surges. 
13

3.0 DETERMINISTIC-PROBABLISTIC APPROACH FOR DERIVING 

LOW-PROBABILITY HURRICANE STORM SURGES

Two fundamentally different methods for estimating design surge levels have been utilized in 

past studies: deterministic-based methods and probability-based methods. Deterministic 

methods typically use the estimated maximum surge value from either a single storm or a small 

set of storms as its design level and do not consider the probability of that surge level. 

Probabilistic methods consider surges from a range of events along with the probabilities of 

those events and attempt to develop a relationship between surge levels and return period. A 

simple example of the deterministic method would be to define a single PMH and to simulate 

surges from that storm, which would yield a single deterministic surge value at a site of interest. 

An example of a probabilistic method would be to simulate the appropriate population of 

historical storms, rank the resulting surge values at a point of interest, and fit the cumulative 

distribution function based on these ranked results with some extremal distribution. There are 

deficiencies with both of these approaches for estimating very-low probability hurricane surges. 

The purpose of this Section is to develop a hybrid approach that considers a natural upper limit 

for hurricane generated surges and allows for natural uncertainty in estimating this upper limit.

3.1 Problems with a Strictly Deterministic Approach

The deterministic (single design storm) approach is clearly suitable for estimating a very-lowprobability surge level in a rigorous sense if 1) the selected design event is known to be the 

event which creates the maximum possible surge at the site of interest or 2) the probability of 

the surge created by the design event is known and accepted as an adequate design criterion. 

In the latter case, subjective words, such as “reasonably be expected” must be replaced by 

definitive, objective values such as “with a probability of exceedance less than z”, where z would 

be a fixed number. Thus, a strictly deterministic approach to the problem of very-low-probability 

design events would imply 1) that we know the precise set of forcing conditions that can create 

the maximum (or at least a given fixed very-low probability) surge at a given location and 2) that 

there was no uncertainty in either the predictive models utilized or the limiting estimates of the 

inputs to the predictive model. Unfortunately, since neither of these conditions is met, a strictly 

deterministic approach may not represent the actual maximum condition (or very-low-probability 

event) expected at a given location. For this reason, it is difficult, and perhaps impossible, to 

generalize a strictly deterministic approach for application in a wide range of coastal 

environments.

3.2 Problems with a Strictly Probabilistic Approach

If the peak surge level at a point only depended on a single scalar variable, such as wind speed, 

the maximum value of that variable could clearly be associated with the maximum surge value. 

However, hurricane surge response at a specific site depends on several storm factors and not 

just a single, scalar variable (e.g. wind speed). Therefore, the maximum surge produced by a 

storm of a given size (as defined by the radius to maximum winds) and wind speed might still be 

exceeded by a storm with a larger radius to maximum winds and precisely the same wind 

speed. Figure 3-1 shows the scatter of storm surge versus a scale based on wind speed (SaffirSimpson Scale), and Figure 3-2 shows the scatter of the storm surge versus a scale based on 

storm size (Powell and Reinhold, 2007). Figure 3-3 shows the scale developed by Irish and 

Resio (2010) based on simplified hydrodynamics. Although the Irish-Resio scale certainly 

improves upon previous scales, the omission of wave set-up contributions, storm forward 
14

speed, and angle of intersection of the storm track with the coast still leave very large scatter in 

the data and confirms that dependence on a single variable is not possible.

Figure 3-1. Comparison of Saffir-Simpson scale to actual measured maximum surge 

values at coast for historical storms (from Irish and Resio, 2010).

Figure 3-2. Comparison of Powell-Reinhold scale to actual measured maximum surge 

values at coast for historical storms (from Irish and Resio, 2010).
15

Figure 3-3. Comparison of simplified hydrodynamics based scale to actual measured 

maximum surge values at coast for historical storms (from Irish and Resio, 

2010).

Several recent studies (IPET, 2009; Resio et al., 2008; Irish et al., 2008; Irish and Resio, 2010) 

have shown that the maximum surge can be estimated as a function of several storm 

parameters:

max max max 0 (, ) (,, , , , ,, ) f f η η θε xy xy pR v Bx =∆ +

 

Equation 3-1

where 

x along coast spatial coordinate

y cross coast spatial coordinate

∆p peripheral pressure minus central pressure

Rmax distance from storm eye to maximum winds

vf forward velocity of the storm

θf angle of storm heading

B Holland B parameter

x0 along coast location of landfall

ε deviation in storm due to potential errors in estimate.

The last term in this equation, in essence, represents the sum of a wide range of omissions and 

errors in our predictive state of the art for surges. Some examples of this are 1) the difference 

between actual (very complex) space-time varying winds in a real hurricane and the parametric 

representation of these winds in a model driven by a small set of parameters; 2) numerical 

surge models are still imperfect and produce errors related to these imperfections (in both the 

physics and numerical approximations utilized within the models); and 3) the coast is always in 
16

a state of change, so the use of present-day topographic/bathymetric representations in 

simulations of a future storm may not be precise.

Before proceeding, it is important to note that the verified accuracy of a numerical model for its 

application to a particular situation/area is absolutely essential to ensuring that any of the results 

are usable for critical applications. As discussed in Resio and Westerink (2008), this absolutely 

requires 1) the application of a model with sufficient resolution to represent important 

bathymetric/topographic features accurately and 2) that all terms contributing to the surge are 

represented in the proper physical context. For modern applications, this latter stipulation has 

shown that a coupled surge-wave model must be applied and the computational domain must 

be sufficiently large to negate the need for empirical factors along an offshore grid boundary. In 

turn, this means that run time requirements for such models tend to be considerably higher than 

for simpler models.

 

Given the general form of Equation 3-1, Joint Probability Methods (JPM’s) can be used to 

estimate the expected probability density functions and cumulative density functions from sets 

of many numerical simulations with an appropriate numerical model (IPET, 2009; Resio et al., 

2008; Irish et al., 2008; Toro et al., 2010a and 2010b; Niedoroda et al., 2010). However, 

present JPM methods are focused on providing estimates of surges for a range of return 

periods in the neighborhood of 50 to 1000 years. Although it has been clearly established that 

estimates from the JPM are more stable than estimates based only on historical hurricanes, the 

confidence limits in estimated values using either of these methods is expected to become very 

large for very low probability surge values.

If the population of hurricanes were known exactly (i.e. the multivariate probability density 

function of all possible combinations of hurricane parameters was known exactly), “boot-strap” 

methods could be used to re-sample from that population to determine N sets of M-year 

samples, where M is often regarded as the “design life” of the decision/design being made. This 

could be used to estimate the range of surge conditions that might be expected in a particular 

M-year period in the future. However, error bands determined in this way do not differentiate 

between initial samples based on a small number of years versus initial samples based on 

many years of data, nor will it allow a simple estimate of the effects of non-stationarity (i.e. 

climate variability) on future samples.

Three main types of uncertainty with respect to the estimation of extremes are relevant to 

understanding hurricane hazards along coasts. First, there is uncertainty that the actual sample 

of storms is representative of the “true” climatology today. Second, there is uncertainty in the 

events that will actually occur within future intervals of time, even if the “true” climatology is 

known exactly. And, third, there is uncertainty that some non-stationary process (sea level rise, 

subsidence, climate change, new development patterns, man-made alterations to the coasts, 

marsh degradation, etc.) will affect future hazards. The first of these has traditionally been 

addressed via sampling theory. The second can be addressed via re-sampling or “boot strap” 

methods. And, the third must be estimated from ancillary information, often not contained within 

the initial hazard estimates themselves.

The first type of uncertainty listed above pertains to what was termed confidence bands (or 

control curves) for estimates of extremes. It cannot be estimated with re-sampling techniques, 

since these techniques use the initial sample as the basis for their re-sampling and implicitly 

assume that the initial sample represents the actual population characteristics. Thus, some 

parametric method must be applied to obtain this information. The data can be fit with many 

classes of distributions. Since we are only using the parametric fits to estimate uncertainty and 
17

not to replace the non-parametric estimates obtained from the JPM, we are somewhat free to 

use any distribution for which the sampling uncertainty is known. Gringorten (1962, 1963) has 

shown that the expected root-mean-square (rms) error of an estimated return period (T) in a 

two-parameter Fisher-Tippett Type I (Gumbel, 1959) distribution is given by

2 1.1000 1.1396 1 T

y y

N σ σ + + =

 

Equation 3-2

where

σT is the rms error at return period, T;

σ is the distribution standard deviation;

N is the number of samples used to estimate the distribution parameters; 

y is the reduced Gumbel variate given by y=(η-a0)/a1;

η is the variate of interest (surge level in this case); and

a0 and a1 are parameters of the Gumbel distribution.

The reduced variate and return period are related by:

ln ln

1

T

y T

    = −         − Equation 3-3

which for T >7 approaches an exponential form given by:

1

2

y T e     − →  

 Equation 3-4

Equation 3-2 shows that the rms error at a fixed return period is related to the distribution 

standard deviation and the square root of a non-dimensional factor involving the ratio of different 

powers of y to the number of samples used to define the parameters. By the method of 

moments, the Gumbel parameters can be shown to be given by:

01 1

6

aa a γμ σ π =− = Equation 3-5

where γ is Euler’s constant (=0.57721...) and μ is the distribution mean. Thus, the distribution 

standard deviation is related to the slope of the line represented by Equation 3-5 and can be 

used for estimating the expected width of the confidence limits for a specified return period.

Although Equation 3-2 was initially derived for applications to annual maxima, it can be adapted 

to any time interval for data sampling in a straightforward manner. For the case of hurricanes, 

the average interval between storms (the inverse of the Poisson frequency used in the 

compound Gumbel-Poisson distribution) can be used to transform Equation 3-2 into the form:

2 1.1000 1.1396 1 T

y y

N

σ σ ′ ′ + + ′ = ′ Equation 3-6

where 

σT’ is the rms error at return period, ˆ T TT ' / =

where Tˆ is the average years between hurricanes; and
18

N’ is the effective number of years used to estimate the distribution parameters.

As an example of how this might be applied, let us examine some actual data from the interval 

1941 to 2005 for hurricanes in the Gulf of Mexico. Since the form of Equation 3-4 is logarithmic, 

the slope is not affected by a multiplicative factor, and thus, the distribution standard deviation 

remains the same. N’ in Equation 3-6 can be estimated from the equivalent total number of 

years in the sample divided byTˆ . The total number of years for this case is 65 (1941 to 2005, 

inclusive) times a factor, Z, which relates the spatial area covered by the sample to the spatial 

extent of a hurricane surge.

 

For relatively intense storms capable of producing surges that are exceeded only every 100 

years or more, the along-coast extent of very high surges at least 60% of the peak value is 

about 60 nm for a storm with a 20-nm radius to maximum winds (IPET 2009). In that study, the 

“local” values used to estimate the distribution parameters were drawn from an alongshore 

section covering ±3.5 degrees longitude along 29.5 degrees north latitude. The value of Z is 

given by:

Distance along coast

Width of a single sample

Z = Equation 3-7

which in this case is 365.5 nm divided by 60 nm, or approximately 6.1. Thus, the effective 

number of years is 396.

Combining Equations 3-4 and 3-6 shows that the asymptotic behavior of the error estimate for 

large return periods will have the functional form:

ln( ) T

T

N

σ

σ′ = ′ Equation 3-8

Since the distribution standard deviation (σ) and the effective number of years are independent 

of the return period, it is apparent that the spread in width of the control band will continue to 

increase in proportion to the logarithm of the return period. Thus, a typical 90% error of 2.5 to 

3.0 ft in the estimates of the 100-year surge value along the northern Gulf of Mexico coast will 

increase by a factor of three in an estimate of the 106 return period, making the equivalent 90% 

error band in the range of 7.5 – 9.0 ft for such an event. And, if a 99% error limit were used as 

the tolerable error threshold, the error band would increase to approximately 11.3 to 13.5 ft. 

Another problem with this approach that is more of an operational nature, is that it would require 

somewhere around 100 to 200 storm surge simulations for a single nuclear power facility site in 

order to cover the range of storm parameter combinations in a JPM approach required for verylow-probability storms. This is due to the fact that the JPM approach covers a much larger range 

in probabilities rather than just focusing on the very high end of the storm surges.

 

The issue of non-stationarity related to changing coastal landscapes, sea level rise, and climate 

variability cannot easily be included within this estimate, since the theoretical foundation for 

these errors is based upon a single, homogeneous population. In areas undergoing rapid land 

loss, such as much of coastal Louisiana, it is particularly important that any simulations used as 

the basis for decision-making consider both the existing coastal landscape and the potential 

future coastal landscape at the end of the expected design life of any critical infrastructure. Even 

in areas where the coastal landscape is not expected to change radically, the issue of 
19

continuing and/or accelerating sea level rise must be dealt with in a quantitatively defensible 

fashion.

The previous discussion shows that there are two substantial problems in the estimation of the 

very-low-probability events using a strictly probabilistic approach: 1) the large error associated 

with extrapolations based on a relatively small number of years to very large return periods and 

2) problems with including non-stationarity into the error bands. Another problem is the lack of a 

strong probabilistic basis for selecting a level of risk appropriate for a surge to exceed a design 

level. This depends strongly on the number of years in the assumed lifetime of the structure 

being designed. It can be shown that for very long return periods, such as the 106 return period 

referenced above, the expected total encounter probability (not the annual encounter 

probability) rises linearly with the number of years in the assumed lifetime, i.e.:

1 11 11

n

n

n P

T T

  =− − ≈− −     Equation 3-9

where Pn is the non-encounter probability of exceedance of the design value in n years. This 

can be expressed in somewhat simpler manner by recognizing that the non-encounter return 

period after n years is related to the initial return period by Tn~T/n for very long return periods 

such as the example here. Thus, a one million year (106

) return period for an occurrence in one 

year would be expected once every 20,000 50-year increments. Risk communication to the 

public should convey this total risk over an expected lifetime as well as the annual risk.

3.3 Development of a Combined Deterministic-Probabilistic 

Approach

Since both the probabilistic-only and the deterministic-only approaches to the estimation of verylow-probability hurricane surges have some deficiencies, it is logical to investigate joining the 

two approaches into a hybrid approach. Such a combination might provide some advantages 

over either approach implemented independently. Thus, instead of using either a probabilisticonly or a deterministic-only approach to the estimation of very-low-probability, the approach 

here attempts to determine which factors affecting hurricane surges can be shown to have 

asymptotic upper limits and which factors still have to be treated within a context that allows for 

natural uncertainty in estimating an upper limit for surges at a specified site. Resio et al. (2008), 

Irish et al. (2008) and Irish and Resio (2010), show that the response of surge levels can be 

addressed as a function of several variables, as shown specifically for the variation of surge 

levels along the coast in Figure 3-4. In this approach, the maximum surge level can be 

approximated as:

max 1 2 max 3 0 4 5 ( ) ( ) ( ) () () η θ =Φ ∆ Φ Φ − Φ Φ p R xx vf f Equation 3-10

where the multiplicative functions Φi should be understood to depend on the specific 

bathymetric/topographic setting of the specific point being investigated, and x-x0 denotes the 

alongshore position of the point of interest relative to the landfall position. As noted by Irish and 

Resio (2010), when the storm size becomes as large as the region of primary surge generation, 

additional increases in storm size do not produce substantial increases in storm surge. If we 

take L* as the width of the primary surge generation region, it can be shown that Φ2 will take a 

form such that
20

max

2 max max *

*

( ) for 

 1 otherwise.

R R R L

L

Φ≈ ≤

=

Equation 3-11

Figure 3-4. Numerically simulated (using ADCIRC) dimensionless alongshore surge 

(ζ/ζpeak) distribution. Demonstrates the similarity in surge scaling for 

hurricanes of different sizes (Rp is an input value to the TC96 model that is 

equivalent to Rmax for practical purposes) and intensities (cp is storm central 

pressure), where x’ is the deviation between a site and the landfall location 

divided by the radius to maximum winds (from Irish et al. 2008).

This is a natural limit related to what might be termed the fetch over which the wind can act to 

generate a significant slope in the water surface and hence forms an upper limit to the effect of 

increasing storm size on maximum surge levels in a storm. Hurricane Ike represents a good 

example of a storm for which the effect of storm size on peak surge levels was mitigated by the 

effective shelf width in the area of landfall and graphical support for this on a simple coast can 

be seen in Figure 3-5.

Irish and Resio (2010) have shown that three of the other four functions in Equation 3-10 have 

asymptotic limits. In extensive tests along the Texas coast and elsewhere, the relative position 

of the point of interest to the landfall location (Φ3) has been shown to behave as seen in Figure 

3-4. As expected the maximum surge occurs near the location where the maximum winds 

come ashore with surge levels decreasing monotonically to either side of this maximum. Φ4 is 

an interesting function in that it reflects two physical mechanisms which tend to have opposite 

effects on surge levels. On one hand, as the storm speeds up, wind speeds inside a hurricane 

increase due to the contribution of these background winds. On the other hand, as the storm 

speeds up the time winds blow over the surge generation area is decreased. As might be 

expected in such a situation, the result of combining these two effects is that the surges typically 

increase to a maximum value at some intermediate forward speed and decrease monotonically 

to either side of this maximum value. The last function with a natural limiting behavior is Φ5

(angle of approach). Changes in track angle increase peak surge by no more than 10% with 

respect to a shore normal approach. Figure 3-6 shows the general behavior of this function.
21

Figure 3-5. Results from numerical ADCIRC simulations showing maximum surge values 

as a function of storm size and storm intensity. The bold vertical line 

corresponds to a pressure differential of 133 mb.

Figure 3-6. Simulated peak surge as a function of hurricane track angle, measured 

counterclockwise from a due north approach. Plus or minus 10%, and 20% 

increases or decreases in value are marked by the dashed and dotted lines, 

respectively (from Irish et al., 2008).

The one function that does not have a clear upper limit in the potential maximum surge 

formulation is the pressure differential term, Φ1 (∆p). To examine the effect of the pressure 

differential on maximum surge, let us examine the simple case of a steady state wind over a 
22

shelf of constant width and depth. In this case, a simple linear approximation for the surge at 

the coast yields:

ρ η

ρ =

2

a d

w

cV L

gh Equation 3-12

where

ρa, ρw are the densities of air and water, respectively;

cd is the coefficient of drag;

V is the wind speed;

L is the shelf width;

g is the acceleration due to gravity; and

h is the water depth on the shelf.

This simple form can also be shown to be appropriate for more complex wind fields with a 

specified geometric similarity, such as found in hurricanes, and more complex offshore 

configurations. For a constant (no wind speed dependence) coefficient of drag, and noting that 

the pressure differential will be linearly proportional to V2

, it is expected that the maximum surge 

in hurricanes will depend linearly on the pressure differential. This result was confirmed 

numerically in a wide range of simulation along the Mississippi coast using simulations 

computed by the SLOSH code (Figure 3-7) (Niedoroda et al., 2010).

 

Figure 3-7. SLOSH results for a set of 44 points along the coast of Mississippi for storms 

of different central pressures.

However, wind speed profile data recently collected in real hurricanes (e.g. Powell et al. 2003, 

and Powell 2006) indicate that wind drag coefficients are not constant but rather increase until 

wind speeds of approximately 30-40 m/sec are reached and then the drag coefficient is reduced 
23

for increasing wind speeds above this range of values. Capping or reducing the wind drag 

coefficient results in a nonlinear surge response to further increase in pressure differential. 

The complex relationship between storm size and maximum wind speeds should also be noted. 

In a natural system such as a hurricane with high winds moving circularly around a pressure 

minimum, the wind and pressure distribution will tend toward a cyclostrophic balance in which 

the outward centripetal acceleration is balanced by the pressure gradient. In this situation, as 

can be verified by hurricane wind vortex models (numerical simulations of the planetary 

boundary layer in hurricanes), the maximum wind speed tends to scale linearly with the square 

root of the pressure differential. If we assume a purely cyclostrophic flow exists, the force 

balance depends on only two terms, the centripetal force directed outward away from the center 

of the storm and the pressure gradient force directed inward toward the center of the storm; 

consequently, in the vicinity of the maximum wind speed, the governing equation for the motions 

is of the form:

∆ =

2

max

max max

V p

R R ; where Vmax is the maximum wind speed Equation 3-13

which is consistent with a linear relationship between velocity squared and the pressure 

differential, independent of storm size. However, as the size of a hurricane becomes larger and 

larger, the geostrophic terms in the force-balance equation become the same order as the 

cyclostrophic terms and this equation changes form to:

∆

+ =

2

max

max

max max

V p fV

R R ; where fVmax is the coriolis acceleration Equation 3-14

In this situation, an increase in the storm size parameter will cause a decrease in the maximum 

wind speed and can have a larger effect on the total storm surge than the increase in size. In 

areas with smaller shelf widths, this effect can lead to a situation in which smaller storms can 

produce larger surges than a larger storm with the same intensity.

Finally, the discussion in Section 2 and data represented in Figures 2-4 and 2-5 indicate that the 

lowest central pressure possible is approximately 880 mb given recent SST. This value could 

be lower if SST within the Gulf of Mexico were to rise due to climate change. However, given a 

likely range of SST, data suggests there is a natural limit to storm intensity. This natural limit,

and the relationships between storm size and wind drag coefficient to wind speed, as previously 

discussed, all suggest the existence of an asymptotic relationship between storm surge and the 

pressure differential term. The uncertainty in estimating this natural limit, however, must be 

considered. A full discussion of the natural limit (MPI) on hurricane central pressure and 

estimating the uncertainty in estimating this limit is provided in Section 4.2.

3.4 Upper Limit Storm Surge Estimation Procedure 

The discussion in Section 3.3 suggests the existence of an upper limit for hurricane generated 

surges in natural environments. The following procedure is recommended for estimating 

maximum surge at a site of interest:

1. A high resolution state-of-the-art coupled wave-surge model with accurate bathymetric-
24

topographic data should be developed and the modeling system validated at the site of 

interest. The reliance on models in this approach requires that these models contain the 

best possible representation of the physics, that they properly resolve all critical scales 

of motion and topographic/bathymetric effects, and that they are calibrated and validated 

with historical data in the area of interest.

2. Develop a suite of synthetic storms. The storm suite should include a range of hurricane 

parameters and combinations of those parameters. For the southern U.S. coast, 

guidance for selecting the parameters to be simulated are:

a. Central Pressure: Storms with an MPI of 880 mb (consistent with Schade 

(2000)) and a central pressure that is 10 mb lower than the MPI.

b. Radius to Maximum Winds: Storms with an offshore Rmax of 30 nm and 

45 nm. These values are larger than any storms in the Gulf of Mexico 

with intensities greater than approximately 930 mb. In addition, as shown 

in Figure 3-5, on a 1 to 10,000 slope for an 880 mb storm, there is little or 

no variation of surge height with a change in storm size above an Rmax of 

approximately 40 nm.

c. Forward Speed: Three storm forward speeds should be simulated, a 

slow, medium, and fast, from approximately 5 to 22 knots. This range is 

based on the joint distribution storm speeds and central pressures in the 

Gulf of Mexico as shown in IPET (2009).

d. Holland B: The Holland B should be set to 1.27 which is the mean value 

for the Gulf of Mexico (IPET 2009).

e. Track: The track should be set to maximize storm surge potential. Irish 

et al. 2008 and Irish and Resio 2010 show that the peak is close to one 

Rmax from the landfall location. The position and orientation of the tracks

should be based on an analysis of historical high surge potential storm 

tracks in the area of interest and have minimal land interference as they 

approach the coast.

The central pressure, radius to maximum winds, and Holland B all vary systematically 

during the storm’s approach to land. Systematic variation in these parameters is 

identical to that used in the IPET (2009) and was adopted for the Gulf of Mexico FEMA 

and USACE studies. For details on the variation in these parameters see Appendix 8 of 

IPET (2009). It should be noted that these values are for the southern U.S. Gulf of 

Mexico coast only and are not applicable for other regions.

3. Applying the validated modeling system, simulate the surges that would be produced by 

these storms at the location of interest and determine the largest predicted surge. The 

modeling system can be applied with the existing mean sea level as the initial water 

level condition or include an estimate of eustatic sea level rise over the project life and 

an adjustment to reflect high tide. If these adjustments are not made to the initial water 

level condition, they must be added later. In areas with a large tidal range and/or high 

rates of sea level rise are estimated, it is recommended that the high water level is 

included in the modeling system.

4. Estimate the uncertainty in the estimate and add to the maximum calculated surge (guidance 

on estimating the uncertainty is provided in Section 4). If the tidal and sea level rise 

adjustments are not included in the simulated water level, they must also be added.
25

Effectively, the approach is deterministic in defining the storm suite. Each of the parameters 

has a range which is assumed to represent, or encompass, the value for that parameter that will 

generate the maximum possible surge. The probabilistic component is to define a 1% threshold 

based on estimated standard deviations in all relevant forcing mechanisms for surge, which 

allows for estimating the uncertainty in all the deterministic estimates.

The above procedure provides an estimate of the still water PMSS. Consideration must also be 

given to flooding potential from wave runup. A detailed analysis of wave runup requires very 

high resolution bathymetric/topographic data at the site location and application of a Boussinesq 

wave model or an approach such as that described by Melby (2012). Wave runup at a site is 

dependent upon the design of the nuclear plant and its protection features and its calculation is 

beyond the scope of this report. 

3.5 Summary

Two fundamentally different methods for estimating design surge levels have been utilized in 

past studies. Deterministic methods typically use the estimated maximum surge value from 

either a single storm or a small set of storms as its design level and do not consider the 

probability of that surge level. Probabilistic methods consider surges from a range of events 

along with the probabilities of those events and attempt to develop a relationship between surge 

levels and return period. Both the deterministic-based and probability-based approaches to the 

estimation of very-low-probability hurricane surges have deficiencies and it is recommended to 

combine the two methods. The hybrid approach determines which factors affecting hurricane 

surges can be shown to have asymptotic upper limits and which factors still have to be treated 

within a context that allows for natural uncertainty in estimating an upper limit for surges at a 

specified site. The discussion in this Section supports the existence of an upper limit for 

hurricane generated surges in natural environments and a procedure for estimating maximum 

surge at a site of interest is recommended for NRC consideration.

27

4.0 APPLICATION OF APPROACH

The Matagorda Bay site served as a platform for developing the initial concepts for very low 

probability surges and is the primary site examined in Sections 4.1 and 4.2. Analyses of the 

upper limit for storm surges at two other sites in Florida are examined in Section 4.3. Section 

4.4 develops a framework for quantifying exceedance probabilities of surges, including 

quantification of the effects of uncertainty on these estimates, and examines the relative 

magnitudes of surges obtained via the asymptotic upper limit method to estimated surge levels 

associated with the 10-6 annual frequency at the Florida sites.

4.1 Modeling System and Execution

The discussion in Section 3 lends support to the possible existence of an upper limit for 

hurricane-generated surges in natural environments; however, it is necessary to validate this 

concept with some actual detailed simulations. The test site selected is in the Matagorda, 

Texas area (Figure 4-1). Two types of tracks span the range of physically realistic major storms 

approaching this site, storms that form in the Bay of Campeche to the south of the site and 

storms that enter into the Gulf of Mexico between Cuba and Yucatan. The details of these 

tracks are not too critical, so they are represented as straight lines for the purpose of these tests 

(Figure 4-2). A suite of 20 storms (Table 4-1) was developed and simulated with a coupled 

system of wind, wave, and coastal circulation models. A schematic diagram of the modeling 

system is shown in Figure 4-3. All site and flood elevations are reported relative to the NAVD88 

datum.

Figure 4-1. Project test site.
28

Figure 4-2. Storm tracks developed with the maximum wind speeds over the point of 

interest.

Table 4-1. Storm parameter values used in Matagorda Bay simulations.

Storm Wind 

m/sec

Pres 

mb

Wlndf 

m/sec

P-lndf 

m/sec

Rp

nm

Holland B Vf

kt

025 59.6 880 46.5 904 30-42 1.35-0.9 5.5

026 58 880 42.4 918.6 45-63 1.35-0.9 5.5

027 61.1 870 48.4 893.8 30-42 1.35-0.9 5.5

028 59.4 870 44.4 908.6 45-63 1.35-0.9 5.5

029 61.4 880 47.5 905.8 30-42 1.35-0.9 11

030 59.2 880 44.5 918.6 45-63 1.35-0.9 11

031 62.8 870 49.3 895.8 30-42 1.35-0.9 11

032 60.6 870 46.4 908.6 45-63 1.35-0.9 11

033 64.3 880 54.6 901.9 30-42 1.35-0.9 22

034 61.8 880 50.9 912.3 45-63 1.35-0.9 22

035 65.6 870 55.9 891.9 30-42 1.35-0.9 22

036 63 870 52.7 902.3 45-63 1.35-0.9 22

037 62.3 880 50 902.8 30-42 1.35-0.9 11

038 60 880 44.4 919.6 45-63 1.35-0.9 11

039 63.7 870 51.9 892.8 30-42 1.35-0.9 11

040 61.4 870 46.3 909.8 45-63 1.35-0.9 11

041 65.1 880 55.1 902.8 30-42 1.35-0.9 22

042 62.2 880 48.8 919.6 45-63 1.35-0.9 22

043 66.4 870 56.5 892.8 30-42 1.35-0.9 22

044 63.5 870 50.5 909.6 45-63 1.35-0.9 22

 Track 1

Track 2
29

Figure 4-3. Schematic of hurricane modeling system.

For each storm, defined by a track and time-varying wind field parameters, the TC96 Planetary 

Boundary Layer (PBL) model (Thompson and Cardone 1996) is applied to construct snapshots 

of wind and atmospheric pressure fields every 15 minutes for driving surge and wave models. 

TC96 generates wind and pressure fields with a highly refined meso-scale moving vortex 

formulation developed originally by Chow (1971) and modified by Cardone et al. (1992). The 

model is based on the equation of horizontal motion, vertically averaged through the depth of 

the planetary boundary layer. 

The depth-integrated circulation model ADCIRC (Luettich et al. 1992, Westerink et al. 1994, 

Luettich and Westerink 2004) is then run to compute the pressure- and wind-driven surge 

component. Imposing the wind and atmospheric pressure fields, the ADCIRC model can 

replicate tide induced and storm-surge water levels and currents. As noted previously in this 

report, the ADCIRC model solves the defined governing equations over complicated bathymetry 

encompassed by irregular seashore boundaries using an unstructured finite-element method. 

This algorithm allows for flexible spatial discretizations over the entire computational domain. 

The advantage of this flexibility in developing a computational grid is that larger elements can be 

used in open-ocean regions where less resolution is needed, whereas smaller elements can be 

applied in the nearshore and estuary areas where finer resolution is required to resolve 

hydrodynamic details and more accurately simulate storm surge propagation onto a complex 

coastal landscape.

In parallel with the initial ADCIRC runs, the large-domain, discrete, time-dependent spectral 

wave model WAM (Komen et al. 1994) is run to calculate directional wave spectra that serve as 

boundary conditions for the local-domain, near-coast wave model STWAVE (Smith et al. 2001, 

Smith 2007). WAM generates the offshore wave field and directional wave spectra. The model 

solves the action balance equation for the spatial and temporal variation of wave action in 

frequency and direction over a fixed longitude-latitude geospatial grid. The numerical model 
30

STWAVE simulates nearshore wave transformation and generation. STWAVE numerically 

solves the steady-state conservation of spectral action balance along backward-traced wave 

rays. The source terms include wind input, nonlinear wave-wave interactions, dissipation within 

the wave field, and surf-zone breaking. STWAVE is a finite-difference model and calculates 

wave spectra on a rectangular grid. The model includes spatially variable wind and surge input 

fields. STWAVE generates the fields of energy-based, zero-moment wave height, peak spectral 

wave period, and mean direction; wave spectra at selected locations; and fields of radiation 

stress gradients. Using initial water levels from ADCIRC, winds that include the effects of 

sheltering due to land boundaries and reduction due to land roughness, and spectral boundary 

conditions from the large-domain wave model, STWAVE is run to produce wave fields and 

estimated radiation stress fields. The radiation stress fields are added to the estimated wind 

stresses, and applied as forcing in the ADCIRC model.

Model accuracy is directly related to how well the model represents the physical system 

(Westerink et al. 2008; Bunya et al. 2009). Many coastal landscapes are characterized by 

complex bathymetry and topography. Natural features such as barrier islands, bays, inlets, 

marshes, lakes and rivers as well as man-made features such as levees, roadways, railways, 

navigation channels, gates, and seawalls all influence surge and wave propagation. The surge 

and waves are not only influenced by the elevation of the landscape features, but also by the 

land cover, such as vegetation or buildings. The ADCIRC modeling system is able to capture 

the influence of these features across the coastal landscape (Wamsley et al.; 2009a, b).

 

Development of the ADCIRC grid utilized for this study was started in the 1990s (Westerink, 

Luettich and Muccino 1994). Considerable advancements were made for the IPET (2007) study 

and high-resolution wave model grids were developed. The IPET grids were then expanded 

and refined even further to create regional models that spanned the entire Louisiana and 

Mississippi coastal zone. The grid has been expanded further to include the Texas coastal 

zone and the mesh applied in this study has a reduced number of nodes in Louisiana and 

Mississippi for efficiency. The ADCIRC, TC96 PBL, and WAM model domains are shown in 

Figure 4-4. Note that the ADCIRC offshore boundary is in the deep Atlantic. Such a boundary 

allows for the model to accurately capture basin-to-basin and shelf-to-basin physics, which is 

important in estimating high water levels that often occur well in advance of a hurricane’s 

landfall. The ADCIRC mesh contains over 2.3 million nodes. Grid resolution in the deep water 

is about 25 km. Figure 4-5 details the high level of resolution in the project area, with nodal 

spacing reaching as low as approximately 100 m in the most highly refined areas. Increased 

resolution across the coastal floodplain allows features such as inlets, rivers, navigation 

channels, levee systems and local topography/ bathymetry to be properly represented 

(Westerink et al. 1994). Levees and roadways are barriers to flood propagation that are 

generally below the defined grid scale. ADCIRC defines these structures as sub-grid scale 

parameterized weirs with a specified height (Westerink et al. 2001) within the domain. The subgrid features such as levees and road systems are also shown in Figure 4-5. Figure 4-6 shows 

the STWAVE grid domain, a structured grid with 200 m resolution. Wave breaking zones must 

be resolved to ensure that the grid scales of the surge and nearshore wave models are 

consistent. The nearshore wave forcing function is properly incorporated by adding resolution 

where significant gradients in the wave radiation stresses exist (IPET 2007; Bunya et al. 2009). 
31

Figure 4-4. ADCIRC (brown), TC96 PBL (red), and WAM (red) model domains.

Figure 4-5. ADCIRC mesh in project area, colors represent bathymetry and topography 

and black lines are mesh elements.
32

Figure 4-6. STWAVE grid.

Accurate modeling of wave and storm surge levels requires accurate wind and pressure field 

input. For historical storms, best wind products are developed by expert meteorologists using 

data assimilation techniques. For synthetic storms, the TC96 PBL model is applied to construct 

snapshots of wind and atmospheric pressure fields every 15 minutes for driving the surge and 

wave models. Storms are defined by a track and time-varying wind field parameters. For each 

storm, a unique set of input conditions is defined. The data file includes the track position in 

space and time, the forward speed and direction, central pressure, pressure scale radius (which 

is related to the radius to maximum winds), a rotation angle, and a pressure profile peakedness 

parameter termed the Holland B factor (Holland, 1980). The wind and pressure field is 

generated and positioned on a fixed longitude/latitude grid system covering the Gulf of Mexico. 

Based on the location of the storm center, these snapshots describe the temporal and spatial 

evolution of a hurricane. The final wind and pressure fields resulting from TC96 are targeted on 

a grid domain. The temporal variation in these fields is typically set to 1800 s, (30-min average 

wind). All wind-fields are marine-exposure (no effective roughness variations for land/sea 

changes), and generated at a 10 m elevation. The effect of ground cover on winds as the 

hurricane makes landfall is accounted for within the ADCIRC storm surge model. In addition, 

ADCIRC applies a wind drag coefficient based on Garratt (1977), which has a cap of 0.0035. 

Example output from the TC96 for storm 027 from the storm suite is given in Figures 4-7 to 4-9. 

Figure 4-7 represents the spatial variation of the maximum wind speed, and Figure 4-8 is the 

minimum overall pressure distribution. The wind field product (Figure 4-7) reflects the storm’s 

path and displays the spatial coverage of high winds, an indication of the breadth in the 

hurricane core. Figure 4-7 also shows the decay in the wind speed magnitude as it makes 

landfall. As this hypothetical storm approaches the coastline, the wind speed decreases from 

approximately 61 m/s at its maximum to around 48 m/s at landfall, indicative of the pressure 

field filling. The minimum pressure distribution (Figure 4-8) clearly shows the storm track 

position, the radius to maximum winds, and where the filling of the pressure field occurs. An 

example plot of the wind speed and wind direction vectors is shown in Figure 4-9. The wind 
33

direction vectors point in the direction the winds are blowing. The wind speed contouring shows 

near continuous lines from the land to sea, indicative of generating an exclusive set of marine 

exposure wind fields. For this storm, the wind speed maximum is found in the right front 

quadrant of the storm.

The WAM offshore wave simulations supply the two-dimensional wave spectra in the coastal 

area to be used as input boundary conditions to the nearshore wave modeling effort supported 

by STWAVE. The WAM directional wave spectra are output every 15-minutes at discrete 

frequency and direction bands at specified save locations for the boundary conditions. Example 

output from WAM is given in Figure 4-10. Figure 4-10 is a plot of the maximum total significant 

wave height field for storm 27 from the storm suite. The envelope of high waves coincides with 

that of the wind core (see Figure 4-7). The maximum overall significant wave height (Hmo) for 

this simulation is approximately 67.2 ft offshore. In the coastal area closer to shore, the Hmo

results diminish to less than 26.2 ft.

The numerical model STWAVE simulates nearshore wave transformation and generation. 

Example output generated from the STWAVE model results are provided in Figure 4-11. Figure 

4-11 shows the maximum significant wave height in the vicinity of Matagorda. Wave period and 

wave direction are also calculated by STWAVE. The significant wave heights, periods, and 

directions in representative sections can be selected as boundary conditions for calculating 

wave runup and overtopping, wave forcing on structures, or for other design purposes.

Figure 4-7. Example of maximum wind speed contours generated by TC96 (Storm 027).
34

Figure 4-8. Example of minimum pressure field contours generated by TC96 (Storm 027).

Figure 4-9. Example snapshot of the wind speed (color contoured) and wind direction at 

the landfall output from TC96 (Storm 027).
35

Figure 4-10. Example of maximum overall total significant wave height contours 

generated by WAM (Storm 027).

ADCIRC estimates the water level across the entire grid at each time step. A time history of 

water levels can be saved at any grid location over the duration of a storm. To provide peak 

water levels, the entire spatial domain is examined during every model time step to determine if 

water levels exceeded the previous time step’s maximum water level at each point in the 

domain. The result of this analysis is a maximum envelope of water level for a given simulation 

and an example of this output generated from ADCIRC is provided in Figure 4-12. Figure 4-12 

is the envelope of maximum water level in the Matagorda, Texas area for storm 27 from the 

storm suite (Table 4-1). The hydrographs and peak water levels obtained from ADCIRC can be 

used to estimate flood risk and for flood damage reduction planning and design purposes.

Table 4-2 shows the surge levels at the site of interest for these test runs, represented as a 

black dot in Figure 4-12, along with all of the other parameters listed in Table 4-1. The surges 

at this point vary by only 2.1 ft (28.8 to 30.9 ft) over the parameter variations executed. The site 

elevation is approximately 28 ft. The dashes in Table 4-2 indicate that the site of interest was 

not inundated during the simulation. In an attempt to emphasize the natural organization 

inherent in the surge results, Figure 4-13 shows the pairs of surge levels for 880 mb and 870 

mb simulations plotted against the pressure differential, with all the other parameters held 

constant. As can be seen here, the surges for the larger pressure differentials are always 

slightly higher than the surges for the smaller pressure differentials. It is also evident that the 

slope of the increase is somewhat larger for Track 1 storms (shown in black) compared to Track 

2 storms (shown in red), with surge levels in the Track 1 storms increasing about 0.8 ft per 10 
36

mb increase in the pressure differential an surge levels in the Track 2 storms increasing about 

0.5 ft per 10 mb increase in the pressure differential.

What is not immediately obvious in Figure 4-13 is that the increase in storm surge levels is 

actually considerably less than expected based on pressure differential scaling. In such scaling, 

we would expect the surge levels to increase linearly with pressure differential (Irish and Resio, 

2010) which, for these simulations, should increase surge levels by about 7.6%. Instead, the 

increases are only about 2.3% to 3.0% for Track 1 storms and by about 1.5% to 1.7% for Track 

2 storms. Three factors play major roles in this nonlinear behavior in surge levels. First, 

although the planetary boundary layer model used for these simulations has been shown to 

produce a relatively linear relationship between the pressure differential and velocity squared 

over a wide range of pressure differentials and storm sizes, this linearity does not extend to very 

large pressure differentials in large storms (see Figure 4-14). Second, the ADCIRC model 

applies a wind drag coefficient formulation based on Garratt (1977) that caps the coefficient at 

0.0035 at wind speeds greater than 40 m/sec. Third, the extent of flooding increases both along 

the coast and across the coast for large storms, which diminishes the effect of a specified 

increase in the pressure differential in very intense storms relative to the effect of the same 

increase in pressure differential in less intense storms.

Figure 4-11. Example of maximum significant wave height generated by STWAVE (Storm 

027).
37

Figure 4-12. Example of envelope of maximum water level generated by ADCIRC.

 

Table 4-2. Surges produced by Matagorda Bay storms.

Surge

ft

Depth 

at Site, 

ft

Wind

m/sec

Pres

mb

W-lndf

m/sec

P-lndf

mb

Rp

nm

Holland 

B

Vf

kt

025 30.11 2.11 59.6 880 46.5 904 30-42 1.35-0.9 5.5

026 28.82 0.82 58 880 42.4 918.6 45-63 1.35-0.9 5.5

027 30.89 2.89 61.1 870 48.4 893.8 30-42 1.35-0.9 5.5

028 29.71 1.71 59.4 870 44.4 908.6 45-63 1.35-0.9 5.5

029 29.51 1.51 61.4 880 47.5 905.8 30-42 1.35-0.9 11

030 --- 0 59.2 880 44.5 918.6 45-63 1.35-0.9 11

031 30.14 2.14 62.8 870 49.3 895.8 30-42 1.35-0.9 11

032 29.19 1.19 60.6 870 46.4 908.6 45-63 1.35-0.9 11

033 --- 0 64.3 880 54.6 901.9 30-42 1.35-0.9 22

034 --- 0 61.8 880 50.9 912.3 45-63 1.35-0.9 22

035 --- 0 65.6 870 55.9 891.9 30-42 1.35-0.9 22

036 --- 0 63 870 52.7 902.3 45-63 1.35-0.9 22

037 29.91 1.91 62.3 880 50 902.8 30-42 1.35-0.9 11

038 29.19 1.19 60 880 44.4 919.6 45-63 1.35-0.9 11

039 30.37 2.37 63.7 870 51.9 892.8 30-42 1.35-0.9 11

040 29.68 1.68 61.4 870 46.3 909.8 45-63 1.35-0.9 11

041 --- 0 65.1 880 55.1 902.8 30-42 1.35-0.9 22

042 --- 0 62.2 880 48.8 919.6 45-63 1.35-0.9 22

043 29.51 1.51 66.4 870 56.5 892.8 30-42 1.35-0.9 22

044 --- 0 63.5 870 50.5 909.6 45-63 1.35-0.9 22
38

Figure 4-13. Lines drawn between pairs of ADCIRC simulations with different central 

pressures for various combinations of fixed storm track, storm size, and 

forward speed.

Figure 4-14 shows the relationship obtained from simulations with the planetary boundary layer 

model used here. The results indicate that up to a pressure differential of about 100 mb, the 

relationship is very linear; however, for larger pressure differentials, at least for the size of storm 

(30 and 45 nm in the offshore area) simulated here, the rate of increase of maximum wind 

speed squared with an increase in pressure differential diminishes. This explains part of the 

reason why the surge levels exhibit a reduced surge response relative to the expected pressure 

differential relationship; however, if we use the maximum wind speed squared scaling for surge 

levels, we still estimate that the increase in surge level of the 870 mb storms over the 880 mb 

storms would be about 5% for the Track 1 storms and 4.5% for the Track 2 storm. This is still 

larger than calculated with the model runs as the wind drag coefficient cutoff further reduces the 

surge response resulting in the nonlinear response. Recent analyses on drag coefficients have 

been made from GPS sonde wind speed profiles (Powell et al. 2003, and Powell 2006) and 

indicate that not only a drag cutoff is supported by data but that reduced drag coefficients may 

be appropriate for very high wind speeds in tropical cyclones. The Garratt formulation in 

ADCIRC applies a wind drag coefficient cutoff at wind speeds of approximately 40 m/sec and 

above, while the new GPS sonde data suggests that the drag coefficient should be reduced at 

these speeds. Reducing the drag coefficient for wind speeds greater than 40 m/sec would 

increase the nonlinear response of surge to increases in storm intensity. Therefore, the 

application of Garratt is conservative. 
39

Figure 4-14. Relationship between maximum velocity squared and pressure differential 

for TC96 PBL model.

4.2 Estimate of Limiting Values for Very-Low Probability Surge 

Levels 

Estimates of what might be the worst possible surge levels (the Probable Maximum Storm 

Surge, PMSS) at the site of interest can now be made. These estimates will be examined from 

both a probabilistic and a deterministic perspective. Similar to the approach used in recent risk 

assessments for flooding in the New Orleans area and elsewhere around the U.S. (IPET 2009; 

Niedoroda et al., 2010), the basic framework for the probabilistic assessment will be based on 

the joint probability of the primary parameters shown to influence surge levels in coastal areas. 

In this context, the Cumulative Distribution Function (CDF) for surge levels can be written as:

0 ( ) ... ( , , , , ) ( | ) F p pR v x p η pfl = ∆ × θ εη ∫ ∫ Equation 4-1

0 0 [ ( , ,,, | , , , ) ] p

pff p f f

p R B

H p R v x B d pdR dv d dx d

ss s

η θ ε θε ∂∆ ∂ ∂

−Ψ ∆ + ∆

∂∂ ∂

where the terms inside the brackets denote averaging across the entire ensemble of storms for 

the quantities within them, i.e.
40

 denotes the average Holland B value for storms in the Gulf of Mexico;

p denotes the average nearshore change in the pressure differential with ;

s

 denotes the average nearshore change

s

p

B

s

R

∂∆

∂

∂

∂ in the storm size with ;

 denotes the average nearshore change in the Holland B parameter with ; where

s

 is the spatial coordinate along the storm direction of travel.

s

B

s

s

∂

∂

There are two terms in Equation 4-1 which are represented probabilistically, the joint probability 

of all of the storm parameters, p(∆p, Rp, vf, θf, x0), and the conditional probability of the error in 

our representation of a storm, p(ε|η). Each of these must be quantified to obtain a realistic 

estimate of the exceedance probability of the events modeled.

0 123 45 ( , ,,, ) p pR v x ∆ pff θ =Λ ⋅Λ ⋅Λ ⋅Λ ⋅Λ Equation 4-2

where

2 max max

2

2

2

0 0 10 0 0

1 0

1 0

( () )

2()

2 max

(() )

2 3

4 0

[ ( ), ( )] ( ) ( | ) exp exp (Gumbel Distribution) ( )

1 ( |) ( )2

1 (|) 2

(| )

ff f

R pR

p

v v

f f

f

Fa x a x p ax p px

p p a x

pR p e

p

p v e

p x

σ

θ

σ

σ π

θ

σ π

θ

∆ − − ∆

− −

∂ ∂        ∆ −   Λ= ∆ = = − −      ∂∆ ∂∆          

Λ= ∆ =

∆

Λ= =

Λ =

2

2

( () )

2 ()

5 0

1

()2

( )

f f x

x e

x

x

θ θ

σ

σ π

− −

=

Λ =Φ

From the IPET (2009), the coefficients for the linear regression for the conditional storm size 

mean are obtained from:

R p max = + −∆ 14. 0.3 * (110. ) Equation 4-3 

with units for Rmax in nm and units for ∆p in mb implied. The standard deviation in this equation 

was estimated to be max σ( ) 0.44 ( ) ∆= ∆ p Rp . To ensure some level of conservatism in the 

application of Equation 4-3, it is modified to the form:

max 14.0 0.3 * (110. ) for 110

 = 14.0 for > 110

R p p

p

= + −∆ ∆ ≤

∆

 Equation 4-4 

which implies a lower limit of 6.16 nm for σ(∆p).
41

Neglecting uncertainty (error) in the estimation of storm surge, the probability of exeedance for a 

combination of storm intensity and storm size can be estimated as:

max max p pR pR pp p ( , ) ( | )( ) ∆ = ∆∆ Equation 4-5

Analyses also documented in IPET (2009) show that the coefficients for the Gumbel Distribution 

in the vicinity of Matagorda Bay are a0=62.67 and a1=7.69. Using these coefficients for a 

Gumbel distribution and a normal distribution for the size distribution from Equation 4-4, the 

exceedance probabilities for any combination of pressure differential and storm size used in our 

simulations can be estimated. The smaller of the two storm sizes simulated was 30 nm in the 

offshore area, the value of the standardized variate, defined as max max ( ) ˆ= ( )

RRp x

σ p

  − ∆     ∆ , for this 

size and a standard deviation of 6.16 nm is 30 14 2.597

6.16

− = , while the value of the standardized 

variate for the larger storm is 45 14 5.032

6.16

− = . The likelihood of a storm as large as, or larger 

than, a given storms is: 

2ˆ ˆ 2 1 () 1 ˆ ˆ 2

x x

F x e dx

π

−

−∞ = − ∫ Equation 4-6

where xˆ is the standardized storm size variate for that storm. For the smaller storm, this yields 

a value of 3.82 x 10-3

; and for the larger storm, this yields a value of 9.94 x 10-8. For the Gumbel 

coefficients determined for this site, the probability of exceedance for a 880 mb hurricane is 

estimated to be 1.38 x 10-4

; and for a 870 hurricane, it is estimated to be 1.38 x 10-5. The 

estimated probability for the hurricane landfall from the IPET study is specifically for the annual 

probability of such a landfall occurring within an alongshore “window” of 1-degree longitude at a 

latitude of 29.5 degrees, or approximately 52.2 nm.

Table 4-3 contains the exceedance probabilities for the 4 combinations of size and pressure 

differential used in our simulations, based only on size and intensity. Recalling that we have 

also restricted the storm approach direction by specifying the track heading at landfall and the 

landfall location is actually more restricted than a storm simply occurring anywhere within a 52.2 

nm window centered on the simulated track, it is likely that the actual probabilities are reduced 

by about another order of magnitude or so over the values listed in Table 4-3. However, an 

exact estimate of such long return period events is not really the focus of this discussion. 

Instead, these probabilities have been quantified only to show that the events being simulated 

are indeed very extreme event storms and cover the range well beyond the 10-6 annual 

frequency level sometimes used in discussions of risk of damage to critical nuclear facility 

infrastructure (NRC, 1986). 

Table 4-3. Annual probabilities of a storm with a combination of size and intensity equal 

to or greater than the storms simulated in this study.

∆p=133 mb ∆p=143 mb

Rp= 30 nm 5.27 x 10-7 5.27 x 10-8

Rp= 45 nm 1.37 x 10-11 1.37 x 10-12
42

Up to this point, it has been shown that, neglecting uncertainty in our estimates, the probabilities 

are very small for the types of storms simulated here. If we were to treat the uncertainty in the 

pressure differential in terms of an extrapolation from the data from Equation 3-2, we would see 

that the estimated width of the confidence band would be about 50 mb for estimates in the 

neighborhood of the 10-6 annual frequency level. Thus, although we have shown that the 

events simulated are expected to be extremely rare, we still need to pursue a quasideterministic upper limit in the storm intensity to avoid having to perform simulations with 820 

mb hurricanes.

 

The MPI of a hurricane has been postulated as an upper limit for extreme tropical cyclone 

intensities at least since the late 1970’s (see for example: World Meteorological Organization, 

1976 and Mooley, 1980). Before that time, theoreticians had recognized the existence of 

thermodynamic and dynamic constraints on the energy available for tropical cyclone 

intensification, even when unencumbered by proximity to land (see for example: Riehl, 1954; 

Miller, 1958; and Malkus and Riehl, 1960). More recently, Emanuel (1986, 1991) and Holland 

(1997) formulated theoretical models for estimating maximum tropical cyclone intensity. In an 

evaluation of the performance of these two MPI models, Tonkin et al. (2000) examined storms 

within 1) the Australian/southwest Pacific region, 2) the northwest Pacific region, and 3) the 

North Atlantic region. Since our primary interest is focused on the Gulf of Mexico, a subsection 

of the North Atlantic region, we will limit our discussion here to results for that region.

Figure 4-15 shows the geographic area encompassed within the “North Atlantic region” as 

defined by Tonkin et al (2000). Figure 2-4 presents the results from Tonkin et al.’s application 

of the Emanuel Model (black dots joined by a solid line), Holland’s model (dashed line), and 

observed intensities (open triangles joined by a solid line). This application used a climatological 

mean Sea Surface Temperature (SST) defined over the period 1950 to 1979. Evans (1993) 

results indicated that there was little gain in predictive skill when actual monthly SST values are 

used in place of the climatological mean.

Figure 4-15. Geographic area used in Tonkin et al. (2000) study.
43

As can be seen in Figure 2-4 and as widely accepted from theoretical considerations, a strong 

relationship exists between climatological SST values and the lowest central pressures. We 

see that, in the range of SST values from 26o to 28o (C), the minimum central pressures of the 

Holland Model, the Emanuel model and the observed intensities are all in approximate 

agreement. Above 28o (C), the observations continue to show decreasing central pressures 

with increasing values of SST; whereas, the Emanuel and Holland models do not.

Figure 2-5, taken from Schade (2000), shows another approximation for the MPI. In this paper, 

Schade suggests that the effect of the SST field on tropical cyclone intensity is twofold. First, 

the large-scale ambient SST field “sets the stage for the tropical cyclone.” Second, the intensity 

of a tropical cyclone is highly sensitive to the reduction of the SST in the interior region of the 

storm due to the response of the ocean to surface winds. Thus, whereas the concept of the 

MPI is well founded, many of its details are still under development. The 85% humidity line 

shown in Figure 2-5 will be taken as the upper limit here, since this is reasonably consistent with 

the upper limit of the data shown in Figure 2-4. 

Figure 4-16 shows the average August to September SST for the Gulf of Mexico during the 

period 1940 to 2006. As can be seen here, the highest average values during this part of the 

year (the peak of hurricane season) have varied from as low as 28.17o C in 1984 to as high as 

29.49o C in 1962. The dotted vertical line in Figure 2-5 shows this historical maximum plotted 

on top of Schade’s results. The heavy solid line along the top of that figure denotes the MPI 

value without consideration of any negative feedback of the type discussed by Schade; thus, it

is expected to represent a maximum possible threshold for the MPI. From Figures 2-4, 2-5, and 

4-16, it can be argued that a value of 880 mb represents a very sensible (perhaps slightly 

conservative) value for the MPI in the Gulf of Mexico, without consideration of significant global 

warming effects on SST’s that might drive them higher than the level of the 1960’s.

Figure 4-16. Variation of average August through October SST in Gulf of Mexico from 

1940 through 2006 (from Extended Reconstructed Sea Surface online 

repository).

Year

Av

era

g

e

S

e

a

S

urfa

c

e

T

e

m

p

erature (C)

1940 1950 1960 1970 1980 1990 2000 28

28.2

28.4

28.6

28.8

29

29.2

29.4
44

In a situation with perfect theories and models, the 880 mb value for central pressure could be 

applied to an exact model of bathymetry, wind, waves, and surges and obtain a deterministic 

limiting value for the PMSS; however, there are at least four sources of variability that should be 

considered in the application of the MPI to the estimation of the maximum surge:

1. Uncertainty in the MPI; 

2. Uncertainty in storm surge prediction; 

3. Potential climate variability over the projected design lifetime; and

4. Tide levels accompanying the maximum surge event. 

Each of these sources of uncertainty listed can be further broken down into contributions from 

two basic types of uncertainty: 1) aleatory uncertainty, which is due to the lack of sample size in 

empirical data used and/or the existence of unresolved/unpredictable variations in system 

behavior, and 2) epistemic uncertainty, which is due to the lack of understanding of the physics 

of and/or relationships within the system.

4.2.1 Uncertainty in the MPI

To estimate the inherent uncertainty in our estimate of the MPI, it should be noted that the 

models used to obtain these estimates are highly parameterized and that the data supporting 

the postulated relationships contain considerable uncertainty, as seen in Figure 2-4. In addition, 

the existing MPI concept does not address the issue of storm size, so one is forced to assume 

that the MPI value is independent of storm size, which is probably not a very good assumption, 

but at least is expected to be conservative. The scatter of points around a linear regression line 

through the observed data (triangles) in Figure 2-4 has a standard deviation of about 4 mb. 

Since a direct estimate of the uncertainty in the MPI is not included within the modeled values, a 

slightly higher value, 5 mb, is taken as an indicator of the uncertainty in our estimate of the MPI.

4.2.2 Possible Errors in Storm Surge Prediction

Most comparisons of model predictions versus observed surge levels involve simulations which 

use “best winds” to drive the coupled wave-surge models (Bunya et al., 2010). Studies of 

computer simulations with parametric winds are conducted less frequently; however, such 

studies are actually much more valuable in understanding and quantifying coastal flooding risks, 

since the risk estimates invariably must use wind-field representations with reduced dimensions 

to be able to characterize the multivariate statistical variations involved in the JPM approach. 

Figure 4-17 shows a comparison of surges predicted by the same coupled wave-surge model 

system as used here against measured high water marks (HWM). This figure and similar 

comparisons for Hurricane Rita indicate that the uncertainty in these predictions can be 

characterized by a standard deviation of about 1.5 ft. This value is somewhat an optimal value 

where considerable effort was spent in developing careful bathymetries and in local validations. 

A somewhat larger value of 2.0 ft is taken as representative of a more general estimate of the 

error in such model predictions.

4.2.3 Potential Climate Variations Over the Design Lifetime

There are many site specific patterns of coastal evolution expected along US coastlines in the 

coming years. The effects of climate variability, sea level rise, and subsidence will all play 

important roles in this evolution. Natural features of the coastal landscape and the vegetation 

types covering landscape features affect surge propagation in coastal areas (Wamsley et al. 
45

2010). However, these effects have not been well quantified to date and there is a large degree 

of uncertainty associated with these changes. The general approach recommended for NRC 

consideration is to separate the sea level change issue from the climate effects on storm 

patterns and intensities, since local subsidence can be such a major component of the former. 

Subsidence and other forms of coastal landscape evolution can be incorporated into the model 

grids if these are expected to contribute significantly to future storm surge levels, such as in 

deltaic areas. However, for most applications, assuming that an estimate for relative mean sea 

level can be obtained for a site of interest, a simple approximation can be made to just add the 

sea level rise linearly to the surge level. Since we are using an MPI approach and not variations 

in storm frequency and intensity here, we can concentrate on the potential impact of climate 

variability on SST’s, which would, in turn, affect the MPI value.

Figure 4-17. Comparison of observed USACE HWMs for Hurricane Katrina and the 

simulation using the PBL wind fields at the recorded USACE HWMs. Thin 

blue lines display a 1:1 correlation as well as 1.5 ft standard deviation on 

each side.

4.2.4 Tide levels accompanying the maximum surge event

Since tide levels are driven by astronomical forcing, rather than meteorological forcing, they are 

generally considered to be independent of hurricane surge levels. To account for this 

possibility, a tidal adjustment (ηtide) equal to the difference between mean higher high water and 

mean tide level should be added in the final computation of the PMSS. The difference between 

mean higher high water and mean tide level can be taken as a simple estimate of the additional 

sea level rise associated with a storm occurring at high tide versus a storm occurring at mid-tide 
46

(the water level used in the numerical simulations. For Matagorda, this value is approximately 

0.4 ft. The tide contribution can be much larger at other locations.

4.2.5 Impact of Uncertainties on the Estimated Upper Limit Surge

So how would all of these uncertainties impact the estimated upper limit surge level? First, the 

case in which the SST values are not affected significantly by climate variability is examined. 

The probability density function for the maximum surge, including uncertainty, can be expressed 

as:

* * 12 1 2 1 2 * 1 2 ( ) ( | , , )( )( ) ( ) F p p MPI p p H η η εε ε ε η ε ε η ε ε MPI d d

∞ ∞

−∞ −∞

= ∆= + + − ∫ ∫ Equation 4-7

where 

ε1 is the uncertainty term related to errors in the estimation of the MPI

ε2 is the uncertainty term related to surge modeling errors; and

ηMPI is the estimated maximum surge for the MPI given the storm set modeled.

Errors for both the estimation in the MPI and the model error follow a Gaussian distribution 

(Resio et al. 2008) and therefore Equation 4-7 can be approximated in a fashion similar to that 

of Equation 4-6. Since there are two different variances involved in these errors, they are

summed before being applied in estimating the likelihood of exceedance, i.e., the standardized 

variate used in Equation 4-6 is:

2 2 1/ 2

1 2

ˆ= ( )

MPI tot x η ε

σ σ

  −     + Equation 4-8

where the subscript “tot” refers to a term with the two sources of uncertainty summed. In this 

form the variances must be converted to the same physical units as the surge values.

 

In Equation 4-8, the first term is related to estimates of the MPI. Contributions to this include the 

uncertainty in the parameterized, quasi-empirical equations used for estimating the MPI. Here 

the 5 mb value noted previously is taken as a very rough estimate of the error in the MPI due to 

potential errors in the parametric model used in predicting the MPI. A simple linear form such 

as p p η

η σ σ ∆∂ = ∂∆

for this should suffice to convert the standard deviation in the estimate of the 

MPI (5 mb) to an estimate for the expected standard deviation in the surge height due to 

uncertainty in the pressure differential of the MPI. Based on the slopes of the lines in Figure 4-

13, we can estimate 

p

∂η

∂∆ to be about 0.8 ft per 10 mb; since the rms for the pressure differential 

(σ∆p) is 5, we obtain a final estimate of approximately 0.4 ft for σ1.

From the information in Figure 4-17, one might estimate that the rms error in model estimates 

for surges is in the neighborhood of 1.5 ft; however, the case of the Katrina comparison is quite 

special, with considerable work done to ensure relatively good results in these comparisons. It 

is not at all clear that a truly “blind” set of predictions for a very low probability storm would have 

an rms error that is this small. As noted previously, the error in predictions of these very large 

storms in such a situation is assumed to be one-third larger, about 2.0 ft. This is an area where 

additional work is needed to provide a more defensible value; however, based on comparisons 
47

for other storms (such as Hurricanes Rita, Gustav, and Ike), the value of 2 ft is reasonable. It is 

interesting to note that the expected effect of errors due to surge modeling uncertainties is 

considerably larger than the effect of uncertainties in the MPI. This is primarily due to the low 

slope of the 

p

∂η

∂∆ term required to relate variations in the MPI to variations in surge for these very 

large storms. Thus, the sum of the two variances is 2 22 2 2

1 2 σ σσ tot =+= + = (0.4) (2.0) 4.16 where σ1

2

is the variance associate with MPI uncertainty and σ2

2 is the variance associated with the model 

prediction uncertainty. The combined total standard deviation is,

22 2 2

1 2 σ σσ tot = += + = (0.4) (2.0) 2.04 , which is less than a 2% increase over the standard 

deviation based on the modeling error alone.

The problem with an unbounded error, such as might be associated with the upper limit of a 

Gaussian probability function, is that there is not a definitive estimate of the PMSS at a site, 

since there is no absolute upper bound to this error distribution. Since we do not have sufficient 

data to dispute this statement, it is difficult to rely on empirical data to establish an upper bound 

for errors. For example, in Figure 4-17, some of the data points show that predicted and 

observed values differ by as much as 8 ft, which is more than would be expected for the 

estimated standard deviation and the number of samples. Therefore, rather than attempting to 

determine an absolute upper bound, it seems advantageous to make use of the fact that our 

events are already characterized as having extremely low probabilities. To allow the uncertainty 

in the modeling to enter into our estimate of the maximum surge, without dominating the 

estimate, we will make use of a 1% threshold of exceedance estimate for our PMSS (equivalent 

to a “2.34-sigma” level). This decreases the overall probability of the expected occurrence of 

this event (as shown in Table 4-3) by about two additional orders of magnitude, but at least 

allows the model uncertainty to be considered.

The effect of climate variability on storm surges over the design lifetime of a structure is the final 

factor considered here. As noted previously, the evolution of coastal landscapes and the 

estimation of sea level rise are both very site specific and should be considered independently 

of the generic surge estimation methodology being described in this report. There have been 

many papers which have addressed possible impacts of climate on the frequency and intensity 

of hurricanes (tropical cyclones). A very good review of this topic can be found in Knutson et al. 

(2010). However, since only the MPI characteristic of storms is being treated, rather than an 

entire distribution of multiple storm characteristics, the investigation is restricted to only the 

impact of climate variability on the MPI. In this context, interest is focused on the likelihood of 

different SST’s and the impact on the expected MPI. 

The actual pattern of summertime SST’s in the Gulf of Mexico (shown in Figure 4-16) resembles 

more of a cyclical pattern than a secular trend. For this reason, it is difficult to use existing data 

to project linearly into the future. Given the lack of projected SST changes specific to the Gulf of 

Mexico, a 1.0o C increase in SST was used to represent a reasonably conservative estimate for 

the potential increase in this parameter over a 100-year facility design life. The 1.0o C is based 

on the measured increase in mean SST in the Northern Atlantic over the last 100 years (Rayner 

et al. 2003). From Figure 2-5, such an increase can lead to about a 14 mb increase in the MPI 

value. This, in turn, increases the associated surge by about 1.2 ft.
48

4.2.6 Putting All Factors into a Single Estimate for the Matagorda Bay Site

The deterministic estimate of the PMSS at the Matagorda Bay site can be taken as the largest 

surge produced by an MPI storm (880 mb) in our storm suite. From Table 4-2 we see that this 

value is 30.1 ft. If we were absolutely certain that this was the correct value for MPI that was 

possible within our study area over the design lifetime of our structure and if we knew that our 

models (including all bathymetric information) were absolutely accurate, this would be a 

reasonable estimate of the PMSS at this site. Since none of these assumptions are justified, we 

should add some additional margins to account for our uncertainty. As previously computed, 

the estimate of the root-mean-square error in our estimates of surge levels due to potential 

inaccuracies in our MPI value and in current state-of-the-art modeling methods (σtot) is 2.04 ft. 

Allowing for a 2σtot margin in our surge estimates will decrease the expected annual frequency 

of an event by about 2 orders of magnitude, which combined with the estimated probability from 

Table 4-3 shows that the estimated annual probability would be 5.27 x 10-9

. Adding the 2σtot

“uncertainty margin” to the deterministic estimate gives us an estimate of 34.2 ft for our 

estimated value of the PMSS, neglecting climate variability. If we add the potential impact of a 

1.0o C increase in SST on the MPI, this would add another 1.2 ft to the estimated PMSS, 

yielding a final value of 35.8 ft. Or, in a simple equation form, we have:

PMSS = PMSS Uncertainty Uncertainty Tidal E deterministic MPI+Models Climate ffects

For our site (feet):

 35.8 = 30.1 + 4.1 + 1.2 + 0.4

+ ++

 Equation 4-9

4.3 Analyses of Surges at Two Sites in Florida

Following the computer runs and analyses for Matagorda Bay, an additional set of surge 

simulations and analyses were conducted for the Levy County and Turkey Point nuclear sites in 

Florida to investigate how well the methodology developed for Matagorda Bay would work 

elsewhere. Figures 4-18 and 4-19 show the model domains for these simulations. Figures 4-20 

and 4-21 show the bathymetric/topographic information used for these model runs, with the 

specific point saved for subsequent analyses shown on each figure. All site and flood 

elevations are reported relative to the NAVD88 datum. It should be noted that the surge 

simulated for Levy County did not inundate the proposed site. Therefore, in order to 

demonstrate the method, the estimated surge near the Crystal River Energy Complex is 

reported for Levy County.

For the Levy County site, based on historical storm tracks, tracks similar to that in Figure 4-22 

are able to develop and maintain very high intensity and size, due to the geometric constraints 

of the surrounding land areas. Strong storms must be imbedded within the westerlies to make 

landfall in the Tampa area. Examples of recent storms in the Gulf of Mexico of this class are 

Opal in 1995 and Wilma in 2005. The tracks in Figure 4-22 were selected to approach at an 

angle that maximizes storm surge. The same storm transformation algorithms used for the 

Matagorda Bay site to decay storm intensity, increase its size, and diminish its Holland B value 

during hurricane approach to land were used here. Table 4-4 provides relevant information on 

the set of storms simulated for this site. 
49

Figure 4-18. ADCIRC mesh near the project area, marked with a red circle and x, for the 

Levy County site in Florida.

Figure 4-19. ADCIRC mesh near the project area, marked with a red circle and x, for the 

Turkey Point site in Florida.
50

Figure 4-20. ADCIRC topography and bathymetry contours near the project area, marked 

with a red circle and x, for the Levy County site in Florida.

Figure 4-21. ADCIRC topography and bathymetry contours near the project area, marked 

with a black circle and x, for the Turkey Point site in Florida.
51

Figure 4-22. Storm tracks, blue lines, for the Levy County site, shown with a red circle 

and x, in Florida.

Table 4-4. Storm parameters and surge for Levy County site.

Storm Surge Wind Pres W-lndf Plndf Rp Holland B Vf

ft m/sec mb m/sec mb nm kt

1 29.89 59.48 880 45.25 910 30-39 1-1.35 5.5

2 31.86 60.98 870 47.19 900 30-39 1-1.35 5.5

3 29.33 60.87 880 47.47 910 30-39 1-1.35 11

4 30.97 62.29 870 49.36 900 30-39 1-1.35 11

5 26.41 64.08 880 52.99 910 30-39 1-1.35 22

6 27.82 65.39 870 54.46 900 30-39 1-1.35 22

7 30.51 57.66 880 44.23 910 45-58.5 1-1.35 5.5

8 32.41 59.05 870 46.14 900 45-58.5 1-1.35 5.5

9 30.68 58.74 880 46.13 910 45-58.5 1-1.35 11

10 32.35 60.12 870 47.97 900 45-58.5 1-1.35 11

11 29.76 61.63 880 50.10 910 45-58.5 1-1.35 22

12 31.14 62.91 870 51.82 900 45-58.5 1-1.35 22

13 10.93 39.81 960 21.96 990 45-58.5 1-1.35 5.5

14 18.04 48.40 930 32.29 960 45-58.5 1-1.35 5.5

15 25.26 54.76 900 39.98 930 45-58.5 1-1.35 5.5

At the Turkey Point site, two critical tracks appeared feasible (Figure 4-23) and both were 

included in the simulations conducted. Since our basis for the storm transformation during 

approach to land is based on Gulf of Mexico data, this transformation was not included in the 

storms affecting the Turkey Point site. Table 4-5 provides relevant information on the set of 

storms simulated for this site.
52

Figure 4-23. Storm tracks, blue lines, for the Turkey Point site, shown with a red circle 

and x, in Florida.

Following the methodology developed for Matagorda Bay, we obtain the following estimates of 

the PMSS for the two sites in Florida, assuming that the MPI value is still in the neighborhood of 

880 mb: 

Levy County (ft)

PMSS = PMSSdeterministic + UncertaintyMPI+Models + UncertaintyClimate +Tidal Effects

 

37.7 = 30.7 + 4.1 + 1.2 + 1.7 Equation 4-10

Turkey Point (ft)

PMSS = PMSSdeterministic + UncertaintyMPI+Models + UncertaintyClimate +Tidal Effects

 

26.1 = 19.7 + 4.1 + 1.2 + 1.1 Equation 4-11

At first glance, these values seem rather high for the site being investigated. Since the 

predictive models have been shown to be reasonably accurate, even for surges of the 

magnitudes generated here, there is no obvious reason to suspect that these surge levels are 

biased high due to the modeling system used. However, the storms simulated in this “upperlimit” analysis are certainly large intense storms, which have not yet been encountered in the 

areas of interest. Because of this, it is important to evaluate the likelihood of the storms used 

here are much less frequent than the value used for other safety considerations (an annual 

frequency of 10-6

). This will be done in Section 4.4.
53

Table 4-5. Storm parameters and surge for Turkey Point site.

Storm Surge Wind Pres W-lndf Plndf Rp Holland B Vf

ft m/sec mb m/sec mb nm kt

1 16.11 59.66 880 59.41 880 30 1.35 5.5

2 16.60 61.15 870 60.87 870 30 1.35 5.5

3 14.67 61.15 880 61.00 880 30 1.35 11

4 15.55 62.57 870 62.42 870 30 1.35 11

5 12.89 63.92 880 63.92 880 30 1.35 22

6 13.39 65.22 870 65.22 870 30 1.35 22

7 15.09 57.60 880 57.57 880 45 1.35 5.5

8 15.52 59.03 870 59.01 870 45 1.35 5.5

9 14.73 58.97 880 58.97 880 45 1.35 11

10 15.16 60.37 870 60.37 870 45 1.35 11

11 12.93 61.11 880 61.00 880 45 1.35 22

12 13.71 62.46 870 62.36 870 45 1.35 22

13 19.72 60.18 880 59.18 880 30 1.35 5.5

14 20.37 61.65 870 60.64 870 30 1.35 5.5

15 18.14 62.76 880 60.85 880 30 1.35 11

16 18.80 64.15 870 62.28 870 30 1.35 11

17 15.62 64.97 880 63.78 880 30 1.35 22

18 16.11 66.29 870 65.10 870 30 1.35 22

19 18.90 58.45 880 57.65 880 45 1.35 5.5

20 19.52 59.87 870 59.06 870 45 1.35 5.5

21 18.31 60.31 880 58.84 880 45 1.35 11

22 18.90 61.64 870 60.24 870 45 1.35 11

23 16.34 62.28 880 61.49 880 45 1.35 22

24 16.90 63.56 870 62.77 870 45 1.35 22

25 11.98 41.58 960 40.29 960 30 1.35 5.5

26 15.58 50.73 930 49.45 930 30 1.35 5.5

27 18.27 56.95 900 55.96 900 30 1.35 5.5

4.4 Analysis of 10-6 Storms at Two Florida Sites

Although uncertainty is often noted as a potential problem for very low probability events, the 

quantification of the effects of uncertainty on the risk has been an evasive problem. A very 

relevant point for licensing nuclear power plants in coastal areas is whether or not the storms 

defined by the upper limit analysis developed in this report are much less likely to occur than the 

accepted standard for safety at these plants, an annual frequency of 10-6

. To begin, historical 

data is analyzed to estimate the central pressure associated with an annual frequency of 10-6

. 

The conditional probability of storm size, with its dependence on storm intensity, is assumed to 

be the same as that used in the Gulf of Mexico study (IPET 2009). This assumption is much 

less conservative than assuming that the conditional storm size distribution is independent of 

storm intensity; since it predicts that large intense storms are much rarer than large moderate 

intensity and weak storms. Under this assumption, the approximate probability of the smaller of 

the two storms (an Rmax of 30 nm) is on the order of 0.01. Thus, when this probability for the 

storm size is combined with the 0.0001 probability for storm intensity, a 10-6 value for the overall 

hazard probability is obtained. 
54

4.4.1 Levy County Site

A careful analysis of hurricane data for the west coast of Florida, as expected, shows that most 

storms move east to west through this area. However, these storms usually have passed over 

land in getting into the Gulf of Mexico and do not produce large storm surges along the west 

coast of the state. In order to focus our analysis on storms of the type that produce significant 

surges along the west coast of Florida, the storm sample is stratified to include only storms with 

a general west to east motion in a latitude-longitude box with boundaries at 81o W and 85o W 

longitude and 25o N and 30o N latitude, and will further limit the storms to those with central 

pressures which are less than 990 mb in this box. Using the most recent reanalysis data 

available from NCDC (HURDAT)1

 

, we find that most storms before about 1940 did not report 

central pressures; consequently, we shall limit our data set for analysis to the interval 1940 to 

2009 (70 years).

Table 4-6 shows a list of the selected storms, their central pressures and the years in which 

they occurred. Table 4-7 gives the results for a Generalized Extreme Value (GEV) analysis in 

terms of the expected central pressure associated with selected return periods (taken here as 

just 1 over the annual frequency) and the standard deviation as a measure of the confidence 

band of this estimate. It should be noted that the difference in the length of coast considered to 

be a “direct hit” in terms of the surge levels produced must be accounted for and the length of 

coast considered in the analysis upon which Table 4-7 is based. In a similar fashion to our 

probabilistic interpretation at the Matagorda Bay site, it is assumed that a direct hit occurs when 

the storm makes landfall within a ±1 Rmax distance along the coast, centered on the location of 

the maximum surge at the site of interest. Since we used an approximate along-coast distance 

of 240 nm, this introduces another factor of 4 into the estimated return periods shown in Table 

4-7. Thus, a 10,000-year value would become the 40,000-year value with this adjustment and 

the 884 mb estimate for the 10,000-year central pressure would become a 903 mb estimate for 

the 10,000-year central pressure within this reduced coastal domain.

Table 4-6. Storms included in analysis of extremes for Levy County site.

Year Name Minimum Central Pressure 

(mb)

1944 Not Named 968

1946 Not Named 979

1947 Not Named 989

1948 Not Named 963

1948 Not Named 975

1950 Easy 958

1953 No Named 985

1964 Isbell 964

1968 Gladys 965

1982 Alberto 985

1998 Mitch 987

1999 Irene 986

2000 Gordon 981

2001 Gabrielle 983

2004 Charley 947

2005 Wilma 950

 1 Available at http://www.nhc.noaa.gov/pastall.shtml
55

Table 4-7. Analysis of central pressures of hurricanes for selected return periods at the 

Levy County site: Results are for a storm striking anywhere along a 240 nm 

stretch of coast.

Return Period Central Pressure (mb) Standard Deviation

20 962 5.8

100 950 9.1

200 941 11.5

500 921 17.0

1000 912 19.4

5000 892 24.9

10000 884 27.3

Typically, the estimates in a table such as Table 4-7 would be used deterministically, and the 

size of the confidence bands would only be noted as a separate piece of information. With this 

deterministic interpretation, the estimate of the 1-in-10,000 central pressure is about 23 mb 

higher than the MPI value and the surges associated with Storm 15 (a 900-mb storm) would 

represent a better estimate of the risk-based surge levels. However, the implication of this is 

that uncertainty has no impact on our risk estimates, which runs counter to intuition.

The traditional form of an extremal distribution can be written in terms of a deterministic 

estimate given by the best-fit GEV Distribution. In the case of the west Florida hurricanes, the 

best-fit distribution was very close to a simple Gumbel distribution, so the Gumbel distribution is 

used here. From the analysis the following estimate of the Cumulative Distribution Function 

(CDF) from Table 4-7 is obtained, with X in this case denoting the value of the pressure 

differential, related to the central pressure by the relationship X=1013-cp:

0

1

0 1

) ( ) exp exp

where

= 31.7 and = 12.34 

( ) is the best fit to the data not adjusted to an annual basis

and the Poisson-Gumbel Distribution for return period is:

b

x a aFX

a

a a

F X

        − ′ = −−                

′

1 ) [1 ( )]

where

 is the annual frequency (= 16/280) and

 is the return period in years; which yields for the annualized CDF, ( ):

1 c) ( ) 1 .

r

r

r

T

F X

T F

F X

T

λ

λ

η

λ

= − ′

= −

 Equation 4-12

It should be noted that the annual frequency factor is simply the number of storms which 

occurred divided by four times the number of years where the additional factor of four in the 

denominator comes from the spatial adjustment mentioned previously.

If no uncertainty existed in our estimate of the CDF for pressure deviations, the encounter risk of 

a particular pressure deviation could be taken directly from Equation 4-12c; however, the risk of 

encountering a particular magnitude of pressure differential (X), for a fixed expected value of 

annual frequency should be understood to be non-zero for other values than the single 

deterministically estimated value; and the effect of possible values deviating from the 
56

deterministic estimate should be considered when forming a “risk-based” estimate of the 

exposure to a particular extreme value. A more realistic treatment of the risk associated with 

the return periods in Table 4-7 can be obtained by quantifying the effects related to their 

probabilistic variation around the deterministic value. The estimated standard deviation, typically 

used to construct control curves around the deterministic estimate, provides a good means of 

quantifying the spread of the probabilities around the deterministic estimate; and in this context, 

the probability of a pressure differential can be written in terms of an integral in two dimensions 

with a delta function to reduce it back to a single dimension:

0

ˆ ˆˆ ˆ ˆ ( ) [ ( ) | ]( )()( ) ( )

where

ˆ ( ) denotes the deterministic estimate of X for a given return period and

 denotes the deviation from the the deterministic surge estimate.

r r

r

p X p X T X p X p X X d dX T

X T

ε εδ ε ε

ε

∞ ∞

−∞

= + + − ∫ ∫ Equation 4-13

In Equation 4-13, the estimate for p(ε) is taken as a Gaussian distribution with the mean value at 

ηˆ and the standard deviation taken from Equation 3-2. However, as seen in Table 4-7, the 

uncertainty in the estimated pressure deviation increases with return period, i.e.:

1

ˆ 1 2 2 (| ) ˆ ( )2

where

( ) is the standard deviation of the esti ˆ ˆ mate at a given value of .

pX e X

ε

σ ε

σ π

σ η η

  −     =

 Equation 4-14

The deviation has a mean value of zero, so no mean value is shown inside the exponential 

function in Equation 4-14.

To integrate Equation 4-13, the range of the deviations was limited to less than or equal to ±5 

standard deviations (with an appropriate normalization coefficient included in the integral to 

ensure that no probability was inadvertently omitted from the total integral) and the relationship 

between the standard deviation and the deterministic estimate of the pressure differential was 

fitted empirically,

[ ] 10000 20

20 20

( ) () ( ( )) ( ( )) ln( ) ln( ) ln(10000) ln(20) r r

T T XT XT T T σ σ

σ σ − = + − − Equation 4-15

where the number subscripts on the return periods denote specific return periods in years. This 

provides a good fit to the data for the entire range of values between return periods of 20 years 

to 10,000 years.

Since the question at hand relates to the return period of the MPI value compared to the 10,000-

year minimum central pressure, results are first converted to a return period representation 

before they are presented, using standard forms for this conversion,

1 ( ) 1 ()

T X r F X = − Equation 4-16a
57

with

0

ˆ ˆˆ ˆ ˆ ( ) [ ( ) ]( )() ( ) ( ) F X p X T X p X p H X X d dX T r r ε ε εε

∞ ∞

−∞

= + + − ∫ ∫ Equation 4-16b

where

H(•) is the Heaviside Function, equal to 1 if • ≥ 0 and equal to 0 if • < 0.

Figure 4-24 shows the results of this integration for three cases compared to the original 

deterministic estimate. Case 1 is the deterministic solution for the return period based on the 

best-fit Gumbel Distribution. Case 2 is a test of the numerical algorithm generated by 

representing the probability of the deviations as a delta function (i.e. all of the probability exactly 

on the deterministic line), which was computed as a test case for the integration algorithm. As 

expected, this case exhibited no significant deviations from Case 1, so the Case 1 and Case 2 

lines are identical. Case 3 shows the results using standard deviations equal to the estimated 

standard deviations divided by two; and Case 4 shows the results for the standard deviations as 

fit to the data in Table 4-7. These results show that the very low probability tail of the 

distribution is markedly affected by standard deviations comparable to those obtained in the fit 

to the Florida west coast data on central pressures. The results shown in Figure 4-24 show that 

the 1 in 10,000 (10-5

) frequency central pressure, based solely on a statistical analysis, is 

approximately 887 mb. This value is slightly higher than the MPI value of 880 mb and would 

likely produce surges in the range of 28.9 to 29.2 ft for a storm with a radius to maximum winds 

equal to 45 nm and in the range of 28.2 to 28.5 ft for a storm with a radius to maximum winds 

equal to 30 nm. It should be noted that the estimate for the 10-6 annual probability surge level 

considered only some of the possible storm combinations. A larger suite of storms (i.e. a larger 

subset from an extended joint probability method) would have to be considered in order to 

establish a better estimate of the 10-6 annual probability surge level. 

4.4.2 Turkey Point Site

In this Section, a similar procedure to that developed in the previous Section is followed. In this 

case, east-to-west moving storms within a latitude-longitude box with boundaries at 77.4o W and 

80.4o W longitude and 23.5o N and 27.5o N latitude are considered, and, similar to the Levy 

County site, the storms are further limited to those with central pressures which are less than 

990 mb in this box. For the same reasons as noted for the Levy County site, the period of 

record is chosen to be 1940 to 2009 (70 year).

Table 4-8 gives a list of the selected storms, their central pressures and the years in which they 

occurred. Table 4-9 gives the results for a GEV analysis in terms of the expected central 

pressure associated with selected return periods (again taken here as just 1 over the annual 

frequency) and the standard deviation for the confidence band of this estimate. Similar to the 

case of Levy County, if we assume that the “direct hit” zone is approximately 60 nm wide, an 

additional factor of four is introduced into the estimates in Table 4-9 to account for the longer 

length of coast (240 nm versus 60 nm) included in the sample of extremes used in Table 4-9 

compared to the “direct hit” length. A note should be given here that, unlike the Levy County 

site, the data for Turkey Point did exhibit considerable curvature away from a Gumbel 

Distribution; however, the analyses was kept consistent and proceeded with usage of the bestfit Gumbel distribution to estimate the effects of uncertainty.
58

Figure 4-24. Comparison of “risk-based” return periods for central pressures without 

uncertainty considered (Cases 1 and 2) and with uncertainty considered 

(Cases 3 and 4) for the Levy County site using data from 1940-2009. Case 4 

represents the actual estimate for the Levy County site.

Table 4-8. Storms included in analysis of extremes for Turkey Point site.

Year Name Minimum Central Pressure 

(mb)

1947 Not Named 947

1949 Not Named 954

1960 Donna 932

1964 Cleo 968

1965 Betsy 952

1966 Inez 985

1979 David 972

1992 Andrew 930

1995 Erin 980

2004 Frances 958

2004 Jeanne 951

2005 Katrina 983

2005 Rita 985
59

Table 4-9: Analysis of central pressures of hurricanes for selected return periods at the 

Turkey Site: Results are for a storm striking anywhere along a 240 nm stretch 

of coast.

Return Period Central Pressure (mb) Standard Deviation

20 950 5.8

100 931 9.1

200 918 11.5

500 889 17.0

1000 877 19.4

5000 848 24.9

10000 835 27.3

Figure 4-25 shows a comparison of the same types of cases analyzed for the Levy County site. 

In this case, the uncertainty is substantially larger; and even by the 5,000 year return period, the 

effect of uncertainty is to lower the central pressure by about 25 mb. The data indicate that the 

hurricane population coming into the Turkey Point area is, in general, more intense than 

hurricane population coming into the west Florida area; therefore the statistically derived central 

pressure is considerable lower than the MPI in the Turkey Point area.

Figure 4-25. Comparison of “risk-based” return periods for central pressures without 

uncertainty considered (Cases 1 and 2) and with uncertainty considered 

(Cases 3 and 4) for the Turkey Point site using data from 1940-2009. Case 4 

represents the actual estimate for the Turkey Point site.
60

4.5 Summary

An example of how a combined deterministic-probabilistic approach can be applied to estimate 

the PMSS (including a first approximation for effects of uncertainty) at three sites (Matagorda 

Bay, Texas; Levy County, Florida; and Turkey Point, Florida) has been presented. Guidance on 

quantifying the uncertainty in climatological parameters and within a state-of-the-art system is

also provided. The uncertainty has traditionally been neglected in past upper-limit estimates of 

surge levels; but the magnitudes of these terms are not negligible. The values of the 

uncertainty terms developed here can serve as reasonable first estimates for the entire Gulf of 

Mexico, since the MPI values and the modeling uncertainty factors are similar throughout this 

region. The recommended estimate for uncertainty due to the estimation of the MPI and the 

models is 4.1 ft and the uncertainty due to climate parameters is estimated at 1.2 ft.

The possibility that the upper limit storms are much larger than the 10-6 annual probability used 

for safety standards at nuclear power plants is also examined at the two Florida sites. As part of 

this effort, the importance of quantifying the impact of uncertainty on estimated surges for a 

fixed frequency level was stressed and a method to accomplish this was developed. In the 

applications here, the estimated central pressures for the 10-4 annual probability were shown to 

be about 15 mb lower when the effects of uncertainty were included. In the two Florida cases 

examined here, the PMSS value for Levy County exceeded the 10-6 annual probability surge. 

Furthermore, at Turkey Point, the annual probability associated with the PMSS was smaller than 

10-6

.
61

5.0 SCREENING METHOD

Appendix C of Regulatory Guide 1.59 contains maps and tables of estimated surges for the U.S. 

Gulf and Atlantic coasts that nuclear power plant applicants can use to determine if flooding 

might be severe enough near their prospective site to warrant more detailed definitions of 

design-basis floods. The USACE was tasked by the NRC Office of Nuclear Regulatory 

Research to develop an updated screening approach that includes data collected and analysis 

methods developed since the publication of Regulatory Guide 1.59. The screening method 

recommended for NRC consideration should include criteria for proceeding or not proceeding 

to more detailed definitions of design-basis floods and explicitly consider local conditions and 

bathymetry that may affect flood level estimates.

 

This Section documents a proposed screening approach to determine if a prospective site is at 

risk of flooding from coastal storms. It begins with a description of surge propagation with an 

emphasis on the importance of the local surrounding coastal landscape and the strength and 

duration of the relevant storm forcing. These complexities drive the development of a 

recommended approach that computes a critical storm surge flood elevation map that is 

compared to a controlling site elevation and provides criteria for proceeding to more detailed 

estimation of design-basis floods. The methodology incorporates an open-coast surge 

calculation, wind wave effects, tide, and uncertainty to estimate a conservative elevation 

threshold that provides the criteria. The recommended method for developing the critical flood 

elevation is demonstrated for sites at Matagorda, TX; Biloxi, MS; Levy County, FL; and Turkey 

Point, FL. The comparison of the computed critical flood elevation to a controlling topographic 

elevation for screening a prospective nuclear power plant site is demonstrated at Matagorda. 

5.1 Processes That Affect Storm Surge

As hurricanes and extra-tropical storms approach the coast, four storm-related phenomena can 

occur to modify local water levels: setup due to wind, low barometric pressure, set up due to 

wave forcing, and rainfall. Storm winds force water towards the coast and typically create the 

greatest change in local water elevation. Low barometric pressure provides a secondary effect, 

creating a bulge in the water surface around the center of the storm. Wave forcing creates a 

local setup on the coast. Rapid storm rainfall can also increase the local water elevation. 

Additional factors not related to the storm itself are the astronomical tide and river flows at the 

time the storm reaches the coast. The spatial scales of the relevant forcing processes, such as 

the wind and wave fields can range from meters in complex shallow areas to hundreds of 

kilometers in large deep basins.

Storm surges are greatly influenced by the geometry of the basin and continental shelf leading 

up to the coastal floodplain. A mildly sloping continental shelf, such as in the Gulf of Mexico, 

results in a higher storm surge as compared to a coast with a steeper bathymetry. The Atlantic 

and Gulf of Mexico basin geometries are very complex in both the “cross-shelf” and “alongshelf” directions. These coasts are characterized by natural features such as bays, inlets, barrier 

islands, and wetlands. Natural feature details at a finer scale, such as coastal streams, 

distributaries in wetlands, and the vegetation types covering landscape features, also affect 

surge propagation in coastal areas. Man-made features, including extensive levee, rail and 

road systems, navigation channels, canals, and culverts must also be resolved.

 

The complexities of modeling surge propagation and the interaction of coastal storms with 

natural coastal features are discussed by Westerink et al. (2008), Resio and Westerink (2008), 
62

and Wamsley et al. (2010). Model accuracy requires 1) the application of a model with 

sufficient spatial resolution to represent important bathymetric/topographic features accurately 

and 2) that all terms contributing to the surge are represented in the proper physical context. 

Processes that affect storm surge inundation include atmospheric pressure, winds, air-sea 

momentum transfer, waves, river flows, tides, and friction due to land cover. Numerical models 

exist that can properly define the physical system and include an appropriate non-linear 

coupling of the relevant processes. A coupled surge-wave model must be applied and the 

computational domain must be sufficiently large to negate the need for empirical factors along 

an offshore grid boundary. Therefore, there is no “short cut” to estimating coastal surges that 

considers all the local conditions for critical applications such as determining flood risk at 

specific prospective nuclear power plant sites. Such an application requires not only resolution 

of the ocean basin, but also detailed representation of the coastal floodplain to be incorporated 

into modeling system meshes or grids. These highly detailed meshes are expensive to 

construct and result in computational run time requirements that are considerably higher than 

for simpler models. In addition, the coastal flood plain is constantly changing due to both 

human development and natural processes which necessitates frequent updating of the 

meshes.

5.2 Requirements for a Screening Approach

The preceding discussion emphasizes that there is not a simple method to properly estimate 

coastal surges for prospective nuclear power plant sites that considers all the local conditions. 

Any prospective nuclear site that is vulnerable to coastal storm surge flooding should be 

required to have a detailed analysis performed. Therefore, the purpose of the screening 

approach should be to identify a critical elevation that defines whether or not a prospective site 

is at risk for coastal surge flooding. The determination of the critical elevation should be 

relatively simple to apply, consistently determined across the coast, and incorporate an 

appropriate level of conservatism.

 

The critical flood elevation should be determined with an appropriate modeling system. 

However, available surge model systems and their application can vary widely. For example, 

each model may apply different formulations of the wind or bottom drag law that can result in 

extremely different surge estimates for the same storm, particularly for large storms. The quality 

of surge estimates is also dependent on the model domains and how boundary conditions are 

applied. Therefore, each screening application should be carefully reviewed to ensure that an 

appropriate determination is made with respect to the coastal surge flood risk at any given site.

A coupled system of wind, wave, and coastal circulation models has been developed and 

implemented for regions in both the Gulf of Mexico and the Atlantic, as described in Section 4. 

The system combines the TC96 PBL model (Thompson and Cardone 1996), the WAM offshore 

(Komen et al 1994) and STWAVE nearshore (Smith et al 2001, Smith 2007) wave models, and 

the ADCIRC (Westerink et al. 2008; Bunya et al. 2010) basin-to-channel scale unstructured grid 

circulation model. The model includes the nonlinear coupling of multiple processes (e.g. 

riverine flow, tide, wind, waves) that contribute to storm surge. The domains are large enough 

to capture the required basin-to-basin and basin-to-shelf physics. The modeling system can be 

run at very high-resolution, accurately representing the physical system with resolution on the 

order of 10 m. The system has undergone extensive validation with Gulf of Mexico storms 

including hurricanes Betsy, Andrew, Ivan, Katrina, and Rita. Based on these extensive 

validation efforts, the details of the models and error associated with surge simulations with this 

system are relatively well known compared to other modeling frameworks. The ADCIRC 
63

modeling framework is therefore recommended for generation of the open coast surge estimate 

for screening purposes.

The open coast surge estimate for screening purposes will need to be generated with meshes 

that do not have detailed representations of the coastal flood plain due to the expense in 

developing these grids. Since a detailed analysis is not part of the screening flood elevation 

estimation, an appropriate level of conservatism should be incorporated into the flood estimates. 

The screening method includes mechanisms to ensure that a reasonable, but conservative, 

estimate of a critical flood elevation is made, as discussed in the following section.

5.3 Screening Method

The coupled system of wind, wave, and coastal circulation models previously discussed is 

appropriate for a detailed coastal surge analysis. The model includes the nonlinear coupling of 

multiple processes and can be run at very high resolution, accurately representing the physical 

system with resolution on the order of 10 m. This allows fine details of the coastal flood plain to 

be resolved that are important to accurately estimate surge levels a specific sites. 

Unfortunately, this high level of detail is expensive to develop in computational meshes and 

requires extensive computer resources to calculate. The coupling of the wave models also 

adds complexity and requires significant resources to compute. However, estimates of opencoast Probable Maximum Storm Surge (PMSS) appropriate for screening can be predicted by 

applying the wind and surge models without resolving the coastal flood plain landward of the 

coastline. The wave setup can then be added separately by applying a factor discussed by 

Resio and Westerink (2008) that represents the ratio of the transfer rate from the wave field to 

the direct wind momentum transfer rate. Tidal effects and predicted sea level rise can also be 

incorporated. Finally, uncertainty must also be considered in the determination of the final 

critical flood elevation.

 

5.3.1 Open Coast PMSS Estimation

Because a conservative estimate of the PMSS is desired, a storm with an extreme upper limit 

for surge potential must be simulated2

. This conservative PMSS for screening purposes will be 

referred to as the SPMSS (Screening PMSS). If the peak surge level at a point only depended 

on a single scalar variable, such as wind speed, the maximum value of that variable could 

clearly be associated with the maximum surge value. However, hurricane surge response at a 

specific site depends on several storm factors and not just a single, scalar variable (i.e. wind 

speed). Several recent studies (IPET 2009; Resio et al., 2008; Irish et al., 2008; Irish and 

Resio, 2010) have shown that the maximum surge can be estimated as a function of several 

storm parameters:

max 1 2 max 3 0 4 5 ( ) ( ) ( ) () () η θ =Φ ∆ Φ Φ − Φ Φ p R xx vf f Equation 5-1

where the multiplicative functions Φi depend on the specific bathymetric/topographic setting at 

the specific point being investigated, Δp is the peripheral pressure minus the central pressure 

(storm intensity), Rmax is the distance from the eye to the maximum winds (storm size), x-x0

denotes the alongshore position of the point of interest relative to the landfall position, vf is the 

forward velocity of the storm, and θf is the angle of storm heading. 

 2 Section 3 provides a detailed discussion on deriving very low probability surge levels. Key concepts are 

reviewed here.
64

The screening storm must consider reasonable parameter values that maximize surge potential. 

As discussed in Section 4, the surge functions associated with each of these parameters have 

asymptotic limits or natural limiting behavior. Irish and Resio (2010) noted that when the storm 

size becomes as large as the region of primary surge generation, additional increases in storm 

size do not produce substantial increases in storm surge. Analysis by Irish and Resio (2010) 

found that increases in offshore storm size above approximately 45 nm in the Gulf of Mexico 

resulted in negligible increases of storm surge. Therefore, for the Gulf of Mexico shelf, a 

reasonable upper limit on storm size for screening purposes is 45 nm. Changes in the forward 

velocity of a storm results in two physical mechanisms that have opposite effects on surge 

levels. Wind speeds inside a hurricane increase with increasing forward velocity of a storm due 

to the contribution of background winds, resulting in a potential increase in surge. Conversely, 

as the storm speeds up, the time winds blow over the surge generation area is decreased, 

resulting in a potential decrease in surge. For open coast simulations not allowing for 

inundation, such as those proposed for the screening method, the importance of the time scales 

for which winds blow over the surge generation area is reduced relative to the increases in wind 

speed. Therefore, a fast moving storm generates greater surges at the coast for these 

simulations and a forward velocity of 22 kt is proposed for screening.

The primary driver of surge potential is storm intensity. The surge function associated with 

storm intensity does not have a clear upper limit. However, the MPI of a hurricane has been 

postulated as an upper limit for extreme tropical cyclone intensities at least since the late 1970’s 

(see for example: World Meteorological Organization, 1976 and Mooley, 1980). Emanuel 

(1986, 1987, 1991) and Holland (1997) formulated theoretical models for estimating maximum 

tropical cyclone intensity. Tonkin et al. (2000) evaluated the performance of these two MPI 

models in the North Atlantic region. Figure 2-4 presents the results from Tonkin et al.’s 

application of the Emanuel Model, Holland’s model, and observed intensities. As can be seen 

in Figure 2-4 and as widely accepted from theoretical considerations, a strong relationship 

exists between climatological SST values and the lowest central pressures. In the range of SST 

values from 26o to 28o (C), the minimum central pressures of the Holland Model, the Emanuel 

model and the observed intensities are all in approximate agreement. Above 28o (C), the 

observations and Holland model continue to show decreasing central pressures with increasing 

values of SST; whereas, the Emanuel model does not. Figure 2-5, taken from Schade (2000), 

shows another approximation for the MPI. Schade (2000) suggests that the effect of the SST 

field on tropical cyclone intensity is twofold: 1) the large-scale ambient SST field “sets the stage 

for the tropical cyclone”; and 2) the intensity of a tropical cyclone is highly sensitive to the 

reduction of the SST in the interior region of the storm due to the response of the ocean to 

surface winds. Therefore, the concept of the MPI is well formed, but many of the details are still 

under investigation.

Figure 4-16 shows the average August to September SST for the Gulf of Mexico during the 

period 1940 to 2006. The highest average values during this part of the year (the peak of 

hurricane season) have varied from as low as 28.17o C in 1984 to as high as 29.49o C in 1962. 

The dotted vertical line in Figure 2-5 shows this historical maximum plotted on top of Schade 

(2000) results. The heavy solid line along the top of Figure 2-5 denotes the MPI value without 

consideration of any negative feedback of the type discussed by Schade; thus, it is expected to 

represent a maximum possible threshold for the MPI. Figures 2-4, 2-5, and 4-16 support a 

reasonable estimate of 880 mb for the MPI in the Gulf of Mexico, without consideration of 

significant global warming effects on SST’s that might drive them higher than the level of the 

1960’s. However, considering that many of details of the MPI are still under development and 

the desire for a conservative estimate for screening purposes, an MPI of 870 mb is proposed.
65

The parameters for the screening storm are summarized in Table 5-1. This storm must be 

simulated on tracks that make landfall along the Gulf of Mexico and Atlantic coasts. For 

different stretches of coastline, as determined by the physical characteristics of the Gulf of 

Mexico and Western Atlantic basins, only certain types of tracks are physically realistic for major 

storms approaching the coast. For example, major storms approaching Matagorda, TX can 

form in the Bay of Campeche to the south or enter the Gulf of Mexico between Cuba and 

Yucatan. For Biloxi, MS, major storms enter the Gulf of Mexico between Florida and Cuba or 

between Cuba and the Yucatan. Figure 5-1 provides examples of the major storm tracks that 

make landfall in these two regions and at the Florida sites.

 

Table 5-1. Screening storm parameters.

Central Pressure (mb) Radius to Maximum Winds 

(nm) Forward Velocity (kt)

870 45 22

Figure 5-1. Location of Matagorda, TX, Biloxi, MS, Levy County, FL, and Turkey Point, 

FL, regions with storm tracks for screening storm.

Open coast surge estimation does not require simulation on a mesh that resolves the coastal 

flood plain and a simpler mesh can be applied. The USACE developed the East Coast 2001 

Western North Atlantic (EC2001) mesh to compute a database of tidal constituents (Mukai et al.

2002). The EC2001 domain encompasses the Western North Atlantic Ocean, the Gulf of 

Mexico, and the Caribbean Sea (Figure 5-2) and can be applied to provide conservative 

estimates of open coast storm surge. The eastern open ocean boundary is along the 60-deg 

west meridian where the bathymetry is almost entirely in the deep ocean. The EC2001 has 

over 250,000 nodes and nearly 500,000 elements. Resolution varies from 25 km in the deep 

ocean to approximately 1 km along the land boundaries. The bathymetry in the mesh is defined 

from multiple databases, including ETOPO5 (National Geophysical Data Center, Nation 

Oceanic and Atmospheric Administration, Boulder, CO, 1988); the Digital Nautical Charts 

bathymetric database (U.S. Department of Defense, National Imagery Mapping Agency, 

Washington DC, 1999); and the NOS raw sounding bathymetric database (NOS Hydrographic 

Survey Digital Database). The coastline boundaries for EC2001 are from the Defense Mapping 

Agency’s World Vector Shoreline database (Soluri and Woodson 1990). The final bathymetry 
66

for EC2001 is shown in Figure 5-3. A complete description of the mesh and its development is 

provided by Mukai et al. (2002).

Figure 5-2. EC2001 finite element grid (from Mukai et al. 2002).

Hurricane simulations on the EC2001 mesh capture the required basin-to-basin and basin-toshelf physics and include the nonlinear coupling of the relevant processes other than the 

transfer of momentum due to waves. The termination of the mesh at the shoreline precludes 

surge propagation inland and surge builds up at the coast, providing a generally conservative 

estimate of open coast surge elevations in the region of interest. To illustrate how surge 

estimates simulated on the EC2001 differ from those made on a mesh with a highly resolved 

coastal flood plain, results from simulations with the screening storm (Table 5-1) that makes 

landfall in the Matagorda, TX region (see Figure 5-1) are compared. The EC2001 and meshes 

in the Matagorda region are plotted in Figures 5-4 and 5-5.
67

Figure 5-3. EC2001 composite bathymetry in meters relative to the geoid (from Mukai et 

al. 2002).

 
68

Figure 5-4. EC2001 mesh and bathymetry in the vicinity of Matagorda, TX.

Figure 5-5. Detailed mesh and bathymetry/topography in the vicinity of Matagorda, TX.
69

The peak surge elevations for the screening storm making landfall in Matagorda with the 

EC2001 and detailed meshes are plotted in Figures 5-6 and 5-7, respectively. The peak surge 

at the coast is higher on the EC2001 mesh because the water is precluded from propagating 

inland. On the detailed mesh, as surge propagates inland, water elevation goes down with 

increasing distance in many areas but can also increase with topography. The peak surge 

elevations realized at inland locations are controlled by the surrounding coastal landscape and 

the strength and duration of the relevant forcing. The duration of the relevant forcing is primarily 

controlled by the forward velocity of the hurricane. Figure 5-8 is a plot of the peak surge 

elevations for a storm with the same parameters as the storm in Table 5-1, except that the 

forward velocity is 11 kt. The slower moving storm increases the duration hurricane winds 

propagate storm surge and results in greater peak surge elevations far inland, which can be 

seen by comparing Figures 5-7 and 5-8.

 

Figure 5-6. Matagorda peak surge elevations for screening storm on the EC2001 mesh.

Figure 5-7. Matagorda peak surge elevations for screening storm on the detailed mesh.
70

A conservative surge estimate based on open coast surge must account for the variability 

associated with propagation inland. To understand how surges may vary spatially in both the 

cross shore and longshore directions, a suite of storms was simulated on a detailed mesh with 

tracks making landfall in the Matagorda, TX, Biloxi, MS, Levy County, FL and Turkey Point, FL 

regions. The suite of storms had pressure and size parameters consistent with those in Table 

5-1. The suite included additional storms with slower forward velocities. In Figure 5-9, the peak 

surge elevations over all storms simulated are plotted versus the maximum surge on the 

EC2001 mesh at several locations across the coastal flood plain within 20 km of the maximum 

surge location at all four locations. The plot shows that the open coast surge estimate on the 

EC2001 is greater than most points in the region of interest. For Biloxi, the peak surge at all 

points across the region of interest simulated on the detailed mesh fall below the peak surge on 

the EC2001. However, at Matagorda, Turkey Point, and Levy County the controlling topography 

allows surge to propagate a longer distance inland, slow moving storms push water up the 

coastal flood plain and the peak water surface elevations at far inland points are greater than 

those at the coast. The maximum difference between the peak surge on the EC2001 mesh and 

the detailed mesh is approximately 5 ft (Figure 5-9), which provides a conservative estimate of 

the peak water level deviation due to variability of surge propagation inland (ηdev). This value 

will be considered a generally applicable correction factor for locations along the Gulf of Mexico 

to account for the variability associated with propagation inland and must be included in the final 

computation of the SPMSS. While the 5 ft correction factor is the maximum calculated for the 

various sites modeled and should provide a sufficient conservative estimate for the majority of 

the U.S. southern coast, this value may not be conservative for every coastal landscape and a 

greater value may be warranted in some circumstances.

Figure 5-8. Peak surge elevations on the detailed mesh in the vicinity of Matagorda, TX 

for a storm with a central pressure of 870 mb, radius to maximum winds of 45 

nm and a forward velocity of 11 kt.
71

Figure 5-9. Peak surges on detailed mesh plotted versus the peak surge for the 

screening storm on the EC2001 mesh.

5.3.2 Tidal Effects

All simulations are run at mean tide level. A storm may, however, occur at high tide which 

would result in higher peak surge elevations. To account for this possibility, a tidal adjustment 

(ηtide) equal to the difference between mean higher high water and mean tide level should be

added in the final computation of the SPMSS.

5.3.3 Wind Wave Effects

Wave setup that occurs due to the momentum transfers from waves must also be included in 

maximum surge elevations. The momentum source, termed a radiation stress, is produced by a 

divergence in the momentum flux within the wave field and is primarily related to wave breaking. 

The momentum loss rate from wave breaking is dependent on the slope and depth of the sea 

bottom, and varies considerably throughout a region of interest and from site to site. The 

introduction of this source can be accomplished by coupling wave and surge models as 

previously discussed and would be required for a detailed analysis. However, an estimate of 

the wave setup can be made based on estimates of the ratio of the transfer rate from the wave 

field to the direct wind momentum transfer rate (R) as discussed by Resio and Westerink 

(2008). The function that defines the variability of R is provided by considering the different 

wave breaking forms assumed in various wave models and theoretical approaches and 

simulated wave momentum loss rates. Figure 5-10, which is based on an approach introduced 

by Resio and Westerink (2008), shows the envelope of the resulting estimates of R on different 

bottom slopes. 
72

Figure 5-10. Approximate upper and lower limits of the ratio of the wave contribution to 

water levels at the coast (wave setup) to the total surge at the coast.

The relationship described by Figure 5-10 can be applied to estimate the wave setup along the 

coast for the SPMSS storm, assuming there is not significant offshore sheltering of waves. The 

only shoreline along the Gulf and Atlantic coasts subject to significant offshore wave sheltering 

is south Florida due to the presence of the Bahamas (see Figure 5-3). Application of Figure 5-

10 in this area results in an overestimate of wave setup as documented in Table 5-2. Table 5-2 

provides the wave setup estimated from Figure 5-10 and the maximum wave setup computed 

with a fully coupled, high resolution modeling system for the Matagorda, TX, Biloxi, MS, Levy 

County, FL, and Turkey Point, FL regions. The wave setup from screening purposes is 

determined by calculating the offshore slope at all four locations according to Irish and Resio 

(2010), obtaining the R value from Figure 5-10, and then solving for the wave setup based on R

and the peak surge calculated at the coast on the EC2001 mesh. Wave setup can be estimated 

as:

mod 1 el

R

R

∗η − Equation 5-2
73

Table 5-2. Estimated wave setup

Wave Setup (ft)

R

(from Figure 5-10)

Function(R, ηmodel)

(Equation 5-2)

Coupled Numerical 

Model*

Matagorda 0.15 4.8 5.0

Biloxi 0.10 3.8 2.7

Levy County 0.05 2.0 1.6

Turkey Point 0.20 6.0 1.7

 *Note: Maximum wave setup across entire area of interest

The maximum wave setup calculated with a detailed coupled model system was determined by 

comparing coupled model system results with and without radiation stress forcing applied. As 

seen in Table 5-2, this approach provides a reasonable estimate of wave setup at all sites, 

except Turkey Point, where offshore waves are subject to sheltering by the Bahamas. The 

wave sheltering results in much lower setup than that predicted with equation 5-2 and the R 

value should be adjusted down for south Florida sites. Based on the analysis here, an R value 

of 0.1 for southeast Florida should provide a reasonable, yet conservative estimate of wave 

setup.

Flooding at a site can also occur as a result of wave runup and overtopping. A detailed analysis 

of wave runup would require the bathymetric/topographic profile at the site location and 

application of a Boussinesq wave model or an approach such as that described by Melby 

(2012). Any wave runup at a site would be dependent upon the design of the nuclear plant and 

it is therefore impractical to estimate at the time a screening analysis is performed. For 

screening purposes, it is therefore proposed to include a freeboard value. The appropriate 

value will vary depending on regional and local conditions and should be carefully considered. 

For example, in the case of a facility not on the open coast and where there is overland surge 

propagation, such as Matagorda TX, 3 ft can be considered a reasonable value based on 

engineering experience. For nuclear facility sites on the open coast, this value may need to be 

greater. The values used here are for illustration purposes and each application should be 

carefully reviewed to ensure a proper freeboard value is applied.

5.3.4 Uncertainty

Three sources of variability that should be considered for estimating the SPMSS: uncertainty in 

the MPI; uncertainty in storm surge prediction; and potential climate variability over the 

projected design lifetime. Because a conservative value of 870 mb for the MPI is being 

considered for the screening storm, the uncertainty in the MPI can be considered accounted for. 

However, the uncertainty in the storm surge prediction and potential climate variability must also 

be considered and added to the final SPMSS value.

The coupled modeling system being applied for the screening storm suite has been validated 

with multiple storms in the Gulf of Mexico. Based on these validations, uncertainty in the model

predictions can be characterized by a standard deviation of about 1.5 ft (see Bunya et al. 2010). 

The uncertainty in model prediction should account for two times the standard deviation, giving 

an uncertainty in model predictions (Umodel) of 3 ft. 

Climate variability must also be considered both with respect to sea level change and climate 

effects on storm patterns and intensities. To account for sea level change, an estimate of the 

relative mean sea level for the project design life must be obtained. For screening purposes, 

the most conservative estimates for sea level rise (SLR) should be applied and based on the 
74

best available information available at the site of interest. (Note that projected drops in sea level 

will not be considered for screening purposes.) This estimate can then be added directly to the 

SPMSS. Relative SLR can be extremely site specific and estimates should be carefully 

considered.

 

The climate impact on the MPI is determined by the impact of climate variability on SST’s. The 

actual pattern of summertime SST’s in the Gulf of Mexico (shown in Figure 4-16) resembles 

more of a cyclical pattern than a secular trend. For this reason, it is difficult to use existing data 

to project linearly into the future. Given the lack of projected SST changes specific to the Gulf of 

Mexico, a value based on the measured mean rise in SST in the northern Atlantic over the past 

100 years of 1.0o C (Rayner et al. 2003) was assumed as the potential increase in this 

parameter over a 100-year design life. From Figure 2-5, a 14 mb increase in the MPI value can 

be estimated for a 1.0o C increase in SST. Based on analysis by Irish and Resio (2010), this will 

increase the associated surge by about 1.2 ft (Uclimate).

5.3.5 Final SPMSS Estimate

All components of the critical flood elevation are described above and must be combined to 

provide a final estimate of the SPMSS. The contributions from the various components can be 

broken down as:

Surge predicted by model from wind and pressure forcing: η model

Wave setup: mod 1 el

R

R

∗η −

Deviation due to variability of surge propagation inland ηdev

Freeboard to account for wave runup: F

Mean higher high water less mean tide level at site location: ηtide

Uncertainty in model storm surge predictions: Umodel

Uncertainty in MPI due to climate variability: Uc ate lim

 Estimate of sea level rise over project life η RSLR

Combining the above in equation form, the PMSS is defined as:

mod mod lim

1

1

SPMSS el dev F U U tide el c ate RSLR R η ηη η

  = + ++ + + +     − Equation 5-3

The modeled screening storm surge on the EC2001 mesh (ηmodel) is 27 ft for Matagorda, 34 ft 

for Biloxi, 38 ft for Levy County, and 24 ft for Turkey Point (see Figure 5-9). The deviation due 

to variability in surge propagation inland is 5 ft for all locations. The difference between mean 

higher high water and mean tide level (ηtide) is approximately 0.4 ft at Matagorda, 0.9 ft at Biloxi, 

1.7 ft at Levy County, and 1.1 ft at Turkey Point. Table 5-2 provides the R values for all 

locations. For illustration purposes, a freeboard (F) of 3 ft will be used for the sites further inland 

(Matagorda and Levy County) and a 4 ft value will be used for the facilities near the open coast. 

However, in actual application a careful consideration should be made of local conditions in 

making this estimate. The uncertainties (Umodel and Uclimate) are the same for all sites and, as 

previously discussed, are equal to 3.0 ft and 1.2 ft, respectively. The computed estimate of 
75

SPMSS must be combined with an estimate of relative sea level rise at a prospective site to 

give a final critical flood elevation. For illustration purposes, the ηRSLR estimate will be based on 

the high eustatic sea level rise function given in the Intergovernmental Panel on Climate 

Change 2007 report. For a 100-year project life, the ηRSLR is estimated to be approximately 3.8 

ft. Therefore, the SPMSS is equal to: 

1 (27) 5 3 0.4 3 1.2 3.8 48.2

1 0.15

SPMSS   = +++ ++ + =     − ft Matagorda Equation 5-4

1 (34) 5 4 0.9 3 1.2 3.8 55.7 1 0.1

SPMSS   = +++ ++ + =     − ft Biloxi Equation 5-5

1 (38) 5 3 1.7 3 1.2 3.8 57.7

1 0.05

SPMSS   = +++ ++ + =     − ft Levy Cty Equation 5-6

1 (24) 5 4 1.1 3 1.2 3.8 44.8 1 0.1

SPMSS   = +++ ++ + =     − ft Turkey Pt Equation 5-7

5.4 Screening Criteria

The computed critical flood elevation is compared to the controlling elevation for the prospective 

site. The controlling elevation is defined as the highest continuous topographic contour 

between the coast and the prospective site. If the controlling elevation is less than the critical 

flood elevation, a detailed surge and wave analysis must be performed. Conversely, if the 

controlling elevation is greater than the critical flood elevation, the site is considered not at risk 

for coastal storm surge flooding and no further analysis would be required.

To demonstrate how the proposed screening method would be applied in practice, a screening 

analysis for a prospective site at Matagorda, TX is presented. The SPMSS elevation at 

Matagorda is 48.2 ft. Figure 5-11 is a topographic map in the vicinity of the prospective site at 

Matagorda, TX. Inspection of Figure 5-11 identifies a controlling elevation of 27 ft. Because the 

controlling elevation is less than the critical flood elevation, a detailed surge and wave analysis 

is required at Matagorda, TX.
76

Figure 5-11. Topographic contours (elevations between 25 and 30 ft) in the vicinity of 

prospective site at Matagorda, TX.

5.5 Summary

This Section documents a screening methodology to determine inundation limits from maximum 

possible intensity storms. The methodology is efficient in that it makes use of a surge modeling 

system applied on a mesh that does not resolve the coastal floodplain. The SPMSS is 

computed through consideration of wind wave effects, tide, and uncertainty and adding these 

contributions to the surge estimate obtained from the numerical model. An estimate of relative 

sea level rise at a site is added to obtain the final SPMSS which provides a critical flood 

elevation that defines a line of safety beyond which critical infrastructure is safe from coastal 

storm surge. If a specific prospective site is being considered, the controlling elevation of the 

site, defined as the highest continuous topographic contour between the coast and the 

prospective site, is compared to the critical flood elevation. If the controlling elevation is less 

than the critical flood elevation, a detailed surge and wave analysis is required. If the controlling 

elevation is greater than the critical flood elevation, no further analysis is required.

The purpose here is to document the overall procedure and little attention is given to the details 

in estimating components of the SPMSS that are highly dependent on local conditions and/or 

may vary temporally as this is beyond the scope of this report. Specifically, it is recommended 

that NRC consider additional analysis be conducted to provide guidance in estimating 

appropriate values of ηdev, F, and ηRSLR. For example, the ηdev, applied in this Section’s 

examples are based on a limited number of simulations. Additional simulations could be 
77

conducted for various coastal landscape types to develop a range of ηdev values that is a 

function of coastal flood plain slope. Given the complexities in making these estimates and the 

fact that available surge model systems and their application can vary widely, each screening 

application should be carefully reviewed to ensure that an appropriate determination is made 

with respect to the coastal surge flood risk at any given site.

79

6.0 SUMMARY AND PMSS ESTIMATION PROCEDURES 

RECOMMENDED FOR NRC CONSIDERATION

Design criteria for nuclear power plants require, in part, that structures, systems, and 

components important to safety be designed to withstand the effects of natural phenomena, 

including floods, without loss of capability to perform their safety functions. The objective of this 

project is to provide the NRC with a technical basis for estimating probable maximum water 

levels due to the storm surge from extreme events along the southern coast of the U.S. for 

consideration in evaluating flood protection for nuclear power plants. Two fundamentally 

different methods for estimating design surge levels have been utilized in past studies. 

Deterministic methods typically use the estimated maximum surge value from either a single 

storm or a small set of storms as its design level and do not consider the probability of that 

surge level. Probabilistic methods consider surges from a range of events along with the 

probabilities of those events and attempt to develop a relationship between surge levels and 

return period. Both the deterministic-based and probability-based approaches to the estimation 

of very-low-probability hurricane surges have deficiencies and it is recommended to combine 

the two methods. The hybrid approach determines which factors affecting hurricane surges can 

be shown to have asymptotic upper limits and which factors should be treated within a context 

that allows for natural uncertainty in estimating an upper limit for surges at a specified site. The 

discussion in Section 3 supports the existence of an upper limit for hurricane generated surges 

in natural environments and a procedure is recommended for estimating maximum surge at a 

site of interest.

Section 4 provided an example of how a combined deterministic-probabilistic approach can be 

applied to estimate the PMSS (including a first approximation for effects of uncertainty). The 

consideration of uncertainty has traditionally been neglected in past upper-limit estimates of 

surge levels; but it has been demonstrated that the magnitudes of these terms are not 

negligible. The possibility that the upper limits of storm surge are much larger than the 10-6

annual probability used for safety standards at nuclear power plants was also examined. As 

part of this effort, the importance of quantifying the impact of uncertainty on estimated surges for 

a fixed frequency level was stressed; and a method to accomplish this was developed. In the 

applications here, the estimated central pressures for the 10-4 annual probability were shown to 

be about 15 mb lower when the effects of uncertainty were included. In the two Florida cases 

examined here, the PMSS value for Levy County exceeded the 10-6 annual probability surge 

and was smaller than the 10-6 annual probability surge for Turkey Point.

The final recommended procedure for estimates of the PMSS at sites within the Gulf of Mexico 

is summarized below:

1. Since it is obvious a limit to the influence of coastal hurricane surges exists, it is 

advantageous to consider a conservative screening filter to avoid requiring detailed 

computations in areas where they are clearly unnecessary. Section 5 establishes such a 

screening filter and develops a proposed approach for a simplified, conservative 

approximation to coast storm flood risk at prospective nuclear power plant sites which 

should be considered before detailed computations are performed. The methodology is

efficient in that it makes use of a surge modeling system applied on a mesh that does not 

resolve the coastal floodplain. The SPMSS is computed through consideration of wind wave 

effects, tide, and uncertainty and adding these contributions to the surge estimate obtained 

from the numerical model. An estimate of relative sea level rise at a site is added to obtain 

the final SPMSS which provides a critical flood elevation that defines a line of safety beyond 
80

which critical infrastructure is safe from coastal storm surge. If a specific prospective site is 

being considered, the controlling elevation of the site, defined as the highest continuous 

topographic contour between the coast and the prospective site, is compared to the critical 

flood elevation. If the controlling elevation is less than the critical flood elevation, a detailed 

surge and wave analysis is required. If the controlling elevation is greater than the critical 

flood elevation, no further analysis is required (i.e. it is not necessary to execute steps 2 to 6 

below).

2. If a detailed analysis is required, a high resolution state-of-the-art coupled wave-surge 

model with accurate bathymetric-topographic data should be developed and the modeling 

system validated at the site of interest. 

3. Develop a suite of synthetic storms. The storm suite should include a range of hurricane 

parameters and combinations of those parameters. For the southern U.S. coast, guidance 

for selecting the parameters to be simulated is:

a. Central Pressure: Storms with an MPI of 880 mb (consistent with Schade (2000)) and a 

central pressure that is 10 mb lower than the MPI.

b. Radius to Maximum Winds: Storms with an offshore Rmax of 30 nm and 45 nm. These 

values are larger than any storms in the Gulf of Mexico with intensities greater than 

approximately 930 mb. In addition, as shown in Figure 3-5, on a 1 to 10,000 slope for an 

880 mb storm, there is little or no variation of surge height with a change in storm size 

above an Rmax of approximately 40 nm.

c. Forward Speed: Three storm forward speeds should be simulated, a slow, medium, and 

fast, from approximately 5 to 22 knots. This range is based on the joint distribution 

storm speeds and central pressures in the Gulf of Mexico as shown in IPET (2009), 

d. Holland B: The Holland B should be set to 1.27 which is the mean value for the Gulf of 

Mexico (IPET 2009).

e. Track: The track should be set to maximize storm surge potential. Irish et al. 2008 and 

Irish and Resio 2010 show that the peak is close to one Rmax from the landfall location. 

The position and orientation of the tracks should be based on an analysis of historical 

high surge potential storm tracks in the area of interest and have minimal land 

interference as they approach the coast.

A typical storm suite is given in Table 4-1. The central pressure, radius to maximum winds, 

and Holland B all vary systematically during the storm’s approach to land. Systematic 

variation in these parameters is identical to that used in the IPET (2009) and was also 

adopted for Gulf of Mexico FEMA and USACE studies. For details on the variation in these 

parameters see Appendix 8 of IPET (2009). It should be noted that these values are for the 

southern U.S. Gulf of Mexico coast only and are not applicable for other regions.

4. Applying the validated modeling system, simulate the surges that would be produced by 

these storms at the location of interest and determine the largest predicted surge. The 

modeling system can applied with the existing mean sea level as the initial water level 

condition or include an estimate of eustatic sea level rise over the project life and an 

adjustment to reflect high tide. If these adjustments are not made to the initial water level 

condition, they must be added later. In areas with a large tidal range and/or high rates of 

sea level rise are estimated, it is recommended that the high water level is included in the 

modeling system.
81

5. Estimate the uncertainty in the estimate and add to the maximum calculated surge. 

Guidance for estimating the uncertainty is provided in Section 4 and a 5.3 ft adjustment is 

recommended. If the tidal and sea level rise adjustments are not included in the simulated 

water level, they must also be added.

6. Consideration must also be given to flooding potential from wave runup. A detailed analysis 

of wave runup requires very high resolution bathymetric/topographic data at the site location 

and application of a Boussinesq wave model or an approach such as that described by Melby 

(2012). Wave runup at a site is dependent upon the design of the nuclear plant and its 

protection features and its calculation is beyond the scope of this report.

The recommended procedure provides a technical basis for improving guidance on 

characterizing very low probability hurricane surge events. Fundamental limitations in the 

existing guidance relate to the modeling of hurricane surge events and the estimation of 

extreme storm parameters. The Bathystrophic Storm Surge model is extremely limited by 

restrictions and simplifications made in order to make the problem computationally tractable 

given the computer resources available in the early to mid 1970’s. The model assumptions and 

simplifications reduce the applicability and accuracy of the model. Existing guidance for 

determination of extreme storm parameters relies on NWS 23, which makes several 

assumptions in the PMH that are now known to be invalid. 

The new approach addresses both of these fundamental limitations in addition to improving on 

the screening method and considering uncertainty that is inherent in the estimation of storm 

parameters and the associated surge levels. Specifically the improvement upon previous 

guidance includes:

• Application of new modeling technology: A modern coupled system of wind, wave, and 

coastal circulation models that properly defines the physical system and includes an 

appropriate non-linear coupling of the relevant processes is recommended. An example of 

such a system is the USACE hurricane modeling system which combines the TC96 PBL 

model for winds, the WAM offshore and STWAVE nearshore wave models, and the ADCIRC 

basin to channel scale unstructured grid circulation model. Any modeling system that is 

applied should be well validated at the site of interest.

• Updated characterization of the MPI storm: Based upon the best available data and 

theoretical concepts, the MPI storm is allowed to attain a somewhat lover central pressure 

than previously considered. The storm size is estimated as a condition probability function 

of storm intensity. In addition, storm parameters are allowed to vary as the storm 

approaches the coast.

• Consideration of uncertainty: Previous guidance did not consider uncertainty in upper-limit 

estimates of surge levels. However, as has been demonstrated, that the magnitude of 

uncertainty is not negligible and it is considered in the new methodology.

• New screening method: The previous screening method was based on a pre-computed 

map of probable maximum surge values that was based on the invalid assumptions in the 

PMH and results from the inadequate Bathystrophic Storm Surge model. The new method 

utilizes the updated characterization of the MPI and appropriate modeling technology. 

83

7.0 REFERENCES

Bodine, B.R., 1971: Storm surge on the open coast: Fundamentals and simplified prediction. 

Technical Memorandum No. 35, U.S. Army Corps of Engineers, Coastal Engineering 

Research Center, Virginia.

Bunya, S., Westerink, J., Dietrich, J.C., Westerink, H.J., Westerink, L.G., Atkinson, J., Ebersole, 

B., Smith, J.M., Resio, D., Jensen, R., Cialone, M.A., Luettich, R. ,Dawson, C., Roberts, 

H.J., and Ratcliff, J. 20010. A High Resolution Coupled Riverine Flow, Tide, Wind, Wind 

Wave and Storm Surge Model for Southern Louisiana and Mississippi: Part I–Model 

Development and Validation. Monthly Weather Review, 138, 345-377.

Cardone, V.J., Greenwood, C.V., and Greenwood, J.A. 1992. Unified program for the 

specification of tropical cyclone boundary layer winds over surfaces of specified roughness. 

Contract Rep. CERC 92-1. U.S. Army Engineer Waterways Experiment Station, Vicksburg.

Chow, S.H. 1971. A study of wind field in the planetary boundary layer of a moving tropical 

cyclone. MSC Thesis, School of Engineering and Science, New York University, New York.

Emanuel, K.A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady state 

maintenance. J. Atmos. Sci., 43, 585-604.

Emanuel, K. A., 1987: The dependence of hurricane intensity on climate. Nature, 326, 483–485.

Emanuel, K. A., 1991: A scheme for representing cumulus convection in large-scale models. J. 

Atmos. Sci., 48, 2313–2335.

Garratt, J.R. 1977. Review of drag coefficients over oceans and continents. Mon Weather 

Rev., 104, 418-442.

Graham, H.E. and D.E. Nunn, 1959. Meteorological considerations pertinent to the Standard 

Project Hurricane, Atlantic and Gulf coasts of the United States, National Hurr. Res. Proj. 

Rep. No. 33, Weather Bureau, U.S. Dept of Commerce, Wash., D.C. 76 p.

Gringorten, I.I. 1962: A simplified method of estimating extreme values from data samples, J. 

Appl. Meterol., 2, 82-89.

Gringorten, I.I. 1963: Extreme-Value Statistics in Meteorology – A Method of Application, Air 

Force Surveys in Geophys. No. 125, A.F. Cambridge Res. Cen., Bedford, MA.

Gumbel, E.J. 1959: Statistics of Extremes, Columbia Univ. Press, New York.

Holland, G., 1980. An analytic model of the wind and pressure profiles in hurricanes. Monthly 

Weather Review, 108, 1212-1218.

Interagency Performance Evaluation Task Force, 2007. Performance evaluation of the New 

Orleans and southeast Louisiana hurricane protection system, vol IV - The Storm. U.S. Army 

Corps of Engineers, Washington, DC. Available at: https://ipet.wes.army.mil/
84

Interagency Performance Evaluation Task Force, 2009. Performance evaluation of the New 

Orleans and southeast Louisiana hurricane protection system, vol VIII – Engineering and 

Operational Risk and Reliability Analysis. U.S. Army Corps of Engineers, Washington, DC. 

Available at: https://ipet.wes.army.mil/

Kennedy, A.B., Gravois, U., Zachry, B.C., Westerink, J.J., Hope, M.E., Dietrich, J.C., Powell, 

M.D., Cox, A.T., Luettich, R.A., Dean, R.G. 2011. Origin of the Hurricane Ike forerunner 

surge. Geophysical Research Letters, 38, L08608, doi:10.1029/2011GL047090.

Irish, J.L., Resio, D.T., and J.J. Ratcliff, 2008: The influence of storm size on hurricane surge, J. 

Phys. Oceanogr., 38 (9), 2003-2013.

Irish, J.L., D.T. Resio, and M.A. Cialone, 2009: A surge response function approach to coastal 

hazard assessment: Part 2, Quantification of spatial attributes of response functions, J. 

Natural Hazards, 51 (1), 183-205,doi:10.1007/s11069-9381-4.

Irish, J.L. and D.T. Resio, 2010: A hydrodynamics-based surge scale for hurricanes, Ocean 

Engr. 37, 69-81.

Knutson, T.R., McBride, J.L., Chan, J., Emanuel, K., Holland, G., Landsea, C., Held, I., Kossin, 

J.P., Srivastava, A.K. and S. Masato, 2010. Tropical cyclones and climate change, Nature 

GeoSci. Rev. Art., Feb. 2010, DOI:10.1038/NGE0779.

Komen, G.J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, S., and Janssen, P.A., 

1994. Dynamics and modelling of ocean waves. Cambridge University Press, Cambridge.

Luettich R.A., Westerink, J.J., and Scheffner, N.W. 1992. ADCIRC: an advanced threedimensional circulation model for shelves, coasts, and estuaries. Report 1, theory and 

methodology of ADCIRC-2DDI and ADCIRC-3DL. Technical report DRP-92-6. U.S. Army 

Engineer Waterways Experiment Station,Vicksburg.

Luettich, R.A., and Westerink, J.J. 2004. Formulation and numerical implementation of the 

2D/3D ADCIRC finite element model version 44, XX. Available at: 

http://adcirc.org/adcirc_theory_2004_12_08.pdf.

Melby, J.A. 2012. Wave runup prediction for flood hazard assessment. ERDC/CHL TR-12-x. 

U.S. Army Engineer Research and Development Center, Vicksburg, MS.

Mooley, 1980 D.A. Mooley, Severe cyclonic storms in the Bay of Bengal, 1877–1977, Mon. 

Weather Rev. 108 (1980), pp. 1647–1655.

Mukai, A.Y., J.J. Westerink, R.A. Luettich, and D. Mark. 2002. Eastcoast 2001, A tidal 

constituent database for Western North Atlantic, Gulf of Mexico, and Carribean Sea. 

ERDC/CHL TR-02-24, U.S. Army Corps of Engineers Engineer Research and Development 

Center, Vicksburg, MS.

Niedoroda, A.W., Resio, D.T., Toro, G.R., Divoky, D., Das, H.S., and C.W. Reed. 2010:

 Analysis of the coastal Mississippi storm surge hazard, Ocean Engr. 37, 82-90.

Nuclear Regulatory Commission, 1986. Safety Goals for the Operations of Nuclear
85

Power Plants; Policy Statement; Republication, 51 FR 28044 & 51 FR 30028, 10 CFR Part 50, 

published 8/21/1986.

Pararas-Carayannis, G., 1975: Verification study of a Bathystrophic storm surge model. 

Technical Memorandum No. 50, U.S. Army Corps of Engineers, Coastal Engineering 

Research Center, Virginia

Powell, M.D., Vickery, P.J., and Reinhold, T.A. 2003. Reduced drag coefficient for high wind 

speeds in tropical cyclones. Nature, 422, 279-283.

Powell, M.D. 2006. Drag coefficient distribution and wind speed dependence in tropical 

cyclones. Final report to the NOAA Joint Hurricane Testbed Program, 26pp.

Powell, M.D. and T.A. Reinhold. 2007: Tropical cyclone destructive potential by integrated 

kinetic energy. Bull. Am. Meteorol. Soc. 88, 513-526.

Rayner et al. 2003. Global analyses of sea surface temperature, sea ice, and night marine air 

temperature since the late nineteenth century. J. Geophys. Res. 108, 4407.

Resio, D.T., Irish, J.L., and M.A. Cialone, 2009: A surge response function approach to coastal 

hazard assessment: Part 1, Basic Concepts, J. Natural Hazards, 51(1), 163-182, 

doi:10.1007/s11069-009-9379-y. 

Resio, D.T., and Westerink, J.J. 2008. Modeling the physics of storm surge. Physics Today, 

61(9),33–38.

Schade, L.R., 2000. Tropical Cyclone Intensity and Sea Surface Temperature. J. Atmosph. 

Sci., 57, 3122-3130. 

Schwerdt, R.W., Ho, F. P., Watkins, R.R., 1979. Meteorological Criteria for Standard Project 

Hurricane and Probable Maximum Hurricane Windfields, Gulf and East Coasts of the United 

States, NOAA Tech Rep NWS 23, National Weather Service, NOAA, Dept of Commerce, 

Silver Spring, MD, 317 p.

Smith, J.M., Sherlock, A.R., and Resio, D.T. 2001. STWAVE: steady-state spectral wave 

model user’s manual for STWAVE, version 3.0. ERDC/CHL SR-01-1. U.S. Army Engineer 

Research and Development Center, Vicksburg.

Smith J. M., and Sherlock, A.R. 2007. Full-plane STWAVE with bottom friction: II. Model 

overview. System-wide water resources program technical note. U.S. Army Engineer 

Research and Development Center, Vicksburg.

Soluri, E. A., and Woodson, V. A. 1990. 1990 World vector shoreline, International 

Hydrographic Review, LXVII(1).

Thompson, E.F., and Cardone, V.J. 1996. Practical modeling of hurricane surface wind fields. 

Journal of Waterway, Port, Coastal, and Ocean Engineering, 122(4):195–205. 

doi:10.1061/(ASCE)0733-950X(1996)122:4(195).

Tonkin, H., Holland, G.J. Holbrook, N., and A. Henderson-Sellers. 2000: An Evaluation of 

Thermodynamic Estimates of climatological maximum potential tropical cyclone intensity, 
86

Mon. Wea. Rev., 128, 746-762.

Toro, G., Resio, D.T., Divoky, D., Niedoroda, A.W., and C. Reed, 2009: Efficient joint probability 

methods for hurricane surge frequency analysis, Ocean Engr. 37, 125-134.

Wamsley, T.V., Cialone, M.A., Smith, J.M., Ebersole, B.A. 2009. Influence of landscape 

restoration and degradation on storm surge and waves in southern Louisiana. Journal of 

Natural Hazards. 51, 1, 207-224.

Wamsley, T.V., Cialone, M.A., Smith, J.M., Atkinson, J.H., and Rosati, J.D. 2010. The potential 

of wetlands in reducing storm surge. Ocean Engineering 37 (1) 59-68. DOI 

10.1016/j.oceaneng.2009.07.018.

Westerink, J.J., Blain, C.A., Luettich, R.A., and Scheffner, N.W. 1994. ADCIRC: an advanced 

three-dimensional circulation model for shelves coasts and estuaries, report 2: users manual 

for ADCIRC-2DDI. Dredging research program technical report DRP-92-6. U.S. Army

Engineer Waterways Experiment Station, Vicksburg, MS.

Westerink, J.J., Luettich, R.A., and Muccino, J.C. 1994. Modeling Tides in the Western North 

Atlantic Using Unstructured Graded Grids, Tellus, 46A, 178-199.

Westerink, J.J., Luettich, R.A., and Militello, A. 2001. Leaky Internal-Barrier Normal-Flow 

Boundaries in the ADCIRC Coastal Hydrodynamics Code, Coastal and Hydraulics 

Engineering Technical Note, U.S. Army Engineer Research and Development Center, 

Vicksburg, MS.

Westerink, J.J., Luettich, R.A., Feyen, J.C., Atkinson, J.H., Dawson, C., Roberts, H.J., Powell, 

M.D., Dunion, J.D., Kubatko, E.J., and Pourtaheri, H. 2008. A basin to channel scale 

unstructured grid hurricane storm surge model applied to southern Louisiana. Monthly 

Weather Review, 136(3):833–864. doi:10.1175/2007MWR1946.1

World Meteorological Organization. 1976. The quantitative evaluation of the risk of disaster 

from tropical cyclones. WMO/TD-No.455, Special Environmental Report.



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OFFICIAL BUSINESS
NUREG/CR-7134 The Estimation of Very-Low Probability Hurricane Storm Surges for 

Design and Licensing of Nuclear Power Plants in Coastal Areas