NIST Technical Note 1482 

METHODOLOGY FOR DEVELOPMENT OF 

DESIGN CRITERIA FOR 

JOINT HURRICANE WIND SPEED 

AND STORM SURGE EVENTS: 

PROOF OF CONCEPT 

NIST Technical Note 1482 

METHODOLOGY FOR DEVELOPMENT OF 

DESIGN CRITERIA FOR 

JOINT HURRICANE WIND SPEED 

AND STORM SURGE EVENTS: 

PROOF OF CONCEPT 

Long T. Phan 

Emil Simiu 

Building and Fire Research Laboratory 

NIST 

Mark A. McInerney 

Arthur A.Taylor 

Bob Glahn 

National Weather Service 

NOAA 

Mark D. Powell 

Oceanic and Atmospheric Research 

NOAA 

April 2007 

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary 

TECHNOLOGY ADMINISTRATION 

Robert Cresanti, Under Secretary of Commerce for Technology 

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 

William A. Jeffrey, Director 

i 

TABLE OF CONTENTS

Acknowledgements ...................................................................................................................... iii 

List of Acronyms and Abbreviations ...........................................................................................v 

List of Figures.............................................................................................................................. vii 

List of Tables ................................................................................................................................ ix 

Abstract......................................................................................................................................... xi 

Chapter 1 

Introduction....................................................................................................................................1 

1.1 Background .................................................................................................................1 

1.2 Overview of Framework for Methodology.................................................................2 

1.3 Objective and Scope of Report ...................................................................................4 

Chapter 2 

Hurricane Storm Tracks, Wind Speeds, and Storm Surge Heights Simulation......................7 

2.1 Hurricane Storm Tracks Simulation ...........................................................................7 

2.2 Wind Speeds and Storm Surge Heights Simulation....................................................8 

2.2.1 SLOSH Model and Wind Field Description...................................................8 

2.2.2 Wind Speeds and Storm Surge Heights at Five Locations of Interest..........12 

Chapter 3 

Joint Distribution and Mean Recurrence Intervals of Wind Speed and 

Storm Surge Height Events.........................................................................................................15 

3.1 Joint Histograms of Wind Speeds and Storm Surge Heights ...................................15 

3.2 Estimated Joint And Marginal Probabilities of Exceedance.....................................19 

 3.2.1 Joint Annual Probabilities of Exceedance .......................................................19 

 3.2.2 Marginal Annual Probabilities of Exceedance.................................................22 

3.3 Estimated Mean Recurrence Intervals of Joint Wind Speed/Storm Surge Events ...24 

3.4 Alternative Methods for Estimating Probability of Exceedance and Mean 

Recurrence Interval...................................................................................................27 

Chapter 4 

Proposed Design Criterion for Structures Subjected to Combined Effect of 

Wind and Storm Surge................................................................................................................29 

4.1 Design Criterion Based on Estimated MRI ..............................................................29 

4.2 Alternative Method for Establishing Design Criterion.............................................29 
ii

Chapter 5 

Summary and Discussion ............................................................................................................31 

5.1 Summary ...................................................................................................................31 

5.2 Discussion .................................................................................................................31 

Chapter 6 

References.....................................................................................................................................33 

Appendix A 

Explanation of SLOSH Simulation Output....................................................................................35 

Appendix B 

Typical SLOSH Simulation Output for the Port of Tampa Site ....................................................37 

Appendix C 

Alternative Methods for Estimating Joint Probability of Exceedance and Mean Recurrence 

Interval..................................................................................................................................43 
iii

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the useful contributions by Dr. Fahim Sadek of the Building 

and Fire Research Laboratory (BFRL), National Institute of Standard and Technology (NIST). 

The authors would also like to thank Dr. H.S. Lew and Mr. Stephen Cauffman of BFRL, NIST, 

and Dr. Will Shaffer of the National Weather Service (NWS), National Oceanic and 

Atmospheric Administration (NOAA) for their thoughtful and expert review of this report.
iv
v

LIST OF ACRONYMS AND ABBREVIATIONS

ADCIRC Advanced Circulation Model 

AFB Air Force Base 

AOML Atlantic Oceanographic and Meteorological Laboratory 

ASCE American Society of Civil Engineers 

BFRL Building and Fire Research Laboratory, NIST 

ETPA Elliptical Tampa SLOSH basin identifier 

FEMA Federal Emergency Management Agency 

FIRM Flood Insurance Rate Map 

FPHLM Florida Public Hurricane Loss Model 

HRD Hurricane Research Division, OAR, NOAA 

MDL Meteorological Development Laboratory, NWS, NOAA 

MRI Mean Recurrence Interval 

NGVD National Geodetic Vertical Datum 

NHC National Hurricane Center 

NIST National Institute of Standards and Technology 

NOAA National Oceanic and Atmospheric Administration 

NWS National Weather Service 

OAR Oceanic and Atmospheric Research 

PDF Probability distribution function 

SLOSH Sea, Lake, and Overland Surges from Hurricanes 

SPH Standard Project Hurricane 
vi
vii

LIST OF FIGURES

Figure 1 Location of Five Sites of Interest in the Tampa Bay Basin ...................................... 5 

Figure 2 Selected Hurricane Storm Tracks from the 55,000-year FPHLM over the 

 area of interest............................................................................................................9 

Figure 3 SLOSH Basins, Courtesy of Ethan Gibney, NHC....................................................10 

Figure 4 Tampa Bay Basin (ETPA) highlighted time step grid points and 25 mi track .range, 

 Courtesy of Ethan Gibney, NHC .............................................................................12 

Figure 5 SLOSH Simulation showing Effect of Hurricane Track Number 17544 

 on the Tampa Bay Basin ..........................................................................................14 

Figure 6(a) Joint Histogram of Peak Wind Speed/Surge Height for Port of Tampa ..................16 

Figure 6(b) Joint Histogram of Peak Wind Speed/Surge Height for Clearwater Beach.............17 

Figure 6(c) Joint Histogram of Peak Wind Speed/Surge Height for St. Petersburg Beach........17 

Figure 6(d) Joint Histogram of Peak Wind Speed/Surge Height for MacDill AFB 18 

Figure 6(e) Joint Histogram of Peak Wind Speed/Surge Height for 

 St. Petersburg on Tampa Bay...................................................................................18 

Figure 7(a) Joint Probability of Exceedance for Port of Tampa Site..........................................20 

Figure 7(b) Joint Probability of Exceedance for Clearwater Beach Site ....................................20 

Figure 7(c) Joint Probability of Exceedance for St. Petersburg Beach Site ...............................21 

Figure 7(d) Joint Probability of Exceedance for MacDill AFB Site...........................................21 

Figure 7(e) Joint Probability of Exceedance for St. Petersburg on Tampa Bay Site..................22 

Figure 8(a) Marginal Probability of Exceedance of Wind Speed for Port of Tampa Site..........23 

Figure 8(b) Marginal Probability of Exceedance of Storm Surge Height 

 for Port of Tampa Site..............................................................................................23 
viii

 
ix

LIST OF TABLES

Table 1 MRI (in Years) for Port of Tampa site......................................................................24 

Table 2 MRI (in Years) for Clearwater Beach site ................................................................25 

Table 3 MRI (in Years) for St. Petersburg Beach site ...........................................................25 

Table 4 MRI (in Years) for MacDill AFB site.......................................................................26 

Table 5 MRI (in Years) for St. Petersburg on Tampa Bay site..............................................26 
x
xi

ABSTRACT

 This report presents proof of concept for a methodology pertaining to combined effects of 

hurricane wind speed/storm surge height events. The methodology was developed jointly by the 

Building and Fire Research Laboratory (BFRL) of the National Institute of Standards and 

Technology (NIST) and the National Weather Service (NWS) and the Oceanic and Atmospheric 

Research (OAR) of the National Oceanic and Atmospheric Administration (NOAA). Its purpose 

is to develop site specific, risk-based design criteria for coastal structures subjected to the 

combined effects of hurricane wind speed and storm surge. The methodology utilizes an 

integrative, interdisciplinary approach that incorporates state-of-the-art knowledge in hurricane 

science, hydrology, probabilistic methods, and structural engineering needs, and involves the 

following steps: (1) selection of a stochastic set of hurricane storm tracks affecting the region of 

interest, (2) hydrodynamic simulation of the region of interest using program SLOSH and the 

selected storm tracks to generate time histories of wind speeds and corresponding time histories 

of storm surge heights at sites within the affected region, and (3) use of hurricane wind speed and 

storm surge height data generated in Steps (1) and (2) to develop (a) probabilistic information on 

joint wind speed/storm surge height events, and (b) risk-consistent structural design criteria. 
xii
Chapter 1 

INTRODUCTION

1.1 BACKGROUND 

At the present time, the design of structures in coastal high hazard area is governed by 

two ASCE standards. For wind and flood loading, the design is governed by ASCE 7-05 

Minimum Design Loads for Buildings and Other Structures [ASCE, 2005]. For flood resistance, 

including high velocity wave action, the design is governed by ASCE 24 Flood Resistant Design 

and Construction [ASCE, 1998]. ASCE 7 provides contours of basic wind speeds for both nonhurricane and hurricane winds. Non-hurricane winds are based on a nominal 50-year mean 

recurrence interval (MRI) and hurricane winds are based on a longer MRI, dependent on 

location. The basic wind speeds provided by ASCE 7 are 3-second gust speeds at 33 ft (10 m) 

above ground in open terrain with scattered obstructions having heights less than 30 ft (9.1 m) 

(see ASCE 7-05, Exposure C). ASCE 24 specifies mainly the elevation and foundation 

requirements for buildings and other structures located in flood hazard areas. 

Neither ASCE 7 nor ASCE 24 addresses the combined effect of hurricane wind speed 

and storm surge as a design condition in a risk consistent manner. However, Table C6-1 of the 

ASCE 7 Commentary reproduces the Saffir/Simpson (S/S) Hurricane Scale, which describes five 

categories of hurricanes and the respective sustained wind speeds (1-minute average at 33 ft (10 

m) elevation) and general storm surge heights (http://www.nhc.noaa.gov/aboutsshs.shtml). (Note 

that, whereas the S/S scale as listed by NOAA does not specify the terrain exposure associated 

with the wind speeds, Table C6-1 of the ASCE 7 Commentary assumes open water exposure.) 

Table C6-2 of the ASCE 7 Commentary provides 3-s peak gust speeds at 33 ft (10 m) elevation 

over open terrain estimated to be equivalent to the 1- min speeds over open water listed in the 

S/S scale. Both the National Hurricane Center (NHC) and ASCE 7 stress that: “Wind speed is 

the determining factor used in categorizing the hurricane,” with the NHC adding “as storm surge 

values are highly dependent on the slope of the continental shelf and the shape of the coastline in 

the landfall region.” Although the S/S Hurricane Scale is widely used by hurricane forecasters, 

the news media, and local and federal agencies responsible for evacuation planning, its use for 

engineering design is limited by the difficulty of relating it to well-defined design criteria that 

account for both wind speed and storm surge height. 

Special design criteria that consider the combined effect of wind speed and storm surge 

have been developed and used in the past for special structures. The New Orleans flood 

protection system was designed on the basis of such design criteria requiring that it resist the 

loads inherent in the Standard Project Hurricane (SPH). The SPH was developed in 1957 based 

on an analysis of past hurricanes of record (from 1900 to 1956) and is defined as the most severe 

hurricane that is considered reasonably characteristic of a region. For the New Orleans, 

Mississippi region, the SPH has the following characteristics: a specified central barometric 

pressure of 27.6 in (935 mb) of mercury, a peripheral pressure of 29.92 in (1013 mb) of mercury, 

a maximum sustained wind speed of 110 mph (49 m/s) (at 30 ft (9.1 m) elevation), a radius of 

maximum winds of 30 mi (48 km), a storm surge of up to 12 ft (3.65 m), and a forward speed of 
2

15 mph (6.7 m/s). The level of risk inherent in the SPH is not known. However, Hurricane 

Katrina, with estimated maximum sustained wind speeds of approximately 125 mph (55.9 m/s, 

consistent with a category 3 hurricane on the S/S Hurricane Scale) and maximum storm surge 

heights of approximately 28 ft (8.5 m) (9 ft to 10 ft (2.7 m to 3.0 m) estimated for New Orleans) 

[NIST Technical Note 1476, 2006], clearly showed that (1) actual storm surge heights can 

substantially exceed the heights listed in the S/S scale for a given hurricane category, and (2) the 

SPH is inadequate as a design criterion for protection against such combination of wind speed 

and storm surge height event as Hurricane Katrina. 

 Thus, at present there is a lack of risk-based design criteria for the design of buildings 

and other structures in coastal, hurricane-prone regions that are subjected to the combined effect 

of wind speed and storm surge. Such risk-based design criteria should be developed (1) by 

accounting for annual probabilities of exceedance of joint wind speed/storm surge events, and (2) 

by considering the effects of topography and bathymetry at the sites of interest, as the storm 

surge at any specific location is highly dependent upon these factors. In this report, we describe 

a methodology, developed as part of the joint effort between the Building and Fire Research 

Laboratory (BFRL) of the National Institute of Standards and Technology (NIST), and the 

National Weather Service (NWS) and the Oceanic and Atmospheric Research (OAR) of the 

National Oceanic and Atmospheric Administration (NOAA), for use in establishing risk-based 

design criteria for structures subjected to the combined effect of wind speeds and storm surges. 

The methodology utilizes an integrative, interdisciplinary approach that incorporates state-of-theart knowledge and tools in hurricane science, hydrology, probabilistic methods, and structural 

engineering needs. 

1.2 OVERVIEW OF FRAMEWORK FOR METHODOLOGY 

 The design criteria for coastal structures subjected to the combined effect of wind speed 

and storm surge will account for probabilities of exceedance of the joint wind speed/storm surge 

height events. These joint probabilities are site-dependent owing to differences in topography 

and bathymetry of the sites and to differences between the respective local hurricane wind 

climates. In addition, the probabilities may be expected to change owing to the evolution of 

coastal basins in time. Thus to calculate the probabilities of exceedance for any specific sites, it 

is necessary to have not only a stochastic set of hurricane storm tracks that would affect the sites 

of interest in a significant way from a structural engineering point of view, but also up-to-date 

information regarding the topography and bathymetry of the areas that contain the sites of 

interest. In general, the methodology for developing the design criteria for joint wind 

speed/storm surge events involves the simulation and selection of a stochastic set of hurricane 

storm tracks, integration of the selected storm tracks into a hydrodynamic simulation model to 

generate time histories of wind speeds and corresponding time histories of storm surge heights at 

a site, and the application of probabilistic methods to develop joint probabilities of exceedance 

and mean recurrence intervals for wind speed/storm surge height events. The following steps 

outline in more detail the framework of this methodology: 
3

 Step 1: Simulation and selection of hurricane storm tracks. 

In this step, a stochastic set of hurricane storm tracks is generated from a 55,000-year 

simulation of the Florida Public Hurricane Loss Model (FPHLM), Version 1.0 [Powell et al., 

2005]. Each hurricane is characterized by a set of climatological parameters, including the 

difference between atmospheric pressures at the hurricane’s periphery and center, the radius of 

maximum wind, and its track. The hurricanes that are deemed capable of causing significant 

property damage in the area containing the site of interest (i.e., are significant from a structural 

engineering viewpoint) are selected using the threat area concept. The detailed description of 

this step is provided in Chapter 2. 

Step 2: Hydrodynamic simulation to generate time histories of wind speeds and 

storm surge heights. 

 In this step, time histories of wind speeds and storm surge heights at a site are generated 

using a numerical-dynamic, tropical storm surge model called SLOSH (Sea, Lake, and Overland 

Surges from Hurricanes) [NOAA Technical Report NWS 48, 1992]. The selected hurricanes in 

step 1 are used to prescribe the environmental conditions in the SLOSH simulation. In addition 

to the time histories of wind speeds and storm surge heights, SLOSH simulation will also 

generate time histories of wind direction to allow for consideration of wind directionality. In this 

report the time histories are saved at a 5 min interval. This interval is sufficiently small so that 

no significant wind speed peaks are likely to be missed, yet not so small as to cause an unduly 

large amount of data to be generated. The detailed description of this step is also provided in 

Chapter 2 of this report. 

 With regard to SLOSH, it should be noted that NOAA uses SLOSH to conduct real-time 

forecasts of potential storm surge from approaching hurricanes and includes these forecasts in 

periodic hurricane advisories. For hurricane Katrina, NOAA, in their advisories prior to landfall, 

predicted based on SLOSH simulation “coastal storm surge flooding of 18 to 22 ft above normal 

tide levels...locally as high as 28 ft along with large and dangerous battering waves...can be 

expected near and to the east of where the center makes landfall.” (Advisory number 24 4PM 

CDT August 28, 2005), and “storm surge flooding of 10 to 15 ft near the tops of the levees is 

possible in the greater New Orleans area.” (Advisory number 26B 8AM CDT August 29, 2005). 

These predictions using SLOSH are consistent with storm surge heights observed for hurricane 

Katrina [see, e.g., NIST Technical Note 1476, 2006]. 

Step 3: Use of hurricane wind speed and storm surge height data generated in 

Steps (1) and (2) to develop (a) probabilistic information on joint wind speed/storm surge height 

events, and (b) risk-consistent structural design criteria. 

 

 In this step, joint histograms of wind speeds and storm surge heights are developed using 

the simulated time histories of the wind speeds and storm surge heights obtained in Steps (1) and 

(2). The joint histograms, and the historically-based mean annual hurricane arrival rate at a site 

of interest, are then used to estimate probabilities of exceedance of yearly events associated with 

the wind speed and storm surge height at the site and corresponding MRIs. The applicability of 

these probabilities to the development of risk-consistent structural design criteria for the 
4

combined effect of wind speed and storm surge is then considered (Chapter 3), and a simple and 

probabilistically rigorous approach to developing such criteria is presented (Chapter 4). 

1.3 OBJECTIVE AND SCOPE OF REPORT 

 The objective of this report, which is the first report in this joint NIST-NOAA effort, is to 

demonstrate proof of concept for the development of an integrative methodology for use in 

establishing risk-based design criteria for the combined effect of wind speeds and storm surge 

heights. As a proof of concept, the methodology is based on the consideration of wind speeds 

regardless of their direction. Effect of wind directionality on wind speeds will be considered in 

the subsequent phase of this work. Note that wind direction is already accounted for in the storm 

surge calculation. 

 In addition, even though at present SLOSH models of coastal basins for the entire Gulf 

and Atlantic coasts are available for use in the hydrodynamic simulations required in step 2, the 

historical hurricane storm tracks necessary for characterizing the storm environments in step 1 

are only available for the State of Florida through the 55,000-year simulation Florida Public 

Hurricane Loss Model (FPHLM, Version 1.0). The scope of this proof of concept phase is 

limited to five specific locations in the Tampa Bay area. These locations were selected because 

they are located in a populated area with substantial construction and are close to the coast and 

thus vulnerable to the combined effect of wind speed and storm surge. Figure 1 shows the five 

locations of interest in the Tampa Bay area. These include: 

Site Lattitude/Longitude 

1. Port of Tampa N27.949/W82.445 

2. Clearwater Beach N27.977/W82.829 

3. St. Petersburg Beach N27.726/W82.744 

4. St. Petersburg on Tampa Bay N27.754/W82.631 

5. MacDill Air Force Base N27.851/W82.510 

 As explained in Section 2.2.1, SLOSH operates on a grid, and surge is calculated for grid 

cells on the order of a kilometer in size in each direction. Therefore, all results in this report 

pertain to calculations made on that basis. While the specific points in the table above are given 

to exact latitude and longitude locations, the calculated values pertain to the grid cell in which 

those points are located. Two of the sites, McDill AFB and St. Petersburg on Tampa Bay, are 

located in cells with an average elevation of 9 and 10 ft, respectively. However, the cells in 

which the other three points are located are closer to sea level. This difference in elevation is 

reflected in the results of Fig. 6. The actual elevations within a cell normally vary, the amount 

depending on the location. 
Figure 1. Locations of Five Sites of Interest in the Tampa Bay Basin 

5
6 
7

Chapter 2 

HURRICANE STORM TRACKS, WIND SPEEDS, AND STORM SURGE 

HEIGHTS SIMULATIONS

2.1 HURRICANE STORM TRACKS SIMULATION 

 As stated in section 1.2, the Tampa Bay, Florida area was chosen as the location for this 

proof of concept phase of our study. A set of hurricane storm tracks that affect the Tampa Bay 

area was selected from the State of Florida FPHLM. To focus on storms capable of causing 

residential property damage in Florida, the FPHLM uses the concept of threat area to best 

capture the statistical characteristics of historical tropical cyclones that have affected the state. 

The area within 1000 km of a location (26.0 N, 82.0W) off the southwest coast of Florida was 

chosen since it captures storms that can affect the panhandle, west, and northeast coasts of 

Florida, as well as storms that approach South Florida from the vicinity of Cuba and the 

Bahamas. 

 The threat area is divided into regions which contain the historical and seasonal 

characteristics of storm motion and intensity change. Genesis location, intensity, and motion for 

each storm are based on the geographic probability distributions of each quantity for a given time 

within the season. We use a stochastic approach to model the storm genesis location, track, and 

intensity evolution. A probability distribution function (PDF) for the initial storm position is 

derived from the historical "genesis'' data. Here we define genesis as the time when the storm 

(tropical depression, tropical storm, or hurricane) forms in or first appears in the threat area. The 

PDF is derived for 0.5 degree latitude/longitude box regions, as well as time of season (month). 

A (uniform) random error term is added so that the storm may form anywhere within the 0.5 

degree box. 

 Discrete PDFs based on historical data provide the initial and subsequent motion and 

intensity of the storm. A storm is simulated by repeatedly sampling from these PDFs via a Monte 

Carlo approach. These PDFs are derived for variable-sized regions centered at every 0.5 degree 

latitude and longitude in the hurricane basin. The size of these regions is determined to be that 

which gives a robust PDF for the quantities of interest (speed, direction, and intensity), up to 

some maximum size. Once the storm has been given an initial condition, its subsequent evolution 

is governed by sampling the PDFs for change in intensity, change in translation speed, and 

change in heading angle in 6 hour increments. The time step is reduced to 1 hour when the storm 

is close to the coastline. 

 The intensity parameter used in the wind model is DelP, the difference between the 

central minimum sea level pressure and an outer peripheral pressure (assumed to be 29.9 in of 

mercury (1013 mb) in our model). Intensity change is modeled by using the observed 

geographic probability distribution of six-hour changes of central pressure as related to the 

relative intensity (Darling, 1991). Intensity change is limited so as to not exceed the maximum 

observed change for a particular geographic region. When a storm center crosses the coastline 

(landfall) the intensity change follows a pressure decay model (discussed below). If the storm 
8

moves back over the sea, the former intensity change model is reinstated. The PDFs for change 

in speed and direction depend on the current speed and direction (binned in discrete intervals), as 

well as geographic location (0.5 degree lat-lon location) and time of season (month). Storms that 

parallel the coast or make several landfalls can be properly simulated with this method. 

 Specification of the central pressure over land uses an exponential decay as a function of 

time after landfall developed by Vickery and Twisdale (1995). The advantage of the filling 

model is that it provides a starting point to invoke an intensity redevelopment for storms that exit 

the coastline and re-intensify over water. When a storm reemerges over water, the intensity is 

modeled along the track the same way it was before landfall using the decayed pressure as an 

initial value. The motion of the vortex is determined by the modeled storm track. The symmetric 

pressure field p(r) is specified by the Holland (1980) pressure profile with the central pressure 

specified according to the intensity modeling in concert with the storm track. A model for the 

Holland B pressure profile parameter was developed based on a subset of the data published by 

Willoughby and Rahn (2004). The radius of maximum wind at landfall is modeled as a function 

of latitude and minimum central barometric pressure Pmin using a database constructed from a 

variety of landfall data including the NWS-38 publication (1987), and extended best track by 

DeMaria et al. (2002), and NOAA HRD archives. 

Using the above method for simulating and selecting hurricane storm tracks affecting the 

point specific locations of interest in the Tampa Bay basin, a total of 19,806 hurricane storm 

tracks were selected. Figure 2 shows a portion of one of the storm tracks selected from the 

FPHLM model, hurricane track number 17526, together with its wind field entering the area of 

interest in the Tampa Bay basin. 

2.2 WIND SPEEDS AND STORM SURGE HEIGHTS SIMULATION 

Wind speeds and storm surge heights at the five selected locations in Tampa Bay caused 

by the 19,806 hurricanes are simulated using the SLOSH model. Below is a brief description of 

SLOSH, SLOSH basins, and the method it uses to generate wind field and associated storm 

surge. 

2.2.1 SLOSH Model and Wind Field Description 

SLOSH is a dynamic, two dimensional numerical model developed by the NWS to 

estimate tropical storm surge flooding. SLOSH works from high resolution curvilinear polar, 

elliptical, or hyperbolic grids separated into 41 unique basins across the Gulf of Mexico, eastern 

seaboard, the Bahamas, Puerto Rico, and Hawaii. Each type of grid is mapped conformally onto 

a Cartesian type of grid for computations, taking care to use the relevant map factors and 

Jacobian – See Figure 3.
Figure 2. Selected hurricane storm track (hurricane number 17526) from the 55,000-year FPHLM over 

9
Figure 3 - SLOSH Basins, Courtesy of Ethan Gibney, NHC 

10
11 

This grid-based coordinate system provides finer mesh near the pole point and becomes 

coarse at outer boundaries. As a result, high resolution data for areas of interest along the coast 

and inlet bays are available. Additionally, sub-grid elements such as channels, barriers, and 

rivers are modeled to improve calculated surge values during processing. Storm surge is 

calculated by solving shallow water equations derived from the transport equations of motion 

and the continuity equation based from input such as topography, bathymetry, and storm track 

which includes change in pressure, radius of maximum winds ( Rmax ), location, wind direction 

and wind speed. Parameters not modeled in the SLOSH include astronomical tides, rainfall, 

river flow, and wind-driven waves. The basic equations solved by the SLOSH model are: 

τ τ f A V AU C x C y

y

h h B

x

h h

g D h B

t

U r i r i

o

i

o

r + + + − ⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂ − − ∂∂ − = − +

∂

∂ ( ) ( ) ( ) ( )

τ τ f A U AV C y C x

x

h h B

y

h h

g D h B

t

V r i r i

o

i

o

r + − + + ⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂ − +

∂

∂ − = − +

∂

∂ ( ) ( ) ( ) ( )

y

V

x

U

t

h

∂

∂ − ∂∂ = − ∂∂ , 

where U and V are the components of transport, g is the gravitational constant, D is the 

depth of quiescent water related to the National Geodetic Vertical Datum (NGVD 29) 

established by geodetic surveys and optical levelings or transits, h is the height of water above 

the NGVD, ho is the hydrostatic water height, f is the Coriolis parameter, τ x and τ y are the 

components of surface stresses, and , , , , , Ar Ai Br Bi Cr and Ci are the bottom stress terms 

[Jelesnianski et al. 1992] 

The surface stress,τ

r

, is an important term in the equations of motion. Generally, the 

wind stress per unit mass on the sea surface is expressed as: 

( , , ) ( , , ) ( , , ) | | x y t x y t

w

a

x y t CD W W r r r

ρ

ρ τ =

where CD is the drag coefficient, ρ w and ρa are densities of water and air, and W is the 

vector wind. The z coordinate of the stress term is s z = z where s z is the distance above the sea 

surface typically 10 meters and where meteorological wind sources retained at the surface utilize 

a constant pressure to be converted to s z [Jelesnianski et al. 1992]. Rather than the vector wind 

field just described, the SLOSH model utilizes a simplified parametric wind model, based on 

pressure and Rmax winds, to calculate surface stresses over water that generate storm surge values 

for the model. One half of the hurricane’s forward speed is added vectorially to the symmetric 

winds to provide asymmetry. Houston et al., 1999 compared SLOSH wind model fields to 

observation-based wind analyses from the NOAA AOML H*Wind system and found that 
12

SLOSH winds were on average 14% lower than the H*Wind analyses at locations between .75 – 

1.5 times the radius of maximum winds. Beyond 1.5 Rmax, wind speed differences tended to be 

larger with cases as large as 27 % lower (Hurricane Bob 1991 off Rhode Island 1991) than 

H*Wind and 15% higher than H*Wind (Hurricane Bob 1991 off North Carolina). 

2.2.2 Wind Speeds and Storm Surge Heights at Five Locations of Interest 

The five locations of interest considered in this proof of concept phase are located within 

the Tampa Bay basin (ETPA), which is characterized by an elliptical/hyperbolic grid extending 

from Citrus County south through Sarasota county and covering approximately 252 statute miles 

(405 km) of coastline (Basin number 32 in Figure 3) - see Figure 4. 

Figure 4 - Tampa Bay Basin (ETPA) highlighted time history grid points and 25 mi track 

range, Courtesy of Ethan Gibney, NHC 
13

To capture hurricane tracks from the FPHLM that affect the five locations of interest in 

this basin a 25 mi (40 km) buffer was established around the basin as shown in yellow in Figure 

4. The total number of tracks identified to cross inside this buffer was 23,166 of the 103,000 

tracks in the 55,000 year simulated track dataset. From these tracks, 19,806 tracks corresponding 

to hurricanes significant from a structural point of view were utilized for this proof of concept 

study to generate the requisite time histories of wind speeds and storm surge heights. Several of 

these selected tracks (hurricane tracks number 17, 243, 254, 290, 760, and 7763) are also 

displayed on Figure 4. 

For the five locations, time histories of wind directions, wind speeds, and storm surge 

heights at 5 min intervals, corresponding to each of the 19,806 selected hurricane storm tracks 

were generated. Figure 5 shows a typical result of SLOSH simulation which indicates the effect, 

at one point in time, of hurricane track number 17544 on the Tampa Bay basin. Appendix A 

shows a typical SLOSH output for the Clearwater Beach location (27.9767N, 82.8366W). In this 

example, the time histories were created by the effect of hurricane storm track number 12364 

generated from 55,000-year simulation for State of Florida FPHLM. 

 . 
Figure 5. SLOSH Simulation showing Effect of Hurricane Track Number 17544 on the Tampa 

14
15

Chapter 3 

JOINT HISTOGRAMS, PROBABILITIES OF EXCEEDANCE, AND MEAN 

RECURRENCE INTERVALS OF WIND SPEED AND STORM SURGE 

HEIGHT EVENTS 

In this Chapter, the time histories of wind speeds and storm surge heights generated in 

step 2 of the methodology described in Chapter 2 are used to develop estimates of joint 

histograms and of corresponding probabilities of exceedance and mean recurrence intervals of 

wind speed/storm surge events. 

3.1 JOINT HISTOGRAMS OF WIND SPEEDS AND STORM SURGE HEIGHTS 

 The same hurricanes are considered for all five sites listed in Chapter 2, since the 

distances between those sites are sufficiently small (less than 20 mi (32 km), see Figure 1). Let n

denote the number of simulated hurricane storm tracks being considered (in this study 

n=19,806). For each hurricane hi (i=1,2,...,n) hydrodynamic simulation using SLOSH yields 

time histories of the wind speed vij and storm surge height sij for all five locations (j is the index 

that denotes the number of time intervals; the corresponding time is tj = jΔt, where Δt is a 5-min 

time interval). Under the effect of the same hurricane hi, the wind speeds vij and the storm surge 

height sij differ from site to site owing to the respective topographies and bathymetries. (As 

indicated in Chapter 2, for the proof of concept purposes of this report we followed the ASCE 7 

Standard wherein wind speeds are specified regardless of their direction, and did not consider 

wind directionality.) 

 For hurricane track hi, a data pair consisting of the maximum wind speed vi,max≡ max(

j

vij) 

and the maximum storm surge height si,max≡ max(

j

sij) at a site can be extracted from the time 

histories of wind speed and storm surge height generated from the SLOSH simulation. Note 

that the speed vi,max and the storm surge height si,max generally do not occur at the same times 

during the life of hurricane hi (for example, Hurricane Katrina’s estimated maximum wind 

speeds of 175 mph (78 m/s) was recorded 18 hours before landfall, when maximum surge 

heights were observed. Also, Appendix B shows results of a typical SLOSH simulation, in this 

case for the Port of Tampa site, where the time of peak wind speed (84 mph at 1359.50 min in 

the storm history, when the surge height is zero (99.9 ft denotes a dry point)) is different from the 

time of peak storm surge height (peak surge height of 3.3 ft occurred at 1564.50 min in the storm 

history.) Therefore, designing a structure or other system under the assumption that they occur 

simultaneously would result in conservative1

 designs. For the 19,806 selected hurricanes, data 

pairs vi,max, si,max (i=1,2,...,19,806) can be similarly extracted for each site of interest from the 

results of 19,806 SLOSH simulations. 

 

1

 In structural engineering terminology a design is referred to as conservative if it results in a structural safety level 

that exceeds minimum requirements prescribed in standard engineering practice. An unconservative design is one 

that results in a structural safety level that does not meet those requirements. 
16

 Next, we rank order the data pairs vi,max, si,max (i=1,2,...,19,806) for each site of interest 

based first on decreasing values of vi,max and then on decreasing values of si,max. The following is 

an example of the data pairs of wind speed and storm surge height occurring at a site after rank 

ordering: 

 vi,max si,max

 (1-minute m/s) (m) 

 

 70 6 

 70 5.5 

 68 6 

 68 5.8 

 68 5.3 

 65 5.5 

 65 4.7 

 60 5.0 

 55 5.2 

 55 4.5 

 ... ... 

 ... ... 

Next, we construct, for each site, a joint histogram that includes the sample of the 

n=19,806 pairs of peak wind speed/storm surge height data just described. These pairs occur 

during the time interval T=55,000 years associated with the n hurricanes. Figures 6(a) to 6(e) 

show the joint histograms of peak wind speeds/storm surge heights derived from the above 

procedure. 

Figure 6(a) Joint Histogram of Peak Wind Speed/Surge Height for Port of Tampa 
17

Figure 6(b) Joint Histogram of Peak Wind Speed/Surge Height for Clearwater Beach

Figure 6(c) Joint Histogram of Peak Wind Speed/Surge Height for St. Petersburg Beach 
18

Figure 6(d) Joint Histogram of Peak Wind Speed/Surge Height for MacDill AFB 

Figure 6(e) Joint Histogram of Peak Wind Speed/Surge Height for 

St. Petersburg on Tampa Bay 
19

As indicated by the respective histograms, events with relatively high wind speed and 

storm surge heights can be expected to occur at the Port of Tampa, Clearwater Beach, and St. 

Petersburg Beach sites (sites 1, 2, and 3). The joint histograms for the MacDill AFB and St. 

Petersburg on Tampa Bay sites (sites 4 and 5), however, indicate that these two sites are mainly 

affected by wind and not by storm surge. This may be a consequence of the local topography 

associated with these two sites (both have high elevations as indicated in Section 1.3.) For 

locations with lower elevations, even by-passing tropical storms can generate sufficient wind 

forcing to flood low lying areas with water levels higher than 0.5 m within Tampa Bay at St. 

Petersburg and Apollo Beach (Houston and Powell 1994). 

 

3.2 ESTIMATED JOINT AND MARGINAL PROBABILITIES OF EXCEEDANCE 

3.2.1 Joint Annual Probabilities of Exceedance 

 From the histograms created in Section 3.1, we next obtain an estimate of the annual 

probability of exceedance, denoted by P(V>v, S>s), of the joint event with wind speed V > v and 

storm surge height S > s, by (1) counting the number of data pairs with wind speeds greater than 

v and storm surge heights greater than s in each of the joint histograms, (2) dividing that number 

by the total number of data pairs, n=19,806, and (3) multiplying the outcome by the mean annual 

hurricane rate of occurrence λ, where λ = n/T = 19,806/55,000 = 0.3601 hurricane/year. Plots of 

the estimated joint annual probability of exceedance of events v,s are shown in Figures 7(a) to 

7(e). Each contour plotted on the wind speed/storm surge height plane on these Figures 

indicates wind speeds and storm surge heights for which the estimated joint annual probabilities 

of exceedance has the same value. 

Figure 7(a) Joint Probability of Exceedance for Port of Tampa Site 
20

Figure 7(b) Joint Probability of Exceedance for Clearwater Beach Site 
21

Figure 7(c) Joint Probability of Exceedance for St. Petersburg Beach Site 

Figure 7(d) Joint Probability of Exceedance for MacDill AFB Site 
22

Figure 7(e) Joint Probability of Exceedance for St. Petersburg on Tampa Bay Site 

3.2.2 Marginal Annual Probabilities of Exceedance 

 

The joint annual probabilities of exceedance computed and shown in Section 3.2.1 can 

also be used to derived the marginal (or unconditional) annual probabilities of exceedance for 

each site, i.e., annual probabilities of exceeding various wind speeds regardless of storm surge 

height and annual probabilities of exceeding various storm surge heights regardless of wind 

speed. Figures 8(a) and (b) below show the marginal annual probabilities of exceedance of wind 

speeds and storm surge heights, respectively, for the Port of Tampa site. 
23

Figure 8(a) Marginal Probability of Exceedance of Wind Speed for Port of Tampa Site 

Figure 8(b) Marginal Probability of Exceedance of Storm Surge for Port of Tampa Site 
24

3.3 ESTIMATED MEAN RECURRENCE INTERVALS OF JOINT WIND 

 SPEED/STORM SURGE EVENTS

 Finally, we obtain the mean recurrence interval (MRI), in years, of event v,s, (i.e., the 

average time between the occurrence of a wind speed of at least v and a storm surge of at least s) 

for each site as the inverse of the bivariate joint annual probability of exceedance of the 

respective site. MRIs corresponding to various joint wind speed/storm surge height events (v, s) 

for the five sites are shown in Tables 1 to 5. It should be noted again that, because the wind 

speeds and storm surge heights considered in these estimates do not occur simultaneously, the 

estimates are conservative for design purposes (see p. 15, footnote 1). 

 

Table 1. MRI (in Years) for Port of Tampa Site 

Wind Storm Surge Height (m) Speed 

(1-min) 

(m/s) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

32.5 30 49 86 158 299 611 1447 2895 13750 55000

35.0 35 53 88 158 299 611 1447 2895 13750 55000

37.5 41 61 92 160 299 611 1447 2895 13750 55000

40.0 51 76 106 172 302 611 1447 2895 13750 55000

42.5 66 99 134 190 313 611 1447 2895 13750 55000

45.0 83 126 165 230 355 625 1447 2895 13750 55000

47.5 115 174 234 324 451 663 1447 2895 13750 55000

50.0 149 224 309 414 556 764 1486 2895 13750 55000

52.5 212 318 455 640 833 1038 1618 3056 13750 55000

55.0 320 433 647 982 1279 1486 2115 3438 13750 55000

57.5 447 598 902 1486 1964 2200 2750 4583 13750 55000

60.0 724 932 1310 2292 3235 3438 3929 5500 13750 55000

62.5 1038 1375 1774 3438 5500 6111 6875 9167 18333 55000

65.0 1774 2115 3056 6875 13750 18333 18333 27500 55000 

67.5 3235 3235 3929 9167 27500 27500 27500 55000 

70.0 5500 5500 6111 13750 55000 55000 55000 
25

Table 2. MRI (in Years) for Clearwater Beach Site 

Wind Storm Surge Height (m) Speed 

(1-min) 

(m/s) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

32.5 32 52 99 237 797 4231 18333 55000 

35.0 36 55 102 242 809 4231 18333 55000 

37.5 41 61 107 253 821 4231 18333 55000 

40.0 50 72 114 264 859 4231 18333 55000 

42.5 63 90 136 286 887 4231 18333 55000 

45.0 80 113 168 324 932 4583 18333 55000 

47.5 109 149 220 385 1058 5000 18333 55000 

50.0 152 205 297 462 1279 6111 18333 55000 

52.5 222 286 404 618 1667 7857 27500 

55.0 340 426 604 982 2500 9167 27500 

57.5 545 679 948 1571 3667 18333 55000 

60.0 932 1170 1528 2500 6111 18333 55000 

62.5 1774 2200 2895 4583 18333 55000 55000 

65.0 2895 3056 4231 7857 18333 55000 55000 

67.5 5000 5500 11000 18333 27500 

70.0 11000 11000 27500 27500 55000 

Table 3. MRI (in Years) for St. Petersburg Beach Site 

Wind Storm Surge Height (m) Speed 

(1-min) 

(m/s) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

32.5 45 69 112 253 655 4583 

35.0 49 71 114 261 679 4583 

37.5 55 75 121 274 714 4583 

40.0 66 84 131 299 764 5500 

42.5 86 103 153 346 846 5500 

45.0 108 127 180 374 887 5500 

47.5 142 162 220 423 965 6875 

50.0 188 206 275 495 1019 6875 

52.5 282 309 420 663 1279 7857 

55.0 401 451 573 859 1719 7857 

57.5 579 640 786 1146 2200 7857 

60.0 932 1038 1341 1667 3235 11000 

62.5 1341 1447 1964 2391 4583 13750 

65.0 2391 2500 3056 3438 9167 27500 

67.5 3929 3929 5000 5500 13750 55000 

70.0 9167 9167 9167 11000 27500 55000 
26

Table 4. MRI (in Years) for MacDill AFB Site 

Wind Storm Surge Height (m) Speed 

(1-min) 

(m/s) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

32.5 165 165 165 284 561 1486 3235 13750 

35.0 165 165 165 284 561 1486 3235 13750 

37.5 167 167 167 285 561 1486 3235 13750 

40.0 180 180 180 291 561 1486 3235 13750 

42.5 200 200 200 306 573 1486 3235 13750 

45.0 249 249 249 362 604 1486 3235 13750 

47.5 333 333 333 466 679 1486 3235 13750 

50.0 447 447 447 611 833 1667 3235 13750 

52.5 696 696 696 902 1122 1897 3235 13750 

55.0 1122 1122 1122 1341 1667 2750 3929 18333 

57.5 1774 1774 1774 2115 2292 3929 5500 18333 

60.0 2619 2619 2619 3235 3438 5500 6875 18333 

62.5 5500 5500 5500 5500 5500 11000 13750 27500 

65.0 7857 7857 7857 7857 7857 18333 27500 55000 

67.5 18333 18333 18333 18333 18333 

70.0 55000 55000 55000 55000 55000 

Table 5. MRI (in Years) for St. Petersburg on Tampa Bay Site 

Wind Storm Surge Height (m) Speed 

(1-min) 

(m/s) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

32.5 753 753 753 753 1897 9167 

35.0 753 753 753 753 1897 9167 

37.5 753 753 753 753 1897 9167 

40.0 753 753 753 753 1897 9167 

42.5 764 764 764 764 1897 9167 

45.0 821 821 821 821 1897 9167 

47.5 982 982 982 982 2037 9167 

50.0 1250 1250 1250 1250 2391 9167 

52.5 1486 1486 1486 1486 2391 9167 

55.0 2391 2391 2391 2391 3438 11000 

57.5 3438 3438 3438 3438 4583 13750 

60.0 4583 4583 4583 4583 5500 13750 

62.5 7857 7857 7857 7857 9167 27500 

65.0 11000 11000 11000 11000 13750 55000 

67.5 27500 27500 27500 27500 55000 

70.0 55000 55000 55000 55000 55000 
27

The interpretation of the results of Table 1 through 5 must take into account the following 

three observations. First, as indicated in Section 3.1, these variates represent the maximum wind 

speed occurring at the site during the life of the hurricane with track hi, and the maximum storm 

surge height occurring at the site during the life of that hurricane; these two variates generally do 

not occur at the same time (see Appendix B). Second, estimates of storm surge height at a site 

are influenced not only by the maximum wind speed, but also by the hurricane’s central 

barometric pressure, radius of maximum wind speed, and speed and direction of its forward 

motion. Thus, hurricanes with wind speeds of Category 3 strength, say, can produce extremely 

high storm surge heights, as has been the case for hurricane Katrina. Third, probabilities of joint 

events consisting of wind speed and storm surge height with respect to NGVD at a site depend 

strongly on the site's geographical position, bathymetry, and topography. 

 The first of those observations explains why the MRIs estimated in this report might be 

smaller than the actual MRIs at a site (i.e., why the MRIs estimated in this report are 

conservative for structural engineering purposes). The second observation explains why the 

ordinates of the joint distributions estimated as shown in this report do not necessarily increase 

monotonically as either of the two variates increases (i.e., the same probabilities of exceedance 

and MRIs for a range of wind speeds and storm surge heights.) The third observation explains 

the significant qualitative differences between the joint histograms, probability distributions, and 

the MRIs estimated for the Port of Tampa, Clearwater Beach, and St. Petersburg sites on the one 

hand, and the MacDill AFB, and St. Petersburg on Tampa Bay sites on the other. However, a 

detailed explanation of those differences would require that extensive studies, which are outside 

the scope of this report, be performed in the future. 

3.4 ALTERNATIVE METHODS FOR ESTIMATING PROBABILITY OF 

EXCEEDANCE AND MEAN RECURRENCE INTERVAL 

 The above method for calculating joint probability of exceedance and mean recurrence 

interval utilized n data pairs. Each data pair consisted of the maximum wind speed 

vi,max≡max(

j

vij) and maximum storm surge height si,max≡max(

j

sij) that occur at different times j in 

the life of hurricane i (i=1,2, 3...,n=19,806). Denote the sample event space defined by the 

above data pairs as SE1. As indicated in Sections 3.1 to 3.3, the joint probabilities of exceedance 

and MRIs developed using event space SE1 are conservative from an engineering design 

viewpoint. 

 

 Other sample event spaces may be considered, for example the sample spaces herein 

denoted by SE2 and SE3. Event space SE2 is defined by pairs consisting of the maximum wind 

speed in each hurricane and the largest of the storm surge heights associated with that speed, and 

pairs consisting of the maximum storm surge height in each hurricane and the largest of the wind 

speeds associated with that height. Event space SE3 is defined by the set of data pairs that 

include the total number of M pairs of wind speeds and corresponding storm surge heights that 

occur during the time period T associated with the n hurricanes (M=m1+ m2+...+mn, and mi is the 

number of pairs of wind speed/storm surge height data in the ith hurricane, i=1,2,...,n=19,806). 

Estimates of joint probabilities of exceedance and mean recurrence intervals for the site of 

interest using the data pairs defined by event spaces SE2 and SE3 are not carried out in this proof 
28

of concept phase. However, the estimation procedures and their shortcomings are discussed in 

Appendix C. 
29

Chapter 4

PROPOSED DESIGN CRITERION FOR STRUCTURES SUBJECTED TO

COMBINED EFFECT OF WIND AND STORM SURGE

The steps outlined in Chapters 2 and 3 - which include the simulation and selection of 

hurricane storm tracks, the hydrodynamic simulation to obtain site-specific wind speeds and 

corresponding storm surge heights, and the application of probabilistic methods to develop joint 

probabilities and mean recurrence intervals for wind speed/storm surge height events - constitute 

a methodology that can be used to develop site-specific, risk-based design criteria for structures 

subjected to the combined effect of wind speed and storm surge. Two possible approaches for 

establishing such structural design criteria using the methodology developed in this study are 

described below. 

4.1 DESIGN CRITERION BASED ON ESTIMATED MRI 

From the MRI table developed as outlined in Chapter 3 for any particular site, the design 

criterion for structures local to that site can be established as follows: 

Ordinary structures shall be designed for the effects of load combinations calculated on 

the basis of wind speed/storm surge height events with a 50-year MRI if the Allowable Stress 

Design method is used, or with a 500-year MRI if the Load and Resistance Factor Design 

method is used. 

 

Special structures shall be designed for load combinations consistent with wind 

speed/storm surge height events with MRIs determined by the authority having jurisdiction. 

The design criterion developed as described in this Section is risk-based and site-specific. 

The use of data pairs consisting of maximum wind speeds and maximum storm surge heights 

(defined by event space SE1 in this report) leads to conservative MRI values. The degree of 

conservatism can be evaluated for specific design situations in a subsequent phase of this study. 

4.2 ALTERNATIVE METHOD FOR ESTABLISHING DESIGN CRITERION 

An alternative approach for establishing the design criterion that is more realistic insofar 

as it does not entail the same degree of conservatism inherent in the above approach (based on 

the event space E1) is described in this section. This alternative approach would likely yield less 

conservative estimates of the requisite exceedance probabilities and mean recurrence intervals, is 

thus more consistent with the requirements of a performance-based design philosophy, and 

entails the following steps: 

 (1) Calculate the combined scalar effect σij of the wind speed and storm surge for each of the 

pairs vij, sij simulated as shown in Chapter 2 (i=1,2,...,n, where n=number of simulated 

hurricanes used in the calculations, and j=1,2,...,mi, where mi is the number of pairs of data 
30

points in hurricane i). The combined effect could, for example, be the maximum stress in a 

member subjected to gravity loads and to loads induced by both wind load and storm surge. A 

second example is the aggregate loss of electrical power in a specified region due to damage to 

overhead power lines induced by wind and damage to underground cables caused by seepage of 

water following a storm surge and the consequent flooding. A third example is the wind-induced 

rotation of buildings with floating foundations that would rise in case of flood (the concept of 

floating foundation has been tried in the Netherlands and is currently being envisaged in the state 

of Louisiana). 

(2) Select, for each hurricane i, the largest of the effects σij, denoted by σi. 

(3) The probabilistic analysis of the univariate time series σi is identical to the analysis applied to 

hurricane wind speeds, regardless of their direction, or to hurricane wind effects representing the 

maximum of the directional effects in each of a large number of simulated hurricanes (see Simiu 

and Miyata, 2006, p. 33). This analysis can yield effects σN corresponding to any mean 

recurrence intervals N specified by the authority having jurisdiction as a function of type of 

design and limit state σlim. 

(4) A limit state σlim is specified by the authority having jurisdiction. 

(5) For a design to be acceptable the relation σN< σlim must be satisfied. 

 

 
31

Chapter 5 

SUMMARY AND DISCUSSION

5.1 SUMMARY 

 In this report, we describe a methodology for developing risk-based design criteria for 

use in designing coastal structures subjected to the combined effects of wind speed and storm 

surge. The methodology requires, as a first step, the selection of a set of stochastic hurricane 

storm tracks that affect the area of interest. For this work, we used the existing FPHLM for 

Florida. The next step involves hydrodynamic simulations of the basin of interest using the 

program SLOSH, with the selected hurricane tracks as input, to develop time histories of wind 

speeds and storm surge heights for the sites within the basin. The final step involves the 

application of probabilistic methods to the time histories of wind speed and storm surge height to 

produce estimates of joint probabilities of exceedance and mean recurrence intervals of wind 

speed/storm surge height events, and a corresponding framework for the development of design 

criteria for the combined effect of wind speed and storm surge that are risk-based and site 

specific. As proof of concept, the methodology was used to provide conservative estimates of 

mean recurrence intervals of wind speed/storm surge height events for five locations in the 

Tampa Bay basin. 

In addition to the approach based on estimates of MRIs of joint wind speed/storm surge 

events at a site, an alternative approach was also proposed for developing design criteria based 

on response, at every time step, to the combined effect of wind speed and storm surge (e.g., 

maximum stress in structural members, aggregate loss of power due to wind induced damage to 

transmission tower or power line, or wind-induced rotation of floating structures). This approach 

is considered more realistic, i.e., the design criterion developed using this alternative approach is 

less conservative compared with the joint MRI approach. 

5.2 DISCUSSION 

 The methodology outlined in Chapters 2 to 4 of this report provides a state of the art 

approach to establishing engineering design criteria for the design of coastal structures or other 

engineering systems, including systems located in the coastal high hazard zones defined by the 

FEMA’s FIRM map and subjected to the combined effect of hurricane wind speed and storm 

surge. However, the methodology has the following limitations: 

• The methodology is applicable only if a stochastic set of hurricane storm tracks and a current 

hydrodynamic model of the area of interest (SLOSH basins) are available. For the State of 

Florida, both of these exist, thus design criteria can be developed for the State of Florida 

using the methodology developed here. Even for Florida the possible evolution in time of 

the bathymetry of the sites needs to be taken into consideration. Furthermore, changes to the 

terrain, including both dunes building during beach restoration projects and destruction due 
32

to hurricane will impact the surge results. For other regions along the eastern seaboard and 

the Gulf coast, while hydrodynamic models of various basins exist, a public stochastic 

hurricane simulation model similar to the State of Florida FPHLM may not be available. 

• The hydrodynamic simulations performed in this proof of concept study using SLOSH did 

not consider the effect of waves and tides, both of which would increase the total water 

levels. Subsequent studies will need to investigate the feasibility of incorporating wave 

modeling, as well as to consider the effect of tides, in the hydrodynamic simulation and of 

comparing results with other simulation tools such as the Advanced Circulation Model for 

Oceanic, Coastal and Estuarine Water (ADCIRC). 

• For simplicity, wind directionality was not considered in this proof of concept phase even 

though time histories of wind direction can be obtained from hydrodynamic simulation by 

SLOSH. Consideration of wind directionality tends to result in decreased wind effects at a 

site. This factor needs to be addressed in a subsequent phase of this study. 
33

Chapter 6 

REFERENCES

ASCE/SEI 7-05, 2005: Minimum Design Loads for Buildings and Other Structures. American 

Society of Civil Engineers. 

ASCE/SEI 24-98, 1998: Flood Resistant Design and Construction. American Society of Civil 

Engineers. 

Darling, R. W. R., 1991: Estimating Probabilities of Hurricane Wind Speeds Using a Large 

Scale Empirical Model, Journal of Climate, 4, 1035-1046. 

DeMaria, M., J. Pennington, and K. Williams, 2002: Description of the Extended Best Track 

File (EBTRK1.4) version 1.4. Available from NESDIS/CIRA/Regional and Mesoscale 

Meteorology Team, Colorado State University, Fort Collin, CO. 

Ho, F. P., J. C. Su, K. L. Hanevich, R. J. Smith, and F. P. Richards, 1987: Hurricane climatology 

for the Atlantic and Gulf coasts of the United States. NOAA Tech Memo NWS 38, NWS Silver 

Spring, MD. 

Holland, G. J., 1980: An analytic model of the wind and pressure profiles in hurricanes, Mon. 

Wea. Rev., 108, 1212-1218. 

Houston, S. H., and M. D. Powell, 1994: Observed and modeled wind and water level response 

from Tropical Storm Marco (1990). Wea. Forecast., 9,427-439. 

Houston, S. H., W. A. Shaffer, M. D. Powell, and J. Chen, 1999: Comparisons of HRD and 

SLOSH surface wind fields in hurricanes: Implications for storm surge and wave modeling. 

Wea. Forecast., 14, 671-686. 

Jelesnianski, C.P., J. Chen, W.A. Shaffer, 1992: SLOSH Sea, Lake, and Overland Surges from 

Hurricanes, NOAA Technical Report NWS 48, Silverspring, Maryland. 

NIST Technical Note 1476, Performance of Physical Structures in Hurricane Katrina and 

Hurricane Rita: A Reconnaissance Report, National Institute of Standards and Technology, 

2006. 

Pennington, J., M. DeMaria, and K. Williams, cited 2000: Development of a 10-year Atlantic 

basin tropical cyclone wind structure climatology. 

(Available online at www.bbsr.edu/rpi/research/demaria/demaria4.html) 
34

Powell, M. D., G. Soukup, S. Cocke, S. Gulati, N. Morisseau-Leroy, S. Hamid, N. Dorst, and L. 

Axe, 2005: State of Florida hurricane loss projection model: Atmospheric science component. J. 

Wind Engineer. and Indust. Aerodyn., 93, 651-674. 

Saffir, H.S., 1989: Florida’s Approach to Hurricane-Resistant Design and Construction, Journal 

of Wind Engineering and Industrial Aerodynamics, Elsevier Science Publishers B.V., 

Amsterdam, The Netherlands, pp. 221-230. 

Simiu, E., and T. Miyata, 2006: Design of Buildings and Bridges for Wind: A Practical Guide 

for ASCE-7 Standard Users and Designers of Special Structures, John Wiley and Sons, Inc. 

Vickery, P. J., and L.A. Twisdale, 2005: Wind Field and Filling Models for Hurricane Wind 

Speed Predictions, Journal of Structural Engineering, 121, 1700-1709. 

Willoughby, H. E., and M. E. Rahn, 2004: Parametric Representation of the Primary Hurricane 

Vortex. Part I: Observations and Evaluation of the Holland (1980) Model. Mon. Wea. Rev., 132, 

3033-3048. 

http://www.nhc.noaa.gov/aboutsshs.shtml 
35

Appendix A 

EXPLANATION OF SLOSH SIMULATION OUTPUT 

Wind Directions, Wind Speeds, and Storm Surge Heights at Clear Water Beach Location 

(27.9767N, 82.8366W) caused by hurricane storm track number 12364 (generated from 55,000-

year simulation for State of Florida FPHLM, Version 1.0) 

RexFile=SLOSHRexFiles/adjSLOSHtrk12364.rex 

 (48 26) (27.9767 -82.8366) 

time (min), i, j, lat, lon, wind dir (0 is wind going eastward), wind speed (1 min MPH), surge (ft) 

 0.00, 48, 26, 27.9767, -82.8366, 132, 29, 2.0 

 4.50, 48, 26, 27.9767, -82.8366, 131, 29, 2.1 

 9.50, 48, 26, 27.9767, -82.8366, 131, 29, 2.2 

 14.50, 48, 26, 27.9767, -82.8366, 131, 29, 2.2 

 19.50, 48, 26, 27.9767, -82.8366, 130, 29, 2.2 

 24.50, 48, 26, 27.9767, -82.8366, 130, 29, 2.2 

 29.50, 48, 26, 27.9767, -82.8366, 130, 29, 2.2 

 34.50, 48, 26, 27.9767, -82.8366, 129, 29, 2.2 

 39.50, 48, 26, 27.9767, -82.8366, 129, 29, 2.2 

 44.50, 48, 26, 27.9767, -82.8366, 129, 29, 2.2 

 49.50, 48, 26, 27.9767, -82.8366, 128, 29, 2.1 

 54.50, 48, 26, 27.9767, -82.8366, 128, 28, 2.1 

.............. 

 674.50, 48, 26, 27.9767, -82.8366, 80, 18, 2.9 

 679.50, 48, 26, 27.9767, -82.8366, 80, 18, 2.9 

 684.50, 48, 26, 27.9767, -82.8366, 80, 18, 2.9 

 689.50, 48, 26, 27.9767, -82.8366, 79, 18, 2.9 

 694.50, 48, 26, 27.9767, -82.8366, 79, 18, 2.9 

 699.50, 48, 26, 27.9767, -82.8366, 79, 17, 2.9 

 704.50, 48, 26, 27.9767, -82.8366, 79, 17, 2.9 

 709.50, 48, 26, 27.9767, -82.8366, 78, 17, 2.8 

 714.50, 48, 26, 27.9767, -82.8366, 78, 17, 2.8 

 719.50, 48, 26, 27.9767, -82.8366, 78, 17, 2.8

Explanation of SLOSH Output:

• Row 1: Identification of hurricane track for the FPHLM used in the simulation 

• Row 2: SLOSH grid locator (i/j) and associated lat/lon of the site of interest 

• Row 3: Keys defining subsequent data columns: 

o Column 1: Time step in minutes 

o Column 2: SLOSH I, of i/j grid locator 

o Column 3: SLOSH J, of i/j grid locator 

o Column 4: Latitude of the site of interest 

o Column 5: Longitude of the site of interest 

o Column 6: Wind direction (0 is wind blowing eastward) 

o Column 7: Wind speed (1-min MPH) 

o Column 8: Storm surge height (ft) 
36
Appendix B 

TYPICAL

SLOSH 

SIMULATION 

OUTPUT FOR 

THE 

PORT OF 

TAMPA 

SI

RexFile=DataSets/SLOSHRexFiles/etpa_SLOSHtrk160.rex (18 10) (27.9475 -82.4448) time (min), i, j, lat, lon, wind dir (0 is wind going eastward), wind speed (1 min MPH), surge (ft)  0.00, 18, 10, 27.9475, -82.4448, -116, 12, 0.0  4.50, 18, 10, 27.9475, -82.4448, -116, 13, 0.0  9.50, 18, 10, 27.9475, -82.4448, -116, 13, 0.0  14.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  19.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  24.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  29.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  34.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  39.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  44.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  49.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  54.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  59.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  64.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  69.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  74.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  79.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  84.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  89.50, 18, 10, 27.9475, -82.4448, -117, 13, 0.0  94.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  99.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  104.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  109.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  114.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  119.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  124.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  129.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  134.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  139.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  144.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  149.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0 

 154.50, 18, 10, 27.9475, -82.4448, -117, 14, 0.0  159.50, 18, 10, 27.9475, -82.4448, -118, 14, 0.0  164.50, 18, 10, 27.9475, -82.4448, -118, 14, 0.0  169.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  174.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  179.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  184.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  189.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  194.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  199.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  204.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  209.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  214.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  219.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  224.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  229.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  234.50, 18, 10, 27.9475, -82.4448, -118, 15, 0.0  239.50, 18, 10, 27.9475, -82.4448, -118, 16, 0.0  244.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  249.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  254.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  259.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  264.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  269.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  274.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  279.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  284.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  289.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  294.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  299.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  304.50, 18, 10, 27.9475, -82.4448, -118, 16, -0.1  309.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  314.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  319.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  324.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  329.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  334.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1  339.50, 18, 10, 27.9475, -82.4448, -119, 17, -0.1 

 344.50, 18, 10, 27.947 349.50, 18, 10, 27.947

 354.50, 18, 10, 27.947 359.50, 18, 10, 27.947 364.50, 18, 10, 27.947 369.50, 18, 10, 27.947 374.50, 18, 10, 27.947 379.50, 18, 10, 27.947 384.50, 18, 10, 27.947 389.50, 18, 10, 27.947 394.50, 18, 10, 27.947 399.50, 18, 10, 27.947 404.50, 18, 10, 27.947 409.50, 18, 10, 27.947 414.50, 18, 10, 27.947 419.50, 18, 10, 27.947 424.50, 18, 10, 27.947 429.50, 18, 10, 27.947 434.50, 18, 10, 27.947 439.50, 18, 10, 27.947 444.50, 18, 10, 27.947 449.50, 18, 10, 27.947 454.50, 18, 10, 27.947 459.50, 18, 10, 27.947 464.50, 18, 10, 27.947 469.50, 18, 10, 27.947 474.50, 18, 10, 27.947 479.50, 18, 10, 27.947 484.50, 18, 10, 27.947 489.50, 18, 10, 27.947 494.50, 18, 10, 27.947 499.50, 18, 10, 27.947 504.50, 18, 10, 27.947 509.50, 18, 10, 27.947 514.50, 18, 10, 27.947 519.50, 18, 10, 27.947 524.50, 18, 10, 27.947 529.50, 18, 10, 27.947

37
 534.50, 18, 10, 27.9475, -82.4448, -123, 20, -0.3 

 539.50, 18, 10, 27.9475, -82.4448, -123, 20, -0.3  544.50, 18, 10, 27.9475, -82.4448, -123, 20, -0.3  549.50, 18, 10, 27.9475, -82.4448, -123, 20, -0.3  554.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.3  559.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.3  564.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.4  569.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.4  574.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.4  579.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.4  584.50, 18, 10, 27.9475, -82.4448, -123, 21, -0.4  589.50, 18, 10, 27.9475, -82.4448, -124, 21, -0.4  594.50, 18, 10, 27.9475, -82.4448, -124, 21, -0.4  599.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  604.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  609.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  614.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  619.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  624.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  629.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  634.50, 18, 10, 27.9475, -82.4448, -124, 22, -0.4  639.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.4  644.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.4  649.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  654.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  659.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  664.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  669.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  674.50, 18, 10, 27.9475, -82.4448, -125, 23, -0.5  679.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  684.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  689.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  694.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  699.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  704.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.5  709.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.6  714.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  719.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.6  724.50, 18, 10, 27.9475, -82.4448, -126, 24, -0.6  729.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  734.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  739.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  744.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  749.50, 18, 10, 27.9475, -82.4448, -126, 25, -0.6  754.50, 18, 10, 27.9475, -82.4448, -126, 26, -0.6 

 759.50, 18, 10, 27.9475, -82.4448, -126, 26, -0.6  764.50, 18, 10, 27.9475, -82.4448, -126, 26, -0.7  769.50, 18, 10, 27.9475, -82.4448, -126, 26, -0.7  774.50, 18, 10, 27.9475, -82.4448, -126, 27, -0.7  779.50, 18, 10, 27.9475, -82.4448, -125, 27, -0.7  784.50, 18, 10, 27.9475, -82.4448, -125, 27, -0.7 

 789.50, 18, 10, 27.9475, -82.4448, -125, 27, -0.7  794.50, 18, 10, 27.9475, -82.4448, -125, 28, -0.7  799.50, 18, 10, 27.9475, -82.4448, -125, 28, -0.7  804.50, 18, 10, 27.9475, -82.4448, -126, 28, -0.8  809.50, 18, 10, 27.9475, -82.4448, -126, 28, -0.8  814.50, 18, 10, 27.9475, -82.4448, -126, 29, -0.8  819.50, 18, 10, 27.9475, -82.4448, -126, 29, -0.8  824.50, 18, 10, 27.9475, -82.4448, -126, 29, -0.8  829.50, 18, 10, 27.9475, -82.4448, -126, 30, -0.8  834.50, 18, 10, 27.9475, -82.4448, -126, 30, -0.8  839.50, 18, 10, 27.9475, -82.4448, -126, 30, -0.9  844.50, 18, 10, 27.9475, -82.4448, -126, 31, -0.9  849.50, 18, 10, 27.9475, -82.4448, -126, 31, -0.9  854.50, 18, 10, 27.9475, -82.4448, -126, 32, -0.9  859.50, 18, 10, 27.9475, -82.4448, -126, 32, -0.9  864.50, 18, 10, 27.9475, -82.4448, -126, 32, -0.9  869.50, 18, 10, 27.9475, -82.4448, -126, 33, -1.0  874.50, 18, 10, 27.9475, -82.4448, -126, 33, -1.0  879.50, 18, 10, 27.9475, -82.4448, -126, 33, -1.0  884.50, 18, 10, 27.9475, -82.4448, -126, 34, -1.0  889.50, 18, 10, 27.9475, -82.4448, -126, 34, -1.0  894.50, 18, 10, 27.9475, -82.4448, -126, 35, -1.1  899.50, 18, 10, 27.9475, -82.4448, -127, 35, -1.1  904.50, 18, 10, 27.9475, -82.4448, -127, 36, -1.1  909.50, 18, 10, 27.9475, -82.4448, -127, 36, -1.1  914.50, 18, 10, 27.9475, -82.4448, -127, 36, -1.1  919.50, 18, 10, 27.9475, -82.4448, -127, 37, -1.2  924.50, 18, 10, 27.9475, -82.4448, -127, 37, -1.2  929.50, 18, 10, 27.9475, -82.4448, -127, 38, -1.2  934.50, 18, 10, 27.9475, -82.4448, -127, 38, -1.2  939.50, 18, 10, 27.9475, -82.4448, -128, 39, -1.3  944.50, 18, 10, 27.9475, -82.4448, -128, 39, -1.3  949.50, 18, 10, 27.9475, -82.4448, -128, 40, -1.3  954.50, 18, 10, 27.9475, -82.4448, -128, 41, -1.3  959.50, 18, 10, 27.9475, -82.4448, -128, 41, -1.3  964.50, 18, 10, 27.9475, -82.4448, -129, 42, -1.4  969.50, 18, 10, 27.9475, -82.4448, -129, 43, -1.4  974.50, 18, 10, 27.9475, -82.4448, -129, 43, -1.4  979.50, 18, 10, 27.9475, -82.4448, -129, 44, -1.5 

 984.50, 18, 10, 27.947 989.50, 18, 10, 27.947 994.50, 18, 10, 27.947 999.50, 18, 10, 27.947 1004.50, 18, 10, 27.947 1009.50, 18, 10, 27.947 1014.50, 18, 10, 27.947 1019.50, 18, 10, 27.947 1024.50, 18, 10, 27.947 1029.50, 18, 10, 27.947 1034.50, 18, 10, 27.947 1039.50, 18, 10, 27.947 1044.50, 18, 10, 27.947 1049.50, 18, 10, 27.947 1054.50, 18, 10, 27.947 1059.50, 18, 10, 27.947 1064.50, 18, 10, 27.947 1069.50, 18, 10, 27.947 1074.50, 18, 10, 27.947

 1079.50, 18, 10, 27.947 1084.50, 18, 10, 27.947 1089.50, 18, 10, 27.947 1094.50, 18, 10, 27.947 1099.50, 18, 10, 27.947 1104.50, 18, 10, 27.947 1109.50, 18, 10, 27.947 1114.50, 18, 10, 27.947 1119.50, 18, 10, 27.947 1124.50, 18, 10, 27.947 1129.50, 18, 10, 27.947 1134.50, 18, 10, 27.947 1139.50, 18, 10, 27.947 1144.50, 18, 10, 27.947 1149.50, 18, 10, 27.947 1154.50, 18, 10, 27.947 1159.50, 18, 10, 27.947 1164.50, 18, 10, 27.947 1169.50, 18, 10, 27.947 1174.50, 18, 10, 27.947 1179.50, 18, 10, 27.947 1184.50, 18, 10, 27.947 1189.50, 18, 10, 27.947 1194.50, 18, 10, 27.947 1199.50, 18, 10, 27.947 1204.50, 18, 10, 27.947

38
 1209.50, 18, 10, 27.9475, -82.4448, 179, 81, 99.9 

 1214.50, 18, 10, 27.9475, -82.4448, 177, 81, 99.9  1219.50, 18, 10, 27.9475, -82.4448, 174, 82, 99.9  1224.50, 18, 10, 27.9475, -82.4448, 171, 82, 99.9  1229.50, 18, 10, 27.9475, -82.4448, 168, 82, 99.9  1234.50, 18, 10, 27.9475, -82.4448, 165, 82, 99.9  1239.50, 18, 10, 27.9475, -82.4448, 162, 82, 99.9  1244.50, 18, 10, 27.9475, -82.4448, 159, 82, 99.9  1249.50, 18, 10, 27.9475, -82.4448, 156, 82, 99.9  1254.50, 18, 10, 27.9475, -82.4448, 152, 82, 99.9  1259.50, 18, 10, 27.9475, -82.4448, 149, 82, 99.9  1264.50, 18, 10, 27.9475, -82.4448, 145, 81, 99.9  1269.50, 18, 10, 27.9475, -82.4448, 141, 81, 99.9  1274.50, 18, 10, 27.9475, -82.4448, 137, 81, 99.9  1279.50, 18, 10, 27.9475, -82.4448, 133, 81, 99.9  1284.50, 18, 10, 27.9475, -82.4448, 129, 81, 99.9  1289.50, 18, 10, 27.9475, -82.4448, 125, 81, 99.9  1294.50, 18, 10, 27.9475, -82.4448, 121, 81, 99.9  1299.50, 18, 10, 27.9475, -82.4448, 117, 81, 99.9  1304.50, 18, 10, 27.9475, -82.4448, 113, 82, 99.9  1309.50, 18, 10, 27.9475, -82.4448, 110, 82, 99.9  1314.50, 18, 10, 27.9475, -82.4448, 106, 82, 99.9  1319.50, 18, 10, 27.9475, -82.4448, 103, 82, 99.9  1324.50, 18, 10, 27.9475, -82.4448, 99, 83, 99.9  1329.50, 18, 10, 27.9475, -82.4448, 96, 83, 99.9  1334.50, 18, 10, 27.9475, -82.4448, 94, 83, 99.9  1339.50, 18, 10, 27.9475, -82.4448, 91, 84, 99.9  1344.50, 18, 10, 27.9475, -82.4448, 89, 84, 99.9  1349.50, 18, 10, 27.9475, -82.4448, 86, 84, 99.9  1354.50, 18, 10, 27.9475, -82.4448, 84, 84, 99.9  1359.50, 18, 10, 27.9475, -82.4448, 83, 84, 99.9  1364.50, 18, 10, 27.9475, -82.4448, 81, 83, 99.9  1369.50, 18, 10, 27.9475, -82.4448, 80, 83, 99.9  1374.50, 18, 10, 27.9475, -82.4448, 78, 82, -1.9  1379.50, 18, 10, 27.9475, -82.4448, 77, 82, -1.9  1384.50, 18, 10, 27.9475, -82.4448, 76, 81, -1.8  1389.50, 18, 10, 27.9475, -82.4448, 75, 81, -1.6  1394.50, 18, 10, 27.9475, -82.4448, 75, 80, -1.4  1399.50, 18, 10, 27.9475, -82.4448, 74, 79, -1.1  1404.50, 18, 10, 27.9475, -82.4448, 73, 78, -0.8  1409.50, 18, 10, 27.9475, -82.4448, 73, 77, -0.4  1414.50, 18, 10, 27.9475, -82.4448, 72, 76, 0.0  1419.50, 18, 10, 27.9475, -82.4448, 72, 75, 0.5  1424.50, 18, 10, 27.9475, -82.4448, 72, 74, 0.9  1429.50, 18, 10, 27.9475, -82.4448, 71, 73, 1.2 

 1434.50, 18, 10, 27.9475, -82.4448, 71, 72, 1.4  1439.50, 18, 10, 27.9475, -82.4448, 71, 74, 1.6  1444.50, 18, 10, 27.9475, -82.4448, 71, 73, 1.7  1449.50, 18, 10, 27.9475, -82.4448, 70, 73, 1.9  1454.50, 18, 10, 27.9475, -82.4448, 69, 72, 2.0  1459.50, 18, 10, 27.9475, -82.4448, 68, 72, 2.2  1464.50, 18, 10, 27.9475, -82.4448, 67, 71, 2.3  1469.50, 18, 10, 27.9475, -82.4448, 67, 70, 2.5  1474.50, 18, 10, 27.9475, -82.4448, 66, 70, 2.6  1479.50, 18, 10, 27.9475, -82.4448, 65, 69, 2.7  1484.50, 18, 10, 27.9475, -82.4448, 65, 68, 2.8  1489.50, 18, 10, 27.9475, -82.4448, 64, 68, 2.8  1494.50, 18, 10, 27.9475, -82.4448, 63, 67, 2.9  1499.50, 18, 10, 27.9475, -82.4448, 63, 67, 2.9  1504.50, 18, 10, 27.9475, -82.4448, 62, 66, 3.0  1509.50, 18, 10, 27.9475, -82.4448, 62, 65, 3.0  1514.50, 18, 10, 27.9475, -82.4448, 61, 65, 3.1  1519.50, 18, 10, 27.9475, -82.4448, 60, 64, 3.1  1524.50, 18, 10, 27.9475, -82.4448, 60, 64, 3.1  1529.50, 18, 10, 27.9475, -82.4448, 59, 63, 3.2  1534.50, 18, 10, 27.9475, -82.4448, 59, 62, 3.2  1539.50, 18, 10, 27.9475, -82.4448, 58, 62, 3.2  1544.50, 18, 10, 27.9475, -82.4448, 57, 61, 3.2  1549.50, 18, 10, 27.9475, -82.4448, 57, 60, 3.2  1554.50, 18, 10, 27.9475, -82.4448, 56, 60, 3.2  1559.50, 18, 10, 27.9475, -82.4448, 56, 59, 3.2 

 1564.50, 18, 10, 27.9475, -82.4448, 55, 58, 3.3  1569.50, 18, 10, 27.9475, -82.4448, 55, 58, 3.3  1574.50, 18, 10, 27.9475, -82.4448, 54, 57, 3.3  1579.50, 18, 10, 27.9475, -82.4448, 54, 57, 3.3  1584.50, 18, 10, 27.9475, -82.4448, 54, 56, 3.3  1589.50, 18, 10, 27.9475, -82.4448, 53, 55, 3.3  1594.50, 18, 10, 27.9475, -82.4448, 53, 55, 3.3  1599.50, 18, 10, 27.9475, -82.4448, 52, 54, 3.3  1604.50, 18, 10, 27.9475, -82.4448, 52, 54, 3.3  1609.50, 18, 10, 27.9475, -82.4448, 51, 53, 3.3  1614.50, 18, 10, 27.9475, -82.4448, 51, 53, 3.2  1619.50, 18, 10, 27.9475, -82.4448, 51, 52, 3.2  1624.50, 18, 10, 27.9475, -82.4448, 51, 52, 3.2  1629.50, 18, 10, 27.9475, -82.4448, 50, 51, 3.2  1634.50, 18, 10, 27.9475, -82.4448, 50, 51, 3.2  1639.50, 18, 10, 27.9475, -82.4448, 50, 50, 3.2  1644.50, 18, 10, 27.9475, -82.4448, 49, 50, 3.1  1649.50, 18, 10, 27.9475, -82.4448, 49, 49, 3.1  1654.50, 18, 10, 27.9475, -82.4448, 48, 49, 3.1 

 1659.50, 18, 10, 27.947 1664.50, 18, 10, 27.947 1669.50, 18, 10, 27.947 1674.50, 18, 10, 27.947 1679.50, 18, 10, 27.947 1684.50, 18, 10, 27.947 1689.50, 18, 10, 27.947 1694.50, 18, 10, 27.947 1699.50, 18, 10, 27.947 1704.50, 18, 10, 27.947 1709.50, 18, 10, 27.947 1714.50, 18, 10, 27.947 1719.50, 18, 10, 27.947 1724.50, 18, 10, 27.947 1729.50, 18, 10, 27.947 1734.50, 18, 10, 27.947 1739.50, 18, 10, 27.947 1744.50, 18, 10, 27.947 1749.50, 18, 10, 27.947 1754.50, 18, 10, 27.947 1759.50, 18, 10, 27.947 1764.50, 18, 10, 27.947 1769.50, 18, 10, 27.947 1774.50, 18, 10, 27.947 1779.50, 18, 10, 27.947 1784.50, 18, 10, 27.947 1789.50, 18, 10, 27.947 1794.50, 18, 10, 27.947 1799.50, 18, 10, 27.947 1804.50, 18, 10, 27.947 1809.50, 18, 10, 27.947 1814.50, 18, 10, 27.947 1819.50, 18, 10, 27.947 1824.50, 18, 10, 27.947 1829.50, 18, 10, 27.947 1834.50, 18, 10, 27.947 1839.50, 18, 10, 27.947 1844.50, 18, 10, 27.947 1849.50, 18, 10, 27.947 1854.50, 18, 10, 27.947 1859.50, 18, 10, 27.947 1864.50, 18, 10, 27.947 1869.50, 18, 10, 27.947 1874.50, 18, 10, 27.947 1879.50, 18, 10, 27.947

39
 1884.50, 18, 10, 27.9475, -82.4448, 36, 33, 2.1 

 1889.50, 18, 10, 27.9475, -82.4448, 36, 32, 2.1  1894.50, 18, 10, 27.9475, -82.4448, 35, 32, 2.0  1899.50, 18, 10, 27.9475, -82.4448, 35, 32, 2.0  1904.50, 18, 10, 27.9475, -82.4448, 35, 31, 2.0  1909.50, 18, 10, 27.9475, -82.4448, 35, 31, 2.0  1914.50, 18, 10, 27.9475, -82.4448, 35, 31, 1.9  1919.50, 18, 10, 27.9475, -82.4448, 34, 31, 1.9  1924.50, 18, 10, 27.9475, -82.4448, 34, 30, 1.9  1929.50, 18, 10, 27.9475, -82.4448, 34, 30, 1.9  1934.50, 18, 10, 27.9475, -82.4448, 34, 30, 1.8  1939.50, 18, 10, 27.9475, -82.4448, 34, 30, 1.8  1944.50, 18, 10, 27.9475, -82.4448, 33, 29, 1.8  1949.50, 18, 10, 27.9475, -82.4448, 33, 29, 1.8  1954.50, 18, 10, 27.9475, -82.4448, 33, 29, 1.7  1959.50, 18, 10, 27.9475, -82.4448, 33, 29, 1.7  1964.50, 18, 10, 27.9475, -82.4448, 33, 28, 1.7  1969.50, 18, 10, 27.9475, -82.4448, 33, 28, 1.7  1974.50, 18, 10, 27.9475, -82.4448, 32, 28, 1.6  1979.50, 18, 10, 27.9475, -82.4448, 32, 28, 1.6  1984.50, 18, 10, 27.9475, -82.4448, 32, 28, 1.6  1989.50, 18, 10, 27.9475, -82.4448, 32, 28, 1.6  1994.50, 18, 10, 27.9475, -82.4448, 32, 27, 1.6  1999.50, 18, 10, 27.9475, -82.4448, 32, 27, 1.5  2004.50, 18, 10, 27.9475, -82.4448, 31, 27, 1.5  2009.50, 18, 10, 27.9475, -82.4448, 31, 27, 1.5  2014.50, 18, 10, 27.9475, -82.4448, 31, 27, 1.5  2019.50, 18, 10, 27.9475, -82.4448, 31, 26, 1.5  2024.50, 18, 10, 27.9475, -82.4448, 31, 26, 1.5  2029.50, 18, 10, 27.9475, -82.4448, 31, 26, 1.4  2034.50, 18, 10, 27.9475, -82.4448, 30, 26, 1.4  2039.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.4  2044.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.4  2049.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.4  2054.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.4  2059.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.4  2064.50, 18, 10, 27.9475, -82.4448, 30, 25, 1.3  2069.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2074.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2079.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2084.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2089.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2094.50, 18, 10, 27.9475, -82.4448, 29, 24, 1.3  2099.50, 18, 10, 27.9475, -82.4448, 28, 24, 1.3  2104.50, 18, 10, 27.9475, -82.4448, 28, 23, 1.2 

 2109.50, 18, 10, 27.9475, -82.4448, 28, 23, 1.2  2114.50, 18, 10, 27.9475, -82.4448, 28, 23, 1.2  2119.50, 18, 10, 27.9475, -82.4448, 28, 23, 1.2  2124.50, 18, 10, 27.9475, -82.4448, 28, 23, 1.2  2129.50, 18, 10, 27.9475, -82.4448, 27, 23, 1.2  2134.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.2  2139.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.2  2144.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.1  2149.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.1  2154.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.1  2159.50, 18, 10, 27.9475, -82.4448, 28, 22, 1.1  2164.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.1  2169.50, 18, 10, 27.9475, -82.4448, 27, 22, 1.1  2174.50, 18, 10, 27.9475, -82.4448, 27, 21, 1.1  2179.50, 18, 10, 27.9475, -82.4448, 27, 21, 1.1  2184.50, 18, 10, 27.9475, -82.4448, 27, 21, 1.1  2189.50, 18, 10, 27.9475, -82.4448, 27, 21, 1.1  2194.50, 18, 10, 27.9475, -82.4448, 26, 21, 1.0  2199.50, 18, 10, 27.9475, -82.4448, 26, 21, 1.0  2204.50, 18, 10, 27.9475, -82.4448, 26, 21, 1.0  2209.50, 18, 10, 27.9475, -82.4448, 26, 21, 1.0  2214.50, 18, 10, 27.9475, -82.4448, 26, 20, 1.0  2219.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2224.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2229.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2234.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2239.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2244.50, 18, 10, 27.9475, -82.4448, 25, 20, 1.0  2249.50, 18, 10, 27.9475, -82.4448, 24, 20, 0.9  2254.50, 18, 10, 27.9475, -82.4448, 24, 20, 0.9  2259.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2264.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2269.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2274.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2279.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2284.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2289.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2294.50, 18, 10, 27.9475, -82.4448, 24, 19, 0.9  2299.50, 18, 10, 27.9475, -82.4448, 23, 19, 0.8  2304.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8  2309.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8  2314.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8  2319.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8  2324.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8  2329.50, 18, 10, 27.9475, -82.4448, 23, 18, 0.8 

 2334.50, 18, 10, 27.947 2339.50, 18, 10, 27.947 2344.50, 18, 10, 27.947 2349.50, 18, 10, 27.947 2354.50, 18, 10, 27.947 2359.50, 18, 10, 27.947 2364.50, 18, 10, 27.947 2369.50, 18, 10, 27.947 2374.50, 18, 10, 27.947 2379.50, 18, 10, 27.947 2384.50, 18, 10, 27.947 2389.50, 18, 10, 27.947 2394.50, 18, 10, 27.947

 2399.50, 18, 10, 27.947 2404.50, 18, 10, 27.947 2409.50, 18, 10, 27.947 2414.50, 18, 10, 27.947 2419.50, 18, 10, 27.947 2424.50, 18, 10, 27.947 2429.50, 18, 10, 27.947 2434.50, 18, 10, 27.947 2439.50, 18, 10, 27.947 2444.50, 18, 10, 27.947 2449.50, 18, 10, 27.947 2454.50, 18, 10, 27.947 2459.50, 18, 10, 27.947 2464.50, 18, 10, 27.947 2469.50, 18, 10, 27.947 2474.50, 18, 10, 27.947 2479.50, 18, 10, 27.947 2484.50, 18, 10, 27.947 2489.50, 18, 10, 27.947 2494.50, 18, 10, 27.947 2499.50, 18, 10, 27.947 2504.50, 18, 10, 27.947 2509.50, 18, 10, 27.947 2514.50, 18, 10, 27.947 2519.50, 18, 10, 27.947 2524.50, 18, 10, 27.947 2529.50, 18, 10, 27.947 2534.50, 18, 10, 27.947 2539.50, 18, 10, 27.947 2544.50, 18, 10, 27.947 2549.50, 18, 10, 27.947 2554.50, 18, 10, 27.947

40
 2559.50, 18, 10, 27.9475, -82.4448, 18, 15, 0.5 

 2564.50, 18, 10, 27.9475, -82.4448, 18, 14, 0.5  2569.50, 18, 10, 27.9475, -82.4448, 18, 14, 0.5  2574.50, 18, 10, 27.9475, -82.4448, 18, 14, 0.5  2579.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2584.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2589.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2594.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2599.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2604.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2609.50, 18, 10, 27.9475, -82.4448, 17, 14, 0.5  2614.50, 18, 10, 27.9475, -82.4448, 16, 14, 0.5  2619.50, 18, 10, 27.9475, -82.4448, 16, 14, 0.5  2624.50, 18, 10, 27.9475, -82.4448, 16, 14, 0.5  2629.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2634.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2639.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2644.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2649.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2654.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2659.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.5  2664.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.4  2669.50, 18, 10, 27.9475, -82.4448, 16, 13, 0.4  2674.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2679.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2684.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2689.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2694.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2699.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2704.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2709.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2714.50, 18, 10, 27.9475, -82.4448, 15, 13, 0.4  2719.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2724.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2729.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2734.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2739.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2744.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2749.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2754.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2759.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2764.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2769.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2774.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2779.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4 

 2784.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2789.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2794.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.4  2799.50, 18, 10, 27.9475, -82.4448, 14, 12, 0.3  2804.50, 18, 10, 27.9475, -82.4448, 14, 11, 0.3  2809.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2814.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2819.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2824.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2829.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2834.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2839.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2844.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2849.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2854.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2859.50, 18, 10, 27.9475, -82.4448, 12, 11, 0.3  2864.50, 18, 10, 27.9475, -82.4448, 12, 11, 0.3  2869.50, 18, 10, 27.9475, -82.4448, 12, 11, 0.3  2874.50, 18, 10, 27.9475, -82.4448, 12, 11, 0.3  2879.50, 18, 10, 27.9475, -82.4448, 14, 11, 0.3  2884.50, 18, 10, 27.9475, -82.4448, 14, 11, 0.3  2889.50, 18, 10, 27.9475, -82.4448, 14, 11, 0.3  2894.50, 18, 10, 27.9475, -82.4448, 14, 11, 0.3  2899.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2904.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2909.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2914.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2919.50, 18, 10, 27.9475, -82.4448, 13, 11, 0.3  2924.50, 18, 10, 27.9475, -82.4448, 13, 10, 0.3  2929.50, 18, 10, 27.9475, -82.4448, 13, 10, 0.3  2934.50, 18, 10, 27.9475, -82.4448, 13, 10, 0.3  2939.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2944.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2949.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2954.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2959.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2964.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2969.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2974.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2979.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2984.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2989.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  2994.50, 18, 10, 27.9475, -82.4448, 11, 10, 0.3  2999.50, 18, 10, 27.9475, -82.4448, 12, 10, 0.3  3004.50, 18, 10, 27.9475, -82.4448, 11, 10, 0.3 

 3009.50, 18, 10, 27.947 3014.50, 18, 10, 27.947 3019.50, 18, 10, 27.947 3024.50, 18, 10, 27.947 3029.50, 18, 10, 27.947 3034.50, 18, 10, 27.947 3039.50, 18, 10, 27.947 3044.50, 18, 10, 27.947 3049.50, 18, 10, 27.947 3054.50, 18, 10, 27.947 3059.50, 18, 10, 27.947 3064.50, 18, 10, 27.947 3069.50, 18, 10, 27.947

 3074.50, 18, 10, 27.947 3079.50, 18, 10, 27.947 3084.50, 18, 10, 27.947 3089.50, 18, 10, 27.947 3094.50, 18, 10, 27.947 3099.50, 18, 10, 27.947 3104.50, 18, 10, 27.947 3109.50, 18, 10, 27.947 3114.50, 18, 10, 27.947 3119.50, 18, 10, 27.947 3124.50, 18, 10, 27.947 3129.50, 18, 10, 27.947 3134.50, 18, 10, 27.947 3139.50, 18, 10, 27.947 3144.50, 18, 10, 27.947 3149.50, 18, 10, 27.947 3154.50, 18, 10, 27.947 3159.50, 18, 10, 27.947 3164.50, 18, 10, 27.947 3169.50, 18, 10, 27.947 3174.50, 18, 10, 27.947 3179.50, 18, 10, 27.947 3184.50, 18, 10, 27.947 3189.50, 18, 10, 27.947 3194.50, 18, 10, 27.947 3199.50, 18, 10, 27.947 3204.50, 18, 10, 27.947 3209.50, 18, 10, 27.947 3214.50, 18, 10, 27.947 3219.50, 18, 10, 27.947 3224.50, 18, 10, 27.947 3229.50, 18, 10, 27.947

41
 3234.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2 

 3239.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3244.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3249.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3254.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3259.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3264.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3269.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3274.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3279.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3284.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3289.50, 18, 10, 27.9475, -82.4448, 8, 8, 0.2  3294.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.2  3299.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.2  3304.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.2  3309.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.2  3314.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.2  3319.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3324.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3329.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3334.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3339.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3344.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3349.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3354.50, 18, 10, 27.9475, -82.4448, 7, 8, 0.1  3359.50, 18, 10, 27.9475, -82.4448, 6, 8, 0.1  3364.50, 18, 10, 27.9475, -82.4448, 6, 8, 0.1  3369.50, 18, 10, 27.9475, -82.4448, 6, 8, 0.1  3374.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1 

 3379.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3384.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3389.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3394.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3399.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3404.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3409.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3414.50, 18, 10, 27.9475, -82.4448, 6, 7, 0.1  3419.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3424.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3429.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3434.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3439.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3444.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3449.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3454.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3459.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3464.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3469.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3474.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3479.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3484.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3489.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3494.50, 18, 10, 27.9475, -82.4448, 5, 7, 0.1  3499.50, 18, 10, 27.9475, -82.4448, 4, 7, 0.1  3504.50, 18, 10, 27.9475, -82.4448, 4, 7, 0.1  3509.50, 18, 10, 27.9475, -82.4448, 4, 7, 0.1  3514.50, 18, 10, 27.9475, -82.4448, 4, 7, 0.1  3519.50, 18, 10, 27.9475, -82.4448, 4, 7, 0.1 

 3524.50, 18, 10, 27.947 3529.50, 18, 10, 27.947 3534.50, 18, 10, 27.947 3539.50, 18, 10, 27.947 3544.50, 18, 10, 27.947 3549.50, 18, 10, 27.947 3554.50, 18, 10, 27.947 3559.50, 18, 10, 27.947 3564.50, 18, 10, 27.947 3569.50, 18, 10, 27.947 3574.50, 18, 10, 27.947 3579.50, 18, 10, 27.947 3584.50, 18, 10, 27.947 3589.50, 18, 10, 27.947 3594.50, 18, 10, 27.947 3599.50, 18, 10, 27.947 3604.50, 18, 10, 27.947 3609.50, 18, 10, 27.947 3614.50, 18, 10, 27.947 3619.50, 18, 10, 27.947 3624.50, 18, 10, 27.947 3629.50, 18, 10, 27.947 3634.50, 18, 10, 27.947 3639.50, 18, 10, 27.947 3644.50, 18, 10, 27.947 3649.50, 18, 10, 27.947 3654.50, 18, 10, 27.947 3659.50, 18, 10, 27.947

42
43

Appendix C 

ALTERNATIVE METHODS FOR ESTIMATING JOINT PROBABILITY OF 

EXCEEDANCE AND MEAN RECURRENCE INTERVAL 

B.1 ESTIMATES CORRESPONDING TO SAMPLE EVENT SPACE SE2 

The members of the sample space SE2 are defined by pairs of maximum wind speed in 

each hurricane and the largest of the storm surge heights associated with that speed, and pairs of 

the maximum storm surge height in each hurricane and the largest of the wind speeds associated 

with that height. We now make this definition more precise. Consider hurricane hi. Associated 

with each j (i.e., at each time tj) are a wind speed vij and a storm surge height sij. The wind speed 

variate being selected as a basis for the subsequent estimates is the maximum wind speed in each 

hurricane, denoted by vi

(1)≡max(

j

vij). There may be several times j at which the same value vi

(1)

occurs. The storm surge height si

(1) associated with the value vi(1) is selected to be the largest of 

the storm surge heights occurring at any of those times. The pair, belonging to hurricane hi, 

selected for incorporation in the data sample of size n used for our estimates is vi

(1), si(1) (the 

explanation for our use of the superscript (1) will become clear forthwith). The following is an 

example of rank ordered pairs of wind speed and storm surge height data in a hurricane hi: 

 vi,max si,max

 (1-minute m/s) (m) 

 

 70 6 

 70 5.5 

 68 6 

 68 5.8 

 68 5.3 

 65 5.5 

 65 4.7 

 60 5.0 

 55 5.2 

 55 4.5 

 ... ... 

 ... ... 

 

where vi

(1)≡ max(

j

vij)= 70 m/s (156 mph). The pair selected for incorporation in the data sample 

is vi

(1), si(1) or, in our example, 70 m/s (156 mph), 6 m (20 ft). However, this pair will not 

necessarily include the largest storm surge height occurring during hurricane hi. For this reason 

we include in the data sample a second pair selected as follows. Let that storm surge height be 

denoted by si

(2) ≡max(

j

sij). The largest of the wind speeds occurring in conjunction with si

(2) is 
44

denoted by vi

(2). The second pair belonging to hurricane hi that is selected for inclusion in the 

sample is vi

(2), si(2). Since i=n, the total number of pairs in the sample is therefore 2n. 

The construction of the histograms of wind speeds and storm surge heights, and the 

estimation of the associated probabilities of exceedance and mean recurrence intervals is similar 

to those discussed in Section 3.1. The difference is that the epoch inherent in the inverse of the 

probability of exceedance is half as small as was the case in Section 3.1, owing to the use of two 

pairs of variates in each hurricane. The advantage of estimates based on sample space SE2 over 

those based on SE1 is that the pairs of variates represent simultaneous wind speeds and storm 

surge heights at the site. However, the information yielded by those estimates can be 

unconservative from a structural engineering point of view, because pairs of variates v,s can 

exist that are more unfavorable from an engineering viewpoint than the pairs of the type vi

(1), si(1)

and type vi

(2), si(2). Such unfavorable pairs are not revealed by analyses based on the sample 

space SE2, owing to the impossibility of rank-ordering between pairs of the type vi

(1), si(1) the one 

hand and type vi

(2), si(2) on the other. 

B.2 ESTIMATES CORRESPONDING TO SAMPLE EVENT SPACE SE3 

For each hurricane hi, pairs of wind speeds vij and storm surge heights sij are available for 

each time is tj = jΔt , where the time step Δt=5 min, and j denotes the number of the time interval. 

For the time interval T=55,000 years the quantities of interest can in principle be 

estimated as follows. For all i and j, create a joint histogram of wind speeds and corresponding 

storm surge heights by placing each of the pairs vij, sij in the bin defined by the coordinates vijΔv/2, vij+Δv/2, sij-Δs/2, sij+Δs/2, where vij and sij are integer multiples of the intervals Δv and Δs, 

respectively. This joint histogram includes the total number M of pairs of wind speeds and 

corresponding storm surge heights that occur during the time interval T associated with the n

hurricanes (M=m1+ m2+...+mn, and mi (i=1,2,...,n=19,806) is the number of pairs of wind 

speed/storm surge height data in the ith hurricane). The probability of exceedance of the values 

v,s can in principle be obtained from the sample of size M, and the mean recurrence interval of 

the pair v,s is then equal to the inverse of that probability, the epoch being in this case 55,000/M 

years. The mean recurrence interval in years is then obtained via multiplication by the yearly rate 

of arrival of the event of the pairs of wind speed and storm surge height, that is, by M/50,000. 

As an illustration, consider the hypothetical case m1 = m2 =...= mn ≈ m, and assume that 

the duration of all hurricanes within the zone in which they affect the site is 50 hours. The time 

step in our calculations is assumed to be Δt = 5 min, so m ≈ 50 hours/(1/12 hour) = 600, and M ≈

600n = 600×19,806 ≈ 12,000,000. Assuming, for example, that in the histogram V > 120 mph 

and S > 7 ft for a total number of times equal to 10,000, we have a probability of exceedance in 

the interval T denoted by ProbT(V>54 m/s (120 mph), S>2.1m (7ft) ≈ 10,000/12,000,000 = 

1/1,200, and the estimated mean recurrence interval is MRIepochT,M = 1,200, in epochs of 

50,000/12,000,000 yr, and the estimated mean recurrence interval in years is MRIyears = 

1,200×50,000/12,000,000 = 50 years. 
45

The approach just outlined does not take into account the important fact that the pairs v,s

within any one of the simulated hurricanes are not independent of each other, but are correlated 

as they belong to the same hurricane and are separated, within each hurricane, by 5-min 

intervals. The correlations can significantly affect the results being sought. In principle, 

knowledge of the cumulative distribution function and of the correlation structure within each 

hurricane could be used to yield realistic estimates. However, the present state of the art does not 

allow such estimates to be readily obtained for non-Gaussian bivariate processes such as those 

representing the simulated time histories of wind speeds and storm surge heights. A considerable 

research effort would be required for the development of procedures allowing such estimates to 

be made. 

 

Choosing an interval longer than 5 min might be viewed as eliminating or reducing the 

severity of the problem just outlined. However, intervals significantly longer than 5 min would 

result in missing significant peaks. In addition, correlations would subsist even if for longer 

intervals between successive pairs v,s. To avoid the problems associated with correlated data it 

would be desirable to select, among the pairs v,s, only the most significant ones. However, in 

general it is not possible to do so directly, since no criterion is available for ranking pairs of data 

in a way that would be satisfactory from an engineering design viewpoint. For example, in some 

applications the pair v=36 m/s (80 mph), s= 1.8 m (6 ft) might be more unfavorable than the pair 

v= 40 m/s (90 mph), s= 1.5 m (5 ft), whereas in other applications the reverse could be true.