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1 OPTIMAL STORM GENERATION FOR EVALUATION OF THE INUNDATION THREAT: DEVELOPMENT AND APPLICATIONS By ANDREW CONDON 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 2011
2 2011 Andrew Condon
3 To my wife Renee parents David and Patricia and Mini and Duke
4 ACKNOWLEDG E MENTS My most sincere thanks go to my wife Renee and to my parents for their endless love and support. I wish to express my gratitude and appreciation to my advisor Dr. Y. Peter Sheng for the financial and moral support in addition to his excellent guidance through my PhD study. I would like to thank th e members of my supervisory comm ittee Dr. Robert Dean Dr. Kurtis Gurley Dr. Forrest Masters and Dr. Corene Matyas This research was conducted under an award from the National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a, as w ell as a University of Florida Alumni Fellowship. A number of professionals provided data, knowledge, and support to aid me in this project. I would particularly like to acknowledge Dr. Don Resio, Dr. Senanu Agbley, and Jamie Rhome for their help. Additio nal thanks to Drs. Justin R. Davis, Vladimir Paramygin, and Bilge Tutak f or their help especially in the early years of my PhD. Thanks to Andy, Tianyi, Jung Woo, and all the other coastal students for the making these years enjoyable.
5 TABLE OF CONTENTS page ACKNOWLEDGEMENTS ................................ ................................ ............................... 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREV IATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 O PTIMAL STORM GENERATION FOR EVALUATION OF THE STORM SURGE INUNDATION THREAT ................................ ................................ ............ 17 Overview ................................ ................................ ................................ ................. 17 Background ................................ ................................ ................................ ............. 18 Hurricane Climatology of Southwest Florida ................................ ........................... 21 Dataset and period of record ................................ ................................ ............ 21 Calculation of storm rate ................................ ................................ ................... 22 Central pressure deficit ................................ ................................ .................... 23 Radius to maximum winds ................................ ................................ ................ 23 Forward speed ................................ ................................ ................................ 24 Storm heading ................................ ................................ ................................ .. 25 Traditional JPM Study ................................ ................................ ............................. 25 Generation of Optimal Storms and Surge Response ................................ .............. 29 Estimation of storm surge frequency using JPM OS SG ................................ ........ 33 Summary ................................ ................................ ................................ ................ 35 3 E VALUATION OF COASTAL INUNDATION HAZARD FOR PRESENT AND FUTURE CLIMATES ................................ ................................ .............................. 54 Overview ................................ ................................ ................................ ................. 54 Background ................................ ................................ ................................ ............. 55 Study Area ................................ ................................ ................................ ........ 59 Current Storm Surge Hazard Products Inundation Maps .............................. 60 Optimal Storm Generation and Storm Surge Modeling ................................ ........... 62 Optimal Storm Ensemble Generation ................................ ............................... 62 CH3D SSMS: CH3D Based Storm Surge Modeling System ............................ 65 Probabilistic Description of Present Hurricane Climatology ................................ .... 67 Dataset and Period of Record ................................ ................................ .......... 67 Calculation of Storm Rate ................................ ................................ ................. 68
6 Central Pressure Deficit ................................ ................................ .................... 68 Radius to Maximum Winds ................................ ................................ ............... 69 Forward Speed ................................ ................................ ................................ 69 Storm Heading ................................ ................................ ................................ 69 Present Flood Hazard ................................ ................................ ............................. 70 Joint Probability Method ................................ ................................ ................... 70 Results ................................ ................................ ................................ ............. 72 Future Flood Hazard ................................ ................................ ............................... 74 Climate Change and Hurricanes ................................ ................................ ...... 74 Sea Level Rise ................................ ................................ ................................ 75 Results ................................ ................................ ................................ ............. 76 Summary ................................ ................................ ................................ ................ 7 8 4 TOWARDS HIGH RESOLUTION, RAPID, PROBABILISTIC EVALUATION OF THE THREAT FROM LANDFALLING HURRICANES ................................ ............ 98 Overview ................................ ................................ ................................ ................. 98 Background ................................ ................................ ................................ ............. 99 Optimal Storm Generation and Multivariate Interpolation ................................ ..... 103 Forecast Inundation Application on Southwest Florida Coast ............................... 107 Hurricane Charley ................................ ................................ .......................... 107 Hurricane Wilma ................................ ................................ ............................. 110 Generation of High Resolution Probabilistic Inundation Response Estimates ...... 112 Summary ................................ ................................ ................................ .............. 115 5 CONCLUSION ................................ ................................ ................................ ...... 134 REFERENCES ................................ ................................ ................................ ............ 140 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 151
7 LIST OF TABLES Table page 2 1 Historical hurricane parameters ................................ ................................ ............. 51 2 2 Synthetic storm parameter values for traditional JPM ................................ ............ 52 2 3 Synthetic storm parameter discretized probability values (weights) ....................... 53 3 1 Historical Hurricane Parameters ................................ ................................ ............ 92 3 2 Synthetic storm parameter values for traditional JPM ................................ ............ 93 3 3 Synthetic storm parameter discretized probability values (weights) ....................... 94 3 4 Risk metrics for th e 10, 50, 100, and 500 year inundation events for climate change scenarios. ................................ ................................ .............................. 95 3 5 Climate change scenarios used for evaluation of the inundation hazard in future climate ................................ ................................ ................................ ................ 96 3 6 Risk metrics for the 10, 50, 100, and 500 year inundation events for climate change scenarios, but at present day sea level. ................................ ................. 97 4 1 Correlation coefficient and average error (m) between simulated (CH3D SSMS) and interpolated (ADAP, NON ADAP) and observed high water marks for Hurric ane Charley ................................ ................................ ............................. 132 4 2 Correlation coefficient and average error (m) between simulated (CH3D SSMS) and interpolated (ADAP, NON ADAP) and observed high water marks for Hurricane Wilma ................................ ................................ ............................... 133
8 LIST OF FIGURES Figure page 2 1 Historical storm tracks for Southwest Florida and s implified shoreline for the western FL coast ................................ ................................ ................................ 37 2 2 Storm rate as obtained by seventh order polynomial fit ................................ ...... 38 2 3 PDFs of hurricane parameters based on hurricane record for Southwest FL. .... 39 2 4 Evaluation of variation of hurricane parameters versus distance t o coast for Southwest Florida. ................................ ................................ .............................. 41 2 5 SLOSH model domain bathymetry and topography for Southwest Florida ......... 42 2 6 Hypothetical storm tracks for traditional JPM study for Southwest Florida ......... 43 2 7 Flood map for the 50, 100, and 500 year inundation events for Southwest Florida produced using the traditi onal JPM and JPM OS SG method. ............... 44 2 8 Comparison between traditional JPM BFE and BFE generated with JPM OS SG using optimal storm database and random database ................................ ... 45 2 9 Root Mean Square Error (RMSE) between inundation return frequencies obtained by the traditional JPM and JPM OS SG for dif ferent number of optimal storms ................................ ................................ ................................ .... 47 2 10 Comparison between traditional MOM and MOM generated with optimal storm database and non optimal (random) storm database ............................... 49 3 1 High resolution CH3D SSMS model domain for Southwest Florida and population density of study area ................................ ................................ ......... 81 3 2 Study area featuring CH3D SSMS model domain and tracks of tropical storms influencing the area since 1940 ................................ .............................. 83 3 3. Comparison between 100 year flood map (BFE) created using the traditional JPM and that created using the and optimal sam ple and random sample ......... 84 3 4 Expected inundation under present day conditio ns for different return periods .. 85 3 5 Risk map for present day sea level and hurricane conditions for Southwest Florida ................................ ................................ ................................ ................ 86 3 6 Projected changes due to climate chang e to hurricanes and sea level. ............. 87 3 7 Spatial extents for the 10, 50, 100, and 500 year inundation events for different scenarios. ................................ ................................ ............................. 88
9 3 8 Spatial extents for the 10, 50, 100, and 500 year inundation events for different sce narios at present day sea level ................................ ....................... 89 3 9 Category 5 MOM for different levels of SLR ................................ ....................... 90 3 10 Category 5 MOM for 150 cm of SLR using dif ferent SLR techniques ................. 91 4 1 High resolution CH3D SSMS model domain for Southwest Florida .............. 117 4 2 Evolution of forecast tracks and parameters for hurricanes Charley and Wilma ................................ ................................ ................................ ............... 118 4 3 Comparison between HWMs and simulated/interpolated results for hurricane Charley ................................ ................................ ................................ ............. 119 4 4 Envelope of high water for best track hurricane Charley simulation in CH3D and Interpolated results ................................ ................................ .................... 121 4 5 HWM comparison between USGS HWMs collected during Hurricane Wilma and CH3D and Interpolated results ................................ ................................ .. 122 4 6 Envelope of high water for best track Hurricane Wilma simulation in CH3D and Interpolated results ................................ ................................ .................... 124 4 7 PDF of hurricane forecast errors ................................ ................................ ...... 125 4 8 Probabilistic envelope of high water for Hurricane Charley .............................. 126 4 9 Probabilistic envelope of high water for Hurricane Wilma ................................ 128 4 10 Evolution of adaptive inundation response with 90 percent chance of occurrence for Hurricane Wilma for different forecast advisories ..................... 130
10 LIST OF ABBREVIATION S BFE Base Flood Elevation CH3D Curvilinear Hydrodynamics in 3D EOHW Envelope of High Water FEMA Federal Emergency Management Agency HWM High Water Mark JPM Joint Probability Method MEOW Maximum Envelope of High Water MOM Maximum of MEOWs NHC National Hurricane Center NOAA National Oceanic and Atmospheric Administration OS Optimal Sampling OSG Optimal Storm Generation RMSE Root Mean Square Error SLOSH Sea, Lake, and Overland Surges from Hurricanes SLR Sea Level Rise SSHS Saffir Simpson Hurricane Scale SSMS Storm Surge Modeling System TS Tropical Storm
11 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 OPTIMAL STORM GENERA TION FOR EVALUATION OF THE INUNDATION THREAT: DEVELOPMENT AND APPLICATIONS By Andrew Condon December 2011 Chair: Y. Peter Sheng Major: Coastal and Oceanographic Engineering In recent years the hazard along U.S. coastlines from inundation produced by hurricane generated storm surge has received a lot of attentio n. Following hurricane Katrina in 2005 there has been a renewed emphasis on producing detailed, high resolution inundation maps. The method of choice for generation of these maps is the Joint Probability Method (JPM). This method involves developing probabilistic d istributions of five important hurricane parameters (i.e. intensity, size, forward speed, heading, and landfall location) based on local climatology specific to the study area. The distributions are discretized into repre sentative values and all possible parameter combinations are simulated with a storm surge modeling system This approach is computationally costly when high resolution; state of the art modeling systems are used. This study develops a technique that combin es an optimal storm gener ation algorithm with multi variate interpolation to greatly reduce the number of necessary model simulations, while preserving the accuracy of the solution. The approach is first verified by comparing the inundation hazard maps prod uced using the interpolation technique with those produced using the actual simulations from a highly efficient numerical
12 model The ap proach is then applied to evaluate the current day and future inundation threat in Southwest Florida, and the optimal sto rm database is developed using a sophisticated modeling system CH3D (Curvilinear grid Hydrodynamics in 3D) SSMS (Storm Surge Modeling System). The current day hazard is confined mainly to coastal locations and areas near the Everglades. The future threat level varies considerably depending on the magnitude of SLR (Sea Level Rise) and changes in hurricane intensity and frequency. SLR is the dominant factor in determining the inundation hazard. The increase in hurricane intensity is generally offset by the decrease in hurricane frequency, resulting in little change in inundation hazard when SLR is not considered. In addition to determining the potential hazard to an area, the optimal storm database is used to produc e high resolution forecasts for an approaching hurricane. The interpolated inundation response is combined with probabilistic descriptions of the hurricane forecast errors to obtain a high resolution probabilistic estimate of the inundation.
13 CHAPTER 1 INTRODUCTION Hurricanes can create havoc and devastation along the coast. Damaging winds, torrential rain, devastating tornados, and flooding storm surges can all accompany a This study will focus on the storm surge, which has been responsible for some of Galveston hurricane, the 1928 Lake Okeechobe e hurricane, and more recently H urricane Katrina in 2005. The storm surge is formed primarily due to the stress of the hurricane winds over the ocean surface with the intense low pressure center of the hurricane also contributing to the storm surge. The effect of waves in the form of wave setup, as well the Coriolis force can also contribute to the surge. In the coastal zone, the complex interaction be tween the storm surge and the local bathymetry and topography can lead to different patterns of inundation. With a concentration of wealth and inundation hazard from storm s urge. For planning and mitigation purposes the hazard to an area from storm surge inundation is typically represented either a s a MEOW (Maximum Envelope of High Water) MOM (Maximum of MEOWs) or a BFE (Base Flood Elevation) map with an associated return p eriod (Glahn et al. 2009) All of these products involve the numerical simulation of many (hundreds for MEOWs to thousands for MOM, BFE) of hypothetical storms for a particular area of interest (i.e. design site, city, county, etc.) There is a large compu tational cost associated with produc tion of these map s using a high resolution, state of the art storm surge modeling system (i.e. CH3D SSMS ( Sheng et al. 2006, 2010a, 2010b; Sheng and Paramygin 2010 ); ADCIRC( Luettich et al. 1992 );
14 CMEPS( Xie et al. 2004; P eng et al. 2004 ); FVCOM( Rego and Li 2009; Weisberg and Zheng 2008 ); etc.) To work around this problem highly efficient, coarse grid hydrodynamic models have been used instead. Following the devastation from H urricane Katrina there has been a renewed emph asis on producing hi gh resolution inundation hazard maps using state of the art numerical model s In addition to the need to address the resolution and accuracy of the inundation products, it is important to note that current inundation maps do not include climate change effects, including c hanges in sea level, hurricane intensity, and hurricane frequency over the coming century. When producing inundation hazard maps that may be used in planning and determining future mitigation strategies, it is important to address what changes could be expected in a future climate and where the largest uncertainty in the results may lie. On a more immediate time scale than that in planning and mitigation studies, current day storm surge forecasting systems typically expe rience the same problem where accuracy and resolution are sacrificed for timeliness T here is a high computational cost associated with generating a high resolution EOHW (Envelope of High Water) from an approaching hurricane using a state of the art storm surge modeling system. A typical forecast cycle is only six hours long, so results are needed quickly. Also there is a degree of error in each hurricane forecast that can affect the accuracy of the EOHW. An ensemble approach that accounts for the forecast error would be most desirable, however this is currently not possible in the forecast window using state of the art storm surge modeling systems
15 This study provides a new method to develop an optimal storm database for a basin. The development of the database is unique in that it can be obtained quickly and without the need of expert knowledge. With the database, multivariate interpolation techniques can be used to quickly develop the inundation response for a given set of hurri cane parameters. The approach is applied to coastal regions of Southwest Florida. The study specifically looks to answer a number of questions. Specifically these questions are: (1) c an an optimal storm generation technique be developed to create an ensemb le of optimal storms for the interpolation of the storm surge r esponse for an area of interest, (2) c an the optimal storm generation technique be easily applied to different coastal basins without (3) w hat is the hurricane c l imatology for Southwest Florida (4) w hat is the current day inundati on threat for Southwest Florida (5) h ow is the inundation threat going to change under v arious future climate scenarios (6) i s there a difference in the inundation response between the common practice of adjusting the bathymetry/topography of a region to obtain the SLR influence and running a state of the art modeling system that incorporates SLR as a change in the initial surface elevation (7) c an the optimal storm database for the re gion inundation from an approaching hurricane and (8) c an high resolution probabilistic forecasts be generated within a forecast cycle by combining the interpolated results with his toric hurricane forecast errors? The preceding questions will be addressed in the following chapters. Chapter 2 provides background on the optimal storm generation technique and the multivariate interpolation scheme used. The approach is verified by comparing the inundation maps
16 produced using the optimal storm database and interpolation scheme with those produced by running all of the necessary numerical simulations. Comparison with a non optimal storm database is also included to demonstrate the importance in the optimal storm selection process The technique is used with a high resolution, state of the art storm surge modeling system, CH3D SSMS ( Curvilinear grid Hydrodynamics in 3D Storm Surge Modeling System) to develop BFE and MOMs for South west Florida under current day conditions in Chapter 3. Potential changes to the inundation hazard due to SLR (Sea Level Rise) and changes in hurricane intensity and frequency are also addressed in Chapter 3. Chapter 4 presents an adaptive forecasting syst em based on the optimal storm database and previous CH3D SSMS forecast simulations. An examination of National Hurricane Center (NHC) forecast errors is included and used to develop a probabilistic forecast which can be generated within a forecast cycle A general summary of the results will be discussed in the last chapter.
17 CHAPTER 2 OPTIMAL STORM GENERA TION FOR EVALUATION OF THE STORM SURGE INUNDATION THREAT 1 Overview To quantify the hazard of hurricane storm surge and coastal inundation in the U.S., storm surge atlas and base flood elevation (BFE) maps are developed. The traditional method for determining the BFE map is the joint probability method (JPM), which requires the simulation of over thousands of hypothetical hurricanes to accurately represent the storm climatology to determine the surge response and return frequency a huge cost using the sophisticated surge and inundation models today. This study presents an efficient and accurate JPM OS (opt imal sampling) for determining inundation return frequencies using piecewise multivariate regression splines coupled with dimension adaptive sparse grids, based on inundation response calculated by a storm surge modeling system. This method involves the in terpolation in five dimensional space of the simulated surge response and the storm characteristics of an optimal set of storms to any set of storm parameters. The interpolated results can be combined with a probabilistic description to obtain the return frequencies. The method is used to calculate the inundation frequencies of SW Florida and compared with the JPM. The results show excellent agreement between simulated and interpolated response with two orders of magnitude reduction in computational cost This technique can be readily applied to other coasts. 1 Submitted for publication as Condon, A. J. and Y. P. Sheng: Optimal storm generation for evaluation of the storm surge inundation threat.
18 Background Since 1995 a more active cycle in north Atlantic Hurricane activity has led to multiple landfalls along the United States coast (Goldenberg et al. 2001; Knutson et al. 2007). The inundat ion generated by these land falling hurricanes has brought renewed emphasis on the accurate estimation of the storm surge hazard in terms of inundation frequencies, in the form of Base Flood Elevation (BFE) maps (FEMA 2008a; IPET 2009; NRC 2009) and the wo rst case scenario, in the form of Maximum of Maximum (MOM) maps. These hazard maps are used by emergency managers, coastal planners, and FEMA for evacuation planning, coastal development planning, and flood insurance rate mapping, respectively. In order to accurately produce these hazard products, it often requires thousands to tens of thousands of numerical model simulations which are computationally costly when state of the art numerical models are used. Optimization of the generation of these products will allow more efficient and accurate development of the hazard maps. A number of methods for estimation of storm surge elevation frequencies exist: Standard Project Hurricane (SPH) (NOAA 1979), Empirical Simulation Technique (EST) (Scheffner et al. 1996 ), Joint Probability Method (JPM) (Myers 1970), Peaks Over Threshold (Lin et al 2010), etc Divoky and Resio (2007) and Agbley and Basco (2008) showed that the most promising method is the JPM, which is the primary method of FEMA for estimation of storm surge return frequencies (FEMA 2007, 2008). However, in its traditional form, the JPM requires thousands to tens of thousands of numerical simulations, which with state of the art numerical modeling systems can be computationally very costly. Recently, c oastal engineers have been developing optimized JPM, i.e., JPM OS (Optimal Sampling), by applying various optimization
19 schemes to significantly reduce the number of necessary simulations while retaining the accuracy of the end product (Divoky and Resio 20 07; Resio 2007; Agbley 2009; Toro et al. 2010a, 2010b; Niedoroda et al. 2010). All of the optimization schemes are built around the traditional application of the JPM. In its traditional form the JPM considers all possible combinations of hurricane charac teristics at landfall (Toro et al. 2010b). Typically hurricanes are characterized by max ), the translational speed (V f land ) The local climatology is analyzed to establish a probabilistic characterization of each variable. The storm surge and inundation response for each parameter combination is obability is combined with the simulated surge and inundation giving the annual probability of exceeding any desired storm stage (Toro et al. 2010b). The need to combine all possible storm parameters to accurately cover the five dimensional space in the J PM formulation is what leads to a large number (tens of thousands) of necessary synthetic storms. The numerical computation of the wind, surge, and wave response from each of these storms can be very time consuming and costly. Due to this large computati onal cost, optimal sampling techniques (JPM OS) have been developed to balance accuracy in the results with computational efficiency. JPM OS schemes fall into two categories: quadrature schemes and interpolation schemes. The quadrature schemes (JPM OS Q) (Toro et al. 2010a, 2010b; Niedoroda et al. 2010) uses an algorithm to select the optimal parameter combinations and assign representative weights to each of the optimal combinations. This turns the multi
20 dimensional JPM integral into a weighted summation with specific weights for the optimal parameter combinations. Two interpolation schemes: the Response Surface (JPM OS RS) scheme (Resio 2007; Niedoroda et al. 2010 Irish et al. 2009 ) and the Sparse Grid method (JPM OS SG) (Agbley 2009) are based on the determination of an optimal set of storms that can be used to interpolate the response for any other storm. In this way the response for all possible parameter combinations can be obtained without the numerical simulation of all combinations (Toro et al. 2010b; Niedoroda et al. 2010). The interpolation schemes can be applied to not only the generation of BFE, but also the development of a MOM map. Both interpolation approaches have proven to be highly efficient at estimating the storm surge return freque ncies, however their implementation can be complex and often expert judgment is needed. This study presents an efficient Optimal Storm Generation (OSG) method for determination of inundation return frequencies, using piecewise multivariate regression spl ines coupled with dimension adaptive sparse grids, based on inundation response calculated by a storm surge modeling system. The interpolation scheme used in this study differs from that used by Agbley (2009) which applies the Sparse Grid method to the hur ricane wind, instead of the inundation response. By applying the Sparse Grid method to the inundation response, local effects due to the coastline configuration, offshore bathymetry, and topography of the land surface is accounted for which cannot be achie ved with a wind model. This efficient and portable method can be implemented in a matter of hours and is easily applied to any coastal domain. The method is applied to Southwest Florida to generate both MOM and BFE maps and compared to the maps made using the traditional methods.
21 In order to determine the return frequencies the local hurricane climatology is reviewed and is presented in Section 2. The traditional JPM is reviewed in Section 3. Section 4 provides details on the OSG scheme and how it is ap plied. Section 5 compares results of MOMs and BFEs using the OSG scheme and the traditional JPM). Additionally a comparison between the results of MOMs and BFE obtained fro m the optimal storm ensemble and a non optimal ensemble are compared. Hurricane Climatology of Southwest Florida Dataset and period of record The historical record for hurricanes in the North Atlantic basin extends back to 1851; however the reliability of data before the air reconnaissance and satel lite era is questionable (Resio 2007). Data from 1940 to the present is considered to be more reliable and the 70 year period from 1940 to 2009 is considered in this study. Data is o btained from the International Best Track Archive for Climate Stewardship (IBTrACS) data set (Knapp et al 2010) This dataset is used along with Ho et al. (1987) to obtain the parameters of interest, ( P, R max V f and X land ) for land falling cyclone s along the simpl ified coastline (generated as described in Ho et al., (1987)) shown in Figure 2 1. The IBTrACS database contains the track information at 6 hour increments as well as the wind speed and central pressure data when available. A total of 28 land falling storms whe re determined to influence the S outhwest coast of Florida during this period. Exiting storms were found to not contribute significantly to the inundation in the area and were not considered in this study. The land falling storms me t the criteria of having reached tropical storm strength within a pre defined area around Southwest Florida and making landfall close enough to the study area to have an influence on the
22 inundation. To quantify which storms have an influence the procedur e of Chouinard and Liu (1997) is followed. A central reference point (CREF) was defined for Fort Myers Beach, FL ( 81.9E, 26.4N). An optimal sampling window is selected which extend s roughly 370 km to the north and 220 km to the south of the CREF. The 220 km extension to the south coincides well with the end of the Florida peninsula and beginning of the Florida Keys. This avoids any conflict in storm characteristics between storms making landfall in the FL Keys and those on the mainland peninsula. Stor ms that do not cross th e approximately 600 km region w ere not considered resulting in 28 land falling storms. The tracks are depicted in Figure 2 1 while the storm parameters at landfall essential to the JPM are summarized in Table 2 1. Calculation of sto rm rate The storm rate i s determined using the method of Chouinard and Liu (1997). In this method the historical hurricane tracks are treated as a Poisson line process and kernel smoothing techniques are used to determine the omni directional rate in terms of storms/year/km. The omni directional rate is based on the distance of a storm from the location of interest X. Weights are assigned based on this information with storms making landfall close to X receiving greater weights t han those making landfall further. Chouinard and Liu (1997) along with Niedoroda et al. (2010) use least squares cross validation to determine the optimal balance between statistical precision and spatial bias as is done in this study. This approach has some advantages over traditional approach u sed in older studies (i.e. FEMA 1988). The biggest advantage being that the traditional arbitrary division of a region of interest into landfall zones can result in poorly weighted statistics and the exclusion o f possibly influential storms (Niedoroda et al. 2010)
23 The omni directional rate i s calculated to be 7.0163E 04 storms/year/km at the CREF following this procedure. Due to the size of the domain a single value is not representative of the entire c oast. Values along the coast a re obtained which shows that the omni directional rate reaches a maximum near the CREF and decreases both to the north and south of this point. Figure 2 2 shows the variation in the omni directional rate as a function of distance from the CREF in kilometers along with the fit of the rate with a seventh order polynomial. Central pressure deficit The central pressure deficit i s examined for all sto rms. In some cases the data are not available for all track locations. The m odel of K naff and Zehr (2007) i s used to compare with the available central pressure data The model shows a strong correlation ( r 2 = 0 .87) with the data and was used to fill in the missing data values. The central pressure deficit pri or to, at, and after landfa ll i s examined (Figure 4a). There is no identifiable trend to the central pressure deficit as a function of distance to the coast for this sample set. As a result the value at landfall is used in the characterization of th e synthetic storms. The data a r e fit to a variety of distributions and a re found to most closely fit by Maximum Likelihood Estimation (MLE) a Generalized Extreme Value (GEV) distribution (Kotz and Nadarajah 2000; Embrechts et al. 1997) w ith shape parameter of 0.3540, scale parameter of 8.9801 and location parameter of 23.4782 as shown in Figure 2 3a. Radius to maximum winds Similar to the central pressure deficit data, the radius to maximum wind data is not complete for all records. A number of models a re applied but the correlation bet ween the available data and the model results i s poor. Due to this only the 19 available R max
24 values are used in the analysis T he change in radius to max imum winds prior to land fall i s found to vary depending on storm (Figure 2 4b) but no trend is iden tifiable. T he data for R max is very sparse making it difficult to try to characterize changes in R max prior to landfall so the R max values at landfall are used to generate the probability density function For radius to maximum winds there is a documented correlation between R max and pressure deficit (Shen 2006; Irish et al. 2008). This relationship was examined for the values at landfall for the storm sample and a weak negative correlation was found. The data was further examined to include all track positions in the Gulf of Mexico, where a stronger negative correlation be tween R max and pressure deficit is present for the hPa ) storms For the weaker storms the distribution is best represented by a lognormal distribution (Figure 2 3d) with no dependence on the central pressure deficit. However for the str onger storms the relationship is similar to that found by Resio (2007) for a different segment of the Gulf Coast. The conditional distribution of R max given central pressure deficit (for > 50 hPa ) is given by a lognormal distribution based on the con ditional mean of R max = 53.6236 and is shown in Figure 2 3(e h) for a number of central pressure deficits. Forward speed The storm forward speed i s found to be independe nt of other variables and shows some variance prior to, at, and afte r landfall. Since no trend in the values prior to landfall could be determined, the values at landfall a re used and found to best fit a Weibull distribution (Devroye, 1986) with the greatest MLE score. The location parameter for the distribution is 15.45 62 and the shape parameter is 3.3798 (Figure 2 3c).
25 Storm heading The storm heading data w ere also examined for any dependency and determined to be independent of the other variables. The heading is represented as a GEV distribution with shape parameter o f 0.3564, scale parameter of 23.5194, and location parameter equal to 26.9055 as shown in Figure 2 3b. Traditional JPM Study The traditional JPM uses the probabilistic descriptions of storm rate and storm characteristics as done above to define a set of s ynthetic storms. These synthetic storms are simulated with a numerical model to determine the flood elevations that would be generated by them (Toro et al. 2010b). The annual rate of occurrence of a specific flood elevation in excess of an arbitrary valu e is given by the JPM integral (Niedoroda et al. 2010): ( 2 1) probability density function of the storm characteristics and the conditional probability that a storm of certain characteristics will generate a flood elevatio n in ; subscript max denotes an annual maximum value (Toro et al. 2010 a ). The integral is evaluated for all possible storm parameter combinations resulting in a rate in terms of events per unit time, which is taken as the annual pro bability. The multidimensional integral in E quation 2 1 cannot easily be determined as written. Typically it is approximated as a weighted summation of discrete storm parame ter values as (Niedoroda et al. 2010):
26 ( 2 2 ) Each term in the summation corresponds to a synthetic storm with an annual rate of occurrence given by i This approximation can be solved by simple quadrature such as the midpoint rule. However to accurately integrate over the entire para meter space tens of thousands of synthetic storms, with multiple values for each of the storm parameters is needed. In practice this is not efficient when state of the art numerical storm surge models are used However the NOAA/NHC Sea, Lake and Overland Surges from Hurricanes (SLOSH) model (Jele s nianski et al. 1992) is highly efficient in simulating the surge response and can be used for this application. SLOSH is a 2 D linear barotropic model which has been officially adopte d by the NHC for forecasting storm surge and producing MOM maps The model estimate s storm surge heights and winds resulting from hurricanes by taking into account storm central pressure, size, forward speed and track (heading and landfall location). SLOSH is very efficient and most forecasting simulations can be completed within a minute. According to the NHC, the SLOSH model is generally accurate within plus or minus 20 percent (Jele s nianski et al. 1992), although SLOSH does not contain all of the dynamic tide a nd wave effects and it uses low resolution computational grids. For more detailed storm surge hazard analysis, the National Academies Committee on FEMA Flood Mapping Accuracy (NRC 2009) proposes the use of a robust storm surge modeling system which includ es the effects of tides, waves, and on land structures, etc on surge and inundation. For this study, the SLOSH model is used to demonstrate the efficiency and accuracy of the Optimal Storm Generation (OSG) method for developing inundation maps. The OSG method used here has also been applied to the region using the
27 robust storm surge modeling system CH3D (Curvilinear grid Hydrodynamics in 3D) SSMS (Storm Surge Modeling System) (Sheng et al. 2010a, 2010b) for estimating inundation threats under current an d future climates, showing promising results (Condon and Sheng 2011b manuscript submitted to Natural Hazards ). The traditional JPM study is carried out with a total of 46,800 hypothetical storms in the Fort Myers (eFM2) SLOSH basin provided by the Nationa l Hurricane Center (Figure 2 5). The hypothetical storm set consists of all combinations of the parameter values in Table 2 max values, 4 V f locations). These storms represent storm parameter combinat ions spaced 9.3 km (5 n. mi.) apart covering the basin. The storm parameter combinations were chosen based on review of past traditional JPM studies (i.e. Myers 1970, 1975; Ho 1974, 1975; Ho and Tracey 1975a, 1975b, 1975c; Ho et al. 1976) and expert analys is (personal communication, Don Resio). Individual tracks for each synthetic storm (Figure 2 6) were constructed as straight line tracks with all parameters held constant until landfall and then allowed to decay, following Vickery (2005). On a single co mputer processor each simulation takes under one minute on average, resulting in approximately one month of wall time to run the entire ensemble. The maximum water level associated with each of the simulations (Envelope of High Water, EOHW) was recorded fo r all 11,100 grid cells in the SLOSH domain. This results in a record of 46,800 peak surge estimates each with a given rate of occurrence based on the storm rate and joint probability of the characteristics for all 11,100 grid cells.
28 The discretization of each storm parameter is shown in Table 2 3. The storm rate is determined based on the joint probabilities of the hurricane characteristics and the storm event rate for the location of landfall as done in Nierdoroda et al. (2010). Fo r each cell a histogram of accumulated storm rate was constructed representing approximations of the surge height density distributions. An error function based on the local tide and precision of the SLOSH model is redistributed over the bins in the histo gram creating a modified version. This is then summed from the highest bin down to the lowest bin to give an estimate of the cumulative surge distribution for the location. With the CDF of the surge, the surge height for any r eturn period can be determine d from the curve. The annual chance of occurrence elevations maps of 2%, 1%, and 0.2% (corresponding to the 50, 100, and 500 year storm) are presented in Figure 2 7 (a, c, e respectively). The results show that the inundation threat to Southwest F lorida i s significant for all re turn periods. The 50 year event produces a maximum inundation depth of 2.79 meters. The event with a 1% annual chance of exceedance produces up to 3.69 meters of inundation and covers a larger spatial extent. The 500 year event p oses a very significant threat with much of the domain experiencing some form of flooding and a maximum depth of 6.13 meters. These values are in line with the values obtained in the Flood Insurance Study for Lee County Florida (FEMA 2008b). The FEMA stu dy differs in a number of ways. The FEMA study considers a much longer time period (1886 1977) that features data of questionable quality. Weaker storms and exiting storms which may not contribute much in terms of storm surge, but do increase the storm e vent rate, are also considered. Additionally a constant storm rate is used, even though the
29 rate was shown to vary by a factor of two throughout the region. The FEMA study features fewer storm sizes, forward speeds and landfall locations, leading to larger errors in the discretization of the associated pdfs. A different, but comparable in physics and resolution model the FEMA standard storm surge model was used and rainfall and river discharge data were combined into the results, aspects that are not inclu ded in the current study. Given the large differences in the two studies is not a surprise that some variance exists. The inclusion of weaker and exiting storms likely leads to the slightly larger values in the FEMA study. The weaker storms do not contribu te much to the storm surge, but do increase the storm rate which leads to higher values for the inundation return frequencies. Also by only considering storms with R max of 15 and 30 nautical miles, small storms such as Charley are ignored. Charley demonstr ated the importance in including a range of storm sizes since it generated such a small surge even though it was extremely intense due to its size. A more efficient mechanism for generation of the same maps is described next. This will allow more sophist icated and accurate numerical models to be used in future studies. Generation of Optimal Storms and Surge Response Optimization schemes for the JPM have recently been developed and were briefly discussed and are detailed in Toro et al. (2010a, 2010b) (JPM OS Q the JPM OS method based on Quadrature interpolation scheme ), Resio (2007) (JPM OS RS the JPM OS method based on Response Surface interpolation scheme ), a nd Irish and Resio (2008, 2009) Both the JPM OS Q and JPM OS RS methods have some feature s which limit the timely application of the methods to any new coastal domain. As pointed out by Toro et al. (2010b), there is subjectivity in the implementation of both
30 schemes that eliminates the possibi lity of automation Additionally the JPM OS Q meth od is limited in the number of dimensions that can be included. Toro et al. (2010b) found that exponentially increasing the number of nodes is required to maintain acceptable error with increasing dimension beyond those currently modeled which eliminates the possibility of including more variables in the JPM formulation (such as tidal amplitude, Holland B parameter, etc). The interpolation scheme described by Agbley (2009) can be modified to eliminate many of the drawbacks of these other JPM OS methods. Agbley (2009) follows many of the same principle s of the JPM OS RS. It involves the interpolation in five dimensional space of the simulated surge response and the storm characteristics of an optimal storm set to obtain the surge response for any set of storm parameters. Specifically Agbley (2009) uses piecewise multivaria te regression splines (Friedman 1991) supported by dimension adaptive spa rse grids (Gerstner and Griebel 2003; Smolyak 1963) to obtain the surge response while using a simple parametr ic wind model (Myers 1954) to rank the importance of the input parameters in the dimension adaptive sparse grid scheme as described below. The use of wind model neglects the contribution of a very important variable, the landfall location, in determining t he inundation response. Our method, on the other hand, couples a storm surge model with the dimension adaptive sparse grid scheme so that all five input variables are accounted for and ranked appropriately for the basin of interest. The traditional JPM can be thought of as a n interpolation problem on a regular grid. Interpolation in multidimensional space on a regular grid requires that support max V f land ) must be specified and regularly spaced which
31 leads to a large number of necessary nodes. To work around this the support nodes can be specified on a sparse grid to drastically reduce the required number of nodes. Work by Gerstner and Griebel (2003) has shown that dimension adaptive sparse grids can be applied to multivariate regression problems such as the surge frequency problem. Sparse grid interpolants involve the careful combination of one dimensional formulae such that multivariate functions can be optimally recovered (Agbley 2009). The basis of all sparse grid method algorithm extends well known univariate interpolation formulas to the multivariate case by using tensor products in a special way resulting in an interpolation method that requires significantly fewer supp ort nodes while preserving the accuracy (Agbley 2009; Klimke and Wohlmuth 2005). The method is hierarchical in structure which allows an estimate of the current approximation error This allows for a level of accuracy to be specified beforehand, generatin g only the support nodes necessary to meet that accuracy. A conventional sparse grid leads to an isotropic grid construction, but in the storm surge response the grid should not be isotropic. Variables such as the central pressure deficit, landfall locati on, and storm size have much more influence over the surge response than the forward speed and storm heading (Agbley 2009; Irish et al. 2008). A scheme that knows the appropriate weights of the variables is needed and this is provided by the formulation o f Gerstner and Griebel (2003). Their scheme can calculate how refinements in each dimension help to reduce the overall interpolation error. The scheme will adapt to these calculations by placing more support nodes in the
32 dimensions that minimize the calc ulated error. This algorithm has been implemented in MATLAB (spinterp) by Klimke and Wohlmuth (2005) and Klimke (2007). The implementation requires coup ling with a numerical model to simulate the response and feed results back into the algorithm. A hig hly efficient numerical model that accurately portrays the physics of the problem and the spatial trends in the response can be used. Agbley (2009) used a simple analytic wind model (Myers 1954) for this task. The drawback to this approach is that the lo cal effects of the domain are not accounted for. Work by Irish et al. (2008) and Irish and Resio (2010) show the importance in the central pressure deficit, storm size, and the local bottom slope in generating storm surge. The surge at the beach is high ly dependent on the underlying bathymetry approaching the shoreline. A simple analytical wind model cannot account for this influence on the surge response. Likewise in the case of inundation, the total flooded area, flooded volume, and flood extent is d ependent on the local topography. In addition features such as rivers, inlets, and bays can change the inundation response for a given wind field. With the above considerations in mind, the highly efficient SLOSH model is coupled with the spinterp toolbo x. The coupling is achieved by generating the first set of predefined nodes by the sparse grid scheme. Synthetic storms are developed based on the five parameter values of each node and simulated using SLOSH. The total inundated volume i s calculated and returned for the next selection of nodes. This procedure is continued until the desired estimated error is obtained. Through this coupling a total of 197 optimal storms a re selected. The procedure is now totally
33 automated with the only necessary input be ing the basin and the parameter range considered (i.e. minimum P, maximum P, etc.). To generate the response of any storm from the recorded response of the 197 optimal storms, multivariate regression is needed. Multivariate regression maps the predictor variables onto the response variables to generate the optimal regression function. The method of Friedman (1991) is used to find multivariate adaptive regression splines (MARS) to fit the data. The MARS approach has the advantage of producing continuous regression functions which makes it reliable for a number of function types and well suited for implementation on sparse grids (Agbley 2009). This method is applied to the S outhwest Florida region as described below. Estimation of storm surge frequency u sing JPM OS SG The optimal track generation technique combined with the MARS interpolation scheme allows for the generation of the inundation response given any five dimensional parameter space within the bounds of the interpolation scheme. The bounds are imposed as the ranges of likely or possible parameter values and were specified to be hPa 13 max 78 km 2.7 f 10.7 ms 1 222 land ). The interpolati on is defined the traditional JPM. The same probability discretization scheme (Table 2 3) was u sed for the JPM OS SG results. The results for the 50, 100 and 500 year inundation return frequencies are shown in Figure 2 7 (b, d, f respectively). A comparison between the traditional JPM results and the JPM OS SG results is shown in
34 Figure 2 8 in red The robust least squared correlation coefficient for all return peri ods is very strong and the average error ( ) between the two methods is minimal. The choice of 197 storms is based on the tradeoff between accuracy of the solution and efficiency in o btaining the solution. Figure 2 9 sh ows the root mean square error (RMSE) between the traditional JPM and the interpolated values for a number of the 197 storm mark for t he various return periods. For larger samples, there is little gain in accuracy. For smaller, more efficient samples the RMSE increases. For this study the 197 storm sample proved to be the optimal balance between efficiency and accuracy. The computation al cost of producing the optimal tracks and the response is dramatically less than that for the traditional JPM. On a single computer processor, the determination of the optimal tracks takes approximately 4 hours. The 197 storm simulations take about 3 h ours and the interpolation and calculation of the return frequencies takes about 1.5 hours. All of these computations on a single CPU can be performed in about 8 hours which is nearly one hundred times more efficient than the traditional JPM. In order to judge the robustness of the optimal storm generation technique, the results for the generation of the BFE maps using the optimal storms was compared to the results using a random sample of 197 storms. The robust least squared correlation coefficient and average error between the results obtained using JPM OS SG and those obtained using the traditional JPM method is shown in blue in Figure 2 8 for the fifty (a), one hundred (b), and five hundred (c) year storms. In all cases the optimal storms
35 show a bett er correlation and a smaller average error than the random storms. However the error and correlation of the random sample is still not too large, which demonstrates the effectiveness of the MARS algorithm in generating the surge response. In addition to the BFE comparison the robustness of the method in generating MOMs was evaluated. Figure 2 10 shows the comparison between the actual MOM generated with 1 490 SLOSH simulations per storm category and that generated using the 197 optimal s torm set (red) and the 197 random storm set (blue) for the category 1 (a), category 3 (b), and category 5 (c) MOMs. In this case the optimal storm sample far outperforms the random storm set especially for the higher category MOMs This is likely due to the fact that this random storm set contains a large number of weaker storms that help generate a decent fit to the category 1 MOM, but poor results for the category 3 and 5 MOMs This underestimation is not as dramatic in the BFE since the stronger storms carry much less weight since they have much lower probability of occurrence. Summary A fully automated and efficient method to determine the surge response for any st orm given the storm parameters i s detailed in this paper This method couples a highly e fficient numerical storm surge model SLOSH, with the JPM OS SG (JPM with Optimal Sampling and Sparse Grid interpolation) interpolation toolbox to generate a set of optimal storms. Multivariate A daptive Regression S plines (MARS) are used to generate the re sponse based on the optimal storms and desired storm characteristics This method i s ap plied in to generate both BFE and MOM maps for quantifying the inundation hazard Southwest Florida In the generation of both h azard products the
36 method shows very pro mising results when compared to the traditional JPM method of generating these maps and a non optimal (random) sample of storms combined with MARS. The op timal storms for a coastal basin can easily be time and can lead to an order of magnitude (or more) reduction in the number of storms and surge simulations needed to generate the inundation maps. The results presented here a re obtained with the highly efficient SLOSH model; however the same optimal storms can be used by more adva nced state of the art storm surge modeling systems to obtain higher resolution and more accurate results.
37 Figure 2 1 Historical storm tracks for Southwest Florida and simplified shoreline (black line) for the western FL coast
38 Figure 2 2 Storm rate as obtained by seventh order polynomial fit through calculated rate every 9.3 km (5 nautical miles ) within the model domain
39 A B C D Figure 2 3 PDFs of hurricane parameters based on hurricane record for Southwest FL. A) Central pressure deficit; B) Storm heading; C) Forward speed; D ) Radius to maximum winds gi ven pressure deficit of 33 hPa ; E ) Radius to maximum winds given pressure deficit of 53 hPa ; F ) Radius to maximum winds given pressure deficit of 73 hPa ; G ) Radius to maximum winds given pressure deficit of 93 hPa ; H ) Radius to maximum winds given pressure deficit of 113 hPa ;
40 E F G H Figure 2 3. Continued
41 A B Figure 2 4 Evaluation of variation of hurricane parameters versus distance to coast for Southwest Florida. A ) Central pressure versus distance to coast for landfalling hu rricanes in Southwest Florida; B ) Radius to maximum winds versus distance to the coast for landfalling hurricanes in Southwest Florida
42 Figure 2 5 SLOSH model domain bathymetry and topography for Southwest Florida
43 Figure 2 6 Hypothetical storm tracks for traditional JPM study for Southwest Florida
44 A B C D E F Figure 2 7 Flood map for the 50, 100, and 500 year inundation events for Southwest Florida produced using the traditional JPM and JPM OS SG method. a) 50 year flood map using Traditional JPM; b) 50 year flood map using JPM OS SG; c) 100 year flood map using Traditional JPM; d) 100 year flood map using JPM OS SG; e) 500 year flood map using Traditional JPM; f) 500 year flood map using JPM OS SG
45 A B Figure 2 8 Comparison between traditional JPM BFE and BFE generated with by JPM OS SG using optimal storm database (red) and comparison between traditional JPM BFE generated with interpolation method and non optimal storm database (blue) Comparison is for the a) 50 year; b) 100 year; and c) 500 year return frequency
46 C Figure 2 8 Continued
47 A B Figure 2 9 Root Mean Square Error (RMSE) between inundation return frequencies obtained by the traditional JPM and JPM OS SG for differe nt number of optimal storms Comparison f or the a) 50 year; b) 100 year; and c) 500 year events
48 C Figure 2 9 Continued
49 A B Figure 2 10 Comparison between traditional MOM and MOM generated with optimal storm database (red) and non optimal (random) storm database (blue) Comparison for a) Category 1; b) Category 3; and c) Category 5 hurricanes
50 C Figure 2 10 Continued
51 Table 2 1 Historical hurricane parameters Historical Storm (year) Central Pressure Deficit ( hPa ) Radius to Maximum Winds ( km) Forward Speed (mph) Storm Heading (N) Notnamed (1944) 45 63 8.0 10 Notnamed (1945) 37 --5.8 62 Notnamed (1946) 27 46 8.5 13 Notnamed (1947) 22 --4.0 12 Notnamed2 (1947) 29 24 6.7 39 Notnamed (1948) 52 13 3.6 24 Notnamed2 (1948) 38 24 7.6 42 Easy (1950) 55 28 2.2 24 Love (1950) 23 --8.0 46 How (1951) 20 --7.2 81 Notnamed (1953) 28 --8.9 51 Hazel (1953) 23 --8.9 46 Judith (1959) 14 --5.8 45 Donna (1960) 75 4 4 4.0 338 Isbell (1964) 45 56 7.2 36 Abby (1968) 20 --4.0 27 Gladys (1968) 36 31 3.6 47 Floyd (1987) 20 --7.6 61 Keith (1988) 18 135 7.6 65 Marco (1990) 14 1 9 4.0 354 Gordon (1994) 18 148 4.0 27 Mitch (1998) 23 278 8.9 62 Irene (1999) 27 74 4.5 33 Gordon (2000) 24 46 4.9 21 Gabrielle (2001) 30 46 8.0 34 Charley (2004) 66 1 9 8.9 15 Wilma (2005) 60 56 7.6 47 Fay (2008) 19 37 2.7 10
52 Table 2 2 Synthetic storm parameter values for traditional JPM P ( hPa ) P ( hPa ) R max ( km) V f (mph) X land 33 (980) 53 (960) 73 (940) 93 (920) 113 (900) 13 26 39 52 65 78 2.7 5.4 8.0 10.7 337.5 0 22.5 45 67.5 90 Spaced every 9.3 km from + 370 to 222 relative to CREF (65 locations)
53 Table 2 3 Synthetic storm parameter discretized probability values (weights) Parameter Value Central Pressure deficit ( hPa ) 33 53 73 93 113 Probability (%) 73.56 17.59 5.53 2.25 1.08 RMW Probability (%) ( km ) 13 6.96 10.38 19.71 40.35 79.39 26 27.54 24.12 29.84 31.58 15.82 39 28.50 23.88 22.21 15.41 3.45 52 19.36 18.67 14.15 7.28 0.93 65 11.34 13.48 8.71 3.56 0.30 78 6.30 9.47 5.38 1.82 0.11 Heading ( N) 22.5 0 22.5 45 67.5 90 Probability (%) 2.51 13.43 31.67 34.75 16.29 1.34 Forward Speed ( m/s ) 2.7 5.4 8.0 10.7 Probability (%) 13.18 44.30 36.19 6.33
54 CHAPTER 3 EVALUATION OF COASTA L INUNDATION HAZARD FOR PRESENT AND FUTU RE CLIMATES 1 Overview Coastal inundation from hurricane storm surges causes catastrophic damage to lives and property, as evidenced by recent hurricanes including Katrina and Wilma in 2005 and Ike in 2008. Changes in hurricane activity and sea level due to a warming climate, together with growing coastal population, are expected to increase the potential for loss of property and lives. Current inundation hazard map s: Base Flood Elevation (BFE) maps and Maximum of Maximums (MOMs ) are computationally expensive to create in order to fully represent the hurricane climatology, and do not account for climate change. This paper evaluates the coastal inundation hazard in S outhwest Florida for present and future climates, using a high resolution storm surge modeling system, CH3D SSMS, and an optimal storm ensemble with multivariate interpolation, while accounting for climate change. Storm surges associated with the optimal storms are simulated with CH3D SSMS and the results are used to obtain the response to any storm via interpolation, allowing accurate representation of the hurricane climatology and efficient generation of hazard maps. Incorporating the impact of anticip ated climate change on hurricane and sea level, the inundation maps for future climate scenarios are made and affected people and property estimated. The future climate scenarios produce little change to coastal inundation, due likely to the reduction of h urricane frequency, except when extreme sea level rise is included. Calculated coastal inundation due to sea level rise without using a coastal surge model is also determined 1 Accepted to Natural Hazards as Condon, A. J. and Y. P. Sheng : Evaluation of coastal inundation hazard for present and future climates
55 and shown to significantly overestimate the inundation due to neglect of land di ssipation. Background Coastal inundation from hurricane induced storm surge and waves can wreak havoc in coastal regions as has been witnessed during recent Hurricanes Ivan, Katrina, Wilma, Ike, and Rita among others. Over the past 15 years North Atlantic hurricane activity has entered a more active cycle and landfalls along the U.S. coast have become more common (Goldenberg et al. 2001; Knutson et al. 2007). Coupled with this, coastal construction and population growth continue to increase making the inu ndation hazard even greater, resulting in 17 of the 30 c ostliest storms (from 1900 2010 using 2010 deflator ) occurring since 1990 (Blake et al. 20 11 ). Hurricane Katrina alone resulted in an estimated $ 105 billion worth of damage and more than 1, 2 00 dea ths (Blake et al. 20 11 ). With the increased potential for such catastrophic damage, the hazard of inundation from hurricanes needs to be quantified in an efficient manner with sufficient spatial resolution to provide useful information to coastal planners and decision makers. The present day coastal inundation hazard analysis takes into account the natural variability in hurricane frequency, size, intensity and track. The hazard analysis is described in detail in recent reports by Federal Emergency Manage ment Agency (FEMA 2008 a ), Interagency Performance Evaluation Taskforce ( IPET 2009), and the National Academies Committee on FEMA Flood Mapping Accuracy (NRC 2009). The analysis requires the use of a robust storm surge modeling system (which includes such processes as tides, waves, and on land structures, etc.) to simulate the response of coastal zone to a statistically generated ensemble of hurricanes using the Joint Probability Method (JPM). This method generally requires a large number (thousands or
56 larg er) of hurricanes in order to adequately represent the past hurricane climatology in a given coastal region. Running this large number of hurricanes with a robust storm surge modeling system requires excessive computational effort. To save computational c ost, existing inundation maps are generally created with a small number of (~100) storms which may not adequately represent the past storm statistics. Effort to more adequately represent the past storm statistics have begun in recent years with the develop ment of the JPM OS method (Resio 2007; Toro et al. 2010a, 2010b; Niedoroda et al. 2010) and limited applications to Louisiana and Mississippi coasts. These methods, however, require expert judgment which limits their applications to other coastal regions w ithout modifications. Moreover, the present day coastal inundation hazard analysis does not include any effect of climate change and anticipated sea level rise (Lin et al. 2010). Evidence suggests that a warming planet may lead to more intense storms (Kn utson et al. 2010), although the frequency of the landfalling hurricanes is expected to be less (Wang and Lee 2008). Wang and Lee (2008) concluded that model projections of ocean warming patterns under future global warming scenarios may be crucial in pre dicting future Atlantic hurricane activity. Additionally, they believe that anthropogenic global warming has a pervasive influence on both oceanic and atmospheric temperatures and circulation as well as water vapor, all of which affect tropical cyclones in complex and not yet fully understood ways. Compounding the issue is the effect of sea level rise (SLR) which could produce a global mean increase in water level of up to 190 cm over the next century when considering the contribution from land ice (Grinst ed et al. 2009; Vermeer and Rahmstorf 2009; Rahmstorf 2010). Combining the continual migration of
57 people to the coast with potential climate change impacts, it is likely that future hurricanes could lead to more costly and deadly damages to the coastal zo ne. To properly plan for the future, potential changes in coastal inundation hazard due to climate change need to be accounted for. Although a few studies (Frazier et al. 2010; Kleinosky et al. 2007; Wu et al. 2002) have examined the impact of SLR on coas tal inundation, these studies did not use any storm surge and inundation modeling system, nor did they include the effect of climate change on hurricane intensity and frequency, hence the results are questionable. Mousavi et al. (2011) and Frey et al. (20 10) both accounted for changes in hurricane intensity and SLR to determine the impact of climate change on inundation in Corpus Christi, TX using a storm surge modeling system. However these studies neglect the expected decrease in hurricane frequency and examine individual historical storms, rather than generating probabilistic hazard analysis (BFE) maps and worst case scenario maps (MOM). Feyen et al. (2006), on the other hand, used a storm surge model to study the effect of SLR alone on coastal inundatio n. Ali (1996, 1999) also incorporated SLR into inundation projections for Bangladesh, however his results were obtained with a stationary, uniform wind, not the dynamic winds expected in a hurricane. Danard et al. (2004) among others investigated the eff ects of SLR on storm surge for non tropical storms, but did not include any changes in storm intensity or frequency. This study will incorporate changes in hurricane intensity and frequency as well as SLR to develop probabilistic hazard maps for Southwest FL. In addition worst case composite maps (MOMs) will be developed for future SLR scenarios.
58 This paper intends to answer the following questions: How will the coastal hazard maps for future climate differ from that for the present climate, and why? How do es a coastal hazard map produced in this study differ from that produced without using a coastal storm surge model? What will a coastal inundation hazard map look like? What is the hazard of coastal inundation induced damage on coastal property and populat ion? To accurately and efficiently quantify the coastal inundation hazard in any coastal zone, we believe it is necessary to (1) use a robust integrated storm surge and inundation modeling system to account for coastal dynamics and atmospheric ocean land interactions; (2) use an efficient and portable JPM OS method to statistically generate a hurricane ensemble with relatively small number (~hundreds) of hurricanes to accurately represent the hurricane statistics; and (3) incorporate the potential impact o f climate change on hurricane intensity and frequency as well as sea level rise. This paper evaluates the present day inundation hazard to the Southwest Florida coast using the integrated storm surge and inundation modeling system CH3D (Curvilinear grid H ydrodynamics in 3D) SSMS (Sheng et al. 2010a, 2010b), and a relatively small (<200 storms) but optimal hurricane ensemble generated by an efficient and portable JPM OS Method (Condon and Sheng 2011a manuscript submitted to Ocean Eng ). The effect of clima te change on hurricane intensity and frequency is incorporated in the JPM OS method. Three sea level rise scenarios for the year 2100 are created and simulated to develop likely coastal inundation hazard. This study will also calculate the coastal inunda tion due to SLR, with and without using a coastal storm
59 surge model, and compare the difference in coastal inundation calculated by these two different methods. Study Area The state of Florida has experienced tremendous growth over the past few decades. Since 1990 the population has increased by over 5.8 million people according to the United States Census ( United States Census 2010 ) The South w est Florida region has seen an explosive population growth particularly since the start of this century. It was estimated that the population for the region would increase by 47% from 2000 to 2010 ( University of Florida 2009 ) and an estimated 138% over the 2000 population by 2030. ( University of Florida 2005 ) With such a large projected increase in population, the region is ideal for evaluation of the present and future coastal inundation hazard This region was selected as the main focus of the NOAA/IOOS (National Atmospheric and Oceanic Administration/Integrated Ocean Observing System) Regional Storm Surg e and Inundation Model Testbed developed by Sheng et al. ( 2011 ). The study area stretches from just south of Tampa Bay to Cape Sable in the Ten Thousand Island region and includ es parts of Manatee, Sarasota, Charlotte, Lee, Collier, and Monroe counties (Figure 3 1 a ). In addition to being an area with explosive population growth in recent decades, there is a concentration of wealth along the coast that is vulnerable to inundation Figure 3 1b shows the population density in the study area which depicts the high density in the coastal regions. The region has been affected by a number of tropical systems over the past 70 years including major hurricanes Donna (1960), Charle y (2004 ), and Wilma (2005) ( Table 3 1 and Figure 3 2 ). Data of U.S. landfalling hurricanes, which account for one third of the North Atlantic
60 hurricanes, have been used extensively for analyzing the potential influence of climate on hurricanes (Emanuel 2005; L an dsea 2005 ). As shown in Figure 3 1, a numerical model grid of this region has been con structed for use with the CH3D ( Sheng 1 987 and 1990 ) Storm Surge Modeling System (CH3D SSMS) ( Sheng et al. 2006, 2010a, 2010b; Sheng and Paramygin 2010 ) The model domai n is currently being used in the NOAA/IOOS Regional Storm Surge and Coastal Inundation Model Testbed which is comparing 5 different storm surge and inundation models : ADCIRC (ADvanced CIRCulation) ( Luettich et al. 1992 ) CH3D SSMS, POM ( Princeton Ocean Mo del ) ( Peng et al. 2004; Oey et al. 2006 ) FVCOM ( Rego and Li 2009; Weisberg and Zheng 2008 ) and SLOSH ( Sea, Lake, and Overland Surges from Hurricanes ) ( Jelisnianski et al. 1992 ) in terms of historical hurricane simulations and coastal inundation maps including M aximum of Maximums (M OMs ) and Base Flood Elevation ( BFEs ) maps ( Sheng et al. 2011 ). Current Storm Surge Hazard Products Inundation Maps Currently the hazard from storm s urge and coastal inundation is described by two different products, i.e., inundation maps: the Maximum of Maximum (MOM) and the Base Flood Elevation (BFE) maps. The MOM (National Hurricane Center 2010a), which is produced based on SLOSH simulations of num erous hurricanes, represents the worst case scenario for a given region for a given Saffir Simpson Hurricane Scale (SSHS) (National Hurricane Center 2010b) storm category. In Florida, the NOAA/NHC (National Hurricane Center) SLOSH group produces the model simulations and the Florida Regional Planning Councils use the SLOSH results to produce MOMs of five hurricane categories. The BFE determines the inundation hazard with an associated (typically 1%) annual chance of occurrence or a particular return period (typically 100
61 (FEMA 2007; NRC 2009). Generation of these products typically requires the numerical simulation of thousands or more of hypothetical hurricanes which represent th e past hurricane statistics, i.e., historical hurricane climatology, for the region. The MOM is the maximum inundation obtained from an ensemble of thousands of hypothetical storms for a specific SSHS category with various tracks (angle, landfall location and forward speed) and storm sizes (radius of maximum winds). FEMA creates BFE maps by use of the Joint Probability Method (JPM) (FEMA 2008) in which the historical climatology of a region is described probabilistically and is combined with the simulat ed surge response covering the entire parameter space to determine the inundation for a set annual probability of occurrence (1%) or return period (100 years). MOM, however, does not contain any probabilistic information such as annual chance of occurrence or return period of any inundation elevation. Combining these hazard analyses with demographic and property value information can portray the risk to a certain area. Both the MOM and BFE, which are intended to relay the potential of coastal inundation, h ave been used widely by emergency managers, coastal planners, and the public, despite the uncertainties associated with the inundation levels shown on these maps (NRC 2009). When a larger storm ensemble is used in the production of inundation maps, there i s less uncertainty associated with the representation of the storm climatology. However, the cost for running a larger ensemble of storms can become excessive. Currently, a single simulation using a state of the art storm surge modeling system can take ho urs to days on a single computer processor, necessitating a cluster with hundreds or thousands of processors.
62 In the past, to reduce the computational cost, model physics and resolution are often compromised and the number of simulations is arbitrarily red uced which leads to inaccurate representation of the storm climatology. More recently, new robust methods (Toro et al. 2010a, 2010b; Resio 2007; Niedoroda et al. 2010; Agbley 2009; Lin et al. 2010) have been developed to create a smaller ensemble of storms for producing BFEs. The JPM optimal sampling (JPM OS) methods have led to a reduction in the number of storms needed for simulations by orders of magnitude, from tens of thousands to only hundreds of storms. With a smaller storm ensemble size, more adva nced numerical modeling systems with better physics and finer model resolution can be used in the storm surge simulations. This paper uses a method developed by Condon and Sheng ( 2011a manuscript submitted to Ocean Eng ), which is modified from Agbley (200 9), to develop an optimal storm ensemble for both the BFE and MOM development. The optimal inundation maps will be combined with economic and population data in Southwest Florida to give a quantitative measure of the inundation risk. Additionally the pro jections of future climate scenarios will be used to determine the coastal inundation hazard expected in the year 2100. Optimal Storm Generation and Storm Surge Modeling Optimal Storm Ensemble Generation Following the destruction caused by Hurricane Katrin a, there is a consensus in the U.S. that it is necessary to more accurately estimate storm surge and inundation hazards in coastal regions (e.g., IPET 2009; NRC 2009). Several recent studies (Resio 2007; Toro et al. 2010a, 2010b; Niedoroda et al. 2010) ha ve been conducted to better represent the storm surge and coastal inundation hazards in terms of the expected return period (or annual chance of occurrence) of such events. The method of choice
63 by FEMA for obtaining inundation frequencies is the Joint Pro bability Method (JPM) (Myers 1970), which traditionally uses the probabilistic descriptions of the historical storm rate and storm characteristics to define a set (or ensemble) of synthetic storms. The synthetic storm set/ensemble is then used by a numeri cal storm surge model to calculate the coastal flood elevations that would be generated by each of those storms. The probabilistic descriptions are combined with the calculated inundation to generate the annual probability of exceeding any desired storm s tage. The approach is widely accepted in the emergency management community and officially adopted by FEMA (Divoky and Resio 2007; Agbley and Basco 2008). The downside to the traditional JPM is that accurate representation of historical storm climatolog y requires tens of thousands of numerical model simulations. storm size R max the translational speed V f location X land based on t he local climatology. A detailed study of the local climatology is usually conducted to develop a discrete probability distribution function (pdf) of each variable. Finer discretization of the pdfs will yield more accurate representation of the climatolo gy, but it would often require tens of thousands of storm surge model simulations. This could translate into hundreds or thousands of computational hours using one of the state of the art storm surge modeling systems mentioned above. Following Katrina, opt imization schemes for the JPM (Toro et al. 2010a, 2010b; Niedoroda et al. 2010; Resio 2007; Agbley 2009) were developed to enable the production of accurate inundation maps with only hundreds of model simulations instead of tens of thousands of model simul ations. These optimized schemes have
64 allowed the production of accurate maps with dramatically reduced computational cost over running the same model with the traditional JPM scheme. For this study, we use a method developed by Condon and Sheng ( 2011a m anuscript submitted to Ocean Eng ), which is modified from the method of Agbley (2009) to make it more transportable and accurate. This method is chosen because it can be fully automated and readily applied to other basins with minimal set up. The methods of Toro et al. (2010a, 2010b), Niedoroda et al. (2010), and Resio (2007) all the methods more difficult and costly to implement. Additionally the quadrature appro ach of Toro et al. (2010a, 2010b) assigns specific weights for the optimal storms selected which is specific to generation of the BFE and cannot be applied for MOM generation. The Condon and Sheng ( 2011a manuscript submitted to Ocean Eng ) method develops an optimal set of (~100) storms, based on the algorithm of Smolyak (1963), from which the surge response for any storm can be obtained using multivariate adaptive regression splines (Friedman 1991). The Condon and Sheng storm generation algorithm modifie adaptivity (Gerstner and Griebel 2003) using the surge response generated with the highly efficient SLOSH (Jele s nianski et al. 1992) model to develop the optimal storms. Condon and Sheng used the optimal sto rm ensemble generation method with the SLOSH model to show that the resulting inundation map is almost identical to that generated using 46,800 storms which fully represent the storm climatology. However, inundation maps generated using randomly selected e nsembles with comparable size to the optimal ensemble result in quite different inundation maps. Figure 3 3 shows a
65 comparison between the results of the BFE with 1% chance of occurrence using a traditional JPM (46,800 simulations) and an optimal (197 simu lations) ensemble. The optimal storm ensemble creates a BFE map with an average error within 0.15 m of that obtained using the traditional JPM but at a fraction of the cost. CH3D SSMS: CH3D Based Storm Surge Modeling System In this study, the high resoluti on storm simulations are performed using CH3D SSMS. CH3D is a hydrodynamic model originally developed by Sheng (1987, 1990) and has been significantly enhanced (e.g. Sheng et al. 2010a; Sheng and Kim 2009). The model can simulate 2 D and 3 D barotropic a nd baroclinic circulation driven by tide, wind, wave, and density gradients. The model uses a boundary fitted non orthogonal curvilinear grid in the horizontal directions and terrain following sigma grid in the vertical direction to allow accurate represe ntation of the complex coastal and estuarine shorelines where forecasting of storm surge, waves and inundation is needed. Based on the finite volume method, CH3D is strictly conservative for momentum, water mass, as well as for temperature and salinity. CH3D uses a robust second order closure model for calculating vertical turbulent mixing (Sheng and Villaret 1989). In the horizontal direction, Smagorinksy type turbulent diffusion coefficients are used. CH3D is used for simulating and forecasting storm surge and circulation in many coastal regions throughout Florida and the U.S. CH3D, which supports flooding and drying, has been dynamically coupled to a wave model SWAN (Booji et al. 1999; Ris et al. 1999; SWAN Team 2009), using the same curvilinear grid, to produce CH3D SSMS, an integrated Storm Surge Modeling System (Sheng et al 2006, 2010a, 2010b). To provide open boundary conditions of water level along the coastal model CH3D domain, CH3D SSMS can use the results of
66 one of several basin scale hydrodyna mic models, including ADCIRC (Luettich et al. 1992), HYCOM (Halliwell et al. 1998 2000 ; Bleck 2002), and NCOM (Ko et al. 2003, 2008). In this study, ADCIRC is used. To provide open boundary condition for SWAN, CH3D SSMS uses the output of a large scale w ave model such as WaveWatch III (Tolman 1999, 2002). CH3D SSMS has been used extensively to simulate storm surge and inundation due to various tropical storms including Hurricane Isabel (Sheng et al. 2010a), Charley (Sheng et al. 2006; Davis et al. 2008; D avis et al. 2010), Ivan (Sheng et al. 2010b), and Wilma ( Paramygin and Sheng 2011, manuscript submitted to J. Geophys. Res. ). Sheng and Paramygin (20 10 ) combined the baroclinic circulation element of CH3D with CH3D SSMS to forecast the storm surge, inunda tion, and 3D baroclinic circulation in northeast Florida during Tropical Storm Fay. For this study CH3D SSMS uses the local CH3D model dynamically coupled with local SWAN wave model. Offshore conditions are provided to CH3D by a coarse grid ADCIRC simulat ion and offshore wave boundary conditions are provided to the local SWAN model by a coarse grid larger scale SWAN domain. Li ttle difference (less than 0.01 %) was found in the final results between using SWAN or WWIII in the offshore for the wave boundary conditions, so SWAN was used to ease nesting with the local scale domain. CH3D SSMS uses wind fields developed by an analytic model based on Holland (1980). The winds are developed as straight line tracks of constant intensity until landfall. For this s tudy, the storm intensity is dissipated following Vickery (2005) post landfall. To save computational cost, this study runs the CH3D model in 2D (vertically based on land use data o btained from United States Geological Survey (NLCD 2006)
67 with an offshore value of 0.02 (dimensionless). The coastal model domain features a minimum horizontal resolution of approximately 20 m in the coastal zone and an overall average grid size of ~ 100m with a maximum of ~700 m offshore. The most up to date LIDAR from NOAA Coastal Services Center (NOAA CSC 2010), topography from United States Geological Survey (USGS 2010), and bathymetry data from NOAA National Geophysical Data Center (NOAA NGDC 2010), have been incorporated into the domain shown in Figure 3 1. Probabilistic Description of Present Hurricane Climatology To determine the coastal inundation hazard to the region, a detailed study of the local hurricane climatology is needed. This was presen ted in Condon and Sheng ( 2011a manuscript submitted to Ocean Eng ) and is summarized here. Dataset and Period of Record Data from 1940 to the present is considered to be more reliable than earlier data since it incorporates aircraft reconnaissance and the satellite era (Resio 2007). To represent the local hurricane climatology, this study uses hurricane data during the 70 year period from 1940 to 2009 obtained from the International Best Track Archive for Climate Stewardship (IBTrACS) data set (Knapp et al. 2010). This dataset is used max V f land for land falling cyclones along the simplified coastline shown in Figure 3 2. A total of 28 land falling storms were determined to influence the southwest coast of Florida during this 70 year period, based on an optimal kernel width calculated by the method of Chouinard and Liu (1997). The tracks are depicted in Figure 3 2 and the p arameters at landfall, which are essential to the JPM, are summarized in Table 3 1.
68 Calculation of Storm Rate The storm rate was determined using the method of Chouinard and Liu (1997). The omni directional rate is based on the distance of a storm from th e location of interest X. Weights are assigned based on this information with storms making landfall close to X receiving greater weights than those making landfall further. Chouinard and Liu (1997) along with Niedoroda et al. (2010) use least squares c ross validation to determine the optimal balance between statistical precision and spatial bias, as is done in this study. The omni directional rate was calculated to be 7.0163E 04 storms/year/km at the Central Reference Point (CREF, defined to be Fort My ers Beach, FL) following this procedure. Due to the size of the domain, a single value is not representative of the entire coast. Values of the omni directional rate were determined every 9.3 km along the coast and show that the rate reaches a maximum ne ar the CREF and decreases both to the north and south of this point. The rate was approximated with a seventh degree polynomial. Central Pressure Deficit The central pressure deficit for all storms 28 storms is examined. In some cases the data is not a vailable for all track locations. The model central pressure of Knaff and Zehr (2007) is used to compare with the available central pressure data. The model central pressure, which shows a strong correlation (r 2 = 0.87) with the data, is used to fill in the missing data values. The values at landfall are fit to a variety of distributions, and through Maximum Likelihood Estimation are found to most closely fit a Generalized Extreme Value (GEV) distribution (Kotz and Nadarajah 2000; Embrechts et al. 1997) with shape parameter of 0.3540, scale parameter of 8.9801 and location parameter of 23.4782.
69 Radius to Maximum Winds Similar to the central pressure deficit data, the radius to maximum wind data is not complete for all records. A number of models are applied but the correlation between the available data and the model results is poor. As a result only the available dat a is used. For the radius to maximum winds, there is a documented correlation between R max and pressure deficit (Shen 2006; Irish and Resio 2008). This relationship is examined for the values at landfall for the storm sample and a weak negative correlat ion is found. The data is further examined to include all track positions in the Gulf of Mexico, where a stronger negative correlation between R max and pressure deficit is determined especially for the storms with a central pressure deficit greater than 5 0 hPa For the weaker storms, the distribution is best represented by a lognormal distribution. For the stronger storms the relationship is similar to that obtained by Resio (2007) for a different segment of the Gulf of Mexico Coast. The conditional di stribution of R max for a given central pressure deficit (for central pressure deficit greater than 50 hPa ) is described by a Lognormal distribution, based on the conditional mean of R max = 53.6236 Forward Speed The Weibull distribution (Devroye 1986) fits the forward speed data with the greatest MLE score. The location parameter for the Weibull distribution is 15.4562 and the shape parameter is 3.3798. Storm Heading The storm heading is represented as a GEV distribution with shape para meter of 0.3564, scale parameter of 23.5194, and location parameter equal to 26.9055.
70 Present Flood Hazard Joint Probability Method The traditional JPM uses the probabilistic descriptions of storm rate and storm characteristics as done above to define a set of hypothetical storms (FEMA 1988). These hypothetical storms are used with a numerical storm surge model to calculate the coastal flood elevations that would be generated by each (Toro et al. 2010b). The annual rate of occurrence of a specific floo d elevation at a point in excess of an arbitrary ( 3 1) This is a function of the mean annual rate of all the joint probability density function of the storm characteristics and the conditional probability that a storm of certain characteristics will generate a flood ; subscript max denotes an annual maximum value. The integral is evaluated for all possible storm parameter combinations. The result of the evaluation of the integral is a rate in terms of events per unit time, which is taken as the annual probability. Th e multidime nsional integral in q uation ( 3 1) cannot be easily determined as written. Typically it is approximated as a weighted summation of discrete storm parameter values as (Niedoroda et al. 2010): ( 3 2) where each term in the summation corresponds to a synthetic storm with an annual rate of occurrence given by This approximation can be solved by simple quadrature such as the m idpoint rule. However to accurately integrate over the entire
71 parameter space tens of thousands of synthetic storms, with multiple values for each of the storm parameters, is needed. In practice this is quite costly using advanced numerical models which can be computationally inefficient. To alleviate this problem, a set of optimal storms is developed using the optimal track generation technique (Condon and Sheng 2011a manuscript submitted to Ocean Eng ). For this basin, under current climate conditions a total of 197 optimal storms were determined. These storms are simulated using CH3D SSMS as described above and the envelope of high is combined with the multivariate adaptive regression spline technique of Friedman (1991) to obtain the inundation response for each of the 46,800 storms listed in Table 3 2. These storms represent possible storm parameter combinations spaced 9.3 km ( five nautical miles ) apart covering t he basin. The storm parameter combinations were chosen based on review of past traditional JPM studies (i.e. Myers 1970, 1975; Ho 1974, 1975; Ho and Tracey 1975a, 1975b, 1975c; Ho et al. 1976) and expert analysis (personal communication, Donald Resio). Th e narrow spacing is important due to the high sensitivity of the surge response on the local topography and location of the storm track as described by Murty (1984). The annual rate for each of the 46,800 storms was based on the statistical characterizatio ns developed above from the past hurricane climatology. The discretization of each storm parameter is shown in Table 3 3. The storm rate is determined based on the joint probabilities and the storm event rate for the location of landfall. The surge heig ht for any return period is determined following the method of Niedoroda et al. (2010) accounting for errors due to the tide (standard deviation of 0.2 m
72 based on Naples, FL tides) and the model (standard deviation of 15 % of the modeled inundation height b ased on IOOS Testbed results). Results Analysis of the present day hazard shows that much of the area is susceptible to hurricane produced storm surge and inundation (Figure 3 4). The inundation in all figures and tables is in excess of 0.305 m (~ 1 foot) in accordance with designation of Special Flood Hazard Area by FEMA (2003). The 10 year inundation hazard is contained almost exclusively to the southern portion of the domain and along the rivers and bays. Although the southern portion contains the Fl orida Everglades and there is little or no development there, there is considerable coastal development along the rivers and bays that are susceptible to low return period events. The higher return periods show much larger flooded area. Table 3 4 shows m etrics to better quantify the extent of the inundation for each return period by reflecting areas that receive at least 0.305 m (~1 foot). The 100 year BFE produced in this study is based on the optimal hurricane ensemble which accurately represents the h urricane climatology, hence should be more accurate than the existing FEMA 100 year BFE which was produced without using the optimal hurricane ensemble. a descriptor of th e economic cost associated with each event. This gives a good representation of the actual value of the property and is obtained from 2009 parcel data for each county from the Florida Geographic Data Library (FGDL 2010). The just value of affected prope rty for a given inundation event is determined by combining the total just value for a parcel with the percentage of damage from USACE depth damage curves (2006). Th e same FGDL database contains information regarding the
73 population distribution through out the domain based on 2000 census data which is presented in Table 3 4. It should be noted that it is extremely unlikely that a certain inundation event will affect the entire domain at the same time. The flooded volume, area, the affected population and the just value of the affected property of a single hurricane will likely be less than that depicted in Table 3 4 and 3 6 since the associated return period will likely not occur at the same time throughout the domain. The 50, 100, and 500 year storms all would result in over 2,500 km 2 of property being affected. The 500 year storm is could affect up to $24 billion worth of property and over half of a million lives (Table 3 4). The 100 year storm, which is the basis for flood insurance rate maps, show s extensive inundation in almost all portions of the domain. As an example of a way to quantify the risk of inundation, an inundation risk map (Figure 3 5) is produced by considering wave heights and water velocity, in addition to surge height, as recomme nded by NRC (2009). By including velocity data, the consequences of the flood hazard on a structure can be determined which produces the risk map. The inundation risk map is constructed by placing all areas that are within the 10 year flood zone in the ex treme risk category. The high risk category consists of those areas in the 50 year flood zone or those that fall in the 100 year flood zone and meet the FEMA velocity zone characteristics (Wave height of 0.64 meter or the product of depth of flow times th e flood velocity squared is greater than or equal to 5.66 m 3 /s 2 ) (FEMA 2007). The medium risk zone consists of the rest of the 100 year flood zone, and the low risk zone is made up of the 500 year flood zone. This map shows that most of the immediate coastline is in the high or greater category. As expected the are as
74 around the low lying Everglades, the barrier islands and beaches, and near the rivers and bays are at the greatest risk. Future Flood Hazard As was done for the current day flood hazard assessment, the future hazard from storm surge can be determined w ith adjustments to the problem to reflect changes in hurricane activity and sea level rise (SLR) due to a warming climate. Climate Change and Hurricanes The effect of a warmer climate on hurricanes is still uncertain (Knutson et al. 2010). In a warming cl imate sea surface temperatures (SSTs) are expected to rise across the Atlantic ( Meehl et al. 2007). SST has long been acknowledged as one of the key factors that influence hurricane formation (Gray 1979) and the maximum intensity (Emanuel 1987). While gl obal climate models have reached a consensus that SST will increase over the next century (Emanuel 2008), models have also concluded that vertical wind shear in the atmosphere will increase as well (Vecchi and Soden 2007; Wang and Li 2008). These two comp onents act to negate each other which make future predictions somewhat uncertain. Based on recent results obtained with finer resolution global climate models and downscaled high resolution regional models, a group of leading climate and hurricane scienti sts have reached a consensus estimate that, by 2100, globally averaged hurricane wind intensity will increase by 2 11% (central pressure deficit by 3 21 %) and the globally averaged frequency of hurricanes will decrease between 6 34% (Knutson et al. 2010). The above projections are used to define future scenarios by adjusting the 3 5. The storm intensity
75 ( central pressure deficit) is modeled as a GEV function which falls into the class of extreme value functions and is parameterized by a location, scale and shape parameter. Katz and Brown (1992) showed that non stationarity (i.e. climate change) can be mod eled probabilistically by changing the function parameters. In the case of the GEV distribution for central pressure deficit, a linear time dependent trend, resulting in the corresponding percent increase of the scenario by 2100, is applied to the locatio n and scale parameter that estimates the change due to climate change (Figure 3 6a). For the storm frequency the percent change for the scenario is applied to each location where the storm rate is calculated and a new fit for the rate is determined (Figur e 3 6b). Sea Level Rise Similar to projections of future hurricane intensity, the literature is full of debate on what future sea level rise may be. Vermeer and Rahmstorf (2009) predict 75 to 190 cm of sea level rise over the next century a large inc rease over most other projections including the IPCC Fourth Assessment Report ( Meehl et al. 2007) which projects sea level to rise 18 to 59 cm globally. Analysis of the past records has shown conflicting views as well. Douglas (1991) concluded that there was a slight deceleration in global mean sea level rise, while Church and White (2006) found a slight acceleration in global records. More recently Houston and Dean (2011) found that SLR is currently not accelerating at a pace necessary to reach the estim ates of the IPCC and Vermeer and Rahmstorf. With so much uncertainty, we consider three sea level change scenarios: 1) and Currents (2010) of the trend in mean sea level for stations near the central Meehl et al. 2007; NRC 2010); Meehl et al. 2007; Vermeer and Rahmstorf 2009;
76 NRC 2010; Rahmstorf 2010). The sea level rise scenarios are shown in Figure 3 6c. The SLR scenarios are modeled by adjusting the mean offshore sea level, allowing it to equilibrate and running the simulations. It is recognized that the bathymetry / topography, land use, barrier islands, etc. will likely change in the next 90 years from their present condition, however it is beyond the scope of this paper to simulate those changes. Local variations in SLR can also be important. An analysis of tide stations on r level data show that the local trend is between 1.8 mm yr 1 (Cedar Key) and 2.24 mm yr 1 (Key West). These rates are just slightly higher than the globally averaged rate of about 1.7 mm yr 1 ( Meehl et al. 2007). Taking an average of the two rates and pr ojecting out to 2100, the local affect is about 3 cm. Given the large uncertainty in the SLR estimates, the local contribution is considered small and the above scenarios are used. Results With the above changes in place, new simulations in CH3D SSMS are carried out with the appropriate changes to sea level and with new optimal storms that reflect the changes in sea level. Figure 3 7 shows the spatial extents for the inundation for each sce nario and return period. Figure 3 7a summarizes the current day scenario as presented above. Figure 3 7b shows the best case future scenario. This scenario features a large reduction in the storm rate and only a slight increase in storm intensity, which is reflected by a reduction in the area affected by the short term inundation events. The increase in intensity and the small increase in sea level is enough to create an increase in flooded area over the present day for the 500 year event (Table 3 4). However for all other events the flooded area is less, as is the affected just value and population. For all cases the flooded volume is less than the current day value.
77 Figure 3 7c shows the spatial extents of various return periods for the mid range cli mate change scenario. For all return periods this represents an increase over the current day scenario. The biggest increase is in the low return period event. The flooded volume for the 10 year storm is more than double that of the present day. This i s in large part due to the additional inundation created by the 50 cm of SLR. The 500 year storm for this scenario will affect nearly 650 thousand people and up to $33 billion worth of property (as defined above to equal or exceed inundation of 0.305 m ). The worst case future scenario depicted in Figure 3 7d shows a very alarming situation. The inundated area increases by over 2.5 times the current day area for the ten year event. This is largely due to the loss of land caused by the 150 cm SLR, but also as a result of the shift to more intense hurricanes. In this scenario the 100 year event, which is the basis for the FIRM, shows that over 675 thousand people will be affected by at least 0.305 m of inundation. This demonstrates that the worst case futu re scenario would lead to a dramatic increase in the requirement of flood insurance with a larg e portion of the residents of Southwest F lorida meeting that requirement. To attempt to separate the influences of sea level rise from those in changes in hurric anes, the three hurricane scenarios are run for present day sea level. Figure 3 8 shows the spatial extents as depicted in Figure 3 7, but at present day sea level. Table 3 6 shows the same metrics as presented in Table 3 4. From Figure 3 8 and T able 3 6 it is clear that sea level rise poses the greatest hazard to inundation. Without consideration of sea level rise, likely changes in hurricane characteristics do not produce a large increase in the inundation hazard. Only the worst case scenario, wh ich features a large increase in hurricane intensity coupled with a slight decrease in
78 hurricane frequency, produces metrics which show a greater hazard than is currently experienced. The influence of the sea level rise can be demonstrated with a MOM for the category 5 storm (taken here as a central pressure deficit of 100 hPa ). The same optimal storm database is used to construct the category 5 MOM depicted in Figure 3 9 for the present day (a), with 21 cm of sea level rise (b), with 50 cm of sea level rise (c), and with 150 cm of sea level rise (d). The technique described here differs from that used in many previous studies (Frazier et al. 2010; Kleinosky et al. 2007; Wu et al. 2002) dealing with SLR and hazard from storm surge. The current study appl ies the SLR at the open boundary and allows it to propagate in where the influence of the topography is accounted for in the surge response, while the three previous studies simply adjusted the topography a set amount corresponding to the specified SLR t his excludes the interaction between the surge and the bathymetry/topography and results in different inundation levels. Figure 3 10 shows the Category 5 MOM with 150 cm of SLR using a coastal model (our technique) (a) and the previously published techniqu e (b), as well as the differences between the two MOMs (c). The previously used technique tends to overestimate the surge in most areas with the exception of the low lying Everglades where resistance to the surge is very weak. Based on this comparison, i t is clear that more robust methods, such as those employed in this study, be used for accurate evaluation of the inundation threat due to SLR. Summary A detailed analysis of the inundation hazard to SW FL has been presented. This analysis is developed b y a combination of optimal storm generation, numerical storm
79 surge and inundation simulation, and multivariate interpolation. The CH3D SSMS model results are used to determine the BFE. In addition, metrics are produced to better quantify the damage from a given surge event in terms of the number of people affected and the cost of the event as well as flooded area and volume. Using the optimal hurricane ensemble to better represent the hurricane climatology, this study produces more accurate BFE for the So uthwest Florida region than that produced by FEMA without using the optimal hurricane ensemble. This work answers the question of how the inundation hazard may change from present climate to future climate scenarios. The inundation hazard is shown to incr ease under both the mid range and worst case future scenarios, due mainly to sea level rise, while changes due to climate effect on hurricane frequency and intensity are less important. When SLR is not considered, only the worst case future scenario resul ts in an increase in inundation hazard. It appears that the expected decrease of hurricane frequency negates the increase of hurricane intensity in producing inundation. Similarly the hazard to coastal property and population was evaluated and depicted. Under present day conditions the high hazard is confined to the Everglades and coastal areas near the rivers and bays of Southwest FL. As depicted in Figure 3 7 and quantified in Table 3 4 much of the area is vulnerable to inundation. The longer term ha zard is much more widespread, for example the hazard from the 500 year event is very large, affecting over half a million residents of Southwest FL and over 5,000 km 2 of land surface with at least 0.305 m of inundation. The hazard increases as SLR is cons idered and the worst case scenario affects over 900,000 residents, resulting in over 7,000 km 2 of property being affected.
80 When SLR is considered, the inundation map generated using a coastal storm surge model differs noticeably from that obtained with a s imple method which applies a uniform change in underlying elevation data as was done by geographers. The simple method significantly overestimates the inundation because it completely ignores the dissipation effect of the land features. For future work, s patial variability in sea level rise (Yin et al. 2010) should also be considered. As prediction of changes in hurricane frequency and intensity becomes less uncertain over time, it will be worthwhile to revisit the topics of this paper. The estimates used herein are based on global estimates. As basin and smaller scale results become available, more accurate depictions of the hazard due to climate change can be developed. Future work can also be conducted to better quantify the correct cut off depth for areas affected by inundation. As mentioned earlier, one foot was used in this study as was done by FEMA in designation of SPHA, but no scientific information supporting this value is readily available. With some effort, the information produced by this s tudy can be incorporated into future coastal planning, coastal construction, and evacuation planning in many different coastal zones in the coming years.
81 A Figure 3 1 High resolution CH3D SSMS model domain for Southwest Florida with focus on Fort Myers and Sanibel Island (A) Population density map for study region (population / km 2 B). Northern boundary is Tampa Bay and southern boundary is Cape Sable
82 B Figure 3 1 Continued
83 Figure 3 2 Study area featuring CH3D SSMS model domain and tracks of tropical storms influencing the area since 1940. Central reference point (CREF) defined as Fort Myers Beach, FL
84 Figure 3 3 Comparison between 100 year flood map (B FE) created using the traditional JPM (46,800 storm simulations) and that created using the optimal method of Condon and Sheng ( 2011a manuscript submitted to Ocean Eng ) (197 storm simulations )
85 A B C D Figure 3 4 Expected inundation (exceeding 30.5 cm) under present day conditions for different return periods. The expected inundation for the A) 10 year; B) 50 year; C ) 100 year; and d) 500 year return periods
86 Figure 3 5 Risk map for present day sea level and hurricane conditions for Southwes t Florida
87 A B C Figure 3 6 Projected changes due to climate change to hurricanes and sea level. Changes to A) storm intensity; B) storm frequency; and C ) sea level for present day conditions (black line) and three future climate scenarios (Best c ase scenario blue dotted; Mid Range scenario green dotted; and Worst case scenario red dotted)
88 A B C D Figure 3 7 Spatial extents for the 10, 50, 100, and 500 year inundation events for different scenarios. F or A) present day; B ) Best c ase future hurricane scenario; C ) Mid Range future hurricane scenario; and D ) Worst case future hurricane scenario;
89 A) B) C) D) Figure 3 8 Spatial extents for the 10, 50, 100, and 500 year inundation events for different scenarios at present da y sea level. For A) present day; B) Best case future hurricane scenario; C) Mid Range future hurricane scenario; and D) Worst case future hurricane scenario;
90 A B C D Figure 3 9 Category 5 MOM for different levels of SLR. A) present day sea level; B) 21 cm of SLR; C) 50 cm of SLR; and D ) 150 cm of SLR
91 A B C Figure 3 10 Category 5 MOM for 150 cm of SLR using different SLR techniques. A ) technique described herein; B ) using simple subtraction of 15 0 cm from base topography; and C) Difference between B and A
92 Table 3 1 Historical Hurricane Parameters Historical Storm (year) Central Pressure Deficit ( hPa ) Radius to Maximum Winds ( km) Forward Speed (m /s ) Storm Heading (N) Notnamed (1944) 45 63 8.0 10 Notnamed (1945) 37 --5.8 62 Notnamed (1946) 27 46 8.5 13 Notnamed (1947) 22 --4.0 12 Notnamed2 (1947) 29 24 6.7 39 Notnamed (1948) 52 13 3.6 24 Notnamed2 (1948) 38 24 7.6 42 Easy (1950) 55 28 2.2 24 Love (1950) 23 --8.0 46 How (1951) 20 --7.2 81 Notnamed (1953) 28 --8.9 51 Hazel (1953) 23 --8.9 46 Judith (1959) 14 --5.8 45 Donna (1960) 75 44 4.0 338 Isbell (1964) 45 56 7.2 36 Abby (1968) 20 --4.0 27 Gladys (1968) 36 31 3.6 47 Floyd (1987) 20 --7.6 61 Keith (1988) 18 135 7.6 65 Marco (1990) 14 19 4.0 354 Gordon (1994) 18 148 4.0 27 Mitch (1998) 23 278 8.9 62 Irene (1999) 27 74 4.5 33 Gordon (2000) 24 46 4.9 21 Gabrielle (2001) 30 46 8.0 34 Charley (2004) 66 19 8.9 15 Wilma (2005) 60 56 7.6 47 Fay (2008) 19 37 2.7 10
93 Table 3 2 Synthetic storm parameter values for traditional JPM P ( hPa ) (P hPa ) R max (n.mi.) V f (mph) X land 33 (980) 53 (960) 73 (940) 93 (920) 113 (900) 13 26 39 52 65 78 2.7 5.4 8.0 10.7 337.5 0 22.5 45 67.5 90 Spaced every 9.3 km. from +370 to 222 relative to CREF (65 locations)
94 Table 3 3 S ynthetic storm parameter discretized probability values (weights) Parameter Value Central Pressure deficit ( hPa ) 33 53 73 93 113 Probability (%) 73.56 17.59 5.53 2.25 1.08 RMW Probability (%) ( km ) 13 6.96 10.38 19.71 40.35 79.39 26 27.54 24.12 29.84 31.58 15.82 39 28.50 23.88 22.21 15.41 3.45 52 19.36 18.67 14.15 7.28 0.93 65 11.34 13.48 8.71 3.56 0.30 78 6.30 9.47 5.38 1.82 0.11 Heading ( N) 22.5 0 22.5 45 67.5 90 Probability (%) 2.51 13.43 31.67 34.75 16.29 1.34 Forward Speed ( m/s ) 2.7 5.4 8.0 10.7 Probability (%) 13.18 44.30 36.19 6.33
95 Table 3 4 Risk metrics for the 10, 50, 100, and 500 year inundation events for scenarios defined in Table 3 5. All statistics reflect inundation greater than 30.5 cm (~ 1foot). Affected population is relative to 2000 census data. Total just value data based on just value of real property as of 2009. Storm Affected Population Just Value of Affected Property (2009 $) Total Flooded Area (km 2 ) Total Flooded Volume (km 3 ) Present Day Scenario 10 Year 6,122 344,871,104 735 0.37 50 Year 102,790 5,066,740,736 2,581 2.13 100 Year 264,910 12,057,786,368 3,471 3.20 500 Year 520,797 24,328,714,240 5,234 6.14 Best Case Future Scenario 10 Year 1,430 103,037,584 349 0.15 50 Year 76,386 3,719,218,688 2,492 2.09 100 Year 190,899 10,494,974,976 3,273 3.00 500 Year 529,697 24,323,721,216 5,246 5.96 Mid Range Future Scenario 10 Year 19,454 1,985,161,856 1,961 1.14 50 Year 188,375 10,506,677,248 3,196 3.25 100 Year 325,718 16,178,281,472 3,954 4.35 500 Year 646,315 33,120,716,800 5,923 7.58 Worst Case Future Scenario 10 Year 249,324 17,302,740,992 3,663 5.04 50 Year 510,234 34,562,613,248 4,935 8.45 100 Yea r 677,577 42,104,897,536 5,811 10.14 500Year 900,777 54,688,997,376 7,224 14.60
96 Table 3 5 Scenarios used for evaluation of the inundation hazard in future climate Worst Case Best Case Mid Range Hurricane Intensity + 21 % + 3 % + 12% Hurricane Frequency 6% 34% 20 % SLR +150 cm +21 cm + 50 cm
97 Table 3 6 Risk metrics for the 10, 50, 100, and 500 year inundation events for scenarios defined in Table 3 5 but at present day sea level All statistics reflect inundation greater than 30.5 cm (~ 1foot). Affected population is relative to 2000 census data. Total just value data based on just value of real property as of 2009. Storm Affected Population Just Value of Affected Property (2009 $) Total Flooded Area (km 2 ) Total Flooded Volume (km 3 ) Present Day Scenario 10 Year 6,122 344,871,104 735 0.37 50 Year 102,790 5,066,740,736 2,581 2.13 100 Year 264,910 12,057,786,368 3,471 3.20 500 Year 520,797 24,328,714,240 5,234 6.14 Best Case Future Scenario 10 Year 0 33,538,700 76 0.03 50 Year 61,028 2,553,325,568 2,202 1.68 100 Year 156,834 8,330,914,304 2,987 2.57 500 Year 472,882 21,026,043,904 4,864 5.42 Mid Range Future Scenario 10 Year 1,032 95,514,880 384 0.17 50 Year 84,113 4,195,028,480 2,438 1.99 100 Year 246,176 11,300,329,472 3,350 3.06 500 Year 513,710 23,780,243,456 5,147 6.01 Worst Case Future Scenario 10 Year 6,380 398,462,272 757 0.38 50 Year 168,174 8,622,438,400 2,976 2.59 100 Year 321,555 14,257,920,000 3,771 3.80 500 Year 565,554 27,654,090,752 5,511 6.89
98 CHAPTER 4 TOWARDS HIGH RESOLUT ION, RAPID, PROBABIL ISTIC EVALUATION OF THE INUNDATION THREAT FR OM LANDFALLING HURRI CANES 1 Overview State of the art coupled hydrodynamic and wave models can predict the inundation threat from an approaching hurricane with high resolution and accuracy. However, these models are not highly efficient and often cannot be run sufficiently fast to provide results two hours prior to advisory issuance within a six hour forecast cycle. Therefore, to produce timely inundation forecast, coarser grid models without wave setup contributions, are typically used which sacrifices resolution and physics. Thi s paper introduces an efficient forecast method by applying a multi dimensional interpolation technique to a pre defined optimal storm database to generate the surge response for any storm based on its landfall characteristics. This technique, which provi applied to the Southwest Florida coast for Hurricane Charley (2004) and Hurricane Wilma (2005) and compares well with deterministic results but is obtained in a fraction of t he time. Due to the quick generation of the inundation response for a single storm, the response of thousands of possible storm parameter combinations can be determined within a forecast cycle. The thousands of parameter combinations are assigned a proba bility based on historic forecast errors to give a probabilistic estimate of the inundation forecast which compare well with observations. 1 To be submitted as Condon, A. J., and Y.P. Sheng: Towards high resolution, rapid, probabilistic evaluation of the inundation threat from landfalling hurricanes
99 Background The extent of coastal inundation from a given hurricane has proven to be difficult to forecast in an efficient manner. High resolution, physics based models such as ADCIRC (ADvanced CIRCulation) (Luettich et al. 1992), CH3D SSMS (Sheng et al. 2006, 2010a, b; Sheng and Paramygin 2010;), POM (Princeton Ocean Model) (Peng et al. 2004; Oey et al. 2006) and FVCOM (Rego and Li 2009; Weisberg and Zheng 2008) have all proven to accurately represent coastal inundation from hurricanes. However these models are all computationally expensive to run, which makes forecasting much more difficult given the tight t ime constraints of a six hour forecast cycle. Typically the National Hurricane Center (NHC) has roughly an hour at most from the time the most recent track/intensity information is received to complete storm surge forecasts for inclusion in the latest advi sory (J. Rhome 2011, personal communication). Dietrich et al. (2011, manuscript submitted to Journal of Scientific Computing ) shows that coupled SWAN and ADCIRC simulations for Hurricane Katrina can take between 2 000 and 10 minutes of wall clock time per day of simulation depending on the computing resources (256 to 8192 computational cores) and solver (implicit or explicit). For similar simulations of Hurricane Katrina, CH3D SSMS runs at about 900 minutes of wall clock time per day of simulation on 8 com putational cores. Both these modeling systems demonstrate that either enormous computational resources or too much wall clock time are needed to develop inundation forecasts in a timely manner. In addition the National more probabilistic forecasts that involve an ensemble of simulations (NRC 2006). Given the one hour time window available to produce a hurricane storm surge forecast, it is currently not possible to run an ensemb le of thousands of storms with a high resolution
100 modeling system. Other attempts to generate a timely estimate of the inundation response have been made. Saffir Simpson Hurricane Scale (SSHS) (Simpson 1974) attempted to relate the storm surge hazard to hurricane intensity. Following the active Atlantic hurricane seasons of 2004 and 2005, it became obvious that storm surge hazard depends on other hurricane characteristics (e.g., size) in addition to intensity. Irish et al. (2008) showed that storm size ca n cause variations of up to 30% in storm surge for a given storm intensity. Kantha (2006) and Powell and Reinhold (2007) developed storm surge classification schemes that look at hurricane characteristics beyond intensity to estimate the storm surge hazar d posed by a particular hurricane. These scales represented an improvement over the SSHS as they accounted for storm size. However, storm surge is also dependent on the landfall location, track heading, and translational speed of the hurricane among other things which these scales do not account for (Jordan and Clayson 2008). Recently the NHC has officially removed storm surge from the SSHS (NOAA NHC 2011a) due to the large differences that can develop in the surge response and inundation for storms with the same intensity but different other characteristics, and identical storms making landfall along different portions of the coast. The offshore bathymetry, coastline configuration, and topography of the affected area play a large role in dictating the ex tent of the inundation. Mildly sloping bathymetry has been shown to generate a larger surge response at the coast than steeper slopes (Irish et al. 2008). Likewise the landfall location can be important as demonstrated by Weisberg and Zheng (2008) for id ealized storm surge simulations in the Tampa Bay area. The topography of the area and roughness of the terrain will dictate the extent of the coastal
101 inundation (Fletcher et al. 1995). Irish and Resio (2010) accounted for the local bathymetry in their hy drodynamics based scale, which gives the best quantitative results for the potential surge at the coast for 28 historical hurricanes compared to SSHS, Powell and Reinhold (2007), and Kantha (2006). However this scale lacks information regarding coastline configuration and topography which is essential in determining the hazard from inundation. In addition to the classification schemes described above to qualitatively estimate inundation hazard, more quantitative measures have been developed. The NHC uses the SLOSH (Sea, Lake, and Overland Surges from Hurricanes) ( Jel e snianski et al. 1992) model operationally to produce hurricane forecasts. SLOSH is extremely efficient, with most approximately 100 hour simulations taking under one minute on a single comput ational core, and is typically accurate within 20 percent (Jelesnianski et al. 1992). The model does not account for dynamic effects of tides and waves, which other forecasting systems incorporate. The largest drawback to the SLOSH forecasts is the coars e resolution (Fort Myers grid has average resolution of 2 km) of the model domains compared to the other models mentioned. With a coarse grid many of the important small scale topographic and bathymetric features are not captured in the model, and the eff ects of waves may not be accurate even if a wave model were coupled to SLOSH. Despite these drawbacks, SLOSH is used in the generation of forecasts and probabilistic products (P Surge) (Glahn et al. 2009; Taylor and Glahn 2008). Irish et al. (2011) has r ecently produced probabilistic maximum hurricane surge forecasts based on surge response functions (Irish et al 2009; Resio et al. 2009), hurricane characteristics, and joint probability statistics. This approach uses high
102 resolution simulation results to generate surge response functions for a given region that can determine the surge response for a set of meteorological parameters. This approach is very promising but has underlying assumptions that the influence of the storm angle and forward speed can be neglected when compared to the storm intensity, size, and landfall location. While their work shows that in most cases this is a fair assumption based on model results, there are outliers which can be important. As pointed out by Rego and Li (2009) and Jelesnianski (1972), neglecting the forward does not account for tides and wave setup, which can contribute significantly to the surge and inundation. This paper addresses the rapid generation of high resolution probabilistic inundation forecasts. The optimal storm generation and multivariate interpolation technique of Condon and Sheng (2 011a, manuscript submitted to Ocean Eng ., 2011b manuscript submitted to Natural Hazard ) is applied to a single storm to generate an estimate of the inundation hazard for Southwest Florida from hurricanes Charley (2004) and Wilma (2005). This is accomplish ed in an adaptive manner to improve accuracy with each forecast. The technique considers the effect of storm intensity, size, landfall location, forward speed, and approach angle on the surge response. The optimal storm database, which includes wave effe cts on surge and inundation, is produced and can be combined with a simple tidal model to account for tidal effects. Analysis of the official NHC forecast errors for the past five years (NOAA NHC 2011; J. Franklin 2011,
103 personal communication) allows for efficient generation of high resolution probabilistic surge estimates as well for each forecast period within the one hour time constraints. Optimal Storm Generation and Multivariate Interpolation For this study an optimal storm ensemble for the Southwest Florida basin (NHC SLOSH efm2 basin) is developed following the method presented in Condon and Sheng (2011a manuscript submitted to Ocean Eng .). In this method a dimension adaptive m to optimally select an ensemble of storms. The method is adapted from that of Agbley (2009) to make it more transportable and accurate for storm surge estimation. This is done by using the dimension adaptive sparse grid formulation of Gerstner and Grie bel (2003) in the form of the spiniterp MATLAB toolbox (Klimke and Wolhmuth 2005; Klimke 2007) and coupling with the SLOSH model (Jelesnianski et al. 1992) to obtain the storm surge simulations that provide the optimal recovery of the surge response for a ny given set of storm parameters. Multivariate regression is used to build the response from the optimal simulation database. This is achieved with multivariate adaptive regressive splines (MARS) as done by Friedman (1991). In Condon and Sheng ( 2011a man uscript submitted to Ocean Eng ., 2011b manuscript submitted to Natural Hazards ) the hurricanes are characterized by five max ), the translational speed (V f (angle of a pproach) and the landfall location (X land ). These studies determined the hazard to the region in present day and future climates through an adapted version of the joint probability method (JPM) which used probabilistic descriptions of these five variabl es combined w ith the surge response from 197 optimal storm simulations for the basin. The 197 high resolution optimal
104 simulations are performed using CH3D SSMS. CH3D (Curvilinear grid Hydrodynamics in 3D) is a hydrodynamic model originally developed by S heng ( 1987, 1990 ) and has been significantly enhanced (e.g. Sheng et al. 2010a; Sheng and Kim 2009 ) The model can simulate 2 D and 3 D barotropic and baroclinic circulation driven by tide s wind s wave s and density gradients. The model uses a boundary fitted non orthogonal curvilinear grid in the horizontal directions and terrain following sigma grid in the vertical direction to allow accurate representation of the complex coastal and estuarine shoreli nes where forecasting of storm surge, waves and inundation is needed. Based on the finite volume method, CH3D is strictly conservative for momentum, water mass, as well as for temperature and salinity. CH3D uses a robust second order closure model for ca lculating vertical turbulent mixing (Sheng and Villaret 1989 ) In the horizontal direction, Smagorinksy type turbulent diffusion coefficients are used. With its ability to simulate flooding and drying, CH3D is used for simulating and forecasting storm su rge and circulation in many coastal regions throughout Florida and the U.S. CH3D has been dynamically coupled to a wave model SWAN (Booji et al. 1999; Ris et al. 1999), using the same curvilinear grid, to produce CH3D SSMS, an integrated Storm Surge Modeli ng System (Sheng et al 2006, 2010a,b, Sheng and Liu 2011). To provide open boundary conditions for CH3D, CH3D SSMS uses basin scale models, such as ADCIRC (Luettich et al. 1992), HYCOM (Halliwell et al. 1998, 2000; Bleck 2002) and NCOM (Barron et al. 2005 ) to simulate hydrodynamic processes in a larger, regional scale domain. To enable efficient simulation, this study couples the CH3D model, with a high resolution coastal grid, to the basin scale model which has a relatively coarse grid in the offshore as well as coastal regions. To provide open
105 boundary condition for SWAN, CH3D SSMS uses the output of a large scale wave model such as WaveWatch III (Tolman 1999, 2002). CH3D SSMS has been used extensively to simulate storm surge and inundation due to various tropical storms including Hurricane Isabel (Sheng et al. 2010a), Charley (Sheng et al. 2006; Davis et al. 2008, 2010), Ivan (Sheng et al., 2010b), and Wilma (Paramygin and Sheng 2011, manuscript submitted to J. Geophys. Res. ). Sheng and Paramygin (2010) combined the baroclinic circulation element of CH3D with CH3D SSMS to forecast the storm surge, inundation, and 3D baroclinic circulation in northeast Florida during Tropical Storm Fay. For this study CH3D SSMS uses the dynamically coupled CH3D SWAN models for the coastal domain. Open boundary conditions for CH3D are provided by a coarse grid ADCIRC model, while open boundary conditions for SWAN are provided by a coarse grid basin scale SWAN and WaveWatch III models. Little difference (less than 0.01% in i nundation) is found between the final results obtained using SWAN or WaveWatch III in the offshore region. Hence SWAN is used for both the offshore region and the coastal region. CH3D SSMS uses wind fields developed by an analytic hurricane wind model base d on Holland (1980). The winds are developed as straight line tracks of constant intensity until landfall. For this study, the storm intensity is dissipated following Vickery (2005) post landfall. To save computational cost, this study runs the CH3D mod el in 2D (vertically coefficient is developed based on land use data obtained from United States Geological Survey (USGS 2011) with an offshore value of 0.02 (dimensionless). The coastal model domain featur es a minimum horizontal resolution of approximately 20 m in the
106 coastal zone and an overall average grid size of ~ 100m with a maximum of ~700 m offshore. The most up to date LIDAR topography data from NOAA Coastal Services Center (NOAA CSC 2011), topogra phy data from United States Geological Survey (USGS 2011), and bathymetry data from NOAA National Geophysical Data Center (NOAA NGDC 2011), have been incorporated into the domain shown in Figure 4 1. In previous studies (Condon and Sheng 2011a manuscript s ubmitted to Ocean Eng ., 2011b manuscript submitted to Natural Hazards ; Toro et al. 2010a, b; Niedoroda et al. 2010) the astronomical tide, an important component of the inundation, is included as an error term in the JPM formulation but not directly simula ted. For this study the astronomical tidal amplitude and phase are considered in the selection of the optimal storm surge simulations. The range of expected tide levels is included in the determination of the optimal simulations. This resulted in a total of 265 optimal simulations for similar estimated error as that obtained with 197 storms and no tides. These are then adjusted to account for the phase by running simulations for both increasing (flood) and decreasing (ebb) tides for all intermediate tida l amplitudes. For amplitudes at the peak or trough of the tidal cycle, only one simulation is run. This resulted in a total of 448 simulations of the surge response in the optimal database. This substantial increase (over the 197 responses without tides ) in the number of necessary optimal storm simulations will be analyzed below. To account for the variations in tide, a simplified sinusoidal tide is applied on the western boundary. This tide is damped and shifted so that the elevation and phase of the p redicted tide at the time of landfall matched that specified in the optimal storm
107 development. The magnitude of the shift and damping is made to match the tidal levels at the NOAA Naples tide gauge (NOAA 2011). Forecast Inundation Application on Southwe st Florida Coast The S outhwest Florida coast experienced landfalls from two distinctly different Hurricane Charley (2004) was a compact and intense hurricane that experienced a major shift in its forecast track just prior to landfall. Hurricane Wilma (2005) was a strong, large hurricane that was well forecasted with little change in track from forecast to forecast. These two storms show very different characteristics which make them ideal for hind cast analysis using our interpolation method. Hurricane Charley Hurricane Charley made landfall near Cayo Costa, just north of Captiva Island around 1945 UTC on A ugust 13, 2004 (Pasch et al. 2011a ). Charley was a very intense (240 k m/hr winds at landfall) and compact (R max of ~ 11 km) storm. The evolution of the hurricane forecast is shown in Figure 4 2a along with the hurricane parameters used in the interpolation. From this it is seen that for most of the forecast period, Charley was believed to be heading towards Tampa Bay. In the final forecast advisory before landfall (Charley advisory 18, c18) the track took an abrupt change from previous advisories, with landfall forecast over 100 km to the south. In addition the size of C harley decreased considerably and the intensity forecast increased. Due to the small size, high intensity, and shifting track Charley is a difficult storm to forecast. The multivariate interpolation method is applied to hurricane Charley in several differ ent ways: with and without consideration of tidal effects, and in an adaptive and non adaptive way. For the Southwest Florida coast the tidal range is about 1.5 m
108 during maximum spring tide conditions. During the tidal cycles prior to landfall the tidal range is generally about 1 m and landfall occurred with a negative ( 0.4 m NAVD88) elevation during ebb tide. Evaluation of the interpolation results are made with and without tide considerations. In addition to the tidal considerations, two different a nalysis methods are considered. The first is to develop the expected inundation based on the optimal storm database (197 storms without tides, 448 with tides) (hereafter called Non Adaptive (NON ADAP)). The second is to fold the previous forecast results into the optimal storm database. This adaptive technique (hereafter called Adaptive (ADAP)) is employed by first determining the expected inundation based on the original optimal storm database for the initial forecast (NHC Forecast advisory 12, for Char ley (c12)) based on the forecast hurricane parameters near landfall using the multivariate interpolation technique. Simultaneously CH3D SSMS would be simulating the surge response based on the forecast track and winds. For the next forecast advisory, the multivariate interpolation technique would be applied to the original optimal storm database plus the response from the previous CH3D SSMS forecast. In this way the results of the previous forecast are folded into the next forecast to improve accuracy. Assuming little change in forecast track and intensity, this method will improve the forecast results by including past simulations in the optimal database which has input parameters that are very similar to the current forecasted parameters. Both the ADAP and NON ADAP techniques can only be as good as the simulation results that are used to make up the optimal storm databases. Figure 4 3a shows a comparison between the simulated CH3D SSMS results using the best track winds and including the simple tide mo del and high water mark (HWM) data collected by the
109 Florida Department of Environmental Protection (FDEP 2004) following hurricane Charley. Figure 4 3b shows the same comparison for CH3D SSMS without tides. There is little difference in the results betwe en the two simulations, with the simulations with tides showing a slightly smaller average error and a larger correlation coefficient. Both simulations show a positive average error indicating that the model tends to overestimate the surge height slightly When the interpolated results are compared to the HWM data, they show that overall the average error remains small as demonstrated in Figure 4 3 and summarized in Table 4 1. Figure 4 3c shows the ADAP results with tides included, 4 3d shows the ADAP results without tides, 4 3e shows the NON ADAP results with tides, and 4 3f show the NON ADAP results without tides. In all cases the results show a slight trend to more scattered results than the actual CH3D SSMS simulations. The results including tides tend to be a little lower than the results without tides, due to the negative tidal amplitude at landfall. There is an improvement both with and without tides when previous forecasts are included as is the case in the ADAP results where simulations using NHC forecast advisories 12 18 are included in the optimal storm database. In general the results without tides show a little better correlation while the results with tides show a slightly smaller average error. It can take up to twice as long to obtain the interpolated results from the optimal database with tides as it does to obtain the results from the database without tides. Figure 4 4 shows the envelope of high water (EOHW) for Charley from the CH3D SSMS simulation with tides (a), without tides (b) and the adaptive interpolated results with (c) and without tides (d). Figure 4 4 shows that the interpolated results do a good
110 job of cap turing the extent and height of the inundation. The results without tides tend to produce slightly greater inundation depths and extents due to the lack of a negative tidal forcing. The adaptive results with tides were obtained in eight minutes, the adap tive results without tides were obtained in five minutes while the full CH3D SSMS simulation with and without tides takes approximately ten hours each to complete with waves effects included. Hurricane Wilma In contrast to hurricane Charley, hurricane Wil ma was well forecasted as shown in Figure 4 2b. Hurricane Wilma made landfall in southwest Florida on Oc tober 24, 2005 (Pasch et al. 2011b ) as a category 3 hurricane with winds of 190 km/hr. Wilma was a very large hurricane (R max ~ 65 km) and did not dev iate much in track, intensity, size, forward speed, or approach angle from forecast to forecast. This is in contrast to Charley which had a large shift in track, intensity, and size during the forecast period. The same approach used with Charley was appli ed to Wilma. Figure 4 5 shows the HWM comparison as in Figure 4 3 and Table 4 2 summarizes the metrics as was done in Table 4 1. Figure 4 5a shows the comparison between the CH3D SSMS results using the best track winds and including tides and the HWM data collected by USGS. Figure 4 5b shows the same comparison but with CH3D SSMS run without tides. Figure 4 5c and 4 5d show the adaptive interpolated comparison with (c) and without (d) tides. Figure 4 5e and 4 5f show the non adaptive interpolated compar ison with (e) and without (f) tides. As was the case with Charley, the inclusion of tides does not seem to have much of an effect on the effectiveness of the model or interpolation scheme to produce results comparable to the HWM data. Wilma made landfall with a very slightly negative tidal elevation ( 0.086 m NAVD88) during ebb tide. This small tidal influence
111 likely explains the lack of a difference between the results. For this region the tidal influence is generally rather small, however inclusion of tides may be more important in other basins. In general there is a much better correlation between all the results and the observed HWMs than for Charley. As mentioned Wilma was a much better forecasted storm which is shown in the improvement in the ada ptive results compared to the non adaptive results as previous forecasts are included in the optimal storm database. Figure 4 6 shows the envelope of high water (EOHW) for Wilma from the CH3D SSMS simulation with tides (a), without tides (b) and the adap tive interpolated results with (c) and without tides (d). As was the case with Charley, the interpolated results do a very good job capturing the inundation extent. The simulations and the interpolated results both capture the surge response well in the populated areas around Sanibel and Captiva Island. The interpolated results tend to be a little low at the peak of the surge in the Florida Everglades. The underestimate can be explained by considering potential errors in the input characteristics. The max V f across the domain as the storm propagates towards shore. To develop the single set of test parameters used to determine the inundation response, the central pressure deficit, radius to maximum winds, and fo rward speed of the hurricane are averaged over the six hour period prior to landfall. The landfall location and angle of approach are taken as those at landfall. This set of test parameters has error built into them since in reality they do vary but a si ngle set is necessary to run the interpolation. Since our method can rapidly develop the high resolution inundation response it is better to develop the
112 response for a number (thousands) of possible storm characteristics to develop a better estimate of th e inundation response as is done next. Generation of High Resolution Probabilistic Inundation Response Estimates The interpolation method has been shown to serve as a good first estimate of the inundation hazard from an approaching hurricane. The method is based on determining by f max V f land ). The storm of interest. There is some error built in since the optimal storm da tabase is built using straight line tracks of constant hurricane characteristics until landfall, while in reality these parameters change prior to and after landfall. As mentioned a six hour e results. Since the method can rapidly produce the inundation response it is possible to include thousands of parameter combinations, each with a probability of occurrence, into the Test Set to develop a probabilistic inundation response in a timely mann er. The Test Set for each storm i s expanded to include likely values based on historical forecast errors. The official NHC forecast track (along and cross track) and intensity errors are obtained for the past five years (NOAA NHC 2011, J. Franklin 2011, p ersonal communication). These are analyzed and fit to a normal distribution to associate a probability with each (Figure 4 7). To determine the central pressure deficit from the wind intensity error, the model of Knaff and Zehr (2007) was used. The land fall location, forward speed, and storm heading can be directly computed from the data. The only variable that is not forecasted is the storm size. To determine a probability distribution for the error in this term, the model of Willoughby and Rahn (2004 ) was
113 used to determine the R max from the latitude and wind intensity. It is seen in Figure 4 7 that for the 000 hour forecast the error is very well confined to a small range and expands as the forecast advances in time. Depending on how far out landfal l is from the current time, the appropriate probability distribution is applied to each parameter. Each parameter is discretized into a number of values and the response for each parameter combination is determined. That response is assigned the joint p robability of the parameter combination based on : (4 1 ) In this case the tides were not included since the response can be computed in less time without tides and they did not contribute any significant improvement to the results. However, as is done by Niedoroda et al. (2010) and Condon and Sheng (2011a manus cript submitted to Ocean Eng ., 2011b manuscript submitted to Natural Hazards ) the tides were included as a secondary error term in the determination of the probabilistic inundation. For each grid cell in the domain a histogram of accumulated storm probabi lity was constructed consisting of 500 2 cm wide elevation bins spanning the range from 0 to 12 meters. These histograms represent approximations of the surge height density distributions. An error function based on the local tide (with standard deviatio n of 0.2 m) and precision of CH3D SSMS (standard deviation ~ 0.15 surge height) is redistributed over the bins in the histogram creating a modified version of the original histogram. This is then summed from the highest bin down to the lowest bin to give an estimate of the cumulative inundation distribution for the grid cell. With the CDF of the inundation, the inundation for any probability can be interpolated from the curve. The inundation response that is 90%, 75%, 50%, 25% and 10% likely to
114 occur is determined. These responses can be determined within the one hour time constraint on a single computational core. Figure 4 8a shows the adaptive interpolated results without tides for hurricane Charley using the single set of Test parameters as shown in F igure 4 4d. Panels b, c, d, e, and f of Figure 4 8 show the inundation heights with a 90, 75, 50, 25, and 10 percent chance of occurrence based on the best track simulation and 000 hour probabilities. Figure 4 8 demonstrates that there is some variance i n the inundation extents and depths; however it is not that great since the storm probabilities for 000 hour forecast are well confined near the actual forecast value so the new Test Set does not feature a very large spread in the storm parameters. Figure 4 9 shows the same panel of plots as Figure 4 8 but for hurricane Wilma. By adjusting the Test Set to include some variation in the storm parameters the resulting EOHW looks very similar to the actual model results for the 90% probabilistic response. Fig ures 4 8 and 4 9 show that by considering a larger Test Set the interpolated inundation response can better match the actual model results. Figure 4 8 and 4 9 a re constructed using the 000 hour forecast probabilities which feature little variance around t he actual forecast. Figure 4 10 demonstrates the evolution of a complete forecast of hurricane Wilma with 90% chance of occurrence. Figure 4 10a shows the inundation response based on Wilma forecast advisory 32. This advisory has landfall forecast appro ximately 24 hours out, so the 024 hour probabilities are used. Figure 4 10b shows the inundation response based of forecast advisory 33 and 024 hour probabilities; 4 10c is the response for advisory 34 and 012 hour probabilities; 4 10d is based on advisor y 35 and 012 hour probabilities; 4 10e shows the response for advisory 36 and 000 hour
115 probabilities; and 4 10f shows the response from the best track winds with the 000 hour forecast error data. Figure 4 10 demonstrates how the surge response changes wit h each forecast based on the input parameters and the forecast error probabilities. The progression of forecasts show an increase in surge as the storm is forecast to become more intense. The spatial extent of the inundation is largest in the earlier for ecasts where the uncertainty in landfall location is greatest. As the forecast becomes more refined and the forecast error decreases the surge response becomes more focused on the area of landfall in the Everglades. Summary The rapid evaluation of the inu ndation threat is necessary for disaster planning when a hu rricane is forecast to affect a coastal area. Current state of the art numerical modeling systems provide accurate estimates of this response, but require a large computational cost to run and may not be able to produce a forecast in the six hour window between forecast advisories. With this in mind a technique for the rapid and high resolution evaluation of the inundation hazard has been developed and presented. algorithm for the selection of optimal storms for a basin. A database of the surge response for the optimal storms can be built using a state of the art storm surge modeling system for the basin. When a hurricane is forecast to affect the basin, multiva riate interpolation can be used to estimate the surge max V f land ) of the approaching hurricane. This technique is tested in S outhwest Florida for hurricanes Charley and Wilma both with and without a simple tidal model. For this basin the use of the tide model did not contribute a large improvement to the results, but does nearly double the time
116 needed to build the surge response. An adaptive method that includes previous for ecasts and simulated surge responses into the optimal database is shown to improve the results, especially when the storm is well forecasted, with little variation in intensity and track over previous forecasts, like Wilma For Wilma the forecast track di d not shift much, leading to a better interpolated inundation response. For Charley there is little difference between the adaptive and non adaptive techniques since the final forecast is very different from previous forecasts. The largest source of error in the method is the parameterization of a hurricane by a single set of five storm characteristics. These characteristics are not constant throughout the forecast but the method builds the surge response based on the optimal storm database that is constr ucted using straight line tracks of constant characteristics. To minimize this error a number of likely changes to the storm characteristics i s considered. This i s done by examining the official NHC forecasts error data and applying a range of variations to each parameter based on this data. Each discrete parameter value is given a probability based on the error data so that the joint probability of each parameter set can be determined. In this way inundation probabilities can be determined for the stor m. The technique presented provides a quick way to determine the expected inundation from an approaching hurricane by utilizing a database of high resolution optimal storm inundation responses generated by a state of the art numerical modeling system. Thi s technique will provide emergency managers the inundation data they need, as well as the probability associated with the inundation in a timely manner so that proper disaster preparation plans can be made.
117 Figure 4 1 High resolu tion CH3D SSMS model domain for Southwest Florida with focus on Fort Myers and Sanibel Island. Northern boundary is Tampa Bay and southern boundary is Cape Sable
118 A B Figure 4 2 Evolution of forecast tracks and parameters fo r hurricanes Charley and Wilma. a) hurricane Charley; and b) hurricane Wilma. Dashed box shows outline of CH3D SSMS model domain. Labeling corresponds to NHC forecast advisorty (i.e. c12 12 th forecast advisory for hurricane Charley)
119 A B C D Figure 4 3 Comparison between HWMs and simulated /interpolated results for hurricane Charley. F rom A ) CH3D SSMS with tides; B ) CH3D SSMS without tides; C ) interpolated results using Ada ptive procedure including tides ; D ) interpolated re sults using Adaptive procedure without ti des ; E ) Non Adap tive results including tides ; and F ) Non Ad aptive results without tides
120 E F Figure 4 3 Co ntinued
121 A B C D Figure 4 4 Envelope of high water for best track hurricane Charley simulation in CH3D and Interpolated results. A) CH3D SSMS with tides; B ) CH3D SS MS without tides; C ) Adaptive interp olated results with tides; and D ) Adaptive interpolated results without tides
122 A B C D Figure 4 5 HWM comparison between USGS HWMs collected during Hurricane Wilma and CH3D and Interpolated results. A ) CH3D SSMS results with tid es; B ) CH 3D SSMS results without tides; C ) Adaptive in terpolated results with tides; D ) Adaptive inter polated results without tides; E ) Non adaptive interp olated result s with tides; and F ) Non adaptive interpolated results without tides
1 23 E F Figure 4 5 Continued
124 A B C D Figure 4 6 Envelope of high water for best track Hurricane Wilma simulation in CH3D and Interpolated results. A ) CH3D SSM S with tides; B) CH3D SSMS without tides; C ) Adaptive interpolated results with tides ; and D ) Adaptive interpolated results without tides
125 A B C D E Figure 4 7 PDF of hurricane f orecast errors A ) track (lan dfall location); B) intensity; C ) sto rm size; D) forward speed; and E ) storm heading; based on 2005 2009 NHC Atlantic Basin forecasts
126 A B C D Figure 4 8 Probabilistic e nvelope of high water for Hurricane Charley a) Adaptive interpolation forecast using best track forecast parameters; b) Probabilistic forecast with 90 percent chance of occurrence; c) Probabilistic forecast with 75 percent chance of occurrence ; d) Probabilistic forecast with 5 0 percent chance of occ urrence ; e) Probabilistic forecast with 25 percent chance of occurrence ; and f) Probabilistic forecast with 1 0 percent chance of occurrence based on 000 hour forecast errors and best track parameters
127 E F Figure 4 8 Continued
128 A B C D Figure 4 9 Probabilistic e nvelope of high water for Hurricane Wilma a) Adaptive interpolation forecast using best track forecast parameters; b) Probabilistic forecast with 90 percent chance of occurrence; c) Probabilistic forecast with 75 percent chance of occ urrence; d) Probabilistic forecast with 50 percent chance of occurrence; e) Probabilistic forecast with 25 percent chance of occurrence; and f) Probabilistic forecast with 10 percent chance of occurrence based on 000 hour forecast errors and best track par ameters
129 E F Figure 4 9 Continued
130 A B C D Figure 4 10 Evolution of adaptive inundation response with 90 percent chance of occurrence for Hurricane Wilma for different forecast advisories. a) Advisory 32; b) Advisory 33; c) Advisory 34; d) Advisory 35; e) Advisory 36; and f) the Best Track
131 E F Figure 4 10 Continued
132 Table 4 1. Correlation coefficient and average error (m) between simulated (CH3D SSMS) and interpolated (ADAP, NON ADAP) and observed high water marks for Hurricane Cha rley CH3D SSMS ADAP NON ADAP R 2 Avg. Error (m) R 2 Avg. Error (m) R 2 Avg. Error (m) With Tides 0.6 0.14 0.47 0.08 0.47 0.064 Without Tides 0.6 0.18 0.55 0.19 0.55 0.23
133 Table 4 2. Correlation coefficient and average error (m) between simulated (CH3D SSMS) and interpolated (ADAP, NON ADAP) and observed high water marks for Hurricane Wilma CH3D SSMS ADAP NON ADAP R 2 Avg. Error (m) R 2 Avg. Error (m) R 2 Avg. Error (m) With Tides 0.8 0.16 0.91 0.013 0.86 0.25 Without Tides 0.81 0.24 0.88 0.0002 0.63 0.096
134 CHAPTER 5 CONCLUSION In this study, a new technique to rapidly generate the high resolution inundation response given a set of storm parameters is presented. The evaluation of the inundation threat due to hurricane generated storm surge is vital for emergency managers and coastal planners. This information is needed for both long term planning and immediate response prior to and after the landfall of a hurrican e. The technique described herein provides a high resolution depiction of the inundation hazard for any set of storm parameters. The inundation response generated for a specific set of storm parameters can be: combined with the response of thousands of oth er storm parameters and combined with probabilistic descriptions of the local climatology to generate Base Flood Elevation (BFE) maps with a certain return period; combined with the response of thousands of other storm parameters and composited into a Maxi mum Envelope of Water (MEOW) or Maximum of MEOWs (MOM) map; used as the first estimate of the inundation response for the given parameters; or combined with the response of thousands of other storm parameters and combined with probabilistic descriptions of historical hurricane forecast errors to generate a probabilistic estimate of the inundation for an approaching hurricane. In order to generate an inundation response for a given set of storm parameters, an optimal storm database needs to be developed firs t. The approach described here allows for the rapid selection of the optimal storms for a basin by utilizing dimension adaptive sparse grids. Sparse grids can achieve greater accuracy in an interpolation as a regular grid with the same number of nodes by e xtending well known univariate interpolation formulas to the multivariate case by using tensor products in a special way.
135 The selection can become even more optimized by including dimension adaptivity which calculates how refinements in each dimension help to reduce the overall interpolation error. A dimension adaptive sparse grid scheme has been coupled with the highly efficient Sea, Lakes, and Overland Surges from Hurricanes ( SLOSH ) storm surge model to select the optimal storms. The response generated by SLOSH is used to refine the next selection of input storm parameters. This system can be set up and run for any coastal basin in the United States so that the optimal storm selection can occur in less The optimal storms were first simul ated in SLOSH and the envelope of high water (EOHW) for each simulation recorded and added to the optimal storm database. For Southwest Florida this totaled 197 simulations. A base flood elevation (BFE) map was generated using the traditional JPM approach which involved 46,800 storm parameter combinations ( simulations ) and by utilizing the 197 storm optimal database and multivariate regression to obtain the response for the 46,800 parameter combinations. The two BFE maps were very well correlated with a cor relation coefficient around 0.9 and an averaged error of around 10 cm or less depending on the return frequency. With the approach verified using SLOSH, a state of the art, high resolution, coupled hydrodynamic and wave modeling system Curvilinear Hydrodyn amics in 3D Storm Surge Modeling System (CH3D SSMS) was used to determine the current and future inundation hazard to Southwest Florida. The current hazard shows over a quarter of a million people in danger from the 100 year event and over half a million from the 500 year event. To determine the future hazard three scenarios affecting sea level and
136 continuation of the linear increase in sea level resulting in 21 cm of se a level rise (SLR) by the year 2100. Hurricane frequency was predicted to decrease by 34 % and hurricane frequency was predicted to increase by 3 of 50 cm, an intensity increase of 12% and frequency decrease of 20 %. ane intensity to increase by 21 % and hurri cane frequency to decrease by 6 %. The results of the interpolated results show that inundation hazard for the 100 year event would actually decrease under increase in the hazard to Southwest Florida. Over half a million residen ts would be at risk from the 50 year event and nearly 900 million people and nearly $ 55 billion worth of property would be affected by the 500 year event. The SLR is the largest contributor to changes in inundation hazard. By just considering changes in th e hurricane intensity greater than that presently experienced indicating that in terms of the probabilistic inundation hazard the decrease in hurricane frequency acts to n egate the increase in hurricane intensity. T he analyzed results were obtained by running CH3D SSMS under the prescribed SLR conditions so that the interaction between the surge and bathymetry and topography was accounted for. A second approach in which the elevation data is simply decreased by the SLR amount was analyzed. A comparison of the two methods show that a simple decrease in the elevation data does not accurately represent the effects of SLR. In general the simple method tends to overestimate the r esponse since the interaction with the topography is not accounted for.
137 The inundation hazard products generated above are ideal for planning and determining mitigation strategies. However when a hurricane is approaching, a more storm specific hazard analy sis is needed to plan evacuations and the dispersal of post storm aid. Current state of the art, high resolution, numerical modeling systems such as CH3D SSMS can take many hours of wall time to generate an estimate of the inundation hazard. The interpol ation technique can be combined with the modeling system to generate storm specific estimates of the inundation hazard. This adaptive procedure is achieved by determining the inundation response for the forecast hurricane parameters and simultaneously runn ing a complete simulation in CH3D SSMS. The CH3D SSMS response is folded into the optimal storm database so that the next forecast using the interpolated storms should be more accurate. The method i s used to determine the inundation response for hurricanes Charley (2004) and Wilma (2005). The results show that the method is a very good first estimate of the surge response. The results for Wilma, which was well forecasted, were better than those for Charley which was a very small and intense hurricane that h ad a very large shift in track. The method has an inherent error in that the hurricane is parameterized by five variables that change over time, but are assumed not to vary in the generation of the optimal storm database. To account for this error, thousan ds of combinations of the inundation response from likely storm parameters are determined. The likely parameters are determined from historical hurricane forecast errors. The joint probability of each parameter combination is calculated to associate probab ility to each inundation response. In this way a probabilistic high resolution inundation forecast is generated
138 within a forecast cycle, something that currently cannot be done with a state of the art modeling system. The work described here provides a con tribution to improving the accuracy and efficiency in inundation forecasting. The major findings for this study can be summarized as: (1) an optimal storm generation technique was developed, (2) the technique can easily be applied to any coastal basin, (3) multivariate interpolation can be used to generate the inundation response for any storm given a set of hurricane input parameters (4) t he re is large advantage in using an optimal storm database to build the inundation response in order to save on co mput ational cost and efficiency, (5) e valuation of the present day inundation threat for Southwest Florida shows over $ 12 Billion worth of property value would be affected by the 100 year storm event (6) c onsideration of future climate change scenarios shows that SLR is likely to cause the largest increases in the inundat ion hazard in a warming climate, (7) t he greater inundation hazard caused by increases in hurricane intensity is mostly offset by the projected decrease in hurricane frequency, (8) i n order to accurately simulate inundation with SLR, complete hydrodynamic model simulations should be per formed that account for the SLR, (9) s imply subtracting an amount of SLR from the base elevation tends to over predict the inundation by not accounting for inter action between the inundatio n and the topography/bathymetry, (10) t n from an approaching hurricane, (11) i nundation forecasts can be generated in an adaptive manner that combines complete storm surge modeling system forecast simulations with those from the pre computed optimal storm database to provide rapid, high resolution inundation
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151 BIOGRAPHICAL SKETCH Andrew Condon was born in 198 2 in B oston, Massachusetts He received his B.S. degree in Meteorology from Florida Institute of Technology in 2005 He started his Ph.D. degree in August 2007 at University of Florida under the supervision of Y. Peter Sheng and received his Ph.D. from the University o f Florida in the fall of 2011 He worked on storm surge modeling and the generation of probabilistic inundation maps He was a National Defense Science and Engineering Graduate (NDSEG) Fellow for three years with funding for his research on the evaluation of the inundation hazard from storm surge