INTEGRATED MODELING OF STORM SURGES DURING HURRICANES ISABEL, CHARLEY, AND FRANCES

Transcription

1 INTEGRATED MODELING OF STORM SURGES DURING HURRICANES ISABEL, CHARLEY, AND FRANCES By VADIM VLADIMIROVICH ALYMOV A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

2 Copyright 2005 by Vadim Vladimirovich Alymov

3 I dedicate this work to Maxim Zakharov.

4 ACKNOWLEDGMENTS My most profound thanks go to my parents, Nadezhda and Vladimir, for their love and endless support. I wish to express my sincere appreciation to my advisor and supervisory committee chairman, Dr. Y. Peter Sheng. I would also like to thank the members of my supervisory committee, Dr. Robert G. Dean, Dr. Ulrich H. Kurzweg, Dr. Robert J. Thieke, and Dr. Andrew B. Kennedy. I would also like to thank Yanfeng Zhang, Vladimir Paramygin, Jeff King, Kijin Park, Taeyun Kim, Jun Lee, Justin Davis, Detong Sun, Dave Christian, Enrique Gutierrez, and Tatiana Lomasko. iv

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS iv LIST OF TABLES ix LIST OF FIGURES xii ABSTRACT xxii CHAPTER 1 INTRODUCTION Literature Review Wave Effect on Surface Stress Wave Effect in Wave-Current Interaction at the Bottom Wave Effect through Radiation Stress Miscellaneous Storm Surge Model Review SLOSH TAOS SPH/WIFM HAZUS ADCIRC SURGE POM coupled with WAVEWATCH-II wave model CH3D THIS STUDY CH3D-SSMS: What Makes it a Better Model? Goals and Questions to be Answered Components of CH3D-SSMS Wind Regional Circulation Model: ADCIRC Regional Wave Model: WAVEWATCH-III Local Circulation Model: CH3D Governing equations Implementation of Wetting-and-Drying Algorithm into CH3D Surface and Bottom Stresses v

6 Wave Enhanced Surface and Bottom Stresses Radiation Stress Local Wave Model: SWAN METHODOLOGY Introduction Coupling Mechanism TEST SIMULATIONS Validation of Wetting-and-Drying Scheme Implemented in CH3D Description Validation Test Case 1: Wall Test Case 2: Wind Test Case 3: Analytical Solution Validation of Atmospheric Pressure Gradient Terms Implemented in CH3D Description Validation Validation of Near-Bottom Wave-Current Interaction Description Validation Pure Oscillatory Flow Current Superimposed on an Oscillatory Flow Validation of Wave Setup Calculated based on SWAN-CH3D coupling Description Validation Validation of Cross and Longshore Currents Based on REF/DIF- CH3D Coupling Description of Cross-shore and Longshore Currents Validation Validation of Wave Height Simulated by SWAN Under Storm Conditions VALIDATION OF THE STORM SURGE MODELING SYSTEM Hurricane Isabel (2003) Description According to NHC Computational Domain Field Data Forcing and Boundary Conditions Results: Simulated Wave Results: Simulated Water Level Error Analysis of Calculated Water Level vi

7 5.1.8 Results: Simulated Flood Level Results: Simulated Currents Hurricane Charley (2004) Description According to NHC Computational Domain Data Results: Simulated Water Level Error Analysis of Calculated Water Level Results: Simulated Flood Level Hurricane Frances (2004) Description According to NHC Computational Domain Data Results: Simulated Water Level Error Analysis of Calculated Water Level Results: Simulated Flood Level FUTURE ENHANCEMENTS AND APPLICATIONS Modeling of Morphological Impacts of Extreme Storms Rip Current Forecasting CONCLUSIONS APPENDIX A SAFFIR-SIMPSON HURRICANE SCALE B FORMULAE TO CALCULATE ERRORS C BEST TRACKS FOR ISABEL, CHARLEY, AND FRANCES D E F WIND SPEED AND DIRECTION DURING HURRICANE ISABEL: WNA AND WINDGEN VS. MEASURED OUTER BANKS/CHESAPEAKE BAY COMPUTATIONAL GRID EX- AMPLE PLOT HURRICANE ISABEL: SIMULATED RESULTS VS. MEASURED DATA230 F.1 Simulated vs. Measured Water Level F.2 Simulated vs. Measured Surge G H HURRICANE CHARLEY: SIMULATED VS. MEASURED WATER LEVEL HURRICANE FRANCES: SIMULATED RESULTS VS. MEASURED DATA vii

8 H.1 Simulated vs. Measured Water Level H.2 Simulated vs. Measured Surge I LOW-PASS FILTER REFERENCES BIOGRAPHICAL SKETCH viii

9 Table LIST OF TABLES page 1 1 A summary of storm surge models Wind data summary Parameters used to create the lookup table Wave parameters used to impose Hurricane Floyd (1999) boundary conditions Comparison of calculated and measured wave height during Hurricane Floyd (1999) Comparison of calculated and measured wave height during Hurricane Floyd (1999) with wave setup being accounted for Wave parameters used to impose Hurricane Bonnie (1998) boundary conditions Comparison of calculated and measured wave height during Hurricane Bonnie (1998) Measured storm tide crests at several sites in North Carolina, Virginia, and Maryland Tide, wind and wave stations used for validation of the model during Hurricane Isabel ADCIRC tidal constituents and their periods used in the CH3D model to simulate Hurricane Isabel Tidal constituent parameters at Duck Pier, NC calculated based on AD- CIRC tidal constituents and IOS program Tidal constituent parameters at Beaufort, NC calculated based on AD- CIRC tidal constituents and IOS program Errors of WNA and WINDGEN wind speed and direction compared with measured at wind stations during Hurricane Isabel A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) ix

10 5 8 Errors of water elevation at tide stations during Hurricane Isabel. The model results are data were compared every 15 minutes Measured peak water elevations at seven stations during Hurricane Isabel using WNA wind and various combinations of storm surge model features Calculated peak storm surge (with tides subtracted) at seven stations during Hurricane Isabel using WNA wind and various combinations of storm surge model features A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) Errors of water elevation at tide stations during Hurricane Charley Measured peak water elevations at four stations during Hurricane Charley using WINDGEN wind and various combinations of storm surge model features Calculated peak storm surge (with tides subtracted) at four stations during Hurricane Charley using WINDGEN wind and various combinations of storm surge model features Comparison between reported high water mark values and flood levels calculated using two techniques A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) Errors of water elevation at tide stations during Hurricane Frances Measured peak water elevations at three stations during Hurricane Frances using WNA wind and various combinations of storm surge model features Calculated peak storm surge (with tides subtracted) at three stations during Hurricane Frances using WNA wind and various combinations of storm surge model features Summary of simulated hurricanes C 1 Best track for Hurricane Isabel, 6-19 September C 2 Best track for Hurricane Charley, 9-14 August C 3 Best track for Hurricane Frances, 31 August - 7 September F 1 A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) x

11 G 1 A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) H 1 A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation) xi

12 Figure LIST OF FIGURES page 2 1 The ADCIRC computational grid The WAVEWATCH-III North Atlantic regional computational grid A diagram of various physical processes. Those in red are accounted for in this methodology A diagram of the coupling process The wall test case: computational layout The wall test case: calculated water surface elevation The wind test case: computational layout The wind test case: calculated water surface elevation Tidal case: comparison with analytic solution at t= Tidal case: comparison with analytic solution at t=π/ Tidal case: comparison with analytic solution at t=π/ Tidal case: comparison with analytic solution at t=π/ Tidal case: comparison with analytic solution at t=2π/ Tidal case: comparison with analytic solution at t=5π/ Tidal case: comparison with analytic solution at t=π Analytical solution of water surface elevation due to atmospheric pressure gradient for a simplified hurricane Difference in water elevation between the analytical and numerical solutions Comparison between measured (Jonsson and Carlsen, 1979) [dashed line with squares] and calculated [solid line] velocity profiles for eight phase angles Vertical profile of the calculated phase lag between horizontal velocities and free stream velocity xii

13 4 16 Comparison between calculated [solid line] bottom stress and bottom stress determined based on measurements during the Jonsson and Carlsen (1979) experiment [dashed line with squares] Comparison between measured (Bakker and Dorn, 1978) [dashed line with squares] and calculated [solid line] velocity profiles for eight phase angles Bottom stress due to wave-current interaction calculated using the 1-D BBL model based on the numerical simulation of the Bakker and Dorn (1978) laboratory experiment Layout of Stive and Wind experimental setup (from Stive and Wind (1982)) Layout of Mory and Hamm experimental setup (from Mory and Hamm (1997)) Comparison between measured and calculated wave setup (Mory and Hamm (1997) experiment) Calculated free surface elevation and current pattern along with the locations where vertical velocity profiles were measured (letters A through N) Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles A, B, C, and N Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles A, B, C, and N Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles D, F, I, and H Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles D, F, I, and H Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles E and G Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles E and G The FRF instrument setup at Duck, NC Best track of Hurricane Isabel (courtesy of NOAA NHC) The Outer Banks and Chesapeake Bay grid domain for Isabel simulation Location of the nine River Input Monitoring sites (courtesy of USGS) xiii

14 5 4 River discharge into Chesapeake Bay data during the month of September, WINDGEN and WNA vs. measured wind speed and direction at Cape Lookout, NC during Hurricane Isabel WINDGEN and WNA vs. measured wind speed and direction at Duck Pier, NC during Hurricane Isabel Significant wave height and peak wave period obtained from WAVEWATCH- III compared with measured wave height at NDBC station Significant wave height and peak wave period obtained from WAVEWATCH- III compared with measured wave height at NDBC station Location of the VIMS instrument package at Gloucester Point, VA Simulated significant wave height vs. measured from the FRF Waverider buoy during Hurricane Isabel Simulated peak wave period vs. measured from the FRF Waverider buoy during Hurricane Isabel Simulated wave direction vs. measured from the FRF Waverider buoy during Hurricane Isabel A test case: wave setup and currents induced by waves approaching the shore from south-west to north-east (top panel), and from north-west to south-east (bottom panel) Simulated significant wave height and peak wave period vs. measured from the FRF pier during Hurricane Isabel Simulated significant wave height and peak wave period vs. measured at VIMS during Hurricane Isabel Comparison of simulated vs. measured water elevation at Beaufort, NC. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Duck, NC. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Chesapeake Bay Bridge, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind xiv

15 5 19 Comparison of simulated vs. measured water elevation at Gloucester Point, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Money Point, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Kiptopeke, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Lewisetta, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Isabel in the Outer Banks/Chesapeake Bay using WNA wind Maximum wave setup elevation relative to NAVD88 calculated during simulation of Hurricane Isabel in the southern part of Outer Banks using WNA wind Simulated storm surge (water level minus tide) at the seven stations throughout the Outer Banks/Chesapeake Bay using WNA wind Separately simulated tide, wave setup, and surge, and their linear superposition at Duck Linearly coupled water elevation vs. water elevation calculated through dynamic coupling at Duck, NC Linearly coupled water elevation vs. water elevation calculated through dynamic coupling at Duck, NC Linearly coupled water elevation vs. water elevation calculated through dynamic coupling near the South River, NC. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again Linearly coupled water elevation vs. water elevation calculated through dynamic coupling on one of the emergent islands of the Outer Banks, NC. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again Linearly coupled water elevation vs. water elevation calculated through dynamic coupling near Gloucester, VA. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again. 136 xv

16 5 32 Maximum simulated inundation in the southern part of the Outer Banks during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in the eastern part of the Outer Banks during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in the Chesapeake Bay during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in the southern part of the Outer Banks during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in the eastern part of the Outer Banks during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in the Chesapeake Bay during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred Pre-storm (top) and post-storm (middle) air photos taken in the southern Outer Banks Pre-storm (top) and post-storm (middle) air photos taken in the eastern Outer Banks Location of Kitty Hawk, NC where currents were measured Location of Gloucester Point, VA where currents were measured Measured (left) and simulated (right) South to North current at Kitty Hawk, NC during Hurricane Isabel Measured (left) and simulated (right) West to East current at Kitty Hawk, NC during Hurricane Isabel Measured (left) and simulated (right) South to North current at Gloucester Point, VA during Hurricane Isabel Measured (left) and simulated (right) West to East current at Gloucester Point, VA during Hurricane Isabel Best track of Hurricane Charley (courtesy of NOAA NHC) The Charlotte Harbor grid domain xvi

17 5 48 WMeasured wind speed vs. WINDGEN and WNA wind data at Ft Myers, FL during Hurricane Charley Measured wind direction vs. WINDGEN and WNA wind data at Ft Myers, FL during Hurricane Charley Measured wind speed vs. WINDGEN and WNA wind data at Naples, FL during Hurricane Charley Measured wind direction vs. WINDGEN and WNA wind data at Naples, FL during Hurricane Charley Comparison of simulated vs. measured water elevation at Big Carlos Pass. Two simulated results are shown: one using WNA wind and another using WINDGEN wind Comparison of simulated vs. measured water elevation at Estero Bay, location 1. Two simulated results are shown: one using WNA wind and another using WINDGEN wind Comparison of simulated vs. measured water elevation at Estero Bay, location 2. Two simulated results are shown: one using WNA wind and another using WINDGEN wind Comparison of simulated vs. measured water elevation at Ft Myers. Two simulated results are shown: one using WNA wind and another using WINDGEN wind Simulated vs. measured water elevation at Estero Bay, location 1. Dashed lines specify the three time instants when wind snapshots were taken WNA wind field snapshot 1 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area WINDGEN wind field snapshot 1 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area WNA wind field snapshot 2 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area WINDGEN wind field snapshot 2 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area WNA wind field snapshot 3 (Aug-14 01:20, Julian Day= ) along with total depth contours in the Estero Bay area WINDGEN wind field snapshot 3 (Aug-14 01:20, Julian Day= ) along with total depth contours in the Estero Bay area xvii

18 5 63 WNA and WINDGEN wind direction vs. measured wind direction at Naples, FL. At the peak of the storm (denoted by number 2), WIND- GEN wind direction matches very well with the measured wind direction and WNA wind direction is off by approximately 30 degrees Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Charley in Charlotte Harbor using WINDGEN wind Simulated storm surge (water level minus tide) at the four stations using WINDGEN wind Maximum simulated inundation in Charlotte Harbor using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred Maximum simulated inundation in Charlotte Harbor using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred Pre-storm (top) and post-storm (middle) air photos taken near Captiva Island. A close-up of our calculated flood map (bottom) verifies the presence of water over the land Pre-storm (top) and post-storm (middle) air photos taken near Sanibel Island Nautical chart of coastal areas in the Charlotte Harbor area impacted by Hurricane Charley Man points at a high water mark left by storm surge caused by Hurricane Charley on North Captiva Island Best track of Hurricane Frances (courtesy of NOAA NHC) The Tampa Bay grid domain Comparison of simulated vs. measured water elevation at Clearwater, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at St Pete, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind Comparison of simulated vs. measured water elevation at Port Manatee, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind xviii

19 5 77 Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Frances in Tampa Bay using WNA wind Simulated storm surge (water level minus tide) at the three stations using WNA wind Maximum simulated inundation in Tampa Bay using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred D 1 WINDGEN and WNA vs. measured wind speed and direction at Cape Lookout, NC during Hurricane Isabel D 2 WINDGEN and WNA vs. measured wind speed and direction at Duck, NC during Hurricane Isabel D 3 WINDGEN and WNA vs. measured wind speed and direction at Chesapeake Light, VA during Hurricane Isabel D 4 WINDGEN and WNA vs. measured wind speed and direction at Chesapeake Bay Bridge, VA during Hurricane Isabel D 5 WINDGEN and WNA vs. measured wind speed and direction at Kiptopeke, VA during Hurricane Isabel D 6 WINDGEN and WNA vs. measured wind speed and direction at Money Point, VA during Hurricane Isabel D 7 WINDGEN and WNA vs. measured wind speed and direction at Gloucester Point, VA during Hurricane Isabel D 8 WINDGEN and WNA vs. measured wind speed and direction at Lewisetta, VA during Hurricane Isabel D 9 WINDGEN and WNA vs. measured wind speed and direction at HPLWS, VA during Hurricane Isabel D 10WINDGEN and WNA vs. measured wind speed and direction at Choptank River, VA during Hurricane Isabel D 11WINDGEN and WNA vs. measured wind speed and direction at North Bay, VA during Hurricane Isabel E 1 Computational grid near Chesapeake Bay mouth E 2 Computational grid in the South Outer Banks area F 1 Comparison of simulated vs. measured water elevation at Beaufort, NC. 231 xix

20 F 2 Comparison of simulated vs. measured water elevation at Duck, NC F 3 Comparison of simulated vs. measured water elevation at Chesapeake Bay Bridge, VA F 4 Comparison of simulated vs. measured water elevation at Gloucester Point, VA F 5 Comparison of simulated vs. measured water elevation at Money Point, VA F 6 Comparison of simulated vs. measured water elevation at Kiptopeke, VA. 236 F 7 Comparison of simulated vs. measured water elevation at, Lewisetta, VA. 237 F 8 Comparison of simulated vs. measured storm surge elevation at Beaufort, NC. Calculated results are based on Simulation 3 using WNA wind. 238 F 9 Comparison of simulated vs. measured storm surge elevation at Duck, NC. Calculated results are based on Simulation 3 using WNA wind F 10 Comparison of simulated vs. measured storm surge elevation at Chesapeake Bay Bridge, VA. Calculated results are based on Simulation 3 using WNA wind F 11 Comparison of simulated vs. measured storm surge elevation at Gloucester Point, VA. Calculated results are based on Simulation 3 using WNA wind F 12 Comparison of simulated vs. measured storm surge elevation at Money Point, VA. Calculated results are based on Simulation 3 using WNA wind. 240 F 13 Comparison of simulated vs. measured storm surge elevation at Kiptopeke, VA. Calculated results are based on Simulation 3 using WNA wind F 14 Comparison of simulated vs. measured storm surge elevation at Lewisetta, VA. Calculated results are based on Simulation 3 using WNA wind G 1 Comparison of simulated vs. measured water elevation at Big Carlos Pass, FL G 2 Comparison of simulated vs. measured water elevation at Estero Bay #1, FL G 3 Comparison of simulated vs. measured water elevation at Estero Bay #2, FL G 4 Comparison of simulated vs. measured water elevation at Ft Myers, FL. 246 xx

21 H 1 Comparison of simulated (using WNA wind) vs. measured water elevation at Clearwater, FL. Calculated results are based on five simulations H 2 Comparison of simulated (using WNA wind) vs. measured water elevation at St Pete, FL. Calculated results are based on five simulations H 3 Comparison of simulated (using WNA wind) vs. measured water elevation at Port Manatee, FL. Calculated results are based on five simulations. 249 H 4 Comparison of simulated vs. measured storm surge elevation at Clearwater, FL. Calculated results are based on Simulation 3 using WNA wind. 250 H 5 Comparison of simulated vs. measured storm surge elevation at St Pete, FL. Calculated results are based on Simulation 3 using WNA wind H 6 Comparison of simulated vs. measured storm surge elevation at Port Manatee, FL. Calculated results are based on Simulation 3 using WNA wind. 251 xxi

22 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INTEGRATED MODELING OF STORM SURGES DURING HURRICANES ISABEL, CHARLEY, AND FRANCES By Vadim Vladimirovich Alymov December 2005 Chair: Y. Peter Sheng Major Department: Civil and Coastal Engineering A storm surge modeling system, CH3D-SSMS, that couples regional and local scale circulation and wave models was developed. The model calculates storm surge elevation during hurricane events using either simple analytic wind field or wind fields produced by sophisticated wind models such as NCEP WNA and WINDGEN. The CH3D model is dynamically coupled with a wave model, SWAN, accounting for wave setup, wave enhanced surface stress, and wave enhanced bottom friction. The model also features a robust flooding and drying scheme that allows simulating of storm induced inundation. The CH3D model is also coupled with a regional scale circulation model, ADCIRC, that provides storm surge elevation conditions along open boundaries. The model was validated by simulating Hurricanes Isabel, Charley, and Frances. The effects of various interactions among storm surge, tide, wind and wave on surge were investigated. For Isabel and Frances, WNA wind was more accurate than WINDGEN wind and produced more accurate storm surge. For Charley, WINDGEN was more accurate than WNA and produced more accurate surge. When Isabel, Charley, and Frances were simulated using tide and wind only, the xxii

23 calculated peak water elevations were always underestimated compared with measured data. The inclusion of wave setup significantly improved the computed surge during Isabel, although for Charley and Frances the effect was less significant. Accounting for wave enhanced surface stress significantly improved the simulated storm surge for all three hurricanes. Accounting for wave induced bottom friction had (1) moderate effect when the Sheng and Villaret formulation was used and (2) significant effect due to overestimated bottom friction when the Grant and Madsen formulation was used. The dynamically coupled water elevation was compared with linearly superimposed results of independently simulated tide, wave setup, and surge. The effect is twofold: over open water, dynamic coupling produces slightly more accurate storm surge, and over land, the inundation calculated through dynamic coupling occurs earlier and is more significant. The effect of excluding the wetting-and-drying feature during storm surge simulations was also examined and found significant. During Charley, when the feature was disabled, the calculated water elevation at its peak was significantly overestimated. xxiii

24 CHAPTER 1 INTRODUCTION Hurricanes are the most devastating and damaging hazards impacting the United States. Today, hurricane damage costs billions of dollars. According to the National Oceanic and Atmospheric Administration (NOAA) (2005), during the last century, 23 hurricanes had each caused damage in excess of $1 billion dollars. Damage from hurricane Andrew (1992) alone was estimated at more than $25 billion dollars in South Florida and Louisiana. Industry data show that 65% of insured losses from natural hazards in the U.S. over the past 50 years are due to hurricanes. From 1990 through 1999 hurricanes caused 140 deaths and $50 billion in property damage in the U.S. Coastal storms account for 71% of recent U.S. disaster losses annually with each event costing roughly $500 million. In 2004, for the first time in history, four major hurricanes, Charley, Frances, Ivan and Jeanne, made landfall in Florida. The 2004 hurricane season will go down as the most costly season on record in the U.S. (NOAA, 2005), with $42 billion estimated damage, deaths totaling 59, and deaths outside of the U.S. at over 3,000. In addition, Florida lost many lives and part of the 2,170 miles of shorelines. A bridge and sections of I-10 were destroyed and transportation interrupted for many days. With population and development continuing to increase along coastal areas, a greater number of people and property are vulnerable to hurricane threat. Hurricanes cannot be controlled but the vulnerability can be reduced through accurate forecasting. The major damage caused by hurricanes is associated with storm surges and coastal flooding. According to NOAA (1999), a storm surge is a large dome of water, 80 to 160 km wide, that sweeps across the coastline near where a hurricane 1

25 2 makes landfall. It can be more than 4.5 m deep at its peak. The surge of high water topped by waves can be devastating. Along the coast, storm surge is the greatest threat to life and property. Not only can hurricanes damage houses and buildings in highly populated coastal residential and commercial areas but also, within just a few hours, they can cause drastic changes in the coastline as an outcome of morphological response. This may result in an ecological imbalance of estuarine systems, especially those that are separated from the ocean by barrier islands, which are a common feature of Florida s coastline. In order to reduce coastal hazards associated with hurricanes, it is necessary to have an accurate prediction model of storm surge and coastal flooding, which is essential for developing cost effective storm mitigation and preparation. Accurate storm surge simulations are also essential for producing accurate flood insurance rate maps (FIRMs) for coastal counties. Florida coastal counties alone contribute more than 40% of the total insurance premiums collected by the National Flood Insurance Program (NFIP) administered by the Federal Emergency Management Agency (FEMA). Sheng and Alymov (2002) showed that the FEMA methodology on flood insurance rates in Pinellas county, Florida (FEMA, 1988), which is based on the 1-D WHAFIS model, overestimates possible damage that may be caused by the 100-year storm event. The use of a more robust storm surge model will likely result in significant savings in insurance premiums. 1.1 Literature Review Surges are induced by the hurricane wind and atmospheric pressure fields, and are significantly affected by the complex coastal bathymetry and topography. In addition, there exist significant nonlinear interactions among surge, wave, wind, and tide. Physical processes governing the development of storm surges during hurricanes are quite complex. Bode and Hardy (1997) pointed out the lack of

26 3 robust storm surge models for tropical storms. During the last ten years, more hurricane and storm surge data have been collected in Florida and elsewhere, providing a good opportunity to develop and validate new storm surge models. Many existing storm surge models contain rather simple physics even though physically measurable attributes, such as water level, actually include the combined effects of physical processes such as waves and tides. They take into account only a few hurricane parameters such as pressure deficit, size of the storm, its translation speed, and direction Wave Effect on Surface Stress According to Janssen (1991) the sea surface stress depends not only on wind speed but roughness due to waves as well. The total stress near the sea surface is the sum of the turbulent part and wave-induced part, τ = τ t + τ w (1 1) where τ t is the turbulent stress which according to the mixing-length hypothesis can be parameterized as follows: ( ) 2 U τ t =ρ a (κz) 2 (1 2) z where κ = 0.4 is von Karman constant; U(z) is the wind speed at height z; ρ a is the air density. Janssen (1991) also introduced the effective roughness length, z e, as opposed to the roughness length, z 0, when waves are absent. The effective roughness length is a function of the wave-induced stress. In derivation of his wave-induced stress, Janssen (1991) used the following wind profile: where u is the friction velocity. U(z) = u ( ) z + κ ln ze z 0 z e (1 3)

27 4 If equation 1 3 is differentiated, squared and compared with equation 1 2 at z = z 0, the following relationship between z 0 and z e is obtained: z e = z 0 1 τ w(z 0 ) τ (1 4) Assuming that Charnok-like expression z 0 = αu 2 /g is valid, the value of α is tuned in such a way that z e = αu 2 /g for old wind sea. The old wind sea term means that waves are no longer developing under current wind condition and the wave-induced stress for such sea diminishes, yielding z e z 0. For young waves (traveling much slower that the wind) almost the entire surface stress is due to waves; therefore, τw / τ approaches one. Zhang and Li (1996) applied the theory of Janssen in their coupling of a thirdgeneration wave model and a two-dimensional storm surge model. Comparing their results with measured data of two storm events that took place in the northern South China Sea, they found that the introduction of a wave dependent drag gives a significant improvement over the use of the Smith and Banke (1975) stress relation which underestimated the surges by 10%. τ = ρc D U 10 U 10 (1 5) where C D = (0.066 U ) Mastenbroek et al. (1993) also studied the effect of a wave-dependent drag coefficient on the generation of storm surges in the North Sea. To estimate the effects of waves on the boundary layer, the theory of Janssen was used. The results were compared to measured data for three storm periods. The calculations with the wave-dependent drag gave a significant improvement. In turn the calculations with the Smith and Banke stress relation underestimated the surges by 20%. Donelan et al. (1993) investigated the aerodynamic roughness of the sea surface, z 0, using data from Lake Ontario, from the North Sea near the Dutch

28 5 coast, and from an exposed site in the Atlantic Ocean off the coast of Nova Scotia. They found that normalized roughness depends strongly on wave age (C p /u ) where C p is the phase speed of the waves at the spectral peak. Their equation for the wave enhanced drag coefficient is C de = ( ln κ ( U 2 10 gz ) ( U 10 2 ) ) 0.9 C p (1 6) The authors normalized roughness by the RMS wave height and using the friction velocity, u, of the wind stress and concluded that in both cases young waves were rougher than mature waves. Xie et al. (2001) investigated the influence of surface waves on ocean currents in the coastal waters by using a coupled wave-current modeling system. They took into account the fact that the wave-induced wind stress is not only a function of wind speed but the wave-modified drag coefficient as well, which in turn is a function of the spectral peak frequency of waves. For young waves the spectral peak frequency is large, and accordingly, the wave-induced surface stress is large. However, for fully developed wind waves the spectral peak frequency is small, and accordingly, the effect of waves on surface stress is relatively small. The authors note that the wave spectral peak frequency increases as the water depth decreases. In their study the magnitude of the peak spectral frequency increases from about 0.6 rad s 1 in the relatively deep offshore water to approximately rad s 1 in the shallow coastal waters. As a consequence, under a constant wind the effect of waves on wind stress is larger in the shallower water than in the deeper water Wave Effect in Wave-Current Interaction at the Bottom Bottom friction is an important factor in wave-current interaction. According to Graber and Madsen (1988), the shape of the wave spectrum in finite-depth

29 6 waters is significantly influenced by the bottom friction. During a storm event when waves are large the area of such an influence extends far offshore. Grant and Madsen (1979) developed an analytical theory to describe the combined motion of waves and currents in the vicinity of a rough bottom and the associated boundary shear stress by considering a combined wave-current friction factor. The magnitude of the maximum boundary shear stress due to combined wave and current is τ b,max = 1 2 f cwρα u b 2 (1 7) where the combined friction factor f cw is a function of u a / u b ; u a is the magnitude of the steady current velocity vector at a height a above the bottom; u b is the maximum near-bottom orbital velocity from linear wave theory; α = 1 + ( u a / u b ) ( u a / u b ) cos φ c ; φ c is the angle made by u a with the direction of wave propagation. Schoellhamer (1993) pointed out weaknesses of the Grant and Madsen (1979) methodology which include the introduction of a fictitious reference velocity at an unknown level, the assumption of the logarithmic layer being constant which is not correct when waves are present. Tang and Grimshaw (1996) adapted the Grant and Madsen (1979) bottom boundary layer theory to study the effect of increased bottom friction due to wind-wave current interaction using a 2-D shallow water numerical model. They showed that the Grant and Madsen (1979) theory may break down in very shallow water where the wave amplitudes become large. To avoid the problem the authors introduced an empirical wave-breaking criterion into the bottom friction formulation: if a W h β, put a W h = β where a W is the wind-wave amplitude at the surface and h is the local depth; β is an empirically determined parameter in the range 0.5 < β < 0.9 based on results for wave breaking.

30 7 Based on their numerical (hence not verified) results, Tang and Grimshaw (1996) concluded that although the wind-wave enhancement of the bottom stress is significant only in the nearshore zone of shallow water, there is a dramatic reduction in the sea surface elevation and the currents in this region. Signell and List (1997) studied the effect of wave-enhanced bottom friction on storm-driven circulation in Massachusetts Bay based on a simplified form of the Grant and Madsen (1979) theory described by Signell et al. (1990). They found that the drag coefficient increases dramatically by a factor of 2-6. The most significant drag coefficient enhancement took place in the shallow regions near the shoreline. In response to the increased bottom drag, however, bottom currents were reduced by 30%-70%. Since the bottom stress is proportional to bottom drag and to the square of the bottom velocity, the mean bottom shear stress increased only by 10%-60% instead of a factor of 2-6. Wang et al. (2000) analyzed several important mechanisms for storm-induced entrainment of estuarine sediments using field measurements. Their study showed that the bottom shear stress, computed using a wave-current interaction model based, again, on the Grant and Madsen (1979) theory, increased significantly during episodic wind events. The currents and waves tended to enhance each other so that the shear stresses during the peaks of storms, computed from the wave-current interaction model, were approximately three times larger than using the traditional quadratic law. A large re-suspension event was caused by a frontal passage when strong wind-driven currents augmented the tidal currents. It was also pointed out in this study that the timing of storm waves with respect to tidal phase was a critical factor. Liu and Dalrymple (1978) proposed a simple empirical model which was also used by Sun and Sheng (2002) in their study of 3-D wave-induced circulation. The

31 8 bottom shear stress is defined as τ b = ρc d ( u b + U wb ) u b (1 8) where U wb is the maximum near-bed wave orbital velocity estimated from linear wave theory; u b is the near-bed wave-averaged velocity; C d is the friction coefficient which can be calculated according to the law of the wall Sheng (1986) C d = κ 2 [ ( )] 2 (1 9) z ln b z 0 where κ is von Karman constant, z 0 = k s /30 with k s being the Nikuradse equivalent sand roughness, and z b is the vertical distance of the lower grid point above the bottom. This simple model assumes that waves and currents are co-linear which is rather unrealistic. As a result of the assumption, the bottom stress will be overestimated when wave and current directions deviate from each other. Xie et al. (2001) also emphasize that surface waves produce two opposite effects on circulation: energy input through surface stress and energy dissipation through bottom stress. The net effect of wave-induced surface and bottom stresses can be quite different under different wind directions. This effect can either enhance or damp the surface current. The authors showed that the effect of waveinduced bottom stress is more significant for alongshore winds than for cross-shore winds. Their results indicated that the effect of waves on currents is mainly present in shallow coastal waters and attenuates rapidly offshore as water depth increases. Xie et al. (2001) also note that the effects of wave-induced surface and bottom stresses also depend on the wind speed. In tropical cyclone situations the wave-induced surface shear stress is generally more important than that due to

32 9 wave-induced bottom stress, and hence the effect of wind waves usually increases the magnitude of storm surge. Johnson and Kofoed-Hansen (2000) studied the influence of bottom friction on sea surface roughness. Their investigations show that the bottom dissipation keeps waves young, which results in increased wind friction Wave Effect through Radiation Stress Waves breaking on a sloping beach produce a wave setup in the nearshore, a rise in the water level above the still water level (the mean sea level in the absence of waves). Higher breakers will produce higher setup than lower breakers. Longshore variation in wave breaker heights will produce longshore currents which cause longshore sediment transport. Wave setup generally occurs in the surf zone. The breaking waves produce excess momentum flux in the shoreward direction which is usually termed radiation stress. As the broken waves continue to propagate toward the shore, the excess momentum flux or radiation stress diminishes. In the steady state, the shoreward decrease in radiation stress is balanced by a shoreward increase in the water level. This raises the water surface elevation within the surf zone to higher than the still water level (SWL) producing setup. It also pushes the water level outside of the surf zone to lower than the SWL producing setdown. It is necessary to account for wave setup within the surf zone during the calculation of storm surge elevation. The reason for that is that the setup may be very significant especially during a storm event. According to Dean and Dalrymple (1991) the wave setup near the shore is about 19% of the breaking wave height. The significant wave height during the 100-year storm estimated by Federal Emergency Management Agency (FEMA) (1988) in the Gulf of Mexico is 8.86 m with the period of 11.5 sec. The breaking wave height during the storm according to Dean and Dalrymple (1991, p. 116) may reach 8.5 m assuming a plane beach,

33 10 and 0 o deep water incident angle. Therefore, the wave setup may reach 1.62 m at the shore, which is a significant value as far as flooding caused by the wave setup is concerned. It would be incorrect to add the calculated wave setup on top of the calculated storm surge elevation linearly since there is a non-linear interaction between the two. Moreover, it is practically impossible to distinctly separate the wave setup from everything else based on the surface elevation data collected in the field. Therefore, wave setup should be introduced in the equations in terms of radiation stresses, so that the calculated surface elevation would include it internally in a non-linear fashion. Longuet-Higgins and Stewart (1964) derived depth-integrated radiation stress quantities that are used in many numerical models including storm surge models accounting for wave-induced setup. Mastenbroek et al. (1993) and Zhang and Li (1996) incorporated radiation stress terms based on the Longuet-Higgins and Stewart (1964) formulation into two-dimensional ocean circulation equations and investigated the importance of radiation stress in calculation of storm surge. Mastenbroek et al. (1993) reported that only in one of the three cases they studied the radiation stress increased the surge some 5%. In the other two cases the effect of the radiation stress was insignificant. Similarly, Zhang and Li (1996) concluded that the inclusion of the radiation stress improves the accuracy of the computed results slightly by 2%. It has to be pointed out that the study by Mastenbroek et al. (1993) took place in the North Sea with stations along the Dutch and British coasts. The authors do not specify how deep the locations of their stations are. It is hard to estimate the importance of the radiation stress if it is not being estimated in relatively shallow water where wave setup is formed under the influence of the breaking waves. Also, the surge model they used does not account for flooding

34 11 and drying. This makes the model inadequate in shallow water regions. The same conclusion is valid for the model used by Zhang and Li (1996). Their grid is located in the northern South China Sea and the depths of their station locations are not specified either. Sheng and Alymov (2002) implemented the Longuet-Higgins and Stewart (1964) radiation stresses in the CH3D (Sheng, 1987) model and simulated 2-D wave setup fields during the 100-year storm event for two study areas in Pinellas County, Florida. The setup value varied from approximately 0.5 m to 1.0 m. There was some effect on wave setup when waves were approaching at 40 o angle which, according to Dean et al. (1995), is the most likely angle of approach of the 100-year storm event in Pinellas County. Also, the study showed that the grid resolution has some effect on calculated wave setup especially in the areas where bathymetry has steeper gradients. Coarse grids are not capable of resolving these bathymetric gradients and as a result the calculated wave setup is typically lower than that calculated using a finer grid. Sun and Sheng (2002) coupled CH3D with the REF/DIF wave model (Kirby and Dalrymple (1994)) and showed significant effects of waves on water level and coastal currents. They compared simulated wave setup to measured laboratory data and found that the calculated wave setup is usually overestimated and proposed that the original wave forcing should be reduced by multiplying wave forcing by a coefficient of 0.8. This is rather an ad hoc approach and the high radiation stresses might have come from overestimated waves calculated by REF/DIF. Recently, some efforts have been made in order to derive vertically varying radiation stress. Mellor (2003) exploited three-dimensional equations of motion decomposing velocities into three components: mean current, wave, and turbulence.

35 12 His radiation stress terms are vertically dependant and, if depth integrated, appear in a more conventional form as in Longuet-Higgins and Stewart (1964) Miscellaneous Davis and Sheng (2002) found that the maximum surge heights depend on the tidal phase when the hurricane landfall occurs: maximum surge height occurs when hurricane landfall occurs at several hours after the peak tide. Sheng and Alymov (2002) simulated the storm surge in Pinellas County using the PEM model (Davis and Sheng, 2002) and found that the maximum surge heights and flooding patterns for the county are dramatically different when the high resolution ALSM data are used as opposed to the USGS 0.25-degree data. Sheng and Alymov (2002) used the 2-D version of CH3D and REF/DIF to simulate the wave setup, and used the SWAN (Holthuijsen et al., 2000) to simulate the wind-induced surge in Pinellas County. However, the calculations of the surge, setup, and wave-induced surge were performed separately and added linearly for simplicity. 1.2 Storm Surge Model Review In this section, the existing storm surge models used by government agencies (e.g., NOAA and FEMA) are reviewed along with some of the models used in the academic world. The features of each model are first summarized in a table at the beginning of this section. Then, each model is described in more detail. The main purpose of this review is to define the limitations of the existing models and point out the advantage of using the storm surge modeling system developed in this study.

36 13 Table 1 1: A summary of storm surge models. Wet- Analy- Assimi- Boundary Wave- Wave- Wave Rain/ River Tide Vali- Opera- Local/ 2-D 3-D ting tical lated Fitted enhanced induced Setup Evapo- Dis- dation tional Regional Model and Wind Wind Grid Surface Bottom ration charge Grid Drying Stress Friction Nesting SLOSH TAOS SURGE SPH/WIFM HAZUS ADCIRC 1 POM 2 CH3D 3 1 Weaver (2004) - Hurricane Georges 2 Moon (2000) - Typhoon Winnie 3 This study - Hurricanes Isabel, Charley, and Frances

37 SLOSH Sea, Lake and Overland Surges from Hurricanes (SLOSH) is a 2-D linear barotropic model developed by Chester Jelesnianski (Jelesnianski et al., 1992). The model is run by the National Hurricane Center to estimate storm surge heights and winds resulting from historical, hypothetical, or predicted hurricanes by taking into account pressure deficit, size, forward speed, track, and winds. The model does not take into account tide, precipitation/evaporation, river flow, wind-driven waves. SLOSH is used by NOAA NWS and the U.S. Army Corps of Engineers to create flood maps representing the Maximum of the Maximum (MOM) storm surge composite of hypothetical storms. Comments: SLOSH is an outdated model which needs to be revised and improved. It tends to produce large uncertainty in the predicted flooded area because of its relatively coarse resolution (0.5-7 km) and inability to fit convoluted shorelines TAOS The Arbiter of Storms (TAOS) model is a 2-D integrated hazards model developed by Charles C. Watson (Watson, 1995; Watson and Johnson, 1999). TAOS is similar to SLOSH and is capable of calculating an estimate of storm surge, wave height, maximum winds, inland flooding, debris and structural damage. The model has been run on over 25 significant historical storms from around the world. Comparing over 500 peak surge observations with TAOS model estimates for the same location and time, the model generates results within 0.3 m 80% of the time, and less than 0.6 m 90% of the time. Comments: As far as the storm surge part is concerned, the TAOS model does not differ much from the SLOSH model, since the storm surge physics are represented in a similar way in both models and, therefore, it does not take into

38 15 account important physical processes associated with storm surge, e.g., waveinduced effects SPH/WIFM Standard Project Hurricane (SPH) and WES Implicit Flooding Model (WIFN) developed by NOAA (Schwerdt et al., 1979; Cialone, 1991) are components of Coastal Engineering Research Center s Coastal Modeling System used by the U.S. Army Corps of Engineers. The SPH is a two-dimensional, parametric model developed in a stretched Cartesian coordinate system for representing wind and atmospheric pressure fields generated by hurricanes. It is based on the Standard Project Hurricane criteria developed by NOAA, and the model s primary outputs are resulting wind velocity and atmospheric pressure fields which can be used in storm surge modeling. The SPH model can be run independently, or it can be invoked from within model WIFM. The WIFM is a two-dimensional, time-dependent, long-wave model for solving the vertically integrated Navier-Stokes equations in a stretched Cartesian coordinate system. The model simulates shallow-water, long-wave hydrodynamics such as tidal circulation and, making use of wind fields produced by SPH, storm surges. WIFM contains many features such as moving boundaries to simulate wetting and drying of low-lying areas and subgrid flow boundaries to simulate small barrier islands, jetties, dunes, or other structural features. Model output includes vertically integrated water velocities and water surface elevations. Comments: WIFM is a simple and outdated model which does not account for wave effect HAZUS HAZUS is a software program developed by FEMA for estimating potential losses from earthquakes, floods, and wind. HAZUS is being developed by FEMA.

39 16 It has the capability to estimate earthquake losses, and flood and wind models are being developed. The Hurricane Loss Estimation Model which is a part of the HAZUS model incorporates sea surface temperature in the boundary layer analysis, and calculates wind speed as a function of central pressure, translation speed, and surface roughness. The model addresses wind pressure, wind borne debris, surge, waves, atmospheric pressure change, duration/fatigue, and rain. The Flood Loss Estimation Model is capable of assessing riverine and coastal flooding. It estimates potential damages to all classes of buildings, essential facilities, transportation and utility lifelines, and agricultural areas. The model estimates debris, shelter and casualties. Direct losses are estimated based on physical damage to structure, contents, and building interiors. The effects of flood warning and velocity are taken into account. The flood model uses geographic information system software to map and display flood hazard data, and the results of damage and loss estimates for building and infrastructure. It also enables users to estimate the effects of flooding on populations ADCIRC ADvanced CIRCulation (ADCIRC) model developed by Rick Luettich (Luettich et al., 1992) solves the equations of motion for a fluid on a rotating earth. These equations are based on hydrostatic pressure and Boussinesq approximations and have been discretized in space using the finite element method and in time using the finite difference method. ADCIRC can be run either as a two-dimensional depth integrated (2DDI) model or as a three-dimensional (3D) model. In either case, elevation is obtained from the solution of the depth-integrated continuity equation in Generalized Wave- Continuity Equation form. Velocity is obtained from the solution of either the

40 17 2DDI or 3D momentum equations. All nonlinear terms have been retained in these equations. ADCIRC can be run using either a Cartesian or a spherical coordinate system. ADCIRC boundary conditions include: specified elevation (harmonic tidal constituents or time series), specified normal flow (harmonic tidal constituents or time series), zero normal flow slip or no slip conditions for velocity, external barrier overflow out of the domain, internal barrier overflow between sections of the domain, surface stress (wind and/or wave radiation stress), atmospheric pressure, outward radiation of waves (Sommerfield condition). ADCIRC can be forced with: elevation boundary conditions, normal flow boundary conditions, surface stress boundary conditions, tidal potential, and earth load/self attraction tide. Comments: ADCIRC is a widely used model. Since the model is based on finite element numerics, it has the ability to exploit very large computational domains with sparse resolution in deep water areas and small grid spacing in shallow water areas or near complex boundaries. Weaver (2004) implemented a one-way coupling of a 2-D version of ADCIRC with a wave model, WAM-3G, to account for radiation stress; no other wave effect was considered. He performed a hindcast of the storm surge during Hurricane Georges (1998) in the North Gulf of Mexico and concluded that the addition of wave forcing improved the overall predictive capabilities and reduced the RMS error of the calculated storm surge by 20% to 50% SURGE SURGE is a 3-D hydrodynamic model of ocean circulation for coastal areas based on the Princeton Ocean Model (POM) developed by Blumberg and Mellor (1987). SURGE simulates and predicts storm surge, flooding, overwash, water recession, and associated horizontal currents. The model makes use of NOAA/NOS

41 18 bathymetry data and hight resolution USGS/NOAA LIDAR survey data. Hurricane Andrew (1992) and Hurricane Carla (1967) were used for model verification in Louisiana and Lavaca Bay, TX, respectively. Comments: The pros of the SURGE model include its three-dimensionality, the ability to used fine resolution computational grids, the capability to simulate wetting-and-drying of the coastal area. The major deficiency is the absence of wave effects, e.g., radiation stress, wave-enhanced surface stress, and wave-induced bottom friction POM coupled with WAVEWATCH-II wave model This is a coupled storm surge model which is based on the synchronous two-way coupling of a third-generation wave model WAVEWATCH-II and a 3-D Princeton Ocean Model (POM) (Moon, 2000, 2005). Analytic wind model (Holland, 1980) is used to calculated hurricane wind field. The model was applied to numerical experiments in the Yellow and East China Seas during Typhoon Winnie (1997). The ocean circulation model calculates currents and surface elevation (new water depth) which is fed back into the wave model to compute the wave dependent drag coefficient to be used in the wave model the next time step. This process is repeated. Each model has its own time step due to the reason that time scales of change of wave parameters and tidal currents are quite different. The wave model has a 360 sec time step and the ocean model has a 1800 sec time step. Therefore, after every 5 time steps of running the wave model the ocean model is run and the coupling takes place. Comments: The POM/WAVEWATCH-II coupling was perhaps the first attempt to exploit a two-way coupling between an ocean circulation model and a wave model. The coupling takes into account the effects of unsteady and inhomogeneous currents, unsteady depth, tides, wind, surface heat flux, river discharge.

42 19 Some of the deficiencies include the inapplicability of the model in shallow water regions; bottom friction depends only on currents, i.e. no effect of waves is considered; wetting-and-drying is not considered; wave setup is not taken into account CH3D CH3D (Curvilinear Hydrodynamics in 3D) is a robust hydrodynamic model originally developed by Sheng (1986, 1990). The model can be used to simulate the estuarine, coastal, and riverine circulation driven by wind, tide, and density gradients. The model uses a boundary fitted curvilinear grid in the horizontal directions to resolve the complex shoreline and geometry, and a terrain-following σ-grid in the vertical direction. The model uses a Smagorinski type horizontal turbulent diffusion coefficient, and a robust turbulence closure model (Sheng and Villaret, 1989) for the vertical turbulent mixing. CH3D has been applied to simulate the 2-D and 3-D circulation in numerous water bodies in Florida (e.g., Tampa Bay, Sarasota Bay, Indian River Lagoon, Florida Bay, Biscayne Bay, St. Johns River, and Lake Okeechobee) and U.S. (e.g., Chesapeake Bay). Many of the CH3D applications, as well as the CH3D formulation and development, are described on In 2002, CH3D was modified to include wetting-and-drying capability (Sheng et al., 2002) and coupled with a wave model SWAN to simulate the flood elevation in Pinellas County during the 100-year storm (Sheng and Alymov, 2002). The wetting-and-drying version of CH3D will be the foundation of the CH3D-SSMS for this study.

43 CHAPTER 2 THIS STUDY This chapter provides a detailed description of the CH3D-SSMS integrated storm surge modeling system including each of the four models it is based on: two regional models, ADCIRC (circulation) and WAVEWATCH-III (wave); and two local models, CH3D (circulation) and SWAN (wave). 2.1 CH3D-SSMS: What Makes it a Better Model? CH3D-SSMS ( is an integrated storm surge modeling system developed by Sheng et al. (2004). The modeling system includes surge-wave-tide-wind coupling in the coastal-estuarine-overland region, as well as coupling between local and regional scales. The table shown at the beginning of Section 1.2 demonstrates that the CH3D-SSMS modeling system has more features than any other existing storm surge model. Such an important element as waves which is included in CH3D through coupling with a wave model, SWAN, is unjustly neglected by most of the other models. Dynamic coupling with tide is also generally ignored assuming that predicted tide can be linearly added on top of the calculated storm surge. Local/Regional coupling is something that is being exploited by many lately. The usefulness of this feature is to be able to predict and forecast storm surge locally using fine grids, which include high resolution shorelines, bathymetry and topography. The boundary conditions for the local model are provided by means of nested coupling with the regional model. Details of the methodology used in this study can be found in Chapter 3. 20

44 Goals and Questions to be Answered Below is a list of goals (G) that are pursued in this study and questions (Q) that the results obtained through this study are supposed to answer. G1) Produce an advanced storm surge model with robust physics by incorporating the nonlinear interaction between surge, tide, wave, and wind and allowing the use of a very fine spatial resolution. The model will be capable of performing in shallow water regions and simulating wetting-and-drying. G2) Produce finely resolved boundary-fitted curvilinear grids for the Outer Banks/Chesapeake Bay, Tampa Bay, and Charlotte Harbor areas by utilizing high-resolution bathymetry and topography data. G3) Validate the modeling system by simulating Hurricanes Isabel (2003), Frances (2004), and Charley (2004) and comparing the calculated results with measured data. G4) Produce flood maps based on simulations of Isabel, Frances, and Charley. G5) Perform a sensitivity analysis of the effect of nonlinear interactions among storm surge, tide, wind, and wave, as well as the effect of wetting-and-drying and the effect of the dynamic coupling versus a linear superposition of separately simulated tide, wave setup, and surge. Q1) How significant is the effect of the nonlinear interaction between the turbulent and wave-induced stresses? Q2) How significant is the effect of the nonlinear interaction between bottom stresses due to currents and waves? Q3) How does wetting-and-drying affect storm surge simulations? Q4) Is dynamic coupling better than linear superposition?

45 Components of CH3D-SSMS Wind Accurate wind field is essential for any storm surge simulation since wind is the primary physical forcing for generating storm surge. First of all, wind blowing onshore causes the water mass to pile up against a sloping beach and propagate inland. Also, wind generates waves whose effect is twofold. They influence the significance of wave setup which is essentially a part of the storm surge plus waves effect surface roughness which in turn impacts the wind stress. Hence, uncertainties in the wind field are generally responsible for errors in storm surge simulations. Several types of wind data are used in this study. The first type is associated with the actual wind measured from buoys in the open ocean or wind towers on land. The National Data Buoy Center (NDBC) is an agency within the National Weather Service (NWS) of the National Oceanic and Atmospheric Administration (NOAA), which operates and maintains a network of data collecting buoys and coastal stations along the U.S. coastline ( shtml). NDBC provides hourly observations of barometric pressure, wind direction, speed and gust, and air temperature from a network of about 90 buoys. NDBC has its own subdivision, Coastal-Marine Automated Network (C-MAN), that was established in response to a need to maintain meteorological observations in U.S. coastal areas. C-MAN consists of 60 stations that are installed on lighthouses, at capes and beaches, on nearshore islands, and on offshore platforms. Another network of stations deployed in the Gulf of Mexico is the Coastal Ocean Monitoring and Prediction System (COMPS). COMPS ( marine.usf.edu/) consists of an array of instrumentation both along the coast and offshore, combined with numerical circulation models. An array of offshore buoys

46 23 take meteorological measurements such as wind, air temperature, humidity, barometric pressure, precipitation, radiation, visibility; and marine measurements such as water level, water temperature, salinity, current velocity, and wave parameters. The above two types of wind data from field measurements are useful for validating wind models, but cannot be used alone to generate the wind field needed for storm surge modeling. Another type of wind data is wind snapshot data which are produced by various wind models, ranging from simple to highly sophisticated. These data cover large areas and are more suitable for storm surge modeling. There are a few different wind snapshot data sets. The summary of this type of wind data is presented in Table 2 1.

47 24 Table 2 1: Wind data summary. Wind Source Type Spatial Vert. Cycles Cycle Mean Analysis/ Assimi- Wind Data (BGD/ Resolu- Level Length/ Sea Forecast/ lated Over Set HUR/ tion Snapshot Level Measured Land CMB) Frequency Pressure NAM NCEP BGD 12 km 10 m 00,06, 84 hrs yes FCAST no yes 12,18 6 hrs NDAS NCEP BGD 12 km 10 m 00,06, 6 hrs yes ANL yes yes 12,18 6 hrs GFDL NCEP HUR varies 35 m 00,06, 126 hrs yes FCAST no yes 12,18 6 hrs GDAS NCEP HUR varies 35 m 00,06, 6 hrs yes ANL yes yes 12,18 6 hrs HRD NOAA HUR 6 km 10 m - varies no MEAS no no WINDGEN Ocean CMB 22 km 10 m 00,06,? hrs yes ANL+FCAST yes yes weather 12,18 1 hr WNA NCEP CMB 28 km 10 m 00,06, 120 hrs no ANL+FCAST yes no 12,18 3 hrs PBL Ocean HUR any 20 m - - yes - no yes weather - - Analytical Holland (1980) HUR any sfc - - yes - no yes - - WRF NCEP BGD 4 km 10 m 00,06, 36/84 hrs yes ANL+FCAST yes yes 12,18 3 hrs MM5 NCEP BGD 12 km 10 m 00,06, 48 hrs yes ANL+FCAST yes yes 12,18 3 hrs BGD/HUR/CMB Background, Hurricane, Combined; NDAS NAM Data Assimilation System; GDAS GFDL Data Assimilation System.

48 25 WNA and WINDGEN winds were extensively utilized in this study. Two other wind models that were tested: a complex Planetary Boundary Layer (PBL) model and a much simpler analytic wind model (Holland, 1980) based on the hypothesis of an exponential decay of atmospheric pressure from the center of a storm. The PBL model is based on Chow (1971) vortex model. The model is capable of calculating vertically averaged through the depth of the PBL velocities during a storm event. The model s governing equation of horizontal motion written in coordinates fixed to the earth is (Cardone et al., 1992) dv dt + f K ( ) V Vg = 1 ( ρ P C + K H V ) C D V h + V ( ) c V + Vc where V = V ave V c is the horizontal wind relative to the center of the cyclone; V g = V g V c is the effective geostrophic flow relative to the center of the cyclone; V ave is the vertically averaged velocity; V c is translation speed of the storm; V g is geostrophic velocity; K is the unit vector in the vertical direction; ρ is the mean air density; f is the Coriolis parameter; K H is the horizontal eddy viscosity; C D is the drag coefficient; h is the depth of the planetary boundary layer; P C is the pressure field representing the tropical cyclone. The interaction between the boundary layer and the free atmosphere is expressed in terms of the geostrophic wind field (vertical velocity at the top of the boundary layer) and the surface stress (frictional dissipation of the kinetic energy (2 1)

49 26 in the boundary layer). Further parameterization of the model includes vertical fluxes of momentum, heat and moisture. This parameterization is based on matching of mean profiles of wind, temperature, and moisture by surface and outer layer similarity theories. The general form of the parametric relations may be written as κu u = (ln [z 0 /h] + A m ) κv u = B m sign (f) κ (θ V θ 0 )/θ = (ln [z 0 /h] 0 + C m ) (2 2) κ (q q 0 )/q = (ln [z 0 /h] + D m ) where u and v are the vertically averaged horizontal velocity components (in the direction of the surface shear and perpendicular to it, respectively); z 0 is the roughness parameter; κ is von Karman s constant; θ V and q are the mean layer virtual potential temperature and specific humidity, respectively (the subscript 0 denotes the value at z 0 ); θ is a potential temperature scale expressed in terms of the heat flux, H; q is a specific humidity scale involving the moisture flux; and A m, B m, C m, and D m are universal functions of dimensionless similarity parameters. Arya (1977) presented the following expressions for the similarity functions in which the depth of the PBL, h, is specified as an independent variable. If h 2 L (unstable) then A m = ln ( h/l) + ln (fh/u ) B m = 1.8 fh u e 0.2h/L C m = ln ( h/l) (2 3)

50 27 and if h L +2 (stable) then A m = 0.96 (h/l) B m = 0.80 (h/l) (2 4) C m = 2.0 (h/l) where L = ρu3 θ V C P κgh capacity. = u2 θ V gθ is the Monin-Obukhov length; C P is the heat For near-neutral conditions, 2 < h/l < 2, A m, B m, and C m are assumed to be given by linear interpolation between the above computed values at h/l = ±2. The PBL model is a sophisticated wind model but the uncertainty in choosing the right parameters makes it hard to use when only a few major storm parameters such as central pressure deficit, translation speed, direction, and radius to maximum winds are known. A simpler analytic wind model by Holland (1980) does not have as many uncertain parameters as the PBL model and it can be very useful in simulating hypothetical storm events. The model is built into the CH3D model and is based on the assumption of exponentially varying atmospheric pressure from the storm center also known as the storm eye: P = P 0 + (P P 0 )e A/rB (2 5) where P 0 is the central atmospheric pressure, P is the atmospheric pressure far away from the center, r is the distance from the center of the storm, and A and B are scaling parameters. Davis (2001) followed a simplifying assumption made by Wilson (1957) to set A to the radius of maximum wind speed, R, and set B equal to 1 in his simulations of Hurricanes Floyd and Irene (1999). Repeating Davis (2001) derivation steps yields

51 28 P a = P 0 (1 e R/r ) (2 6) where P a is the relative atmospheric pressure and P 0 = P 0 P is the central pressure drop of the storm. The cyclostrophic wind velocity, U c, is U c = The geostrophic wind velocity, U g, is The gradient wind velocity, U G, is P 0 ρ a R r e R/r (2 7) U g = P 0 fρ a R r 2 e R/r (2 8) ( ) U G = U c γ2 + 1 γ (2 9) where γ = 1 2 ( V s + U ) c U c U g (2 10) and the resolved part, V s, of the translational velocity of the storm, V s is V s = V s sin(θ) (2 11) where θ is the angle from the direction of bearing of the storm, β, to any point inside the storm. The surface wind velocity, U s, in the x and y directions is then written as U sx = KU G cos(90 + θ + β + φ) (2 12) U sy = KU G sin(90 + θ + β + φ) (2 13)

52 29 where φ is an inward rotation angle of 18 o and K is the ratio of surface wind velocity to gradient wind velocity Regional Circulation Model: ADCIRC ADCIRC is ADvanced CIRCulation model that solves the equations of motion for a fluid on a rotating earth. These equations are based on hydrostatic pressure and Boussinesq approximations and have been discretized in space using the finite element method and in time using the finite difference method. ADCIRC can be run either as a two-dimensional depth integrated (2DDI) model or as a three-dimensional (3D) model. In either case, elevation is obtained from the solution of the depth-integrated continuity equation in Generalized Wave- Continuity Equation form. Velocity is obtained from the solution of either the 2DDI or 3D momentum equations. All nonlinear terms have been retained in these equations. ADCIRC can be run using either a Cartesian or a spherical coordinate system. ADCIRC boundary conditions include: specified elevation (harmonic tidal constituents or time series), specified normal flow (harmonic tidal constituents or time series), zero normal flow slip or no slip conditions for velocity, external barrier overflow out of the domain, internal barrier overflow between sections of the domain, surface stress (wind and/or wave radiation stress), atmospheric pressure, outward radiation of waves (Sommerfield condition). ADCIRC can be forced with: elevation boundary conditions, normal flow boundary conditions, surface stress boundary conditions, tidal potential, and earth load/self attraction tide. The advantage of using ADCIRC is that its computational grid (shown in Figure 2 1) covers the western part of the North Atlantic including the Gulf of Mexico and the Caribbean and consists of only elements and nodes with varying grid spacing which is coarse offshore (up to 100 km) but finer near the coast (5-6 km in the Chesapeake Bay and Tampa Bay areas). This makes the

53 30 model computationally efficient without much of a slow down when coupled with the local circulation model, CH3D. Both models can use the same time step. Some of the deficiencies that ADCIRC has include its inability to exploit boundary fitted grids. Near land, shoreline approximation can be reached by increasing the resolution of the computational grid. The ADCIRC computational grid that was provided to us had rather coarse resolution (5-6 km) along the coastline which would result in losing some accuracy of the calculated storm surge in the nearshore regions. Also, the version of ADCIRC which was used in this study does not calculate wetting-and-drying. Overall, ADCIRC is a robust circulation model which can be useful in estimating the response of the ocean to a moving hurricane on a large regional scale and providing boundary conditions to local circulation models. 40 USA LAT 30 Gulf of Mexico North Atlantic LON Figure 2 1: The ADCIRC computational grid.

54 Regional Wave Model: WAVEWATCH-III WAVEWATCH-III (Tolman (1997) and Tolman (1999)) is a third generation NOAA/NCEP operational wave model. It solves the spectral action density balance equation for wave number-direction spectra. The implicit assumption of these equations is that the medium (depth and current) as well as the wave field vary on time and space scales that are much larger than the corresponding scales of a single wave. Furthermore, the physics included in the model do not cover conditions where the waves are severely depth-limited. This implies that the model can generally by applied on spatial scales (grid increments) larger than 1 to 10 km, and outside the surf zone. The governing equations include refraction and straining of the wave field due to temporal and spatial variations of the mean water depth and the mean current (tides, surges etc.), and wave growth and decay due to the actions of wind, nonlinear resonant interactions, dissipation ( whitecapping ) and bottom friction. Wave propagation is considered to be linear. Relevant nonlinear effects such as resonant interactions are therefore included in the source terms (physics). The WAVEWATCH-III North Atlantic computational grid (shown in Figure 2 2) covers the western North Atlantic including the Gulf of Mexico and Caribbean. The size of the grid is with spatial resolution of 0.25 degrees ( 28 km). WAVEWATCH-III products are 6-hour hindcast and 120-hour forecast with 6-hour intervals. Regional analysis wave data for Hurricanes Isabel (2003), Charley (2004), and Frances (2004) were provided by courtesy of NOAA/NCEP. As will be explained in Chapter 3, we do not actually run WAVEWATCH- III which provides boundary conditions for the local wave model, SWAN. WAVEWATCH-III wave forcing was obtained by the courtesy of NOAA/NCEP. This is one of the advantages of using the model: no computational burden is involved at all except for the preprocessing phase. Another reason for using

55 32 WAVEWATCH-III is that, as will be shown in Section 5.1.4, the model produces good results compared with measured data during hurricane events USA LAT Gulf of Mexico North Atlantic LON Figure 2 2: The WAVEWATCH-III North Atlantic regional computational grid Local Circulation Model: CH3D CH3D (Sheng, 1987, 1990) is a 3-D curvilinear-grid hydrodynamic model. The model solves the continuity equation and two momentum equations in a nonorthogonal boundary fitted coordinate system. The equations are derived from the Navier-Stokes equations using four simplifying approximations. First, it is assumed that water is incompressible, which results in a simplified continuity equation. Second, based on the fact that characteristic vertical length scale is

56 33 much smaller than the horizontal length scale, the vertical velocity is small and vertical acceleration may be neglected. Thus, the vertical momentum equation can be reduced to the hydrostatic pressure relation. Third, with the Boussinesq approximation, an average density can be used in the equations except in the buoyancy term. Finally, the eddy-viscosity concept, which assumes that the turbulent Reynolds stresses are the product of the mean velocity gradients and eddy viscosities Governing equations The equations include such terms as time variation, nonlinear inertia, surface slope, Coriolis force, horizontal diffusion, vertical diffusion, and radiation stress. u x + v y + w z = 0, (2 14) u t + uu x + uv y + uw z + 1 S xx ρ w x + 1 S xy ρ w y = g ζ x 1 ρ w P a x + fv + A H ( 2 u x u y 2 ) + z (A V u ), (2 15) z v t + vu x + vv y + vw z + 1 S yx ρ w x + 1 S yy ρ w y = g ζ y 1 P a ρ w y fu + A v H ( 2 x + 2 v 2 y ) + 2 z (A v ), (2 16) V z where u(x, y, z, t), v(x, y, z, t), and w(x, y, z, t) are the velocity vector components [LT 1 ] in x-, y-, and z-coordinate directions, respectively; t is time [T]; ζ(x, y, t) is the free surface elevation [L]; g is the acceleration of gravity [LT 2 ]; A H and A V are the horizontal and vertical turbulent eddy coefficients, respectively [L 2 T 1 ]; S xx, S xy, S yy are radiation stresses, P a is atmospheric pressure and f is the Coriolis component [T 1 ]. The necessary conditions for the solution are the definition of the computational domain, the initial conditions on the domain, and the boundary conditions.

57 34 Water elevation is first solved by using a pre-conditioned conjugate gradient method for the Poisson equation of water elevation. Contravariant velocity components are then obtained by solving the momentum equations. A three dimensional advection-diffusion equation for salinity is solved coincidentally with the equations of motion and continuity, which allows for variable density and baroclinic forcing. In Cartesian coordinates, the conservation of salt and temperature can be written as: S t + us x + vs y + ws z T t + ut x + vt y + wt z = x (D S H x ) + y (D S H y ) + z (D S v ), (2 17) z = x (K T H x ) + y (K T H y ) + z (K T v ), (2 18) z where S is salinity and T is temperature, D H, K H, D v and K v are turbulent eddy diffusivity coefficients for salinity and temperature in horizontal and vertical direction, respectively. After defining dimensionless variables as (x, y, z ) = (x, y, zx r /Z r )/X r (u, v, w ) = (u, v, wx r /Z r )/U r t = tf ζ = gζ/(fu r X r ) S ij = S ij /(ρ w U 2 r ) (2 19) Pa = P a /(ρ w fu r X r ) = (ρ w gϑ)/(ρ w fu r X r ) where ϑ is pressure head A H = A H/A Hr A V = A V /A V r equations 2 14 through 2 16 become dimensionless: u x + v y + w z = 0 (2 20)

58 35 ( u uu t + R 0 x + uv y + uw ) z = ζ x ϑ x + v + E HA H ( v vu t + R 0 x + vv y + vw ) z = ζ y ϑ y u + E HA H ( Sxx + R 0 x + S ) xy y ( ) 2 u x + 2 u 2 y 2 ( Syx + R 0 x + S ) yy y ( ) 2 v x + 2 v 2 y 2 ( ) u + E V A V z z ( ) v + E V A V z z (2 21) (2 22) where R 0 = U r fx r Rossby Number E H = A Hr fx 2 r Horizontal Ekman Number E V = A V r fz 2 r Vertical Ekman Number (2 23) In a curvilinear non-orthogonal boundary fitted grid system, the nondimensional form of the continuity and x and y momentum equations can be written as: ζ t + γ [ g0 ξ ( g 0 Hu) + η ( g 0 Hv)] + γ Hω σ = 0, (2 24) 1 Hu H t ζ 11 = (g ξ ζ ϑ ϑ + g12 ) (g11 + g12 η ξ η ) + ( g 12 u + g 22 v) (2 25) g0 g0 R 0 {x g η [ 0 ξ (y g0 S ξ xx + y η g0 S xy ) + η (y g0 S ξ xy + y η g0 S yy )]} y η [ ξ (x g0 S ξ xx + x η g0 S xy ) + η (x g0 S ξ xy + x η g0 S yy )] R 0 g 0 H {x η[ ξ (y g0 Huu + y ξ η g0 Huv) + η (y g0 Huv + y ξ η g0 Hvv)] y η [ ξ (x g0 Huu + x ξ η g0 Huv) + η (x g0 Huv + x ξ η g0 Hvv)] Huω g 0 σ } + E v H 2 σ (A u v σ + E A (Horizontal Diffusion of u) H H R 0 0 ρ ρ H H 0 11 [H (g + F 2 g12 )dσ + (g11 + g12 ξ η ξ η )( ρdσ + σρ)] r σ σ

59 36 1 Hv H t ζ 21 = (g ξ ζ ϑ ϑ + g22 ) (g21 + g22 η ξ η ) ( g 11 u + g 21 v) (2 26) g0 g0 R 0 {x g η [ 0 ξ (y g0 S ξ yx + y η g0 S yy ) + η (y g0 S ξ yx + y η g0 S yy )] y η [ ξ (x g0 S ξ xx + x η g0 S yx ) + η (x g0 S ξ yx + x η g0 S yy )]} R 0 g 0 H {x [ ξ ξ (y g0 Huv + y ξ η g0 Hvv) + η (y g0 Huv + y ξ η g0 Hvv)] y ξ [ ξ (x g0 Huu + x ξ η g0 Huv) + η (x g0 Huv + x ξ η g0 Hvv)] Hvω g 0 σ } + E v H 2 σ (A v v σ + E HA H (Horizontal Diffusion of v) R 0 0 ρ ρ H H 0 21 [H (g + F 2 g22 )dσ + (g21 + g22 ξ η ξ η )( ρdσ + σρ)] r σ σ where σ = z ζ h + ζ = z ζ σ stretching in the vertical (2 27) H gξη = x x g ηξ = ξ η + y y Horizontal measures of lengths (2 28) ξ η ( x y g0 = ξ η x ) 2 y Jacobian of horizontal transformation (2 29) η ξ The salinity transport equation can be written as HS t = E v HS cv ( ) S HωS D v R σ σ 0 σ R 0 [ g0 ξ ( g 0 HuS) + η ( g 0 HvS)] + E h [ S g0 ch ξ ( S 11 g 0 Hg ξ + g 0 Hg )], (2 30) η 12 S + E h [ S g0 ch η ( S 21 g 0 Hg ξ + S 22 g 0 Hg η )] Mode splitting technique is applied in CH3D to solve the full three-dimensional equations. First, external mode is used to solve the vertically integrated equations of motion and continuity over the whole domain. Then the three-dimensional

60 37 equations of motion, continuity and transport for a given cell is solved in the internal mode. In the current version of CH3D, sweeping method is used in the external mode. The i-sweep couples the continuity and u-momentum equations and solve for intermediate elevation and new step velocity u; Then j-sweep combines the continuity and v-momentum equations and solve for new step elevation and velocity v. The boundary conditions that must be specified are the tidal and wind forcing, river inflow, and salinity profiles along open boundaries. The tide, river inflow can be specified as either constant or time varying. The initial conditions which must be specified are the three dimensional flow field, salinity field as well as the water surface elevation. The parameterization of turbulence in the model has three options, a constant eddy coefficient, a Richardson-number dependent eddy coefficient, and a simplified application of the second-order turbulence closure model. Slightly modified version of a robust wetting-and-drying scheme by Casulli and Cheng (1992) is incorporated into the CH3D model as described in Davis (1996) and Sheng et al. (2002). Due to the use of the non-orthogonal boundary fitted equations of motion and continuity, the model can handle fairly complex geometries without excessive number of grid cells. In addition, the code uses a sigma-stretching in the vertical direction which allows for variation in the bottom bathymetry. The model simulates the storm surge and tide subjected to prescribed hurricane wind and offshore tide forcing. The model has been tested with analytical solution as well as storm surge data during real storms (Peene et al., 1993). Coupled with some wave models (REF/DIF and SWAN), the CH3D model has also been used to estimate wave setup (e.g., Sun and Sheng (2002); Sheng and Alymov (2002)).

61 38 To allow efficient simulations, the CH3D model has been modified to allow parallel operation on a shared memory computer (Davis and Sheng, 2000) and (Davis and Sheng, 2002) Implementation of Wetting-and-Drying Algorithm into CH3D The wetting-and-drying algorithm as described by Casulli and Cheng (1992) has been implemented in CH3D (Sheng et al., 2002). First, the algorithm is implemented into the vertically averaged equations of CH3D. During each time step, the vertically averaged equations of CH3D are first solved, and a new shoreline is calculated. This new shoreline is then implemented in the calculation of the three-dimensional baroclinic flow field. In the curvilinear coordinate system, the two-dimensional vertically averaged, non-dimensional equations can be written as ζ t + γ [ g0 ξ ( g 0 Hu) + η ( g 0 Hv)] = 0 (2 31) u t v t + g11 ζ ξ g 12 g0 u g 22 g0 v F ξ = 0 (2 32) + g22 ζ η + g 11 g0 u + g 21 g0 v F η = 0 (2 33) where F ξ and F η are the remaining nonlinear, horizontal diffusion, wind stress, bottom friction, radiation stress, atmospheric pressure gradient and surface slope in the opposite directions terms, and u, v are depth-averaged velocities defined as u = 1 H ζ h udz (2 34) v = 1 H ζ h vdz (2 35) where H = h + ζ is total water depth.

62 39 The finite difference form of the simplified equations 2 31, 2 32, and 2 33 can be written as ζ n+1 i,j ζ n i,j t + + γθ 1 g0,i,j,s ξ ( g 0,u,i+1,j H n u,i+1,j un+1 i+1,j ( g 0,u,i,j H n u,i,j un+1 i,j )) γθ 1 g0,i,j,s η ( g 0,v,i,j+1 H n v,i,j+1 vn+1 i,j+1 ( g 0,v,i,j H n v,i,j vn+1 i,j )) + γ(1 θ 1) g0,i,j,s ξ ( g 0,u,i+1,j H n u,i+1,j un ( g i+1,j 0,u,i,j H n u,i,j un )) (2 36) i,j + γ(1 θ 1) g0,i,j,s η ( g 0,v,i,j+1 H n v,i,j+1 vn i,j+1 ( g 0,v,i,j H n v,i,j vn i,j )) = 0 u n+1 i,j u n i,j t + g11 θ u,i,j 1H n u,i,j ξ (ζ n+1 ζ n+1 ) + g11 (1 θ u,i,j 1)H n u,i,j (ζ n i,j i 1,j i,j ξ ζ n ) i 1,j g 12,u,i,j g0,u,i,j u n i,j g 22,u,i,j g0,u,i,j v n i,j F n ξ,i,j = 0 (2 37) v n+1 i,j v n i,j t + g22 θ v,i,j 1H n v,i,j (ζ n+1 ζ n+1 i,j i,j 1 η ) + g22 (1 θ v,i,j 1)H n v,i,j (ζ n i,j η ζ n ) i,j 1 + g θ 11,v,i,j 2 u n+1 + g (1 θ 11,v,i,j 2) u n i,j i,j g0,v,i,j g0,v,i,j + g 21,v,i,j θ 2 g0,v,i,j v n+1 i,j + g 21,v,i,j (1 θ 2) g0,v,i,j v n i,j F n η,i,j = 0 (2 38) where θ 1 and θ 2 are the degrees of the implicitness of the surface slope and Coriolis terms. Substituting the vertically averaged velocity finite difference equations into the continuity equation yields: Π n nw,i,j ζ n+1 i 1,j+1 + Πn n,i,j ζ n+1 i,j+1 + Πn ne,i,j ζ n+1 i+1,j + Π n w,i,j ζ n+1 i 1,j + Πn c,i,j ζ n+1 i,j + Π n e,i,j ζ n+1 i+1,j+1 + Π n sw,i,j ζ n+1 i 1,j 1 + Πn s,i,j ζ n+1 i,j 1 + Πn se,i,j ζ n+1 i+1,j 1 = (RHS)n i,j (2 39) where

63 40 Π n = Γ i,j+1 t nw,i,j ξ θ 1β u,i,j+1 g 11 u,i,j+1 Π n ne,i,j = + Γ i,j t ξ θ 1β u,i+1,j+1 g 11 u,i+1,j+1 Π n = Π n n,i,j nw,i,j Πn Φ ne,i,j v,i,j+1 Π n = + Γ i,j t sw,i,j ξ θ 1β u,i,j 1 g 11 u,i,j 1 4 Π n se,i,j = Γ i,j 4 t ξ θ 1β u,i+1,j 1 g 11 u,i+1,j 1 (2 40) Π n s,i,j = Π n sw,i,j Πn se,i,j Φ v,i,j Π n = + Γ i,j t w,i,j 4 Π n e,i,j = Γ i,j 4 ξ θ 1β u,i,j g 11 Γ i,j+1 u,i,j 4 t ξ θ 1β u,i+1,j g 11 + Γ i,j+1 u,i+1,j t ξ θ 1β u,i,j g 11 u,i,j Φ u,i,j 4 t ξ θ 1β u,i+1,j g 11 u,i+1,j Φ u,i+1,j Π n c,i,j = + g o,s,i,j Π n w,i,j Πn e,i,j Πn n,i,j Πn s,i,j Πn nw,i,j Πn ne,i,j Πn sw,i,j Πn se,i,j and (RHS) n i,j = ζ n go,s,i,j + t i,j ξ H n α β go,u,i,j γθ u,i,j u,i,j u,i,j 1 t ξ H n α β go,u,i+1,j γθ u,i+1,j u,i+1,j u,i+1,j 1 + t η H n α β go,v,i,j γθ v,i,j v,i,j v,i,j 1 t η H n α β go,v,i,j+1 γθ v,i,j+1 v,i,j+1 v,i,j+1 1 where + t(1 θ 1) ( g ξ o,u,i,j H n u,i,j un g i,j o,u,i+1,j H n u,i+1,j un )γ (2 41) i+1,j + t(1 θ 1) ( g η o,v,i,j H n v,i,j vn g i,j o,v,i,j+1 H n v,i,j+1 vn )γ i,j+1 Γ i,j (α u,i,j β u,i,j + α u,i+1,j β u,i+1,j + α u,i,j 1 β u,i,j 1 + α u,i+1,j+1 β u,i+1,j+1 ) 4 + Γ i,j+1 (α u,i,j β u,i,j + α u,i,j+1 β u,i,j+1 + α u,i+1,j β u,i+1,j + α u,i+1,j+1 β u,i+1,j+1 ) 4

64 41 α u,i,j = tf n u,i,j + un i,j + vn i,j t g 22,u,i,j go,u,i,j α v,i,j = tf n v,i,j + vn i,j vn i,j t(1 θ 2) g 21,v,i,j go,v,i,j t η (ζ n i,j ζ n i,j 1 )(1 θ 1)g 22 v,i,j t ξ (ζ n i,j ζ n i 1,j )(1 θ 1)g 11 u,i,j u n i,j t(1 θ 2) g 11,v,i,j go,v,i,j β u,i,j = 1 (2 42) β v,i,j = tθ 2 g 21 v,i,j go,v,i,j Γ i,j = θ 1 θ 2 t η H n v,i,j β v,i,j tg11 v,i,j γ Φ u,i,j = t ξ θ 1H n u,i,j Φ v,i,j = t η θ 1H n v,i,j t ξ θ 1β go,u,i,j u,i,j g 11 γ u,i,j t η θ 1β go,v,i,j v,i,j g 22 γ v,i,j The system of equations is a nine-diagonal system of linear equations that can be solved for water surface elevation by the conjugate gradient method. By following Casulli and Cheng (1992), the normalized form of the equation can be written as: Π n nw,i,j Π n c,i,j Π Π n n c,i 1,j+1 ζ n+1 i 1,j+1 + Π n n,i,j c,i 1,j+1 Π n c,i,j Π Π n n c,i,j+1 ζ n+1 i,j+1 c,i,j+1 Π n ne,i,j + Π n c,i,j Π Π n n c,i+1,j+1 ζ n+1 c,i+1,j+1 i+1,j+1 + Π n w,i,j Π n c,i,j Π n c,i 1,j Π n c,i 1,j ζ n+1 i 1,j + Π n c,i,j ζn+1 i,j = (RHS)n i,j Π n c,i,j (2 43) Π n e,i,j + Π n c,i,j Π Π n n c,i+1,j ζ n+1 c,i+1,j Π n s,i,j i+1,j + + Π n c,i,j Π Π n n c,i,j 1 ζ n+1 c,i,j 1 which, by letting i,j 1 + Π n sw,i,j Π n c,i,j Π n c,i 1,j 1 Π n c,i 1,j 1 ζ n+1 i 1,j 1 Π n sw,i,j Π n c,i,j Π n c,i+1,j 1 Π n c,i+1,j 1 ζ n+1 i+1,j 1 e i,j = Π n c,i,j ζn+1 i,j (2 44) is equivalent to

65 42 a nw,i,j e i 1,j+1 + a n,i,j e i,j+1 + a ne,i,j e i,j +a w,i,j e i 1,j + e i,j + a e,i,j e i+1,j = (2 45) b i,j + a sw,i,j e i 1,j 1 + a s,i,j e i,j 1 + a se,i,j e i+1,j 1 where a nw,i,j = a n,i,j = a ne,i,j = a w,i,j = Π n nw,i,j Π n c,i,j Π n c,i 1,j+1 Π n n,i,j Π n c,i,j Π n c,i,j+1 Π n ne,i,j Π n c,i,j Π n c,i+1,j+1 Π n w,i,j Π n c,i,j Π n c,i 1,j a e,i,j = Π n e,i,j Π n c,i,j Π n c,i+1,j (2 46) a sw,i,j = a s,i,j = a se,i,j = b i,j = RHSn i,j Π n c,i,j Π n sw,i,j Π n c,i,j Π n c,i 1,j 1 Π n s,i,j Π n c,i,j Π n c,i,j 1 Π n se,i,j Π n c,i,j Π n c,i+1,j 1 The conjugate gradient algorithm (Casulli and Cheng, 1992) solves the system as described in Davis (1996): (1) Guess e (0) i,j (2) Set p (0) i,j = r(0) i,j = e(0) i,j + a nw,i,je (0) i 1,j+1 + a n,i,je (0) i,j+1 + a ne,i,je (0) i,j+1 + a w,i,je (0) i 1,j + a e,i,j e (0) i+1,j + a sw,i,je (0) i 1,j 1 + a s,i,je (0) i,j 1 + a se,i,je (0) i+1,j 1 b i,j (2 47) (3) For k=0, 1, 2,... and until (r(k), r(k)) < ɛ, calculate e (k+1) i,j = e (k) i,j α(k) p (k) i,j (2 48) where

66 43 α (k) = (r(k),r (k) ) (p (k),mp (k) ) r(k+1) i,j = r (k) i,j α(k) (Mp (k) ) i,j p (k+1) i,j = r (k+1) i,j + β (k) p (k) i,j (2 49) where β (k) = (r(k+1),r (k+1) ) (r (k),r (k) ) (2 50) In the equation, Mp is solved as follows (Mp (k) ) i,j = p (k) i,j + a nw,i,jp (k) i 1,j+1 + a n,i,jp (k) i,j+1 + a ne,i,jp (k) i+1,j+1 + a w,i,j p (k) i 1,j + a e,i,jp (k) i+1,j + a sw,i,j p (k) i 1,j 1 + a s,i,jp (k) i,j 1 + a se,i,jp (k) i+1,j 1 (2 51) Once the free surface has been computed through the computational domain, before proceeding to the next time step the new total depth at u and v horizontal locations have to be updated. H n+1 u,i,j = h u,i,j + max ( ) ζi 1,j, n ζi,j n H n+1 v,i,j = h v,i,j + max ( ζ n i,j 1, ζ n i,j A resulting zero value of the total depth in the cell center H n+1 i,j ) (2 52) = h i,j + ζ n i,j means the cell is dry and it may be flooded when the total water depth becomes positive. Since the CH3D model uses the total depth as a denominator in some of its equations terms, the zero total depth value is not always a good way of distinguishing between wet and dry cells. Also, very small total depth might bring in instability, e.g., very strong wind blowing over extremely shallow water will result in a highly unpredictable behavior of horizontal velocities which may grow unrealistically high and cause the model to blow up. To solve the problem, a critical total depth value as opposed to the zero total depth value was used to distinguish between wet and dry cells. If the total depth of a cell is smaller than the critical value then the cell is dry, otherwise it is wet. The value of 30

67 44 cm performed well under hurricane strong wind conditions. Under conditions less extreme a smaller value of the critical total depth may be more practical Surface and Bottom Stresses The boundary condition imposed at the free surface as wind stress is calculated using τ w x = ρ a C d u w W s τ w y = ρ a C d v w W s (2 53) where W s = (u 2 w + vw) 2 is the total wind speed. The drag coefficient, C d is calculated using Garratt (1977) formulation: C d = ( W s ) (2 54) The boundary condition at the bottom is expressed in terms of bottom stress given by the quadratic law: τ bx = ρc d u b (u 2 b + vb 2) (2 55) τ by = ρc d v b (u 2 b + vb 2) where u b and v b are bottom velocities and C d is the drag coefficient which is defined using the formulation of Sheng (1983): C d = (κ/ln(z 1 /z 0 )) 2 (2 56) where κ = 0.4 is the von Karman constant. The formulation states that the coefficient is a function of the size of the bottom roughness, z 0, and the height at which u b is measured, z 1 is within the constant flux layer above the bottom. The size of the bottom roughness can be expressed in terms of the Nikuradse equivalent sand grain size, k s, using the relation z 0 = k s /30.

68 45 In the two-dimensional mode, the bottom boundary conditions are given using a Chezy formulation: u τ bx = ρa v z = gu U 2 + V 2 Cz 2 (2 57) v τ by = ρa v z = gv U 2 + V 2 Cz 2 (2 58) where U and V are depth averaged velocities, and C z is the Chezy friction coefficient defined as: C z = 4.64 R 1 6 n (2 59) where R is the hydraulic radius which can be approximated by the total depth given in centimeters, and n is Manning s n Wave Enhanced Surface and Bottom Stresses When the CH3D model is coupled with a wave model (e.g., SWAN), different formulations developed by Donelan et al. (1993) for surface roughness, z 0, and drag coefficient, C d are used to calculate wind stress at the free surface. Both are functions of wave age. When waves are young the roughness increases making the wind stress higher as opposed to when waves are not taken into consideration. ( ) ( ) z 0 = W s W s g C p (2 60) where W s is the wind speed at a 10 m altitude. Following the relation between z 0 and C d, z 0 = z exp( κ/ C d (z)), yields the wave enhanced drag coefficient C de = κ ( ( ln W 2 s gz ) ( W s 2 ) ) 0.9 C p (2 61) where C p is wave phase speed and W s /C p represents the inverse wave age.

69 46 Wave enhancement of bottom stress is implemented in CH3D using two methodologies. The first methodology exploits the Grant and Madsen (1979) theory described in a simplified form by Signell et al. (1990). The second methodology makes use of a one-dimensional wave-current bottom boundary layer model (Sheng and Villaret, 1989) as described in Sheng and Villaret (1989) and Sun (2001). The Grant and Madsen (1979) formulation is given by the typical quadratic law with one distinction: C de is the wave enhanced drag coefficient. τ bx = ρc de u b (u 2 b + vb 2) (2 62) τ by = ρc de v b (u 2 b + vb 2) The main idea used in the formulation in order to find C de is that τ b max = τ C + τ W (2 63) where τ C is the bottom stress due to current and τ W is the maximum stress due to waves which can be defined as τ W = 1 2 ρf W UW 2 (2 64) where U W is the near-bottom wave orbital velocity and f W is the wave friction factor which depends on the bottom roughness, k s and the near-bottom excursion amplitude A B = U W /ω and whose values are obtained using the empirical expressions from Grant and Madsen (1982): f W = 0.13 (k s /A B ) 0.40 if k s /A B < (k s /A B ) 0.62 if 0.08 < k s /A B < if k s /A B > 1.0 (2 65)

70 47 With u B determined, an iteration procedure is used to determine C de at z r. With an initial guess of C de, the steady shear stress component u B is u B = C de u C (2 66) The combined wave-current shear velocity u CW is defined by u CW = τ b,max /ρ (2 67) From equation 2 63, u CW is determined as u CW = u 2 W + u2 B (2 68) The apparent bottom roughness k BC, which indicates the turbulence level due to the combination of the wave boundary layer and the physical bottom roughness, is expressed as where the exponent β is given by k BC = k s [ 24 u CW u W ] β A B (2 69) k s β = 1 u B u CW (2 70) The apparent roughness is then used to determine the velocity profile in the constant stress region above the wave boundary layer using the law-of-the-wall relation u = u ( ) B z + h κ ln k BC /30 The final expression for the wave enhanced drag coefficient is (2 71) ( ) 2 κ C de = (2 72) ln (30z r /k BC ) where z r is a reference height chosen to lie above the wave boundary layer and k BC is the apparent bottom roughness which accounts for the turbulence induced by

71 48 both the wave boundary layer and physical bottom roughness. According to Signell et al. (1990), the reference height was specified as 20 cm and k s = 0.1 cm was selected to correspond to a drag coefficient of at one meter above the bed in the absence of waves. Once the effective drag coefficient C de is calculated, it is used in CH3D to compute bottom stress as defined by equation As was pointed out in Section 1.1.2, the Grant and Madsen (1979) methodology has some deficiencies which include a fictitious reference velocity at an unknown level and the assumption of the logarithmic layer being constant which is not correct when waves are present. Sun (2001) used a 1-D wave-current bottom boundary layer model based on Sheng and Villaret (1989) to calculate bottom shear stress through nonlinear interaction between waves and currents. This model was adopted and implemented in CH3D in the following paragraphs. The governing equations for the combined wave-current bottom boundary layer model are the vertical one-dimensional equations of motion: u t = 1 p ρ x + z v t = 1 p ρ y + z Boundary conditions at the bottom are: ( u A v z ( A v v z ) ) (2 73) (2 74) τ bx = A v u z = ρc du 1 u v 2 1 (2 75) τ by = A v v z = ρc dv 1 u v 2 1 (2 76) where u 1, v 1 are velocity components at the lowest grid point, z 1, and C d is computed by: [ ] 2 κ C d = (2 77) ln (z 1 /z 0 )

72 49 where z 0 is the bottom roughness (it was set to 0.1 cm) and κ is the von Karman constant. The smallest grid spacing near the bottom is 0.03 cm. Boundary conditions above the bottom boundary layer which was set to 30 cm are: τ sx = A v u z = 0 (2 78) τ sy = A v v z = 0 (2 79) To drive an oscillatory motion due to waves, a pressure gradient from the linear wave theory is applied: ( 1 ) p ρ x ( 1 ) p ρ y w w = 1 cosh (kz) gkh sin ϕ cos (σt) (2 80) 2 cosh (kh) = 1 cosh (kz) gkh cos ϕ cos (σt) (2 81) 2 cosh (kh) where g is gravitational acceleration, k is wave number, H is wave height, ϕ is wave direction, and σ is angular wave frequency. To drive a current, a constant pressure gradient is applied in the y direction: ( 1 ) p ρ y c = const (2 82) The eddy viscosity A v is determined using a TKE closure model developed by Sheng and Villaret (1989). The model solves an equation for the turbulent kinetic energy, q 2 : q 2 t = 2 u w u z 2 v w v z z ) (qλ q2 q3 z 4Λ (2 83) The second-order correlation terms of fluctuating velocities are solved using the following equilibrium condition: u w = v w = 81Γ 4 (2 84) where

73 50 ( q ) 2 Γ = (2 85) Λ ( q ) 4 = 81 (2 86) Λ The macro-scale Λ is determined by the following integral constraints: dλ dz 0.65 Λ C 1 H Λ C 1 H p (2 87) Λ C 2 δ q 2 Λ q N where C 1 is between 0.1 and 0.25, H is the total depth, H p is the depth of pycnocline, C 2 ranging between 0.1 and 0.25 is the fractional cut-off limitation of turbulent macro-scale based on δ q 2, the spread of the turbulence determined from the turbulent kinetic energy profile, and N is the Brunt-Vaisala frequency defined as: ( N = g ) 1/2 ρ (2 88) ρ z Sheng and Villaret (1989) and Sun (2001) validated the model for an oscillatory boundary layer by comparing the calculated velocity profiles with velocity profiles obtained in the Jonsson and Carlsen (1979) experiment on the oscillatory boundary layer under rough turbulent flow conditions. Two test simulations (refer to Section 4.3.2) were performed to validate the model: for a pure oscillatory flow (Jonsson and Carlsen, 1979) and uniform current superimposed on an oscillatory flow (Bakker and Dorn, 1978). The model results of both tests agreed well with the experimental data. A series of model runs (a total of runs) using various combinations of water depth, wave height, wave period, wave direction and current magnitude

74 51 (shown in Table 2 2) was performed in order to develop a look-up table of bottom stress due to wave-current interaction. When the table is used in CH3D, the bottom stress value in each grid cell is determined based on the value obtained by interpolating the table values in a five-dimensional space (i.e., water depth, wave height, wave period, wave direction, current magnitude). The current is specified at the lowest grid point, z 1, where CH3D calculates its bottom currents. Therefore, the water depth (i.e., water column within which the 1-D model is applied) is defined as 1 (h+ζ) z 2 KM 0, and the wave height corresponded to the z 1 point is determined according to the linear wave theory: H (z=z1 ) = H (z=ζ) sinh k(h + z 1 ) sinh k(h + ζ) (2 89) where h is local water depth, ζ is water surface elevation, KM is the number of vertical layers in CH3D, and H (z=ζ) is wave height at the surface. Table 2 2: Parameters used to create the lookup table. Parameter Water Depth Wave Height Wave Period Wave Direction Current Values 0.5 m to 5.0 m with 0.5 m increments 0.0 m to 2.0 m with 0.2 m increments 2 s to 16 s with 1 s increments 0 deg to 315 deg with 45 deg increments 0.0 m/s to 1.0 m/s with 0.1 m/s increments Radiation Stress In its governing equations, CH3D has radiation stress terms to account for wave setup when coupled with a wave model (see equations 2 15 and 2 16). Two formulations are implemented in the model: vertically uniform (Longuet-Higgins and Stewart, 1964) and vertically varying (Mellor, 2003).

75 52 The derivation of the vertically uniform radiation stress and the relation between radiation stress gradients and wave setup follows in the manner of Dean and Dalrymple (1991). If a wave is propagating at some angle θ to the x axis (representing onshore direction), then the radiation stress in this direction will be: S xx = E [ n ( cos 2 θ + 1 ) 1 ] 2 (2 90) Similarly, the radiation stress in the transverse (longshore) direction will be: S yy = E [ n ( sin 2 θ + 1 ) 1 ] 2 (2 91) where n is the ratio of group velocity to wave celerity. There is an additional term which represents the flux in the x direction of the y component of momentum S xy = E n sin 2θ (2 92) 2 In a simple 1-D case, the relation between the radiation stress and wave setup can be expressed as follows: 1 ds xx ρg (h + η) dx = d η dx (2 93) where η is the mean water surface slope or wave setup. In 2-D case, a system of two differential equations has to be solved: ( 1 dsxx ρg (h + η) dx 1 ρg (h + η) ( dsyx dx + ds ) xy = d η dy dx ) + ds yy dy = d η dy (2 94) (2 95) Mellor (2003) derived equations for three-dimensional ocean circulation models that handle surface waves. In his derivation radiation stresses vary vertically and

76 53 are expressed as follows: S αβ = khe [ ] kα k β k F CSF 2 CC + δ αβ (F CS F CC F SS F CS ) (2 96) where H is the total depth; σ = (z ζ)/h ; k is the wave number whose x and y components are k α and k β, respectively; E is the total wave energy; δ αβ is the Kronecker delta; and F SS = F CS = F SC = F CC = sinh KH(1+σ) sinh KH cosh KH(1+σ) sinh KH sinh KH(1+σ) cosh KH cosh KH(1+σ) cosh KH If Mellor s equations are integrated vertically, his radiation stresses become identical to those of Longuet-Higgins and Stewart (1964). Since CH3D calculates the water surface elevation in the external mode where vertically integrated equations are used, the calculated wave setup will be the same no matter which radiation stress formulation is used. The difference between the two formulations will take place in the velocity field Local Wave Model: SWAN The SWAN (Simulating WAves Nearshore) model (Booij et al., 1999) is a (2 97) third-generation wave model which computes random, short-crested wind-generated waves in coastal regions and inland waters. It accounts for wave propagation in time and space, shoaling, refraction due to current and depth, frequency shifting due to currents and non-stationary depth, wave generation by wind, bottom friction, depth-induced breaking, and transmission through and reflection from obstacles. The model was developed at Delft University of Technology, the Netherlands. SWAN is used in coastal applications by many institutions in the United States and Europe.

77 54 SWAN is can be applied to a boundary-fitted curvilinear grid which is irregular, quadrangular, and not necessarily orthogonal. It calculates many important wave and wave related parameters such as significant wave height, swell wave height, mean wave direction, peak wave direction, direction of energy transport, mean absolute wave period, mean relative wave period, current velocity, energy dissipation due to bottom friction, wave breaking and whitecapping, fraction of breaking waves due to depth-induced breaking, transport of energy, wave induced force, the RMS-value of the maxima of the orbital velocity near the bottom, the RMS-value of the orbital velocity near the bottom, average wavelength, average wave steepness, and some others. In SWAN the waves are described with the two-dimensional wave action density spectrum N(σ, θ) equal to the energy density divided by the relative frequency: N(σ, θ) = E(σ, θ)/σ. The evolution of the wave spectrum is described by the spectral action balance equation which for Cartesian coordinates is: t N + x c xn + y c yn + σ c σn + θ c θn = S σ (2 98) The first term in the left-hand side of this equation represents the local rate of change of action density in time, the second and third term represent propagation of action in geographical space (with propagation velocities c x and c y in x- and y-space, respectively). The fourth term represents shifting of the relative frequency due to variations in depths and currents (with propagation velocity c σ in σ-space). The fifth term represents depth-induced and current-induced refraction (with propagation velocity c θ in theta-space). The expressions for these propagation speeds are taken from linear wave theory. The term S(= S(σ, θ)) at the right hand side of the action balance equation is the source term in terms of energy

78 55 density representing the effects of generation, dissipation and nonlinear wave-wave interactions. Transfer of wind energy to the waves is described in SWAN with a resonance mechanism and a feed-back mechanism. The corresponding source term for these mechanisms is commonly described as the sum of linear and exponential growth: S in (σ, θ) = A + B E (σ, θ) (2 99) in which A and B depend on wave frequency and direction, and wind speed and direction. The dissipation term of wave energy is represented by the summation of three different contributions: whitecapping S ds,w (σ, θ), bottom friction S ds,b (σ, θ) and depth-induced breaking S ds,br (σ, θ). Whitecapping is primarily controlled by the steepness of the waves. In SWAN the whitecapping formulations are based on a pulse-based model: S ds,w (σ, θ) = Γ σ k k E (σ, θ) (2 100) where Γ is a steepness dependent coefficient, k is wave number and σ and k denote a mean frequency and a mean wave number, respectively. Depth-induced dissipation may be caused by bottom friction which can generally be represented as: σ 2 S ds,b (σ, θ) = C bottom g 2 sinh 2 E (σ, θ) (2 101) (kd) in which C bottom is a bottom friction coefficient. JONSWAP suggested to use an empirically obtained constant. It performs well in many different conditions as long as a suitable value is chosen (typically different for swell and wind sea). The total dissipation (i.e., integrated over the spectrum) due to depth-induced wave breaking in shallow water can be well modeled with the dissipation of a bore

79 56 applied to the breaking waves in a random field. The expression used in SWAN is: S ds,br (σ, θ) = D tot E tot E (σ, θ) (2 102) where E tot is the total wave energy and D tot (which is negative) is the rate of dissipation of the total energy due to wave breaking. In deep water, quadruplet wave-wave interactions dominate the evolution of the spectrum. They transfer wave energy from the spectral peak to lower frequencies (thus moving the peak frequency to lower values) and to higher frequencies (where the energy is dissipated by whitecapping). In very shallow water, triad wave-wave interactions transfer energy from lower frequencies to higher frequencies often resulting in higher harmonics (low-frequency energy generation by triad wave-wave interactions is not considered here). In SWAN the computations are carried out with the Discrete Interaction Approximation and the Lumped Triad Approximation. SWAN has been successfully tested and applied to storm conditions in simulation of 1995 Hurricane Luis by Wornom et al. (2001). The model is currently used by the Naval Research Laboratory which created three sub-regional scale wave forecasting systems for the National Weather Services Coastal Storms Program (Rogers, 2005). One of their systems, northeast Florida system, was validated for the period of September 2003 when Hurricane Isabel took place and for the period of August 2004 when Hurricane Charley went across the Florida peninsula. The results of these validations show that one can have confidence in applying the SWAN model to shallow-water regions during severe storm evens such as hurricanes. Sheng and Alymov (2002) used an extremely large and fine grid in their SWAN simulations. The size of the grid was grid cells with the grid spacing of 5 m. Although to run a simulation on such a fine grid requires a lot of

80 57 computer memory and computational time, it is worthwhile doing it. For storm surge modeling such fine resolution may not be necessary. Increasing the grid spacing to m will allow to still have finely resolved domain but also place the open boundary many tens of kilometers offshore. Some of the deficiencies of the SWAN model include the assumption of the wave spectrum being Gaussian which may not be true in the breaker zone (Ochi, 1998), and the incapability of replicating extreme dissipation imparted by muddy bottom (Kaihatu and Sheremet, 2004).

81 CHAPTER 3 METHODOLOGY 3.1 Introduction When it comes to numerical simulation of a storm surge, various physical processes have to be taken into account. These processes can be either forces driving the circulation (e.g., wind, tide, atmospheric pressure, river flow) or the outcome of the forces (e.g., waves, currents, sediment transport). There is also an interaction between these physical processes that takes place at the air-sea interface and bottom. At the air-sea interface it is turbulent stress and stress due to waves, evaporation and precipitation. On the bottom, there is bottom stress due to tidal currents and waves. A diagram of the various physical processes is shown in Fig 3 1. Those in red are accounted for in the methodology presented herein. One of the major advantages of this methodology is that unlike many other storm surge models, the water elevation is calculated dynamically and not in parts which include storm surge, tide and wave setup in the surf zone. It is all done as a whole due to the reason that all these parts that water elevation consists of interact between each other in a non-linear fashion and it would be physically incorrect to neglect this interaction. 3.2 Coupling Mechanism By definition, a storm surge is an increase (or decrease) in water level associated with some significant meteorological event, e.g. persistent strong winds and change in atmospheric pressure (as in a tropical cyclone). This means that there are two major components in storm surge modeling: an atmospheric model which calculates wind speed, wind direction and atmospheric pressure during a hurricane 58

82 59 Geostrophic layer Geostrophic winds Wave run-up Wave setup Water run-off Currents River inflow Evaporation Precipitation Sediment transport PBL Atmospheric pressure gradients Momentum transfer Hurricane Heat transfer Bottom stress due to: 1) Tidal currents 2) Waves Turbulent stress + Stress due to waves Mass flux Waves Surge + Tide elevation Salinity + Density stratification Figure 3 1: A diagram of various physical processes. Those in red are accounted for in this methodology.

83 60 event; and a circulation model which calculates surface water elevation and currents based on the meteorological conditions provided by the atmospheric model. As was stated earlier, wave effects can become a significant factor during storm events. Waves breaking in the surf zone transfer their momentum to the water column which results in wave set-up or increase in water elevation from the breaker point to the point where the waves completely dissipate by running up the beach. Wave setup is mainly a function of the breaking wave height. Stormy seas generate large waves which break further offshore as opposed to waves during regular conditions, thus extending the surf zone. As a result, a larger area is affected by the rising water due to wave set-up which can be significant and has to be accounted for. Therefore, adding a wave model as another component of storm surge calculation adds robustness to the entire storm surge modeling system. Horizontal scale and grid spacing are also important aspects of storm surge modeling. Since hurricanes affect large areas, computational domains must be large as well. Having small grid spacing results in more accurate results but it also means more computational cells and, as a result, more computational resources and time. Models of two different scales are used in storm surge modeling in general and this study in particular: (1) Regional models which simulate large regions (e.g., the North Atlantic), have a relatively coarse spatial resolution and provide boundary conditions for local models; (2) Local models which simulate smaller areas of particular interest (e.g., Tampa Bay or Chesapeake Bay) and have fine spatial resolution. The methodology presented herein consists of four models. Two regional models, ADCIRC and WAVEWATCH-III, and two local models CH3D and SWAN. ADCIRC and CH3D are circulation models, and WAVEWATCH-III and SWAN are wave models.

84 61 As for the atmospheric model, results from two sophisticated atmospheric models, NCEP WNA and WINDGEN, were used. Verification of these model results for Hurricanes Isabel (2003), Charley (2004), and Frances (2004) can be found in Chapter 5. For simulation of storm surge during a particular hurricane, the basic coupling process is as follows: First, wind and atmospheric pressure snapshots are initialized, i.e., the wind and atmospheric pressure data from one of the wind models are processed to make them available for the circulation models, ADCIRC and CH3D. Second, wave boundary conditions for the local wave model, SWAN, are initialized by processing the wave data calculated by the regional wave model, WAVEWATCH-III, by NOAA. Third, tidal constituents along the open boundaries of the local circulation model, CH3D, are initialized. These constituents are based on the ADCIRC tidal database ( CATS/tides/tides.htm) and were obtained for each hurricane prior to their simulations. At the conclusion of the initialization phase, the simulation phase starts. There are three models that are involved in the actual simulation: ADCIRC, CH3D, and SWAN. There are two types of coupling between these models. The first one is one-way coupling meaning that the results of model A are fed to model B whose results are not fed back to model A. This type of coupling occurs between ADCIRC and CH3D. The accuracy of results calculated by the local model, CH3D, depends on accurate representation of physical processes inside the computational domain and CH3D boundary conditions. The open boundary conditions can be provided either by available field data or through coupling with a regional scale model such as ADCIRC. The ADCIRC domain covers the Eastern North Atlantic, the Gulf of

85 62 Mexico and the Caribbean Sea. Therefore, ADCIRC is capable of providing water elevation along open boundaries of a local model (CH3D) domain (e.g., North Carolina or Florida) during hurricane events when the actual hurricane is located thousands of kilometers away. Both models can run concurrently using the same time step. ADCIRC results are not affected by results of CH3D. The same one-way coupling is used to couple WAVEWATCH-III and SWAN. The second type of coupling is two-way coupling which is also known as dynamic coupling, where the results calculated by model A are fed to model B whose results are fed back to model A. This type of coupling is used to couple the local circulation model, CH3D, and the local wave model, SWAN. CH3D solves for water elevation and currents. It also accounts for situations when land cells become flooded and vice versa. SWAN computes wave conditions within the same curvilinear grid as used in CH3D. Since wave conditions change relatively slowly, the wave model simulation was conducted every 30 minutes to ease the computational burden. This means that after thirty 60-second CH3D time steps, the two models mutually exchange information. CH3D loads in wave information (wave height, wave period, and wave direction) to account for wave setup. SWAN, in return, updates bathymetry that changes in time due to tide, storm surge, wave setup, and inundation of previous land areas. The current field used in SWAN simulation gets updated as well. Also, the updated wind field is passed onto the wave model via CH3D. A diagram of the entire coupling process from initialization to concurrent simulation and coupling of ADCIRC, CH3D, and SWAN is shown in Figure 3 2.

86 63! +, %-) '*+#!'&#./# 0,( 3! " # $# %!&' ( ( & ) % % 4 )! *# #!# %!&' ) # $# Figure 3 2: A diagram of the coupling process.

87 CHAPTER 4 TEST SIMULATIONS 4.1 Validation of Wetting-and-Drying Scheme Implemented in CH3D Description Dealing with storm surge in shallow water coastal areas brings the issue of capability of taking into account of wetting-and-drying right to the front. The ability to account for wetting-and-drying is essential in storm surge modeling since the main question to be answered by storm surge prediction models is not how high the surge may rise near the shore during a hurricane event but how far the surge might propagate inland, what land areas might be affected and how much damage it may cause. Some methodologies that try to account for flooding (e.g., FEMA) do not do it dynamically, that is, they just calculate the maximum surge level and extend it from the coastal area to the land. This is a rather simple approach and it does not consider the actual physical processes that move the water up the beach over the land. Also, the maximum storm surge level is a fixed number, which is independent of time. Therefore, this approach cannot tell when in time a land area will be inundated and once it gets inundated, how long it will stay flooded. Storm surge models that do not have wetting-and-drying scheme incorporated in them cannot produce accurate storm surge near the coastline. Hubbert and McInnes (1999) showed that their storm surge heights at the coast produced by fixed coastline version of the model were overestimated by 17% compared with the inundation version of their model. This overestimation comes as a result of the water being piled up near the coast by the action of high wind and the fixed coastline storm surge model not allowing the water to propagate inland. 64

88 65 The CH3D model is capable of accounting for wetting-and-drying. The method is based on a lightly modified version of a robust wetting-and-drying scheme developed by Casulli and Cheng (1992). The technical description can be found in Section The idea is, every time step the model calculates free surface elevation which is then used to calculate total depth. If the total depth in a computational cell exceeds some critical value (i.e., 30 cm), then the cell is considered to be wet, otherwise dry Validation In order to validate the wetting-and-drying scheme, three test cases were performed: (1) the wall case, (2) the wind case, and (3) the analytical solution case. The first two cases are rather qualitative and the third test is very robust and quantitative Test Case 1: Wall The purpose of the test is to see how a cell, which is dry initially, becomes wet by being affected by its neighbor wet cell. The layout of the wall test case is shown in Figure 4 1 below. There is a vertical wall in middle of the computational domain which extends from the bottom to half of the vertical column. Initially, the grid cells to the left of the wall are filled with water and the ones to the right are dry. There are four output locations in the middle of each vertical column. The results of computed water surface elevation in each output location are shown in Figure 4 2. The results are in agreement with what one would expect. The water surface elevation in columns 1 and 2 drops quickly and tends to reach half of the total water depth as time progresses. On the other hand, water surface elevation in columns 3 and 4 rapidly increases as water fills up the part of the domain to the right of the wall. It also tends to reach half of the total depth. Eventually, the

89 66 Z water level wet X dry Figure 4 1: The wall test case: computational layout. water surface elevation becomes equal to half of the total depth throughout the entire domain. Water Surface Elevation (cm) Column 1 Column 2 Column 3 Column Julian Day Figure 4 2: The wall test case: calculated water surface elevation Test Case 2: Wind The wind test case was performed in order to see how a dry cell may become wet by the action of wind stress which forces mass flux to flow from a wet cell to its neighbor dry cell. This is a real situation, strong wind blowing onshore will

90 67 make the water pile up against the beach and move the water mass inland causing flooding. The computational layout of the test is shown in Figure 4 3. The bed is mildly sloped (1:100,000) and the wind (0.1 dyne/cm 2 ) blows onshore. There are four output locations. Location 1 is initially dry and becomes wet during the simulation. Locations 2 through 4 are wet at all times. The results of water surface elevation calculated in each location are shown in Figure wind (0.1 dyne/cm 2 ) Elevation (cm) initial water level x = 1000 m Grid Cell in the Cross-shore Figure 4 3: The wind test case: computational layout. The results are consistent with what one would expect. In Location 1, which is initially dry, surface elevation does not change during some period of time due to the reason that the water which is piling up against the beach has not yet reached the location. To clarify the behavior of the blue line in Figure 4 4, it has to be noted that it was plotted the way that when a cell is dry it has no value for water elevation. Later on, when Location 1 gets inundated by the water that is being pushed onshore by the blowing wind, the water elevation starts to grow from the initial elevation which is ground level. Location 2 is initially under water and water surface elevation increases in time as expected. Location 3 is a little offshore and the water surface elevation increases

91 68 Water Surface Elevation (cm) Location 1 Location 2 Location 3 Location Julian Day Figure 4 4: The wind test case: calculated water surface elevation. more rapidly than that of Location 2 as a result of Location 3 being closer to the open boundary where the wind is blowing from and, therefore, it takes less time for the wind to reach Location 3 and start to pile up water there. Location 4 is farther offshore near the open boundary. Water surface elevation starts to grow in the beginning but then it starts to decline due conservation of mass Test Case 3: Analytical Solution As was mentioned before, the first two test cases were rather qualitative. In order to give a quantitative analysis of the wetting and drying scheme implemented in the CH3D model, a robust analytical solution developed by Carrier and Greenspan (1958) for propagation of waves on a linearly sloping beach was applied. The one-dimensional nonlinear shallow water equation can be written as: η t + t [(η + h )u ] = 0 (4 1) u u + u t x + g η x = 0 (4 2)

92 69 The obtained solution to the equation in the form of a potential is as follows: ϕ(σ, λ) = 8A 0 J 0 ( σ 2 ) sin(λ 2 ) (4 3) where A 0 is an arbitrary amplitude parameter and J 0 is a zero Bessel function of the first kind. This potential represents a standing wave solution resulting from a perfect reflection of a unit frequency wave. The following computational layout was set up to solve for η(x, t) and u(x, t) for given location, x, and time, t. A orthogonal grid 62 km long and 10 km wide with bottom sloping at 1:2500. The depth, h, varies from 2 m above the mean sea level to 22.8 m below the mean sea level at x=57 km. The grid spacing in the longshore y-direction is fixed and equal to 2 km whereas the grid spacing in the cross-shore x-direction varies. For the first 10.5 km (going offshore) the grid spacing is fixed at 100 m, then from 10.5 km to 15 km, the grid spacing linearly grows from 100 m to 1 km adding 100 m every grid cell. From 15 km to 62 km, the grid spacing is fixed at 1 km. The tidal forcing applied in the model at x=57 km is ζ(t) = A cos( 2π t) (4 4) T where the amplitude, A, is cm and the period, T, is 3600 s. During this simulation the non-linear terms in the CH3D model were turned on since the analytic solution was derived using those terms. The results of comparison of calculated surface elevation with analytic solution at different times are shown in Figures 4 5 through Validation of Atmospheric Pressure Gradient Terms Implemented in CH3D Description Atmospheric pressure is an important factor to be considered in storm surge modeling. Changes in atmospheric pressure drive winds and in addition to that,

93 Surface Elevation (cm) Time = 0 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theoretical Solution Numerical Solution X (m) Figure 4 5: Tidal case: comparison with analytic solution at t= Surface Elevation (cm) Time = π/6 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theoretical Solution Numerical Solution X (m) Figure 4 6: Tidal case: comparison with analytic solution at t=π/6.

94 Surface Elevation (cm) Time = π/3 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theoretical Solution Numerical Solution X (m) Figure 4 7: Tidal case: comparison with analytic solution at t=π/ Surface Elevation (cm) Time = π/2 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theoretical Solution Numerical Solution X (m) Figure 4 8: Tidal case: comparison with analytic solution at t=π/2.

95 Surface Elevation (cm) Time = 2π/3 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theoretical Solution Numerical Solution X (m) Figure 4 9: Tidal case: comparison with analytic solution at t=2π/ Surface Elevation (cm) Time = 5π/6 Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theretical Solution Numerical Solution X (m) Figure 4 10: Tidal case: comparison with analytic solution at t=5π/6.

96 Surface Elevation (cm) Time = π Surface Elevation (cm) X (m) Shoreline Mean Sea Level Theretical Solution Numerical Solution X (m) Figure 4 11: Tidal case: comparison with analytic solution at t=π. atmospheric pressure gradient gives rise to water surface elevation in the ocean. The significance of the rise depends on the magnitude of the gradient. In Cartesian coordinate system, the momentum equation including air pressure term can be written as: u t + advection = P a ρ w x g ζ + diffusion (4 5) x v t + advection = P a ρ w y g ζ + diffusion (4 6) y Since the air pressure term can be written as water head P a = ρ w gϑ, equations 4 5 and 4 6 can be rewritten as: u t v t ϑ + advection = g x g ζ + diffusion (4 7) x ϑ + advection = g y g ζ + diffusion (4 8) y

97 74 In curvilinear coordinate system after non-dimensionalization, the equations transform into the following form: U t = H(g11 ϑ ξ ϑ ζ + g12 ) H(g11 η ξ ζ + g12 ) + otherterms (4 9) η V t = H(g21 ϑ ξ ϑ ζ + g22 ) H(g21 η ξ ζ + g22 ) + otherterms (4 10) η where other terms include nonlinear terms, Coriolis term, diffusion terms, surface and bottom friction terms. The air pressure terms in equations 4 9 and 4 10 are treated fully explicitly when the 2D equations are solved Validation In order to validate the air pressure gradient term, a numerical solution based on the governing CH3D equations was compared with analytical solution derived by Holland (1980) and simplified as in Wilson (1957) (see Section 2.3.1). The local pressure in a storm can be written as: P a = P 0 + (P P 0 )e R/r (4 11) where P 0 is the pressure in the center of the storm, P is the free stream pressure, r is the distance from the center of the storm, and R is the radius to maximum wind. For steady state condition, the water surface elevation due to the pressure gradient of the storm can be written as: ϑ = P a ρ w g + C (4 12) where C is specified by boundary conditions or simply zero in case of steady state conditions. The computational domain for the test was a 100 km 100 km rectangular grid. The following parameters were used for analytical storm: atmospheric pressure at center, P 0 = 960 mb;

98 75 free stream pressure, P = 1013 mb; radius to maximum wind, R = 30 km. The analytical solution of water level is shown in Figure 4 12 and the difference between the analytical solution and numerical solution is shown in Figure The difference is on the order of cm, which validates the accuracy of the implemented in the CH3D model atmospheric pressure gradient terms. Figure 4 12: Analytical solution of water surface elevation due to atmospheric pressure gradient for a simplified hurricane. 4.3 Validation of Near-Bottom Wave-Current Interaction Description As was pointed out earlier in Section , a 1-D wave-current bottom boundary layer (BBL) model is exploited in CH3D to calculate bottom shear stress through nonlinear interaction between waves and currents. The eddy viscosity in the model is determined using a TKE closure model developed by Sheng and

99 76 Figure 4 13: Difference in water elevation between the analytical and numerical solutions. Villaret (1989). The BBL model s governing equations and integral constrains can also be found in that section Validation In order to validate the wave-current BBL model, numerical simulations of two laboratory experiments were performed: 1) for a pure oscillatory flow, and 2) for a uniform current superimposed on an oscillatory flow Pure Oscillatory Flow Jonsson and Carlsen (1979) carried out a laboratory experiment in a U-shaped water tunnel during which they measured oscillatory velocities throughout the water column and, based on the measurements, determined bottom stresses. The following parameters were used during the experiment: Water Depth = 10 m; Wave Height = 5.3 m;

100 77 Wave Period = 8.39 s; Bottom Roughness = cm. In the numerical simulations, the vertical computational grid was setup in a way that the grid spacing near the bottom was on the order of cm; it grew as the distance from the bottom increased. The computational time step was 0.01 s. As can be seen in Figure 4 14, the calculated velocity profiles are in good agreement with measured velocities. The RMS errors are shown for each individual profile and for all profiles altogether. The relative RMS errors were calculated based on the maximum range of measured velocities ( 440 cm/s). It has to be noted that one of the sources of the calculated error may be attributed to the asymmetry of the measured free stream velocity above the boundary layer. The measurements showed that the free stream velocity ranged from -220 cm/s to 201 cm/s whereas the oscillatory flow imposed through boundary conditions in the model was implied symmetrically and ranged from -210 cm/s to 210 cm/s. 0 7/4π π/ /2π π/2 5/4π 3/4π π Depth (cm) : 10.5 (2.4%) π/4: 7.4 (1.7%) π/2: 6.7 (1.5%) 3/4 π: 13.4 (3.0%) π: 13.4 (3.0%) 5/4 π: 12.6 (2.9%) 3/2 π: 23.6 (5.4%) 7/4 π: 11.1 (2.5%) 12.3 (2.8%) RMS Errors (Relative RMS Errors) Velocity (cm/s) Figure 4 14: Comparison between measured (Jonsson and Carlsen, 1979) [dashed line with squares] and calculated [solid line] velocity profiles for eight phase angles.

101 78 Figure 4 15 shows the phase lags of horizontal velocities at various levels. The horizontal velocity near the bottom shows a phase lead of 24 o. The above model results are consistent with the results of Sheng (1982) and Sheng and Villaret (1989), which used a Reynolds stress model and a TKE model Z (cm) Phase Lag (rad) Figure 4 15: Vertical profile of the calculated phase lag between horizontal velocities and free stream velocity. Figure 4 16 shows how the calculated bottom stress compares against the bottom stress determined based on the velocity measurements during the experiment. The relative RMS error was calculated based on the maximum range of measured bottom stress ( 880 dyne/cm 2 ). From this comparison, it can be concluded that the calculated and measured bottom stresses agree well, which validates the use of the 1-D BBL model for computing velocities and bottom stresses in the oscillatory bottom boundary layer Current Superimposed on an Oscillatory Flow To validate the 1-D BBL model when both waves and currents are present, a numerical simulation of the Bakker and Dorn (1978) laboratory experiment was performed. The water depth during the experiment was 0.3 m. The oscillatory flow

102 RMS error = 48.7 Relative RMS error = 5.5% Bottom Stress (dyne/cm 2) Phase (rad) Figure 4 16: Comparison between calculated [solid line] bottom stress and bottom stress determined based on measurements during the Jonsson and Carlsen (1979) experiment [dashed line with squares]. with a period T = 2 s was imposed though oscillatory motion boundary condition according to: ( ) ( 2π U OSC = U 1 sin T t ψ 1 + U 2 sin 2 2π ) ( T t ψ 2 + U 3 sin 3 2π ) T t ψ 3 (4 13) where velocity amplitudes of the three harmonics were defined as: U 1 = 24.3 cm/s, U 2 = 6.3 cm/s, U 3 = 5.8 cm/s; and their corresponding phase angles were defined as: ψ 1 = 52.7 o, ψ 2 = o, ψ 3 = o. The bottom roughness was 0.07 cm and the current velocity specified at the top of a 6.2 cm thick bottom boundary layer was 22.7 cm/s. A comparison between measured and calculated velocity profiles shown in Figure 4 17 demonstrates that the numerical results are in good agreement with measured velocities which validates the use of the model for computing velocity profiles within turbulent bottom boundary layer for combined wave-current flows.

103 80 The RMS errors are shown for each individual profile and for all profiles altogether. The relative RMS errors were calculated based on the maximum range of measured velocities ( 55 cm/s) π/4 7/4π π/2 3/2π 3/4π 5/4π π 2 1 Depth (cm) 0: 2.0 (3.6%) π/4: 1.4 (2.5%) π/2: 1.5 (2.7%) 3/4π: 2.0 (3.6%) π: 2.5 (4.5%) 5/4π: 2.0 (3.6%) 3/2π: 1.8 (3.3%) 7/4π: 2.5 (4.5%) 2.0 (3.6%) RMS Errors (Relative RMS Errors) Velocity (cm/s) Figure 4 17: Comparison between measured (Bakker and Dorn, 1978) [dashed line with squares] and calculated [solid line] velocity profiles for eight phase angles. Bakker and Dorn (1978) did not determine bottom shear stress based on their measurements, thus Figure 4 18 shows only the calculated bottom stress over one wave cycle along with its average value. 4.4 Validation of Wave Setup Calculated based on SWAN-CH3D coupling Description As was discussed in Section 1.1.3, breaking waves produce excess momentum flux in the shoreward direction, radiation stress. The shoreward decrease in radiation stress is balanced by a shoreward increase in the water level, wave setup. Wave setup varies in cross-shore and longshore directions as a result of complex bathymetry. The width of the surf zone depends on the beach slope and incident

104 81 50 Bottom Stress (dyne/cm 2 ) Avg. bottom stress = Phase (rad) Figure 4 18: Bottom stress due to wave-current interaction calculated using the 1-D BBL model based on the numerical simulation of the Bakker and Dorn (1978) laboratory experiment. wave height. For the same beach slope, a modest wave breaks closer to the shore while a larger wave breaks further offshore. As was pointed out in Section , two formulations are implemented in CH3D: vertically uniform (Longuet-Higgins and Stewart, 1964) and vertically varying (Mellor, 2003). When coupled with SWAN, CH3D accounts for wave setup, which is an important factor in storm surge modeling and has to be considered Validation Wave setup is calculated by means of coupling two models. First, the wave model (SWAN) calculates 2-D wave field and passes it to the circulation model (CH3D) which calculates radiation stresses and water elevation, which when any other forcing mechanisms such as tide, wind or atmospheric pressure gradient are not accounted for, represents wave setup. Two laboratory experiments were simulated in order to validate the wave setup calculation methodology.

105 82 The first experiment was by Stive and Wind (1982). In the experiment the authors studied variations of radiation stress and mean water level for the twodimensional shoaling and breaking of progressive, periodic waves on a plane, gently slopping laboratory beach. The experiment was conducted in a wave flume which is 55 m long, 1 m wide and 1 m high (see Figure 4 19). A plane concrete beach with a 1:40 slope was installed. The slope consists of three parts (i) a sloping zone which starts in a water depth of 0.85 m where waves are generated, (ii) a zone with a constant depth of 0.70 m to enable the installation of instruments, and (iii) another sloping beach zone. Figure 4 19: Layout of Stive and Wind experimental setup (from Stive and Wind (1982)). The experiment was simulated using a slightly different computational domain. The reason for the modification was that the width of the wave flume used in the experiment was only 1 m and its length was approximately 45 m. In the SWAN model there are affected areas with errors along lateral boundaries spreading to the shore at an angle of approximately 30 o. Therefore, the lateral boundaries should be sufficiently far away from the area of interest to avoid propagation of the error into this area. Thus, the domain in the transverse direction was expanded from 1 m to 20 m. Since the problem is essentially one-dimensional the width of the domain should not matter as long as the area of interest is not affected by the lateral boundaries. During the experiment the following wave parameters were used by the wave generator: wave height H rms =0.159 m, which was converted to significant wave height since the SWAN model does not operate with monochromatic waves,

106 83 H sig =1.42 H rms =0.226 m, and wave period T =1.79 s. The maximum wave setup measured up the sloping beach was equal to 1.8 cm. The maximum simulated wave setup value was also equal to 1.8 cm. The second experiment was by Mory and Hamm (1997). In this experiment the authors studied the impact of a detached breakwater on coastal morphology in a 3-D wave basin. The basin (see Figure 4 20), 30 m 30 m by size, consists of three parts (i) a zone 4.4 m wide with a constant depth of 0.33 m which is the closest to the wave maker, (ii) an underwater plane beach with the slope of 1:50, and (iii) an emerged plane beach with the slope of 1:20. A detached breakwater 6.66 m long and 0.87 m wide was built perpendicular to one of the lateral walls. Figure 4 20: Layout of Mory and Hamm experimental setup (from Mory and Hamm (1997)). One of their tests, which was extensively studied experimentally and numerically, was for a JONSWAP distribution incident wave generated by the wave maker with H sig =11.5 cm and T peak =1.69 s. JONSWAP distribution is one of the options used in SWAN. The other two distributions that the model is capable of simulating are Gaussian and Pierson-Moskowitz. Detailed measurements of wave heights,

107 84 setup and currents were made during the experiment. Wave setup was measured at 6 locations along a transect perpendicular to the shoreline. The accuracy of the measured wave setup values was 0.02 cm. Comparison of measured and simulated wave setup is shown in Figure Figure 4 21: Comparison between measured and calculated wave setup (Mory and Hamm (1997) experiment). The results compare very well with the average RMS error being 0.04 cm, which is on the order of accuracy of measured wave setup, and the average relative error between all stations being 6.25%. 4.5 Validation of Cross and Longshore Currents Based on REF/DIF-CH3D Coupling Description of Cross-shore and Longshore Currents Waves breaking on a sloping beach cause a large amount of energy to release and turn into turbulence. As they continue breaking, the wave momentum flux decreases as a result of decreasing wave height. This causes the generation of longer period waves and currents. Wave-induced currents, both long-shore and cross-shore, are the primary driving forces of bottom sediment transport.

108 85 Sun and Sheng (2002) studied the importance of wave-induced currents and other wave related effects on the general nearshore circulation. In order to account for these effects, a couple of wave-related features were incorporated in CH3D. First, a new so called surface roller term was implemented. Svendsen (1984) showed that the surface roller of breaking waves plays an important part in mass, momentum and energy balance in the surf zone and is the primary driving mechanism for the undertow. The roller represents an increase in radiation stress which according to Svendsen (1984) can be written as follows: S + xx = 0.9 h L ρgh2 b (4 14) where, S xx + is the increase of the radiation stress above the wave trough, L is the wave length, h is water depth, and H b is the breaking wave height. The second implemented term was an additional term to the vertical eddy viscosity in order to account for wave effects. Following Battjes (1975) and Vriend and Stive (1987) the wave-enhanced vertical eddy viscosity has the following form: A z = A zc + Mh (D b /ρ) 1/3 (4 15) where, A zc is the eddy viscosity related to the mean currents as computed by the equilibrium closure model implemented in the CH3D model. D b is the wave energy dissipation resulted from wave breaking and bottom friction, h is the water depth and M is a constant. The wave energy dissipation, D b, was calculated according to Battjes and Janssen (1978) as follows: D b = 1 gq b Hm 2 4 T (4 16) where Q b is the fraction of breaking waves, H m is the maximum wave height that can exist at this depth, and T is the wave period. The fraction of breaking waves was calculated from the following implicit relation:

109 86 where E tot is the total wave energy Validation 1 Q b ln Q b = 8 E tot H 2 m (4 17) The Mory and Hamm (1997) experimental data were used for validation. The experiment studied the impact of a detached breakwater on coastal morphology. A detailed description of the experimental setup can be found in Section Since diffraction is not modeled in SWAN, the wave field computed by SWAN may not be accurate in the immediate vicinity of obstacles and will certainly not be accurate in harbors or behind breakwaters. Therefore, instead of the SWAN model the REF/DIF, a nearshore wave transformation model developed by Kirby and Dalrymple (1994) was used. One of the experiments was conducted using a monochromatic incident wave generated by the wave maker with a wave height of m and a wave period of 1.69 s. The most prominent phenomenon observed during the experiment was a strong eddy behind the detached breakwater which can also be seen in Figure 4 22 that shows calculated free surface elevation along with calculated current pattern. The locations where vertical velocity profiles were measured during the experiment are depicted by letters A through N. To simulate the experiment, the REF/DIF model was used to calculate wave parameters and provide radiation stresses to drive the hydrodynamic model. After shoaling and approaching the breakwater, the waves diffracted behind the breakwater and eventually broke on the beach. Maximum current velocity for the eddy was more than 0.3 m/s which agrees well with observations. The velocity of longshore current on the open beach was on the order of 0.1 m/s or less, also in good agreement with the observation. The eddy was almost uniform over depth compared with the distinctive 3-D structure of the currents on the open beach

110 87 Free Surface Elevation (cm) cm/s 15 I Y (m) 10 F N C 5 B E H 0 A D G X (m) Figure 4 22: Calculated free surface elevation and current pattern along with the locations where vertical velocity profiles were measured (letters A through N).

111 88 due to the presence of the undertow. Overall, the current model results in this study show very good agreement with measurements qualitatively and fairly good agreement quantitatively. Many runs using various combinations of different parameters such as wave breaking parameter, κ, bottom roughness, z 0, and vertical eddy viscosity equation constant, M, were performed. Two values for κ were used, 0.55 and The range of z 0 was from cm to 0.4 cm, whereas constant M varied form to For each run the relative RMS error of the vertical velocity profiles (total 10 profiles) was calculated. The RMS error ranged from to The lowest relative RMS error (=0.190) was achieved when the following parameter values were used: κ=0.55; z 0 =0.005 cm; M= Smaller value of κ as opposed to more conventional wave breaking parameter values ( 0.8) performed better due to the reason that the REF/DIF model tended to overestimate the wave height which led to overestimation of computed radiation stresses. Comparison of measured and simulated (with the lowest RMS error) long- and cross-shore velocity profiles is shown in Figures 4 23 through Validation of Wave Height Simulated by SWAN Under Storm Conditions Any model needs to be validated. Since the focus of this study is storm surge modeling, it was necessary to test the SWAN wave model under severe storm conditions. Field Research Facility (FRF) at Duck, NC was chosen to be the area of testing. Figure 4 29 shows a diagram of the instrument setup. Waves are measured at three locations: #630 (approximately 3900 m offshore), #625 (at the tip of the pier, 570 m offshore), and #641 (240 m offshore). Two hurricane events were tested: Hurricane Floyd (September 1999) and Hurricane Bonnie (August 1998). The computational grid was set up the way

112 89 Profile A Profile B Z (cm) Z (cm) Longshore vel (cm/s) 0 Profile C Longshore vel (cm/s) 0 Profile N Z (cm) Z (cm) Longshore vel (cm/s) Longshore vel (cm/s) Figure 4 23: Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles A, B, C, and N. Profile A Profile B Z (cm) Z (cm) Cross-shore vel (cm/s) 0 Profile C Cross-shore vel (cm/s) 0 Profile N Z (cm) Z (cm) Cross-shore vel (cm/s) Cross-shore vel (cm/s) Figure 4 24: Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles A, B, C, and N.

113 90 Profile D Profile F Z (cm) Z (cm) Longshore vel (cm/s) 0 Profile I Longshore vel (cm/s) 0 Profile H Z (cm) Z (cm) Longshore vel (cm/s) Longshore vel (cm/s) Figure 4 25: Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles D, F, I, and H. Profile D Profile F Z (cm) Z (cm) Cross-shore vel (cm/s) 0 Profile I Cross-shore vel (cm/s) 0 Profile H Z (cm) Z (cm) Cross-shore vel (cm/s) Cross-shore vel (cm/s) Figure 4 26: Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles D, F, I, and H.

114 91 Profile E Profile G Z (cm) Z (cm) Longshore vel (cm/s) Longshore vel (cm/s) Figure 4 27: Simulated (red dashed line) vs. measured (green solid line) longshore velocities: profiles E and G. Profile E Profile G Z (cm) Z (cm) Cross-shore vel (cm/s) Cross-shore vel (cm/s) Figure 4 28: Simulated (red dashed line) vs. measured (green solid line) cross-shore velocities: profiles E and G. Figure 4 29: The FRF instrument setup at Duck, NC ( army.mil/frfdata.html).

115 92 that the offshore open boundary lay parallel to the shore at the location of wave gage #630. This was done for the purpose of exploiting wave parameters such as wave height, period and direction measured at this location as the open boundary conditions used in the SWAN model. Thus, the grid went approximately 3900 m offshore in the cross-shore direction and 3400 m in the alongshore direction. Bottom surveys at FRF are done every month. In order to use bathymetry as close to reality as possible, bathymetric data collected during the month of September 1999 were utilized to create the grid. Table 4 1 shows Hurricane Floyd wave/wind information used as the input for SWAN at the time when the offshore station recorded the largest wave height during the hurricane Floyd event (=4.78 m). Table 4 1: Wave parameters used to impose Hurricane Floyd (1999) boundary conditions. Parameter Value Julian Day H sig (#630) 4.78 m T peak 10.5 s Wave Direction 98 o (True North) Wind Speed 5.3 m/s Wind Direction 62 o (True North) Tide 0.58 m The tide value was added on top of the bathymetry assuming it was constant throughout the domain. Table 4 2 shows comparison between calculated and measured significant wave height at two locations along the pier. Table 4 2: Comparison of calculated and measured wave height during Hurricane Floyd (1999). Station # Measured H sig, m H sig calculated by SWAN, m Relative Error, % Since wave setup during storm events can be a significant factor affecting the mean water level, another simulation was made. First, the CH3D model was used

116 93 to calculate wave setup as a function of cross and long-shore directions. The wave setup value was then added on top of the SWL and the wave field was recalculated using the SWAN model. Comparison between calculated and measured significant wave height at the two locations along the pier taking into account wave setup is shown in Table 4 3. Table 4 3: Comparison of calculated and measured wave height during Hurricane Floyd (1999) with wave setup being accounted for. Station # Measured H sig, m H sig calculated by SWAN, m Relative Error, % The comparison shows an excellent agreement between measured and simulated wave height. The inclusion of wave setup helped reduce the relative error. Analogously, Tables 4 4 and 4 5 show Hurricane Bonnie wave/wind information and comparison of the results, respectively. Table 4 4: Wave parameters used to impose Hurricane Bonnie (1998) boundary conditions. Parameter Value Julian Day H sig (#630) 3.95 m T peak 11.1 s Wave Direction 98 o (True North) Wind Speed 20.7 m/s Wind Direction 111 o (True North) Tide 0.28 m Table 4 5: Comparison of calculated and measured wave height during Hurricane Bonnie (1998). Station # Measured H sig, m H sig calculated by SWAN, m Relative Error, % FRF bathymetric surveys collected during the month of August of 1998 were used to create a computational grid, which covered the same domain and had

117 94 the same dimensions as the one used in case of Hurricane Floyd. Wave setup was accounted for in the same fashion as before, which helped slightly reduce the relative error.

118 CHAPTER 5 VALIDATION OF THE STORM SURGE MODELING SYSTEM In this chapter the validation of the modeling system is discussed. The main criterion for model validation is how well the simulated results compare with measured data. Three hurricanes are considered: (1) Isabel (2003) in the Outer Banks, NC and Chesapeake Bay, VA area, (2) Charley (2004) in Charlotte Harbor, FL, and (3) Frances (2004) in Tampa Bay. A thorough error analysis of wind, wave and water elevation was performed. Each hurricane was simulated several times using various combinations of six model features, e.g., tide, wind, wave setup, wave enhanced surface stress, wave enhanced bottom friction, and wetting-and-drying. The goal of these simulations is to identify those processes that are dominant for each hurricane. 5.1 Hurricane Isabel (2003) Description According to NHC Hurricane Isabel is considered to be one of the most significant tropical cyclones to affect portions of northeastern North Carolina and east-central Virginia since Hurricane Hazel in 1954 and the Chesapeake-Potomac Hurricane of The hurricane reached Category 5 status on the Saffir-Simpson Hurricane Scale (see Appendix A for detailed description of the scale). It made landfall near Drum Inlet on the Outer Banks of North Carolina as a Category 2 hurricane around 17:00 UTC on September 18. Official reports state that 51 people died as a result of the storm (17 directly), with an official damage estimate of $3.37 billion. The track chart of Isabel is given in Figure 5 1. Isabel brought hurricane conditions to portions of eastern North Carolina and southeastern Virginia. According to NOAA s National Hurricane Center, the highest observed sustained wind over 95

119 96 Figure 5 1: Best track of Hurricane Isabel (courtesy of NOAA NHC). land was 35 m/s with gusts up to 44 m/s at an instrumented tower near Cape Hatteras, NC at 16:22 UTC on September 18. Another tower in Elizabeth City, NC reported 33 m/s sustained wind with a gust to 43 m/s at 18:53 UTC that day. The National Ocean Service station at Cape Hatteras reported 35 m/s sustained wind with a gust to 43 m/s before contact was lost. The Coastal Marine Automated Stations (C-MAN) at Chesapeake Light, VA and Duck, NC reported similar winds. Gloucester Point, VA reported 31 m/s sustained winds with a gust to 41 m/s at 22:00 UTC on September 18, while the Norfolk Naval Air Station reported 26 m/s sustained winds with a gust to 37 m/s at 21:00 UTC that day. The wind record from the most seriously affected areas is incomplete, as several observing stations were either destroyed or lost power as Isabel passed. The storm surge of Hurricane Isabel was 0.3 to 1.0 m higher than it was forecast, especially in the northern Chesapeake Bay and Potomac Basins. Table 5 1

120 97 provides measured storm surge crests at several sites in North Carolina, Virginia, and Maryland. Table 5 1: Measured storm tide crests at several sites in North Carolina, Virginia, and Maryland. Location Storm Tide (m, NAVD88) Wilmington, NC 0.68 Beaufort, NC 1.23 Cape Hatteras, NC 2.04 Oregon Inlet Marina, NC 1.48 Duck, NC 1.83 Money Point, VA 2.06 Chesapeake Bay Bridge, VA 1.87 Sewell s Point, VA 1.99 Scotland, VA 1.75 King s Mill, VA 1.61 Gloucester Point, VA 1.46 Colonial Beach, VA 1.66 Kiptopeke, VA 1.54 Wachapreague, VA 1.86 Richmond, VA 2.44 Washington, D.C Baltimore, MD 2.24 Annapolis, MD 1.97 Tolchester Beach, MD 2.16 Cambridge, MD 1.57 Ocean City Inlet, MD 0.80 Philadelphia, PA 1.83 Reedy Point, DE 1.75 Lewes, DE 1.30 Cape May, NJ 1.18 Burlington, NJ Computational Domain Hurricane Isabel made landfall in the South Outer Banks area near Drum Inlet, NC. Due to a particular complexity of the area, the effect of the hurricane was spread out over a vast domain including East Outer Banks, Croatan-Albemarle- Pamlico Estuary System, and Chesapeake Bay. A computational grid that covers

121 98 all the affected areas was created. The grid (Figure 5 2) contains two open boundaries: The southern open boundary starts at Wilmington, NC and goes 300 km to the east where the continental shelf ends, while the eastern open boundary extends 578 km to the north. Both open boundaries are far away from the coastline of the areas affected by the hurricane. The distance from the South Outer Banks to the southern open boundary ranges from 40 to 80 km whereas the distance from the East Outer Banks to the eastern open boundary is between 40 and 60 km. The area of the computational domain is 134,385 km 2 with a total of 548,240 computational grid cells and an average grid spacing of 500 m. 192,608 (35%) of those computational cells are water cells. The grid covers the entire Chesapeake Bay and all of its river basins including land cells for calculation of wetting and drying. The USGS National Elevation Data set ( was used for calculating topography by spatial interpolation over the land. The data have a resolution of approximately 30 m. The GEODAS bathymetric data set was used for depth interpolation over the water. Both data sets were converted to the standard NAVD88 vertical datum. The high resolution DOT shoreline was utilized to distinguish between land and water. Since the CH3D model can be applied to boundary-fitted curvilinear grids, the computational mesh was created so it accurately fitted the shoreline and small scale topographic features such as inlets and islands (see example plots in Appendix E). The grid extends inland far enough to the heights of tens of meters so that it would be impossible for the water to reach the inland grid boundaries during hurricane events Field Data A large amount of various data was collected during the passage of Hurricane Isabel over the Outer Banks and Chesapeake Bay areas. A summary of the collected tide, wind, and wave data that are used for validation of the model during Hurricane Isabel is presented in Table 5 2.

122 Figure 5 2: The Outer Banks and Chesapeake Bay grid domain for Isabel simulation. 99

123 100 Table 5 2: Tide, wind and wave stations used for validation of the model during Hurricane Isabel. Station Lat Lon Easting Northing Water Elev. Data Wind Data Wave Data Current Data ( o N) ( o W) (UTM18, m) (UTM18, m) Source Source Source Source Vert. Datum Anemometer Height (m) Depth (m) Depth (m) Cape Lookout C-MAN 9.8 Beaufort NOAA NAVD88 Kitty Hawk FRF 8.5 Duck Pier NOAA C-MAN FRF FRF NAVD Duck FRF 17.0 Chesapeake Bay NOAA NOAA Bridge NAVD88? Chesapeake Light C-MAN 43.3 Gloucester Point VIMS VIMS VIMS VIMS NAVD88? Kiptopeke NOAA NOAA NAVD88? Lewisetta NOAA NOAA NAVD88? Money Point NOAA NOAA NAVD88? HPLWS CBOS? Choptank River CBOS? North Bay CBOS?

124 101 River discharge data were obtained from USGS Chesapeake Bay River Input Monitoring Program ( html). There are a total of nine river basins that discharge into the bay. Figure 5 3 shows the location of the nine river input monitoring sites. River discharge values at these stations during the month of September, 2003 are shown in Figure 5 4. As can be seen in the figure, after Hurricane Isabel made landfall (around Julian Day 261), there was a significant increase (up to 40 times) in river discharge. Figure 5 3: Location of the nine River Input Monitoring sites (courtesy of USGS) Forcing and Boundary Conditions The major boundary condition that must be specified along the open boundaries of a coastal model domain is tide. Ideally, water surface elevation measured along open boundaries can be used to specify the boundary condition. However, due to the paucity of real time tide data, it is usual to specify tidal constituents along the open boundaries. Recently, a tidal database was created using the AD- CIRC model (Luettich et al., 1992) for the Western North Atlantic, Caribbean

125 Susquehanna Potomac James Appomattox Pamunkey Rappahannock Mattaponi Patuxent Choptank River Discharge (m 3 /s) Julian Day Isabel made landfall on Julian Day Figure 5 4: River discharge into Chesapeake Bay data during the month of September, and Gulf of Mexico (all waters west of the 60 o W Meridian and east of the North American continent). M2, S2, N2, K2, O1, K1, Q1, M4, M6 and STEADY tidal constituents are included. Seven constituents are used in the CH3D model during simulation of Hurricane Isabel. The constituents and their corresponding periods are listed in Table 5 3. Table 5 3: ADCIRC tidal constituents and their periods used in the CH3D model to simulate Hurricane Isabel. Constituent Period, hours K O Q M N S K It should be noted that although the tidal database was partially validated (except nonlinearly generated constituents M4, M6, and STEADY) by Mukai et al. (2001), there are still errors associated with the constituents. In order to improve

126 103 tidal simulation by reducing errors associated with the ADCIRC constituents in the Outer Banks/Chesapeake Bay area, an analysis of tidal constituents based on a comparison between simulated and measured water elevation was performed. The analysis was done using the IOS program (Foreman, 1977) for calculating tidal constituents based on measured or simulated time series of water elevation. A two-month period, Sep-15, 2003 through Nov-15, 2003, was chosen with two time series of measured water elevations available during that period of time at two tidal stations: Duck Pier, NC and Beaufort, NC. The Duck Pier analysis corresponds to the eastern open boundary and the Beaufort analysis corresponds to the southern open boundary. Tables 5 4 and 5 5 below show how constituent parameters (amplitude and phase) compare with each other. Table 5 4: Tidal constituent parameters at Duck Pier, NC calculated based on ADCIRC tidal constituents and IOS program. Simulated (ADCIRC) Measured (IOS) Difference (ADCIRC-IOS) Constituent Amplitude Phase Amplitude Phase Amplitude Phase cm o cm o cm o K O Q M N S K N/A N/A N/A N/A These results show that there are some discrepancies between constituents based on measured water elevation and ADCIRC constituents. These discrepancies are more pronounced at the Beaufort location. That is consistent with our preliminary simulations of Hurricane Isabel when simulated water elevation was noticeably out of phase at Beaufort. In order to improve Hurricane Isabel simulation results, the ADCIRC tidal constituents used in the CH3D model along the open boundaries were adjusted according to the amplitude and phase differences shown above. The Duck Pier

127 104 Table 5 5: Tidal constituent parameters at Beaufort, NC calculated based on AD- CIRC tidal constituents and IOS program. Simulated (ADCIRC) Measured (IOS) Difference (ADCIRC-IOS) Constituent Amplitude Phase Amplitude Phase Amplitude Phase cm o cm o cm o K O Q M N S K N/A N/A N/A N/A adjustment was applied to the entire eastern open boundary and the Beaufort adjustment was applied to the southern open boundary. As a result, the simulated tide was in much better agreement with measured tide, which was very important. Wind is a major force driving a storm surge. So when it comes to using wind in a storm surge model, it is very important to validate the wind because its accuracy will be a significant factor in the overall accuracy of model s output. Two analysis wind fields were used to drive the model: WINDGEN and WNA (refer to Table 2 1) for more information on these wind fields). Figures 5 5 through 5 6 show comparison between measured wind speed and direction at the Cape Lookout and Duck Pier stations, and wind speed and direction obtained from WINDGEN and WNA wind field data sets during Hurricane Isabel. The comparison for all wind stations within the computational domain, listed in Table 5 2, is shown in Appendix D. A thorough error analysis of WNA and WINDGEN wind speed and wind direction is shown in Table 5 6. Formulas used to calculate the errors can be found in Appendix B.

128 105 Cape Lookout Cape Lookout Measured (C-MAN) WNA WINDGEN Measured (C-MAN) WNA WINDGEN Wind Speed (m/s) Wind Direction (deg) Julian Day Julian Day Figure 5 5: WINDGEN and WNA vs. measured wind speed and direction at Cape Lookout, NC during Hurricane Isabel. Duck Pier Duck Pier Measured (C-MAN) WNA WINDGEN Measured (C-MAN) WNA WINDGEN Wind Speed (m/s) Wind Direction (deg) Julian Day Julian Day Figure 5 6: WINDGEN and WNA vs. measured wind speed and direction at Duck Pier, NC during Hurricane Isabel.

129 106 Table 5 6: Errors of WNA and WINDGEN wind speed and direction compared with measured at wind stations during Hurricane Isabel. WNA WNA WINDGEN WINDGEN speed (m/s) dir (deg) speed (m/s) dir (deg) Cape Lookout RMS error Mean absolute error Max absolute error on Julian Day Duck RMS error Mean absolute error Max absolute error on Julian Day Chesapeake Light RMS error Mean absolute error Max absolute error on Julian Day Chesapeake Bay Bridge RMS error Mean absolute error Max absolute error on Julian Day Kiptopeke RMS error Mean absolute error Max absolute error on Julian Day Gloucester Point RMS error Mean absolute error Max absolute error on Julian Day Money Point RMS error Mean absolute error Max absolute error on Julian Day HPLWS RMS error Continued on next page

130 107 Table 5 6 continued from previous page WNA WNA WINDGEN WINDGEN speed (m/s) dir (deg) speed (m/s) dir (deg) Mean absolute error Max absolute error on Julian Day Choptank River RMS error Mean absolute error Max absolute error on Julian Day Lewisetta RMS error Mean absolute error Max absolute error on Julian Day North Bay RMS error Mean absolute error Max absolute error on Julian Day Both wind data sets compare well with the data over the Outer Banks and near the mouth of the Chesapeake Bay, with the WNA wind being slightly more accurate. Inside the Chesapeake Bay, the WINDGEN wind is more accurate than WNA but the overall accuracy is much worse when compared to the wind data over the Outer Banks. Evidently, both the WNA and WINDGEN wind models do not perform well over the land and the Chesapeake Bay area as they do over the open water. This is disappointing because some of the water elevation stations lie within the area where the WNA and WINDGEN winds were not adequate, and thus it would be hard to judge the quality of the performance of the storm surge model based on the poor wind accuracy. Wave boundary conditions were obtained from the regional wave model, WAVEWATCH-III. Figures 5 7 and 5 8 show a comparison between significant wave height and peak wave period obtained from the WAVEWATCH-III model

131 108 NDBC Station NDBC Station Measured H SIG WWIII H SIG Measured T peak WWIII T peak H SIG (m) T peak (sec) Julian Day 9/1, /7, /17, /27, Julian Day 9/1, /7, /17, /27, 2003 Figure 5 7: Significant wave height and peak wave period obtained from WAVEWATCH-III compared with measured wave height at NDBC station H SIG (m) Measured H SIG WWIII H SIG NDBC Station Julian Day 9/1, /7, /17, /27, 2003 T peak (sec) Measured T peak WWIII T peak NDBC Station Julian Day 9/1, /7, /17, /27, T Figure 5 8: Significant wave height and peak wave period obtained from WAVEWATCH-III compared with measured wave height at NDBC station and measured at NDBC stations and 41002, a couple hundred kilometers off the coast of North Carolina during the month of September, It is interesting to note that the Hurricane Isabel track passed right between the two wave buoys. These figures show that the simulated and measured wave parameters are in good agreement. Though, as shown in Figure 5 8, the significant wave height is underestimated right before the wave height peak associated with Hurricane Isabel near Julian Day 260. This will have some effect on wave height calculated by the SWAN model inside our local computational domain. The effect is discussed in Section of this chapter.

132 Results: Simulated Wave One important component that contributes to a storm surge in the nearshore zone is wave setup which is created by spatial gradients of radiation stresses produced by breaking waves. The radiation stresses depend on wave parameters such as wave height, wave period, and wave direction (see Section 4.4 for wave setup validation). Thus, in order to obtain accurate estimate on wave setup, it is essential to have accurate simulation of nearshore wave fields. The SWAN wave model (see Section 2.3.5) was used to simulate wave fields during Hurricane Isabel. Three sets of wave data were available for comparison with simulated wave results. Two data sets came from the Field Research Facilities (FRF) at Duck, NC (see Figure 4 29 for the entire FRF instrument setup); and the third set was provided by Virginia Institute of Marine Science (VIMS) which measured waves at Gloucester Point, VA (see Figure 5 9 for the location of the VIMS instrument package). First, let us compare the simulated and measured wave parameters at the Figure 5 9: Location of the VIMS instrument package at Gloucester Point, VA.

133 110 FRF Waverider approximately 4 km offshore (these data will be further referred to as the Duck 630 data). The depth at the location is 17 m. The maximum significant wave height measured at the FRF Waverider buoy during Hurricane Isabel was 8.1 m, while the largest wave (crest to trough) recorded on September 18 at 19:11 UTC, was 12.1 m. The ratio of the largest wave to local water depth, 12.1/17 = 0.71, is close to the range when waves might start to break. The simulated vs. measured significant wave height, peak wave period and wave direction are shown in Figures 5 10, 5 11, and 5 12, respectively. It should be pointed out that all simulated results presented in this section were obtained using the WNA wind, since the WINDGEN wind for Hurricane Isabel was slightly less accurate. The simulated wave height matches well with the measured data with Duck Measured Calculated (SWAN) 6 H SIG (m) Julian Day Figure 5 10: Simulated significant wave height vs. measured from the FRF Waverider buoy during Hurricane Isabel. slight underestimation at the peak. There is also a phase lag right before the peak which might be due to swell waves generated outside of the computational domain which could not be properly simulated by the SWAN model because, as was discussed in Section 5.1.4, the wave height boundary conditions obtained from

134 111 the regional WAVEWATCH-III model were slightly underestimated right before Hurricane Isabel passed over the area. The consequence of such wave height underestimation will most likely result in lower than expected wave setup right before the peak of the storm. Despite that, however, the peak wave height values match well, which should result in an accurate calculated wave setup contribution to the overall peak storm surge level. The calculated peak wave period matches the measured peak period very well, so Duck Measured Calculated (SWAN) Wave Period (sec) Julian Day Figure 5 11: Simulated peak wave period vs. measured from the FRF Waverider buoy during Hurricane Isabel. does the calculated wave direction, especially during the peak of the storm when the difference was less than 5 degrees, an excellent agreement. Wave direction is an important factor in calculation of wave setup. Wave rays approaching the shore perpendicularly will cause higher wave setup as opposed to the case when they approach the shore in an oblique manner (Sheng and Alymov, 2002). Wave direction can also influence the estimation of cross-shore and longshore currents. Figure 5 13 shows results obtained from a test case simulation of the Stive and Wind (1982) laboratory experiment, with a shoreline on the

135 112 right and incident waves on the left side where H sig = m and T = 1.79 sec. The top panel plot shows the calculated wave setup and currents caused by waves approaching the shore at a 45 o angle (from south-west to north-east). The calculated wave setup and currents caused by waves approaching the shore at -45 o (from north-west to south-east) are shown in the bottom panel plot. Northerly and southerly longshore currents are formed in both plots. Since no other forcing mechanism (wind or tide) was considered in this simulation, currents are generated by wave action only through radiation stresses and wave setup. Duck Measured Calculated (SWAN) Wave Direction (deg) Julian Day Figure 5 12: Simulated wave direction vs. measured from the FRF Waverider buoy during Hurricane Isabel. Now, let us compare simulated and measured wave parameters at the end of the FRF pier approximately 600 m offshore (these data will be referred to as the Duck 625 data). The depth at this location is 8.4 m and the maximum measured significant wave height during Hurricane Isabel was 3.7 m. The simulated vs. measured significant wave height and peak wave period comparisons are shown in Figure There was no record of wave direction at that location. The trend in simulated significant wave height at the FRF pier is similar to that at the Duck

136 113 Wave Setup, cm Y (m) X (m) L A N D Y (m) X (m) L A N D Figure 5 13: A test case: wave setup and currents induced by waves approaching the shore from south-west to north-east (top panel), and from north-west to south-east (bottom panel).

137 114 Duck Pier (625) Duck Pier (625) 4 Measured Calculated (SWAN) 25 Measured Calculated (SWAN) 20 3 H SIG (m) 2 Wave Period (sec) Julian Day Julian Day Figure 5 14: Simulated significant wave height and peak wave period vs. measured from the FRF pier during Hurricane Isabel. 630 location. The peak values match well but the simulated wave height did not capture the increase of the measured data wave height approximately one day before the actual storm came in. This is more likely due to the inability of the SWAN model to account for large swell waves that are coming from outside of the computational domain. As was pointed out earlier in this section, the underestimation of wave height before the peak of the storm will result in lower than expected wave setup during that time. But due to the fact that the peak wave height values match well, the contribution of the calculated wave setup to the overall storm surge during its peak at the end of the FRF pier should be accurate. The calculated peak wave period is again in good agreement with the observed one. Now, let us compare simulated and measured wave parameters at Gloucester Point, VA (these data will be referred to as the VIMS data). The depth at the location is around 8.5 m, while the maximum measured significant wave height during Hurricane Isabel was 1.7 m. The simulated vs. measured significant wave height and peak wave period comparisons are shown in Figure There was no record of wave direction at that location. The calculated significant wave height is slightly overestimated based on comparison with measured wave height, although

138 115 VIMS VIMS 2 7 Measured Calculated (SWAN) 6 Measured Calculated (SWAN) H SIG (m) 1 Wave Period (sec) Julian Dday Julian Dday Figure 5 15: Simulated significant wave height and peak wave period vs. measured at VIMS during Hurricane Isabel. the peaks agree well. The main reason behind this is the strong WNA wind which in reality was slightly weaker (see Figure D 7 in Appendix D). The result of the slight wave height overestimation at VIMS will be a slightly higher than expected wave setup in that location. The calculated peak wave period agrees well with observed Results: Simulated Water Level In order to establish how well the modeling system performs during hurricanes when different forcing mechanisms are present, several simulations of Hurricane Isabel were carried out using WNA or WINDGEN wind and including or excluding wave effect. Simulated water elevation, using WNA and WINDGEN wind (both include wave effect), are compared with measured water elevation at seven stations in Figures 5 16 through All the other simulated versus measured water elevation results during Hurricane Isabel are shown in Appendix F. It can be noted that the peak values of the calculated water surface elevation match the measured water elevation well at Duck, Chesapeake Bay Bridge, and Gloucester Point. The simulated wind at the Outer Banks and lower Chesapeake Bay agree well with data and, as a result, the simulated water elevations agree well

139 116 Beaufort, NC 150 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 16: Comparison of simulated vs. measured water elevation at Beaufort, NC. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. Duck Pier, NC 200 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 17: Comparison of simulated vs. measured water elevation at Duck, NC. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind.

140 117 Chesapeake Bay Bridge, VA 200 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 18: Comparison of simulated vs. measured water elevation at Chesapeake Bay Bridge, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. 200 Gloucester Point, VA 250 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 19: Comparison of simulated vs. measured water elevation at Gloucester Point, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind.

141 118 Money Point, VA 250 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) 200 Water Elevation (NAVD88, cm) Julian Day Figure 5 20: Comparison of simulated vs. measured water elevation at Money Point, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. Kiptopeke, VA 150 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 21: Comparison of simulated vs. measured water elevation at Kiptopeke, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind.

142 119 Lewisetta, VA 150 Measured Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Water Elevation (NAVD88, cm) Julian Day Figure 5 22: Comparison of simulated vs. measured water elevation at Lewisetta, VA. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. with measured data. Right before the peak, a slight underestimation can be observed at all the stations. As was pointed out in the previous section, the computed wave height before the peak was underestimated due to the underestimated wave boundary conditions provided to SWAN by the regional WAVEWATCH-III model. This underestimation resulted in lower than expected wave setup right before the peak of the storm. The wave height at the peak of the storm was accurately simulated, which resulted in adequate contribution of calculated wave setup to the simulated water level at that time. Maximum simulated water elevations (including tide, surge and wave setup, and relative to NAVD88) in the Outer Banks and Chesapeake Bay during Isabel, calculated using WNA wind, are shown in Figure High water elevations can be seen not only in the area where Isabel made landfall but also throughout the entire Outer Banks and lower Chesapeake Bay. The highest value reached 4.0 m at the tip of the Outer Banks near Buxton, NC. The computed water level reached 3.2

143 120 m just south of Pamlico Sound near the upper South River, NC. In Virginia, the highest calculated water level of 3.5 m can be observed in Cobb Bay near Cheriton and Butler Creek near Brays Landing. The maximum water level in the upper James River, VA reached 3.0 m. Figure 5 24 shows the maximum wave setup elevation calculated during Isabel using WNA wind. As can be seen in this figure, wave setup reached 1.2 m and flooded parts of the chain of emergent barrier islands in the southern Outer Banks. This demonstrates that wave setup can be a significant factor and contributor to storm surge level and inundation. Figure 5 25 shows the storm surge at all seven stations with tides subtracted from the simulated water level which includes all forcing mechanisms (tide, wind, wave setup, wave enhanced surface and bottom friction). The calculated storm surge at the seven stations shows a wide range: from 1.3 m near Duck, NC to 2.0 m near Gloucester Point, VA. It should be noted that during the peak of the surge, the tide was at its high stage. In fact, at Duck, NC the tide was at its highest level of 0.45 m. By the time Isabel approached Chesapeake Bay, the tide had already passed its peak and started to recede. Plots showing comparison between the simulated storm surge elevation and measured storm surge elevation can be found in Appendix F. Throughout the model domain, it took 19 to 26 hours from the point when the surge level started to rise to the point when the surge retreated, with shorter periods occurred over the Outer Banks and longer ones in the lower Chesapeake Bay. For example, although Duck, NC and Gloucester Point, VA started to experience the incoming storm surge at approximately the same time, even after it had risen to its maximum level at Duck, the surge kept on rising at Gloucester Point.

144 Figure 5 23: Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Isabel in the Outer Banks/Chesapeake Bay using WNA wind. 121

145 122 Figure 5 24: Maximum wave setup elevation relative to NAVD88 calculated during simulation of Hurricane Isabel in the southern part of Outer Banks using WNA wind. Surge Elevation (cm) 200 Beaufort Duck Chesapeake Bay Bridge Gloucester Point 150 Money Point Kiptopeke Lewisetta Julian Day Figure 5 25: Simulated storm surge (water level minus tide) at the seven stations throughout the Outer Banks/Chesapeake Bay using WNA wind.

146 Error Analysis Error analysis is a good way of estimating how well the calculated water elevation compares with water level measured at tide stations throughout the computational domain. It has to be pointed out that measured water elevation consists of two parts: tide and storm surge itself. Theoretically, the storm surge part can also be split into two constituents, one due to wind action and the other due to wave setup. But practically it is impossible to filter out the wave setup from the storm surge and therefore it would be reasonable if we left the storm surge elevation intact. Tide, on the other hand, can be filtered out using the Doodson and Warburg (1941) 39-hourly average tidal filter as described by Groves (1955). An error between measured and calculated water elevation can be attributed to either tide or storm surge or their combination. In order to estimate the contribution of each source of error, a pure tide simulation was performed and its results were compared with tidal elevation which was filtered out from measured water elevation using Doodson and Warburg (1941) 39-hourly average tidal filter. Pure tide simulation means that the only boundary force imposed during that simulation was tide and all other forcing mechanisms such as wind and wave were not considered. In order to weigh the effect of each component involved in the non-linear interaction between the surge, tide, wind, and wave, several simulations were made by including different component combinations. Turning the wetting-and-drying feature on and off was an option as well. Table 5 7 specifies the six specific features included in five simulations.

147 124 Table 5 7: A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation). Factors Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Tide Wind Wave Setup - Wave Enhanced Surface Stress Wave Enhanced Bottom Stress Wetting-and-Drying - Table 5 8 shows the RMS, Mean Absolute, and Maximum Absolute errors (see Appendix B for definitions) of calculated water elevation during Hurricane Isabel. Errors of peak values (measured peak elevation minus simulated peak elevation) and timing errors (the time when measured peak elevation occurred minus the time when simulated peak elevation occurred) are also shown. A separate column in the table displays the errors attributed to pure tide. Tidal range is also shown for each station. 1 Donelan et al. (1993) formulation was used 2 Grant and Madsen (1979) formulation was used 3 Sheng and Villaret (1989) formulation was used

148 125 Table 5 8: Errors of water elevation at tide stations during Hurricane Isabel. The model results are data were compared every 15 minutes. WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Station: Beaufort (depth = 4.0 m; tidal range = 115 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Station: Duck (depth = 5.8 m; tidal range = 140 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Station: Chesapeake Bay Bridge (depth = 10.6 m; tidal range = 110 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Continued on next page

149 126 Table 5 8 continued from previous page WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Station: Gloucester Point (depth = 8.5 m; tidal range = 80) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Station: Money Point (depth = 13.1 m; tidal range = 100 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Station: Lewisetta (depth = 3.0 m; tidal range = 45 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Station: Kiptopeke (depth = 2.4 m; tidal range = 95 cm) RMS Error (cm) Mean Abs Error (cm) Continued on next page

150 127 Table 5 8 continued from previous page WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak (cm) Timing at Peak (min) Avg RMS Error (cm) Avg Err. at Peak (cm) Avg Timing Error (min)

151 128 Based on this error analysis, especially on the average RMS errors and average absolute errors at the peak water elevation, it can be concluded that the WNA wind produced slightly better surge simulation results than the WINDGEN wind. This is consistent with the overall analysis of wind data shown in Table 5 6, which justifies the importance of wind accuracy: more accurate wind produces more accurate water elevation results. The accuracy of the simulated water elevation depended on the accurate simulation of tide which was accurate across the Outer Banks up to the mouth of the Chesapeake Bay, with the average RMS error of approximately 4 cm. Inside the bay, the accuracy of the calculated tide worsened, with the average RMS error increasing to 6 cm. So did the accuracy of the simulated water elevation, which was also accompanied with the worse accuracy of the WNA wind inside the Chesapeake Bay as opposed to that over the Outer Banks. Overall, Simulation 3 produced better results in terms of smaller RMS errors and better comparison with measured water surface elevation at its peak. Water level calculated using wave enhanced bottom friction based on the Sheng and Villaret (1989) formulation (Simulation 4 b ) was slightly worse. Simulation 4 a which accounted for wave enhanced bottom friction (Grant and Madsen (1979) formulation) was even worse due to overestimated bottom friction. Simulation 5 which did not account for wetting-and-drying improved the results inside Chesapeake Bay, but the only reason for this improvement was that the calculated water elevation was significantly underestimated there, so when the flooding was turned off, the water elevation was able to gain cm more, thus making it look better. The timing errors are very small (based on Simulation 4 b using WNA wind, 0 to 16 min) for the three Outer Bank stations (Beaufort, Duck, and Chesapeake Bay Bridge). For the other four stations inside Chesapeake Bay the errors are much

152 129 larger (45 min to almost 3 hours). This is consistent with the fact that the WNA wind was more accurate in the Outer Banks area compared with the wind in the Chesapeake Bay area. Also, more accurate over the Outer Banks area WNA wind produced smaller timing errors compared with less accurate WINDGEN wind in that area. And more accurate over the Chesapeake Bay WINDGEN wind produced smaller timing errors compared with less accurate WNA wind in that area. Table 5 9 shows peak water elevation values calculated during these simulations along with the measured value. The table also displays percent increase or decrease relative to the simulation in the previous simulation column (e.g., at Gloucester Point, the Simulation 2 value 3% relative to the Simulation 1 value, and the Simulation 4 a and 4 b values 12% and 2% relative to the Simulation 3 value, respectively). Percent value for each station was normalized by the measured value at this station. Including wave and radiation stress terms (Simulation 2) increased the calculated water level by 1-17%. More significant wave setup effect was observed along the Outer Banks and less significant inside Chesapeake Bay. This is in accordance with the wave height distribution over the area: larger breaking waves resulted in higher wave setup. In the Chesapeake Bay, waves were not as high as near the Outer Banks, thus the wave setup was lower. Adding wave enhanced surface stress helped further increase (in most cases) the computed water elevation by 5-18%. At Beaufort, the increase was not very significant (2%), and at Kiptopeke, a 1% decrease was observed. This happened because during the peak of the storm, the wind was blowing primarily offshore. Waves increased the stress thus pushing more water offshore and creating a slight set-down. Accounting for wave enhanced bottom friction using the Grant and Madsen (1979) model decreased the calculated water elevation by 1-14%. The importance of the wave enhanced bottom friction was more significant inside

153 130 shallower Chesapeake Bay. It is known that the Grant and Madsen (1979) model tends to overestimate the wave enhanced bottom stress (Sheng, 1982), although there was insufficient data during Hurricane Isabel to confirm this. To improve the uncertainty of the wave-enhanced bottom stress, a one-dimensional turbulent boundary layer model with TKE closure (Sheng and Villaret, 1989) was used to develop a look-up table (see Section ) for calculating wave enhanced bottom stress in a wide range of combined wave-current boundary layer flows. When wetting-and-drying scheme was not activated during the calculation, the peak water level value, in general, grew an extra 2-20%, although the elevation actually dropped near Duck. After analyzing the flood map obtained during Simulation 4 b when wetting-and-drying was activated, it turned out that this part of the grid had high enough topographic elevation so it did not get flooded during Isabel. Therefore, when wetting-and-drying was disabled, the calculated water elevation would not be affected much anyway. Why did the elevation actually drop? It happened because when the CH3D model runs in no wetting-and-drying mode, a minimum depth has to be specified. During Simulation 5, this depth was set to 10 m, meaning that any grid cell whose depth was less than 10 m was forced to be 10 m. Normally, the minimum depth should be set as low as possible to reduce the number of cells to be affected by the cut-off depth. Picking a small value might cause the model to become unstable, especially under severe wind conditions, and blow-up which did happen when the minimum depth was set to less than 10 m. The actual depth at Duck is less than 6 m, so during Simulation 5, it was set to 10 m. Such deepening of the bathymetry caused a slight decrease in the calculated water surface elevation. This case brings out a problem related to storm surge models without wetting-and-drying. Most such models, including ADCIRC, have a cut-off depth. This may result in inaccurate storm surge simulations.

154 131 Table 5 9: Measured peak water elevations at seven stations during Hurricane Isabel using WNA wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Meas. cm cm cm cm cm cm cm Beaufort % 72 2% 66 6% 67 5% 81 13% 107 Duck % 172 6% 171 1% 171 1% 166 3% 171 Ches. Bay Br % 148 8% 141 4% 147 1% 149 1% 168 Gloucester Pt % % % 205 2% % 199 Money Point % 172 6% 160 6% 168 2% 178 5% 192 Kiptopeke % 83 1% 72 8% 80 2% 99 14% 138 Lewisetta % 89 5% 71 14% 85 3% 96 8% 131

155 132 Table 5 10: Calculated peak storm surge (with tides subtracted) at seven stations during Hurricane Isabel using WNA wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Meas. cm cm cm cm cm cm cm Beaufort % 38 5% 39 1% 39 1% 38 1% 83 Duck % 131 8% 131 0% 131 0% 126 4% 131 Ches. Bay Br % 118 5% 115 2% 117 1% 126 6% 142 Gloucester Pt % % % 195 5% 200 3% 170 Money Point % 133 1% 127 4% 130 2% 146 9% 171 Kiptopeke % 98 2% 88 9% 94 4% % 108 Lewisetta % 95 5% 76 16% 91 3% % 118

156 133 Table 5 10 shows peak storm surge values (tide was subtracted from water elevation) computed during these simulations. Percent increase or decrease was calculated the same way it was calculated in the previous table. The results demonstrate that including wave setup increased and improved the calculated surge, especially at Beaufort and Duck. Its effect ranged between 3-18%. Wave-enhanced wind also made the computed surge look better by increasing the values by 1-16%. The wave-enhanced bottom stress calculated using the Grant and Madsen (1979) model, mostly made the surge look worse by decreasing the peak surge values by 0-16%. Wave enhanced bottom stress calculated using the Sheng and Villaret (1989) formulation (Simulation 4 b ) decreased the surge less dramatically, by 0-5%. When the wetting-and-drying feature was inactive, the surge level inside Chesapeake Bay grew by 3-14%. Another interesting fact can be deduced from comparing water elevation calculated by linear superposition of separately simulated tide, wave setup, and surge with water elevation calculated through the dynamic coupling. Figure 5 26 shows the individually calculated tide, wave setup, and surge, and their linear superposition at Duck. Figure 5 27 shows how the linearly coupled water elevation at Duck stacks up against the water elevation which was calculated through dynamic coupling of the circulation and wave models. The measured water elevation is shown as well. Similarly, Figure 5 28 shows how linearly and dynamically coupled results compare at Gloucester Point. As can be seen from these figures, at the peak the linearly coupled water elevation is only slightly higher than the dynamically coupled one. Does this mean that the dynamic coupling in storm surge modeling does not bring in a significant improvement? Not necessarily. This might be the case when one is not concerned about flooding, otherwise the major difference between linear and dynamic coupling can be observed over inundated areas. Indeed, Figures 5 29 through 5 31 show

157 Duck, NC Tide Wave Setup Surge Linearly Coupled (Tide + Wave Setup + Surge) Water Elevation (NAVD88, cm) Julian Day Figure 5 26: Separately simulated tide, wave setup, and surge, and their linear superposition at Duck. 200 Duck, NC Measured Linearly Coupled (Tide + Wave Setup + Surge) Dynamically Coupled Water Elevation (NAVD88, cm) Julian Day Figure 5 27: Linearly coupled water elevation vs. water elevation calculated through dynamic coupling at Duck, NC.

158 Measured Linearly Coupled (Tide + Wave Setup + Surge) Dynamically Coupled 200 Gloucester Point, VA Water Elevation (NAVD88, cm) Julian Day Figure 5 28: Linearly coupled water elevation vs. water elevation calculated through dynamic coupling at Duck, NC. water elevation calculated linearly and dynamically at three inland locations that were flooded during Isabel: 1) south of Pamlico Sound near the South River, 2) on one of the emergent islands of the Outer Banks, and 3) near Gloucester in Chesapeake Bay. The topographic elevations (relative to NAVD88) at the three locations are 1.23 m, 0.77 m, and 0.87 m, respectively. As can be seen from the figures, at the beginning all three locations are dry. Then, in the middle of the storm, they get inundated and after the storm passes they get dry again. The difference between water elevations calculated linearly and dynamically is significant during the peak of the storm. The reason behind that is that when tide and wave setup were calculated separately, their elevation was not high enough to flood those locations. Thus, only separately calculated surge was able to flood those areas but it was significantly lower than the one calculated through the dynamic coupling. Also, when coupled linearly, the location near South River was flooded 10 hours after the area was flooded using the dynamic coupling.

159 136 Near South River, NC Linearly Coupled (Tide + Wave Setup + Surge) Dynamically Coupled 300 Water Elevation (NAVD88, cm) Julian Day Figure 5 29: Linearly coupled water elevation vs. water elevation calculated through dynamic coupling near the South River, NC. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again. Outer Banks, NC 200 Linearly Coupled (Tide + Wave Setup + Surge) Dynamically Coupled Water Elevation (NAVD88, cm) Julian Day Figure 5 30: Linearly coupled water elevation vs. water elevation calculated through dynamic coupling on one of the emergent islands of the Outer Banks, NC. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again.

160 137 Near Gloucester, VA Linearly Coupled (Tide + Wave Setup + Surge) Dynamically Coupled 250 Water Elevation (NAVD88, cm) Julian Day Figure 5 31: Linearly coupled water elevation vs. water elevation calculated through dynamic coupling near Gloucester, VA. The location is initially dry and gets flooded during Isabel. After the surge recedes, it becomes dry again Results: Simulated Flood Level A robust wetting-and-drying scheme incorporated in the modeling system allows to estimate inundation caused by hurricanes. Figures 5 32 through 5 37 show the highest simulated inundation caused by Hurricane Isabel during its passage over the Outer Banks and Chesapeake Bay using WNA wind. The plots also identify the time when the highest flood level occurred. Similarly, Figures 5 35 through 5 37 show the maximum simulated inundation using WINDGEN wind. Simulation 3 (see Table 5 7) using WNA wind produced the best comparison between measured and simulated water elevations at all the water elevation data stations throughout the computational domain. Therefore, this simulation was considered as the base simulation for estimating the amount of inundation caused by Isabel. The flooded area affected 7675 km 2 of land, mostly the surroundings of the Croatan-Albemarle-Pamlico Estuary System.

161 Figure 5 32: Maximum simulated inundation in the southern part of the Outer Banks during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 138

162 Figure 5 33: Maximum simulated inundation in the eastern part of the Outer Banks during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 139

163 Figure 5 34: Maximum simulated inundation in the Chesapeake Bay during Hurricane Isabel using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 140

164 Figure 5 35: Maximum simulated inundation in the southern part of the Outer Banks during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 141

165 Figure 5 36: Maximum simulated inundation in the eastern part of the Outer Banks during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 142

166 Figure 5 37: Maximum simulated inundation in the Chesapeake Bay during Hurricane Isabel using WINDGEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 143

167 144 There was no direct inundation data available against which to compare our flood maps. The only data that could be found to compare the calculated inundated areas are air photos taken before and after Isabel passed over the domain. Figures 5 38 and 5 39 show pre-storm and post-storm air photos taken at two locations, in the southern and eastern Outer Banks, respectively (see Figure 5 2 for location information). By examining the pre-storm and post-storm photos, it can be seen that these areas were subject to extensive inundation during Isabel. The bottom panels in the figures demonstrate close-ups of our computed inundation maps which also display the presence of water over the land. This validation cannot be considered complete and is rather qualitative because the actual measured flood level is unknown but, despite that, it shows a good potential of the storm surge modeling system for predicting inundation.

168 Figure 5 38: Pre-storm (top) and post-storm (middle) air photos taken in the southern Outer Banks (courtesy of USGS, hurricanes/) showing that the area was inundated during the time when Isabel passed over it. A close-up of our calculated flood map (bottom) verifies the presence of water over the land. 145

169 Figure 5 39: Pre-storm (top) and post-storm (middle) air photos taken in the eastern Outer Banks (courtesy of USGS, showing that the area was inundated during the time when Isabel passed over it. A close-up of our calculated flood map (bottom) verifies the presence of water over the land. 146

170 Results: Simulated Currents As a three-dimensional model, CH3D is capable of calculating horizontal currents throughout the water column. Under relatively calm conditions, currents are caused by the action of tide near the shoreline plus density stratification in the horizontal and vertical directions due to salinity and water temperature variation near inlets and in estuaries. During storm events wind and wave contribute to the currents significantly, mostly in the upper layers of the water column. During the passage of Hurricane Isabel, current profiles were measured at two locations. The first location is near Kitty Hawk, NC (see Figure 5 40) approximately 3 km offshore in 8.8 m depth. This location is away from inlets and any other fresh water sources. Therefore, currents there are mostly driven by tide, wind and wave. The second location is inside Chesapeake Bay near Gloucester Point, VA (see Figure 5 41) where currents are affected not only by the action of tide but salinity stratification as well. The depth at the location is 8.5 m. Figure 5 40: Location of Kitty Hawk, NC where currents were measured. It is of interest to compare measured currents to those calculated by our storm surge modeling system in general and the CH3D model in particular, primarily

171 148 Figure 5 41: Location of Gloucester Point, VA where currents were measured. to examine how robust the current-wave coupling algorithms in CH3D are. The coupling accounts for wave setup through either depth uniform (Longuet-Higgins and Stewart, 1964) or vertically varying (Mellor, 2003) radiation stresses, waveenhanced surface stress and wave-induced bottom friction. The currents were classified as the South to North current and West to East current. The latter can be looked at as the along-channel current at Gloucester Point and as the cross-shore current near Kitty Hawk (although not exactly due to the shoreline orientation in that area) and the former can be considered, again to some degree, as the longshore current near Kitty Hawk. Eight vertical layers were used in the CH3D model to simulate currents during Isabel. Comparison between measured and calculated South to North and West to East currents at Kitty Hawk is shown in Figures 5 42 and The Gloucester Point comparison is shown in Figures 5 44 and Simulated currents at Kitty Hawk agree well with measured data, although at the peak of the storm the West to East simulated current is overestimated. Simulated currents at Gloucester Point are in worse agreement with measured

172 149 Figure 5 42: Measured (left) and simulated (right) South to North current at Kitty Hawk, NC during Hurricane Isabel. Figure 5 43: Measured (left) and simulated (right) West to East current at Kitty Hawk, NC during Hurricane Isabel. data, especially in the West-East direction. This is partially due to the close proximity of the current meter to the shoreline. Near the shoreline, flow simulated by the model closely follows the shoreline orientation. In order to effectively account for horizontal diffusion, there has to be enough grid cells between the instrument location and the shoreline. Refining the grid in the area helped increase the accuracy of simulated currents but it was not enough to achieve as accurate agreement with measured data as it was achieved at Kitty Hawk.

173 150 Figure 5 44: Measured (left) and simulated (right) South to North current at Gloucester Point, VA during Hurricane Isabel. Figure 5 45: Measured (left) and simulated (right) West to East current at Gloucester Point, VA during Hurricane Isabel.

174 Hurricane Charley (2004) Description According to NHC Hurricane Charley was the third named storm and the second hurricane of the 2004 Atlantic hurricane season. It caused major damage to parts of Cuba as it crossed the island as a Category 2 hurricane, and strengthened further before reaching the U.S. It made landfall west of Fort Myers, Florida, as a Category 4 hurricane on the Saffir-Simpson Hurricane Scale. It was the strongest hurricane to strike the area since Hurricane Donna in After moving northward along the East Coast of the U.S., it eventually dissipated near Cape Cod. The track of Charley is given in Figure The storm moved rapidly across the Caribbean, Figure 5 46: Best track of Hurricane Charley (courtesy of NOAA NHC). and reached hurricane strength on August 11, 150 km south of Kingston, Jamaica. Hurricane Charley then passed just south of Jamaica, and the next morning passed between Grand Cayman and Little Cayman. On the night of August 12,

175 152 Charley passed just east of the Isle of Youth, then over mainland Cuba, just west of downtown Havana. After passing over Cuba, Charley crossed the Straits of Florida. Around 13:00 UTC, Charley passed over the Dry Tortugas. Tropical storm force winds of 41 mph (65 km/h) were recorded at Key West International Airport, 115 km east. The course Charley took at this time caught many by surprise. Instead of following the predicted track through the Tampa-St. Petersburg area, Charley made an abrupt turn to the northeast, heading for Fort Myers and Sanibel Island. Nevertheless, this track was well within the official forecast s margin of error. At the same time as it turned, Charley rapidly strengthened, going from a Category 2 storm at 110 mph (170 km/h) to a Category 4 storm at 145 mph (235 km/h) in only three hours. This rapid intensification was outside the official forecast, which called for only a slight strengthening before landfall. The change in strength was so drastic that the NHC issued a special hurricane advisory outside of its normal schedule. It is possible that the winds were even stronger at landfall, possibly at or near Category 5 strength (155 mph or 250 km/h), based on later images and assessments. Charley became the second tropical storm to strike Florida in 24 hours when Tropical Storm Bonnie struck the Florida panhandle in Apalachicola at 14:00 UTC on August 12, 22 hours before Charley went over the Dry Tortugas. This made 2004 the first year two named storms have struck the same state in the same 24-hour period since Mainland landfall occurred only 29 hours apart. On August 13 at 19:45 UTC, Charley made landfall at Cayo Costa, north of Fort Myers. Charley moved inland near Charlotte Harbor shortly afterwards. Near midnight local time (August 14, 04:00 UTC), Charley began moving back over water, exiting Florida near Daytona Beach. It returned to land around 15:00 UTC near North Myrtle Beach, SC still retaining hurricane strength. Charley

176 153 continued to run off and on land up the East Coast of the United States, and dissipated near Cape Cod around mid-day on August 15. Charley s strongest gusts were measured at 180 mph (290 km/h) at Punta Gorda. One death in Jamaica, four deaths in Cuba, and 10 deaths in the United States were directly attributed to Charley. Property damage from Charley was estimated by the NHC at $14 billion. This makes Charley the second most costly hurricane in American history, behind Hurricane Andrew s $26 billion in 1992, and above Hurricane Hugo s $7 billion ($9.4 billion in 2000 dollars) in Computational Domain The computational grid used to simulate Hurricane Charley (see Figure 5 47) contains three open boundaries. The southern open boundary starts just north of Naples, FL and extends 60 km offshore. The northern open boundary starts near Venice, FL and stretches 50 km offshore. The length of the western open boundary is 107 km. The area of the computational domain is approximately 10,350 km 2 with the total number of computational grid cells of 22, ,127 (45%) of those computational cells are water cells. Grid spacing varies from 2 km near the offshore open boundary to 200 m within San Carlos Bay and Estero Bay. The grid covers the entire Charlotte Harbor with all of its river basins such as Caloosahatchee, Peace, and Myakka rivers. The grid contains land cells to account for wetting-anddrying. The USGS National Elevation Data set ( was used for topographic interpolation over the land. The horizontal resolution of the topographic data is approximately 30 m. The GEODAS bathymetric data set was used for depth interpolation over the water. Both data sets were converted to the standard NAVD88 vertical datum. A high resolution DOT shoreline was utilized to distinguish between land and water. Since the CH3D model is capable of using curvilinear grids, the computational mesh was created so it precisely fitted the shoreline and resolved small scale topographic features such as inlets and

177 154 islands. The grid extends far inland so that it would be practically impossible for the water to reach the inland grid boundaries during coastal inundation. Figure 5 47: The Charlotte Harbor grid domain Data During the passage of Hurricane Charley across the Charlotte Harbor area, water level was recorded at four locations: Ft Myers, which is located on the Caloosahatchee river; Big Carlos Pass located by the entrance to Estero Bay in the southern part of the computational domain; and two stations inside Estero Bay, one in the northern part of the bay and the other one in the southern part. Both, wind speed and direction were measured at two stations: one station at Ft Myers and another one located at Naples. The Naples station is located approximately 10 km south of our model domain s southern open boundary. Such

178 155 proximity allowed us to make use of the wind data for comparison with WNA and WINDGEN wind. Figures 5 48 through 5 51 demonstrate a comparison analysis between measured wind speed and direction at the two wind stations vs. those obtained using WNA and WINDGEN wind data. The Ft Myers station was inoperative for 2.5 hours during the time when Charley was passing over the area. The wind direction measured at Ft Myers was almost constant all the time which was a little strange. The same trend was observed after analyzing the data over a 3-month period prior to Charley. Since wind direction measured at Naples was in good agreement with WNA and WINDGEN wind direction, wind direction data at Ft Myers were considered erroneous and were not used. The WINDGEN wind at the two stations was stronger than the WNA wind, though it was hard to judge which one of the two was better because the station at Ft Myers broke down before the wind reached its maximum and the Naples station was a little too far from the center of the hurricane. Ft Myers 25 WNA WINDGEN Measured 20 Wind Speed (m/s) Julian Day Figure 5 48: WMeasured wind speed vs. WINDGEN and WNA wind data at Ft Myers, FL during Hurricane Charley.

179 156 Ft Myers 350 WNA WINDGEN Measured 300 Wind Direction (deg) Julian Day Figure 5 49: Measured wind direction vs. WINDGEN and WNA wind data at Ft Myers, FL during Hurricane Charley. 25 WNA WINDGEN Measured Naples 20 Wind Speed (m/s) Julian Day Figure 5 50: Measured wind speed vs. WINDGEN and WNA wind data at Naples, FL during Hurricane Charley.

180 157 Naples 350 WNA WINDGEN Measured 300 Wind Direction (deg) Julian Day Figure 5 51: Measured wind direction vs. WINDGEN and WNA wind data at Naples, FL during Hurricane Charley Results: Simulated Water Level In order to establish how well the modeling system performs during hurricanes when different forcing mechanisms are present, several simulations of Hurricane Charley were carried out using WNA or WINDGEN wind and including or excluding wave effects. Simulated water elevation, using WNA and WINDGEN wind (both include wave effect), are compared with measured water elevation at four stations in Figures 5 52 through All the other simulated versus measured water elevation results during Hurricane Charley are shown in Appendix G. As can be seen in the figures, simulated water elevation using WNA wind was significantly underestimated at all four locations. In contrast to these results, simulated water elevation using WINDGEN wind looked much better, matching the surge peak very well at Big Carlos Pass, slightly overestimating the surge peak at both locations in Estero Bay, and underestimating the peak surge value at Ft Myers. Such discrepancy in the simulated water elevations using the two winds is a result of large difference between WNA and WINDGEN wind fields during the

181 158 Big Carlos Pass Simulation (WNA wind) Simulation (WINDGEN wind) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 52: Comparison of simulated vs. measured water elevation at Big Carlos Pass. Two simulated results are shown: one using WNA wind and another using WINDGEN wind. Estero Bay 1 Simulation (WNA wind) Simulation (WINDGEN wind) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 53: Comparison of simulated vs. measured water elevation at Estero Bay, location 1. Two simulated results are shown: one using WNA wind and another using WINDGEN wind.

182 159 Estero Bay 2 Simulation (WNA wind) Simulation (WINDGEN wind) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 54: Comparison of simulated vs. measured water elevation at Estero Bay, location 2. Two simulated results are shown: one using WNA wind and another using WINDGEN wind. Ft Myers 100 Simulation (WNA wind) Simulation (WINDGEN wind) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 55: Comparison of simulated vs. measured water elevation at Ft Myers. Two simulated results are shown: one using WNA wind and another using WIND- GEN wind.

183 160 time when the strongest winds were experienced in the area. In order to investigate this problem, wind snapshots in the Estero Bay area were taken at three instants shown in Figure 5 56: (1) before the storm peak (Aug-13 16:50 UTC, Julian Day= ), (2) right at the peak (Aug-13 20:40 UTC, Julian Day= ), and (3) after the storm peak (Aug-14 01:20 UTC, Julian Day= ). Figure 5 56 shows the measured and simulated (using WNA and WINDGEN wind) water surface elevation at Estero Bay location 1. It also specifies the times when the wind snapshots were taken. From Figures 5 57 through 5 62 that depict wind speed and Estero Bay Simulated (WNA wind) Simulated (WINDGEN wind) Measured 100 Water Elevation (cm) Julian Day Figure 5 56: Simulated vs. measured water elevation at Estero Bay, location 1. Dashed lines specify the three time instants when wind snapshots were taken. direction along with total water depth contours in the Estero Bay area, the most significant difference between WNA and WINDGEN wind fields can be found in snapshot 2, which was taken at the peak of the storm surge in Estero Bay. There is an evident discrepancy in wind direction which is responsible for the significant difference in water elevation. Now the question is: How confident are we in picking WINDGEN wind over WNA wind even though water elevation simulated using WINDGEN wind

184 161 Total Depth, cm Y 2.915E E E E X Figure 5 57: WNA wind field snapshot 1 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area. Total Depth, cm Y 2.915E E E E X Figure 5 58: WINDGEN wind field snapshot 1 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area.

185 162 Total Depth, cm Y 2.915E E E E X Figure 5 59: WNA wind field snapshot 2 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area. Total Depth, cm Y 2.915E E E E X Figure 5 60: WINDGEN wind field snapshot 2 (Aug-13 20:55, Julian Day= ) along with total depth contours in the Estero Bay area.

186 163 Total Depth, cm Y 2.915E E E E X Figure 5 61: WNA wind field snapshot 3 (Aug-14 01:20, Julian Day= ) along with total depth contours in the Estero Bay area. Total Depth, cm Y 2.915E E E E X Figure 5 62: WINDGEN wind field snapshot 3 (Aug-14 01:20, Julian Day= ) along with total depth contours in the Estero Bay area.

187 164 compares with measured water elevation much better than that calculated using WNA wind. Figure 5 63 shows a comparison between WNA and WINDGEN wind direction vs. actual wind direction measured at Naples, FL which is approximately 30 km south of Estero Bay. As can be seen from the figure, at the time of high surge (when snapshot 2 was taken), WINDGEN wind direction compares very well with the measured wind direction and the WNA wind direction is off by approximately 30 degrees. This leads to the conclusion that WINDGEN wind field is more reliable when it mattered most (i.e. when the storm was at its peak) and the significant underestimation of storm surge calculated using WNA wind is due to the incorrect wind information provided to the modeling system by the WNA wind. This should not be a surprise because WNA wind is not known to resolve the hurricane wind field accurately. Maximum water elevation relative to NAVD88 Naples 350 Wind Direction (deg) WNA WINDGEN Measured Julian Day Figure 5 63: WNA and WINDGEN wind direction vs. measured wind direction at Naples, FL. At the peak of the storm (denoted by number 2), WINDGEN wind direction matches very well with the measured wind direction and WNA wind direction is off by approximately 30 degrees. (includes tide, surge and wave setup) calculated during simulation of Hurricane Charley in Charlotte Harbor using WINDGEN wind is shown in Figure As

188 165 can be seen in the figure, the maximum values reached 1.9 m near Estero Bay causing extensive inundation in that area. Figure 5 65 shows simulated storm surge at all four stations which was obtained by subtracting simulated tide (no other forcing mechanism was included) from simulated water levels which include all forcing mechanisms (tide, wind, wave setup, wave enhanced surface and bottom friction). The results show that the calculated storm surge within Estero Bay was around 1.2 m. It is worth noting that during the peak of the storm, the tide was in its outgoing stage at a level of approximately -0.1 m. Therefore, if the storm were to have occurred at high tide the surge level would have been 0.5 to 0.6 m higher. It took approximately 11 hours from the point when the surge level started to rise to the point when the surge receded. For comparison, it took nearly 30 hours for storm surge caused by Hurricane Frances in the Tampa Bay area to recede. Charley was a fast moving hurricane whereas Frances was moving very slowly.

189 Figure 5 64: Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Charley in Charlotte Harbor using WINDGEN wind. 166

190 167 Ft Myers Big Carlos Pass Estero Bay 1 Estero Bay Surge Elevation (cm) Julian Day Figure 5 65: Simulated storm surge (water level minus tide) at the four stations using WINDGEN wind.

191 Error Analysis As was discussed in section 5.1.7, error analysis is a good way of comparing calculated water elevation to measured water level. In that section it was also pointed out that an error between measured and calculated water elevation can be attributed to either tide or storm surge or their combination. An estimation of the contribution of tide to the total error was done by performing a pure tide simulation and comparing its results with tidal elevation which was filtered out from measured water elevation using Doodson and Warburg (1941) 39-hourly average tidal filter. In order to weigh the effect of each component involved in the non-linear interaction between the surge, tide, wind, and wave, several simulations were made by including different component combinations. Turning the wetting-and-drying feature on and off was an option as well. Table 5 11 specifies which simulation had what features. Table 5 11: A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation). Factors Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Tide Wind Wave Setup - Wave Enhanced Surface Stress Wave Enhanced Bottom Stress Wetting-and-Drying - 1 Donelan et al. (1993) formulation was used 2 Grant and Madsen (1979) formulation was used 3 Sheng and Villaret (1989) formulation was used

192 169 Table 5 12 shows the RMS, Mean Absolute, and Maximum Absolute errors of calculated water elevation during Hurricane Charley (see Appendix B for formulas used to calculate the errors). Errors of peak values (measured peak elevation minus simulated peak elevation) and timing errors (time when measured peak elevation occurred minus time when simulated peak elevation occurred) are also shown. A separate column in the table displays the errors attributed to pure tide. Tidal range is also shown for each station.

193 170 Table 5 12: Errors of water elevation at tide stations during Hurricane Charley. WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Ft Myears (depth = 3.2 m; tidal range = 50 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) - 99 Error at Peak Timing at Peak (min) Big Carlos Pass (depth = 3.8 m; tidal range = 90 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak Timing at Peak (min) Estero Bay 1 (depth = 2.8 m; tidal range = 105 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak Timing at Peak (min) Estero Bay 2 (depth = 2.2 m; tidal range = 110) Continued on next page

194 171 Table 5 12 continued from previous page WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at the Peak Timing at Peak (min) Avg RMS Error (cm) Avg Err. at Peak (cm) Avg Timing Error (min)

195 172 Based on RMS errors and average absolute errors shown in the table above, it can be concluded that the WINDGEN wind gave significantly more accurate surge elevations than the WNA wind. The peak water elevations calculated using WNA wind were not very well pronounced, therefore errors at the peak and timing errors at the peak were not calculated and are not shown in Table The accuracy of the simulated tide was not very good, with the average RMS error of 9 to 10 cm, which might be due to a significant contribution of non-linear tidal constituents which were not included in the boundary condition of this model simulation. The simulated water elevation at Ft Myers was significantly underestimated, whereas at the other three stations the results looked very good. It is hard to say what caused the Ft Myers elevation to be so low. The station is located on the Caloosahatchee River, approximately 25 km inland. The wind station located there broke down before the storm reached its maximum strength in the area, thus the accuracy of the wind data used in the model near Ft Myers is uncertain. Overall, excluding the Ft Myers station, Simulation 4 b produced better results in terms of smaller RMS errors and better comparison with measured water surface elevation at its peak. Simulation 5, when the wetting-and-drying feature was disabled, significantly worsen the results for the three stations within Estero Bay. On the other hand, Simulation 5 significantly improved the computed water level at Ft Myers. This happened because without wetting more water was pushed up the Caloosahatchee River significantly increasing the water elevation there. The timing errors are in excellent agreement with measured data for all four stations (5 to 45 min, with the average error around 20 min). Table 5 13 shows the peak water elevation values calculated during these simulations along with the measured ones. By normalizing the difference between consecutive simulations by the peak measured water level, we can calculate percent

196 173 increase or decrease that each component introduced at the time when the peak water elevation was observed (e.g., at Big Carlos Pass, the Simulation 2 value 3% relative to the Simulation 1 value, and the Simulation 4 a and 4 b values 7% and 2% relative to the Simulation 3 value, respectively). Including radiation stress terms increased the calculated water level by 1-5%. Adding wave enhanced surface stress helped further increase the computed water elevation by 6-15%. Accounting for wave enhanced bottom friction decreased the calculated water elevation by 7-16% and 1-8% using Grant and Madsen (1979) and Sheng and Villaret (1989) formulations, respectively. When wetting-and-drying scheme was not engaged during the calculation the peak water level value grew an extra 18-49%. Table 5 14 shows peak storm surge values (tide was subtracted from water elevation) calculated during these simulations. Percent increase or decrease was calculated the same way it was calculated in the previous table.

197 174 Table 5 13: Measured peak water elevations at four stations during Hurricane Charley using WINDGEN wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Meas. cm cm cm cm cm cm cm Ft Myers % 63 6% 53 16% 55 8% % 99 Big Carlos Pass % % 105 7% 98 2% % 119 Estero Bay # % % % 112 4% % 112 Estero Bay # % % 110 9% 102 1% % 102 Table 5 14: Calculated peak storm surge (with tides subtracted) at four stations during Hurricane Charley using WINDGEN wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 cm cm cm cm cm cm Ft Myers % 54 9% 48 12% 46 8% 88 42% Big Carlos Pass % % 113 7% 103 2% % Estero Bay # % % % 120 4% % Estero Bay # % % 118 5% 104 2% %

198 175 The results reveal that including wave setup increased and improved the calculated surge by 2-5%. This increase was not as significant as it was observed during Hurricane Isabel (3-18%) due the reason that waves were not as high during Charley as they were during Isabel and all four stations were located in estuaries (Estero Bay and Caloosahatchee River), and thus were sheltered, whereas some of the Isabel stations such as Beaufort, Duck, and Chespeake Bay Bridge were located on the open ocean front. The wave-enhanced wind was a significant factor in increasing and improving the calculated storm surge. Its effect ranged within 9-13%. Such significance can be explained by the fact that the waves entering the computational domain were not very high, around 4 m in height with approximately 9 sec period (for comparison, during Isabel waves were as high as 15 m with 14 sec wave period). With strong wind blowing onshore, the small, short period waves were not fully developed, in other words, they were still young and energetic. Young seas increase sea surface roughness and, as a result, surface stress also increases. Wave-enhanced bottom stress based on the Sheng and Villaret (1989) formulation (Simulation 4 b ) decreased the peak surge values by 2-4% near Estero Bay and by 8% at Ft Myers station where the more significant effect can be explained by the remoteness of the station and shallow depths in the area, 2 to 4 m. When the wetting-and-drying feature was inactive, the water level grew significantly by 13-42%. This significant increase can be explained by the fact that most of the calculated flooding would have occurred in the vicinity of Estero Bay, so when the flooding feature was inactive, the water could not propagate inland thus piling up near the shore and significantly overestimating the calculated storm surge.

199 Results: Simulated Flood Level The wetting-and-drying scheme incorporated in the modeling system allowed the estimation of inundation caused by Hurricane Charley during its passage over the Charlotte Harbor area. Figures 5 66 and 5 67 show maximum simulated inundation caused by Charley during Simulation 4 (see Table 5 11) using WINDGEN and WNA winds, respectively. The bottom plots in the figures identify the time when the highest flood level occurred. Since the WNA wind was weaker than WINDGEN, it produced less inundation. Simulation 4 using WINDGEN wind produced the best comparison between measured and simulated water elevation at three stations within Estero Bay where most of the flooding occurred. Thus, this simulation was taken as the base simulation for estimating the amount of inundation caused by Charley. The flooded area affected 530 km 2 of land, mostly the surroundings of Estero Bay, San Carlos Bay, Sanibel Island, and Pine Island.

200 Figure 5 66: Maximum simulated inundation in Charlotte Harbor using WIND- GEN wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 177

201 Figure 5 67: Maximum simulated inundation in Charlotte Harbor using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 178

202 179 In order to validate the calculated inundation, air photos taken before and after Charley passed over the domain were compared with our calculated flood maps. Figures 5 68 and 5 69 show pre-storm and post-storm air photos taken at two locations, Captiva Island and Sanibel Island, respectively (see Figure 5 47 for location information). As can be seen from these figures, both islands were subject to extensive inundation during Charley. The bottom panels in each figure display close-ups of our computed inundation maps which also verify the presence of water over the islands. This validation is rather qualitative but nonetheless important. A more quantitative flood analysis was done based on some evidences obtained from Hurricane Charley Post-Storm Conditions and Impact report (Clark and LaGrone, 2004). In this report, four locations were examined on presence of high water marks left by the flood caused by Hurricane Charley. The locations are: Gasparilla Island, North Captiva Island, Captiva Island, and Estero Island (see Figure 5 70 for locations). In order to see how our model results stack up against the reported storm surge values, two techniques of evaluating water marks were applied: Technique 1 uses the storm surge level computed from the integrated storm surge modeling system, and Technique 2 adds a wave height to the storm surge level calculated by Technique 1. The wave height was calculated according to the methodology of Federal Emergency Management Agency (FEMA) (1988) for estimating flood zones: Flood Level = Surge H controlling (5 1) Since H controlling = 1.6 H sig Flood Level = Surge H sig (5 2) Table 5 15 below shows comparison between reported high water mark values and those calculated by the two techniques.

203 Figure 5 68: Pre-storm (top) and post-storm (middle) air photos taken by Captiva Island (courtesy of USGS, showing that the area was inundated during the time when Charley passed over it. A close-up of our calculated flood map (bottom) verifies the presence of water over the land. 180

204 Figure 5 69: Pre-storm (top) and post-storm (middle) air photos taken by Sanibel Island (courtesy of USGS, showing that the area was inundated during the time when Charley passed over it. A close-up of our calculated flood map (bottom) verifies the presence of water over the land. 181

205 182 Figure 5 70: Nautical chart of coastal areas in the Charlotte Harbor area impacted by Hurricane Charley (from Clark and LaGrone (2004)). Table 5 15: Comparison between reported high water mark values and flood levels calculated using two techniques High Water Mark Value, ft Location Reported Simulated by Technique 1 Simulated by Technique 2 Gasparilla Island N. Captiva Island Captiva Island Estero Island

206 183 Technique 2 gives results closer to the reported values but since it is not very clear how accurately the water marks were measured and what vertical datum was used to measure the water marks (see Figure 5 71), this analysis and its results are somewhat uncertain. Despite the uncertainties in the accuracy of measured high water marks, the results calculated by Technique 2 would be a more fair comparison because the high water marks were most likely left by wave crests, not just storm surge. Figure 5 71: Man points at a high water mark left by storm surge caused by Hurricane Charley on North Captiva Island (from Clark and LaGrone (2004)).

207 Hurricane Frances (2004) Description According to NHC Hurricane Frances was the sixth named storm and the fourth hurricane of the 2004 Atlantic hurricane season. The storm s maximum sustained wind speeds were 145 mph (230 km/h), giving it a strength of Category 4 on the Saffir-Simpson Hurricane Scale. It affected the central regions of Florida just three weeks after Hurricane Charley, which was the United States s second costliest hurricane with about $14 billion in damage. Frances then moved northward into Georgia where it weakened to a tropical depression. The track chart of Frances is given in Figure Figure 5 72: Best track of Hurricane Frances (courtesy of NOAA NHC). A strong tropical wave developed into a tropical depression late on August 24, It was then 1,400 km west-southwest of Cape Verde, and about 2,700 km east of the Windward Islands. The next day it was upgraded and named Tropical Storm Frances. The storm was upgraded to a hurricane on August 26.

208 185 Frances strengthened rapidly, reaching Category 3 intensity 24 hours later on the 27th and Category 4 the next day. Initially forecast to turn north and potentially threaten Bermuda, conditions changed and Frances s predicted track shifted westward toward the Bahamas. Frances s intensity fluctuated as it travelled west over the next several days, dropping back to a Category 3 storm before restrengthening. This drop and subsequent restrengthening was likely caused by an eyewall replacement cycle, according to the National Hurricane Center. Over the next several days, Frances passed just north of the Antilles, with only its outer rain bands affecting the British Virgin Islands and the Dominican Republic. On the evening of September 1, Frances passed to the north of Grand Turk in the Turks and Caicos Islands. Although Frances did not strike the island directly, hurricane force winds were reported there. On September 2, Frances struck the Bahamas directly, passing directly over San Salvador Island and very near to Cat Island, and passing over Eleuthera on September 3. Reports from Long Island said that parts of the island remained underwater after the storm had passed, with numerous homes and other structures damaged. On Saturday, September 4, the airport at Freeport, Grand Bahama was reported to be under 6 to 8 feet of water. One drowning death was reported in Freeport, Grand Bahama. On September 3, Frances weakened slightly as it passed into the vicinity of Abaco Island and directly over Grand Bahama. The storm weakened from a Category 3 to 2 prior to passing over Grand Bahama and also lessened in forward speed. Parts of South Florida began to be affected by squalls and the outer rainbands of the hurricane at this time. Gusts as low as 40 mph (60 km/h) to as high as 87 mph (140 km/h) were reported from Jupiter Inlet to Miami. Frances moved extremely slowly, from 5 to 10 mph (8 to 16 km/h), as it crossed the warm Gulf Stream between the Bahamas and Florida, leading to

209 186 fears it could rapidly restrengthen. It remained stable at Category 2 hurricane and battered the east coast of Florida, especially between Fort Pierce and West Palm Beach, for most of September 4. At 03:00 UTC on September 5, the western edge of Frances s eyewall began moving onshore. Because of Frances s large eye of roughly 130 km across and slow motion, the center of circulation remained offshore for several more hours. At 05:00 UTC, the center of the broad eye of Frances finally was over Florida, near Sewall s Point, Stuart, Jensen Beach and Port Salerno. Late on September 5, it picked up speed and crossed the Florida Peninsula, emerging over the Gulf of Mexico near Tampa as a tropical storm. After a short trip over water, Frances again struck land near St. Marks, Florida. Frances headed inland, weakening to a tropical depression and causing heavy rainfall over the southern US. Tropical Depression Frances continued north, maintaining its circulation longer than expected. US forecasters at the Hydrometeorological Prediction Center continued issuing advisories on the remnants of Frances until the system crossed the Canadian border into Quebec, where up to 8 inches (200 mm) of rain fell, causing significant flooding. Two deaths have been reported in the Bahamas. 32 deaths are blamed on the storm in Florida, two in Georgia and one in South Carolina. The insured claims of Frances have been determined to be about $4 billion. Some areas of Florida received over 13 inches of rain. Frances also spawned 117 tornados from Florida to as far north as Virginia. This amount beats the record number of tornados for a hurricane, which was 115 for Hurricane Beulah in Computational Domain The grid (see Figure 5 73) contains three open boundaries. The southern open boundary starts at Venice, FL and extends 28 km offshore. The northern open boundary starts near Crystal Beach, FL and stretches 36 km offshore. The

210 187 length of the western open boundary is 120 km. The area of the computational domain is approximately 7,000 km 2 with the total number of computational grid cells of 54,476 and the average grid spacing of approximately 350 m. 28,317 (52%) of those computational cells are water cells. The grid covers the entire Tampa Bay with all of its river basins and Sarasota Bay as well. The grid contains land cells in order to use it for wetting-and-drying. The USGS National Elevation Data set ( was used for topographic interpolation over the land. The horizontal resolution of the topographic data is approximately 30 m. The GEODAS bathymetric data set was used for depth interpolation over the water. Both data sets were converted to the standard NAVD88 vertical datum. A high resolution shoreline was utilized to distinguish between land and water. The computational mesh was created to fit the shoreline and resolve small scale topographic features such as inlets and islands. The grid extends inland far enough to the heights of at least 5 meters so that it would be practically impossible for the water to reach the inland grid boundaries during coastal inundation Data Three NOAA tide stations in the area were able to record water elevation during the passage of Hurricane Frances across Florida. These stations are: Clearwater Beach which is located outside Tampa Bay on the Gulf coast in 3.5 m depth, in the northern part of the north of the computational domain; St Pete which is located inside Tampa Bay near St Petersburg in 7.3 m depth; and Port Manatee which is located across the bay from St Pete station in 0.7 m depth. All three stations show that during the period when the eye of Frances was crossing over the Florida peninsula, there was a slight set down of water level due to strong winds blowing offshore. Once the hurricane moved further along such that the wind started blowing onshore and into the bay, the water level started to increase. Since the hurricane moved across Florida slowly allowing strong winds blowing into the

211 Figure 5 73: The Tampa Bay grid domain. 188

212 189 bay for 20 hours, the water level rose steadily gaining up to 165 cm (at St Pete station) from the point when the level reached its lowest value Results: Simulated Water Level In order to establish how well the modeling system performs during hurricanes when different forcing mechanisms are present, several simulations of Hurricane Frances were carried out using WNA or WINDGEN wind and including or excluding wave effects. Simulated water elevations, using WNA and WINDGEN wind (both include wave effect), are compared with measured water elevation at three stations in Figures 5 74 through All the other simulated versus measured water elevation results during Frances are shown in Appendix H. Clearwater Beach, FL 100 Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 74: Comparison of simulated vs. measured water elevation at Clearwater, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Frances in Tampa Bay using WNA wind is shown in Figure As can be seen in the figure, the maximum

213 190 St Pete, FL Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Measured 100 Water Elevation (NAVD88, cm) Julian Day Figure 5 75: Comparison of simulated vs. measured water elevation at St Pete, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind. Port Manatee, FL 100 Simulated (WNA wind, wave) Simulated (WINDGEN wind, wave) Measured Water Elevation (NAVD88, cm) Julian Day Figure 5 76: Comparison of simulated vs. measured water elevation at Port Manatee, FL. Two simulated results are shown: one using WNA wind and the other using WINDGEN wind.

214 191 values reached 2.0 m in the north eastern part of the bay, near McKay Bay and Upper Tampa Bay Park, flooding some of the land in those areas. Figure 5 78 shows simulated storm surge at all four stations which was obtained by subtracting simulated tide (no other forcing mechanism was included) from simulated water levels which included all forcing mechanisms (tide, wind, wave setup, wave enhanced surface and bottom friction). The results show that the calculated storm surge ranged from 0.6 to 0.8 m. It should be noted that during the peak of the surge, the tide was at its low stage at an approximate level of -0.3 m. Therefore, if the peak of the storm were to coincide with a high tide the surge level would have been 0.6 to 0.7 m higher. An interesting fact is revealed by looking at the difference between the times when the water elevation and storm surge level reached their peak values: The surge reached its maximum approximately 4 hours after the water elevation maximum occurred. Another interesting fact is found by observing the simulated storm surge at St Pete and Port Manatee during Julian days : During that time Frances was crossing the Florida peninsula approaching the Tampa Bay area with its winds blowing primarily from north to south. As a result, the surge level decreased at St Pete which is on the northern side of the bay causing set-down, and increased at Port Manatee which is across the bay from St Pete. After the hurricane approached the north eastern part of Tampa Bay coming from the east, the wind direction started to change from north-to-south to west-to-east causing the water level at Port Manatee to slightly decrease for some time until the point when the eye of Hurricane Frances moved closer to the Gulf of Mexico slightly increasing its strength and started pushing the water into Tampa Bay causing the major storm surge to increase. Despite the fact that the storm surge level was not too high (thanks to low tide during the peak), it took approximately 30 hours from the point when the

215 Figure 5 77: Maximum water elevation relative to NAVD88 (includes tide, surge and wave setup) calculated during simulation of Hurricane Frances in Tampa Bay using WNA wind. 192

216 193 surge level started to rise to the point when the surge receded. The main reason for that is the slow moving Hurricane Frances (5-10 mph). For comparison, it took only 11 hours for the storm surge caused by Hurricane Charley to recede when it made landfall and went over the Charlotte Harbor area. 100 Clearwater Beach Port Manatee St Pete Surge Elevation (cm) Julian Day Figure 5 78: Simulated storm surge (water level minus tide) at the three stations using WNA wind Error Analysis As was discussed in section 5.1.7, error analysis is a good way of comparing calculated water elevation to measured water level. In that section it was also pointed out that an error between measured and calculated water elevation can be attributed to either tide or storm surge or their combination. An estimation of the contribution of tide to the total error was done by performing a pure tide simulation and comparing its results with tidal elevation which was filtered out from measured water elevation using Doodson and Warburg (1941) 39-hourly average tidal filter. In order to weigh the effect of each component involved in the non-linear interaction between the surge, tide, wind, and wave, several simulations were made

217 194 by including different component combinations. Turning the wetting-and-drying feature on and off was an option as well. Table 5 16 specifies which simulation had what features. Table 5 16: A list of simulations with various combinations of six model features ( symbol denotes the feature was included during the simulation). Factors Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Tide Wind Wave Setup - Wave Enhanced Surface Stress Wave Enhanced Bottom Stress Wetting-and-Drying - Table 5 17 shows the RMS, Mean Absolute, and Maximum Absolute errors of calculated water elevation during Hurricane Frances (see Appendix B for formulas used to calculate the errors). Errors of peak values (measured peak elevation minus simulated peak elevation) and timing errors (time when measured peak elevation occurred minus time when simulated peak elevation occurred) are also shown. A separate column in the table displays the errors attributed to pure tide. Tidal range is also shown for each station. 1 Donelan et al. (1993) formulation was used 2 Grant and Madsen (1979) formulation was used 3 Sheng and Villaret (1989) formulation was used

218 195 Table 5 17: Errors of water elevation at tide stations during Hurricane Frances. WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Clearwater Beach (depth = 3.5 m; tidal range = 110 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) - 86 Error at Peak Timing at Peak (min) St Pete (depth = 7.3 m; tidal range = 95 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak Timing at Peak (min) Port Manatee (depth = 0.7 m; tidal range = 90 cm) RMS Error (cm) Mean Abs Error (cm) Max Abs Error (cm) Meas. Surge Peak (cm) Error at Peak Timing at Peak (min) Avg RMS Error (cm) Continued on next page

219 Table 5 17 continued from previous page WNA wind WINDGEN wind Tide Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Avg Err. at Peak (cm) Avg Timing Error (min)

220 197 Based on RMS errors and average absolute errors shown in the table above, a conclusion can be drawn that the WNA wind gave significantly better simulated storm surge values than the WINDGEN wind. The accuracy of the simulated tide was good, with the average RMS of approximately 5 cm. The simulated water elevation at all three stations was underestimated, which might have come as a results of the underestimated WNA wind speed. Again, even sophisticated hurricane wind models do not do a very good job near land or over estuaries, such as Tampa Bay, which results in an underestimated storm surge. This seems to be the weakest link in getting very accurate storm surge simulation results. Overall, Simulation 3 produced better results in terms of smaller RMS errors and better comparison with measured water surface elevation at its peak. Water level calculated using wave enhanced bottom friction based on the Sheng and Villaret (1989) formulation (Simulation 4 b ) was slightly worse. Wave enhanced bottom friction based on the Grant and Madsen (1979) theory (Simulation 4 a ) further reduced already underestimated surge within Tampa Bay: at St Pete and Port Manatee stations, due to its relative shallowness. The timing errors are acceptable (based on Simulation 4 b using WNA wind, 45 to 73 min) for all three stations. More accurate WNA wind produced smaller timing errors compared with less accurate WINDGEN wind. Table 5 18 shows the peak water elevation values calculated during these simulations along with the measured values. By normalizing the difference between consecutive simulations by the peak measured water level, the percent error of the effect of each component included in the non-linear interaction was calculated at the time when the peak water elevation was observed (e.g., at St Pete, the Simulation 2 value 1% relative to the Simulation 1 value, and the Simulation 4 a and 4 b values 13% and 6% relative to the Simulation 3 value, respectively).

221 198 Including radiation stress terms increased the calculated water level by 1-2%. It was somewhat surprising to see such a weak wave effect, especially at Clearwater Beach which openly faces the approaching waves. For example, the analogous effect during Isabel was 3-18%. This might be reasoned by the fact that the maximum wave height of 1.4 m occurred on Sep-5 at 23:00 UTC while the maximum water elevation value was observed on Sep-6 at 13:00 UTC. Similarly, the maximum calculated wave height at St Pete and Port Manatee was 0.65 m and 0.55 m, respectively, and occurred around Sep-5, 18:00 UTC while the calculated water elevation reached its peak 18 hours later. The wave fields were calculated using the SWAN model. The boundary conditions were obtained from the regional wave model, WAVEWATCH-III. Since there was no wave station in the vicinity of the computational domain, the accuracy of the computed waves could not be verified. Adding wave enhanced surface stress helped further increase the computed water elevation by 2-7%. Accounting for wave enhanced bottom friction decreased the calculated water elevation by 0-13% and 0-6% for Simulations 4 a and 4 b, respectively. When wetting-and-drying scheme was not engaged during the calculation, the peak water level value grew an extra 5-7%. Table 5 19 shows peak storm surge values (tide was subtracted from water elevation) calculated during these simulations. Percent increase or decrease was calculated the same way it was calculated in the previous table.

222 199 Table 5 18: Measured peak water elevations at three stations during Hurricane Frances using WNA wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Meas. cm cm cm cm cm cm cm Clearwater Bch % 63 2% 63 0% 63 0% 67 5% 86 St Pete % 92 7% 77 13% 85 6% 85 7% 116 Port Manatee % 81 6% 69 11% 76 5% 76 7% 105 Table 5 19: Calculated peak storm surge (with tides subtracted) at three stations during Hurricane Frances using WNA wind and various combinations of storm surge model features. Sim1 Sim2 Sim3 Sim4 a Sim4 b Sim5 Meas. cm cm cm cm cm cm cm Clearwater Bch % 60 6% 60 0% 60 0% 62 3% 69 St Pete % 85 13% 84 1% 84 1% 85 1% 96 Port Manatee % 71 12% 70 1% 70 1% 71 1% 77

223 200 Unlike Hurricanes Isabel and Frances when the maximum surge and maximum water elevation were observed at approximately the same time, during Frances, the surge reached its maximum approximately 4 hours after the water elevation maximum occurred. Therefore, wave, wind, and flood conditions were slightly different from the conditions reflected in Table Wave setup, again, had an insignificant effect on storm surge at it peak, 0-4%. Wave enhanced surface stress improved the calculated surge increasing it by 6-13%. Wave enhanced bottom stress effect (both formulations) was very insignificant decreasing the surge by 1%. Turning off the wetting-and-drying feature increased the surge by only 1-3%, which can be explained by the fact that most of the flooding occurred a few hours earlier during the high tide when the wetting-and-drying effect appeared to be more significant, 5-7% Results: Simulated Flood Level The wetting-and-drying scheme incorporated in the modeling system allowed the estimation of inundation in the Tampa Bay area. Figure 5 79 shows maximum simulated inundation caused by Frances calculated during Simulation 3 (see Table 5 16) using WNA wind. The bottom plot identifies the time when the highest flood level occurred. Based on Table 5 17, the WNA wind produced better comparison between measured and simulated water elevation at Clearwater Beach, St Pete, and Port Manatee stations. Simulation 4 had too much dissipation due to wave enhanced bottom friction which significantly reduced the calculated water surface elevation in comparison with measured water elevation. Thus, Simulation 3 was taken as the base simulation for estimating the amount of inundation caused by Frances. The flooded area affected 187 km 2 of land, mostly along the eastern shores of the bay.

224 Figure 5 79: Maximum simulated inundation in Tampa Bay using WNA wind (top panel). The bottom panel shows the time during which the maximum flood occurred. 201