A new approach to spatially explicit flood loss characterization via hazard simulation Jeffrey Czajkowski Wharton Risk Management Center University of Pennsylvania; Willis Research Network Luciana K. Cunha Dept. of Civil and Environmental Engineering Princeton University; Willis Research Network Erwann Michel-Kerjan Wharton Risk Management Center University of Pennsylvania James A. Smith Dept. of Civil and Environmental Engineering Princeton University Willis Research Network December 2014 Working Paper # 2014-12 _____________________________________________________________________ Risk Management and Decision Processes Center The Wharton School, University of Pennsylvania 3730 Walnut Street, Jon Huntsman Hall, Suite 500 Philadelphia, PA, 19104 USA Phone: 215‐898‐5688 Fax: 215‐573‐2130 http://opim.wharton.upenn.edu/risk/ ___________________________________________________________________________ THE WHARTON RISK MANAGEMENT AND DECISION PROCESSES CENTER Established in 1984, the Wharton Risk Management and Decision Processes Center develops and promotes effective corporate and public policies for low‐probability events with potentially catastrophic consequences through the integration of risk assessment, and risk perception with risk management strategies. 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From these findings, the Wharton Risk Center’s research team – over 50 faculty, fellows and doctoral students – is able to design new approaches to enable individuals and organizations to make better decisions regarding risk under various regulatory and market conditions. The Center is also concerned with training leading decision makers. It actively engages multiple viewpoints, including top‐level representatives from industry, government, international organizations, interest groups and academics through its research and policy publications, and through sponsored seminars, roundtables and forums. More information is available at http://wharton.upenn.edu/riskcenter . A new approach to spatially explicit flood loss characterization via hazard simulation 1 2 3 December 18, 2014 4 5 6 7 8 9 Jeffrey Czajkowski1,3 , Luciana K. Cunha2,3 , Erwann Michel-Kerjan1 , James A. Smith2,3 1 2 3 Wharton Risk Management and Decision Processes Center, University of Pennsylvania, Philadelphia, PA, USA Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA Willis Research Network, London, UK 10 11 12 Corresponding author: Jeffrey Czajkowski, The Wharton School, University of Pennsylvania, Huntsman Hall, Suite 500, 3730 Walnut Street, Philadelphia, PA, 19104, USA; [email protected]; +(1) 215 898-8047 13 14 15 16 17 18 19 20 21 22 23 24 25 Among all natural disasters, floods have historically been the primary cause of human and economic losses around the world. Improving flood risk management in any large river basin requires multi-scale characterization of the hazard and associated losses. Such characterization is typically not available in a precise and timely manner, yet. We propose a novel and multidisciplinary approach to do just that, which relies on a computationally efficient hydrological model that simulates streamflow for scales ranging from small creeks to large rivers. We adopt a normalized index, the flood peak ratio (FPR), to characterize flood magnitude across multiple spatial scales. The FPR is a key statistical predictor for associated flood losses. Because it is based on a simulation procedure that utilizes readily available remote sensing data, our approach can be broadly utilized, even for ungauged and poorly gauged basins, providing the necessary information for public and private sector actors to effectively reduce flood loss and save lives. 26 27 28 29 30 31 32 33 34 35 36 Of all natural disasters, floods are the most costly(1) and have affected the most people(2). Losses from worldwide flood events nearly doubled in the 10 years from 2000 to 2009 compared with the prior decade. This trend shows no sign of abating and most countries are exposed to flood hazard, making flood mitigation a universal challenge. Recent large-scale riverine flood events, on which this article focuses, in countries as diverse as Australia (in 2010), China (in 2010 and 2013), Germany (in 2013), Morocco (in 2010), Thailand (in 2011), the UK (2012 and 2014) and the US demonstrate the urgency to improve preparedness of exposed areas. Effective flood risk management activities – risk reduction, emergency response, recovery – require an accurate and timely characterization of the hazard and its possible consequence (losses) at a given location and for the entire affected region(3). Current high annual economic damage and human losses caused by riverine floods, combined with projected increases in flood intensity and frequency 1 37 38 39 due to climate change and land cover change(4,5), highlights the need for such information. However, methods that are able to accurately simulate or observe flood magnitudes over large areas, across multiple spatial scales, and in a timely manner are typically unavailable. 40 41 42 43 44 45 46 47 Ideally, floods would be characterized by detailed maps of inundated areas, depths and duration. Even though detailed hydraulic models have advanced in recent years, they still have significant limitations for operational use over large areas, including high implementation cost, excessive computational time, and large data requirements(6,7,8,9). The direct use of rainfall data to predict flood loss is not satisfactory because this method neglects the critical land surface processes that control floods. Dense stream-gauging networks are useful to characterize floods, however there are few settings from a global perspective with adequate gauging density for flood hazard assessment (10,11,12,13). 48 49 50 51 52 53 54 55 To overcome these issues, we propose a novel and interdisciplinary methodology that links flood hazard to flood impacts, and allows us to better understand relationships between them. We introduce a computationally efficient multi-scale hydrological model, and a normalized flood index, the flood peak ratio (FPR), to spatially characterize flood intensity. The FPR compares the intensity of the flood event with the intensity of events that have happened in the past, and more importantly provides a suitable metric for a multi-scale approach to evaluate flood hazard. With a spatially explicit characterization of flood intensity, we are able to investigate the relationship between hazard and economic damages, estimated here based on insured losses. 56 57 58 59 60 The significant contribution of our proposed methodology is that it can be applied to any region of the world, since it requires only data that is available worldwide(14,15,16). This new capacity will be of tremendous value to a large number of public and private sector stakeholders dealing with flood disaster preparedness and loss indemnification (e.g., emergency services, relief agencies, insurers) in low- and high-income countries alike. 61 Methods for the Local Characterization of Flooding 62 63 64 65 66 We apply our methodology to the Delaware River Basin (DRB), which has a drainage area of 17,560 km2 at Trenton, New Jersey (NJ) and an exceptionally dense stream gauging network of 72 sites. Moreover, the DRB experiences frequent and intense riverine flooding(17). Figure 1 shows the location of the DRB in relation to the states of New York (NY), Pennsylvania (PA), and NJ. 67 68 69 70 71 72 While the main channel of the Delaware River is un-dammed, 38 major dams (50 feet in height or with normal storage capacity of 25 thousand acre-feet or more) control the flow of the Delaware River tributaries(18). A highly controlled environment imposes difficulties for flood simulation; we address this issue by applying a filter to estimate the outflow from the dams. The filter replicates the delay and attenuation in streamflow caused by the reservoirs and is able to represent outflow during extreme flood events (Cunha et al, in preparation). 73 74 We characterize the DRB flood hazard through observed and simulated streamflow data. Each method presents advantages and limitations (see M1 for further details). Observed 2 75 76 77 78 79 80 81 82 83 streamflow is typically measured at specific points in the river network by stream gauges. To obtain a spatially continuous representation of flood peaks, we interpolate the observed station data provided by the 72 gauges using an inverse distance weighted approach. This method has been applied by Villarini and Smith(19) to estimate peak flow over the eastern US for major floods. Flood hazard quantification using stream gauging data is sensitive to the density of the network, the spatial variability of the flood event, the interpolation method used, and the number of flow control structures in the basin that introduce unnatural flow alteration. The sparse nature of stream gauging networks in many settings limits the utility of data-driven approaches to characterize the spatial extent of flooding. 84 85 86 87 88 89 90 91 92 93 94 95 96 On the other hand, the main advantage of the hydrologic simulation approach is that it can be applied in sparse stream-gauge settings. Furthermore, it takes into consideration the river network structure’s role in shaping the spatial pattern of flooding. While many distributed hydrological models represent a region by dividing it into a number of regular spatial elements (see Kampf and Burges(20) for a list of models), a watershed is made up of hillslopes, where rainfall-runoff transformation occurs, and the river network, that transports the runoff through the drainage basin. Our simulated streamflow methodology discretizes the landscape into these natural elements (hillslopes and river network links) and solves the mass conservation equations for each(21). With this natural discretization of the terrain we obtain a more accurate representation of the river network, which is an essential component of a flood simulation model(22). This model conceptualization allows us to obtain a spatially explicit characterization of floods; hydrographs and peak flow are simulated across multiple scales for each link of the river network in a computationally efficient way(23). 97 98 99 100 We simulate streamflow using CUENCAS, a spatially explicit physically based hydrological model. Prior flood research using CUENCAS has been presented by Mantilla and Gupta(24), Mandapaka et al.(25); Cunha et al.(5); Cunha et al.(26), Seo et al.(27), Ayalew et al.(28), Ayalew et al.(29). Cunha et al. (in preparation) describes the implementation of CUENCAS to the DRB. 101 102 103 104 105 The datasets required to implement the model include: (1) digital elevation model for the river network extraction and for the estimation of hydraulic geometry parameters; (2) rainfall as hydrometeorological forcing, (3) land cover, and soil datasets for landscape characterization; and (4) initial soil moisture conditions. Most importantly these datasets are widely available from satellite remote sensing systems 106 107 108 109 110 111 112 113 To remove streamflow dependency on drainage area we utilize the flood peak ratio (FPR) approach(19). The FPR is the event flood peak divided by the 10-year flood peak flow value. FPRs larger than 1 indicate a flood event with return period larger than 10 years. The FPR based on observed streamflow has been successfully applied to characterize flood data(30,31) and flood losses(11) over large regions. A required step to apply this methodology is to estimate regional values for the 10-years peak flow (see M2 for details). To provide a direct link between FPR and flood severity we followed the methodology employed by Villarini et al.(32) and estimate the FPR that correspond to each of the National Weather Service (NWS) flood categories – action, minor, 3 114 115 moderate, and major flooding.1 In Extended Data Figure 1 we present box plots with FPR values for each NWS flood category for sites in the DRB. 116 Summary of flood characterization and losses from four major events 117 118 119 120 121 122 123 124 125 We investigate four recent (2004, 2005, 2006 and 2011) extreme flood events in the Delaware River Basin. Smith et al.(33) presented a detailed description of the Delaware River flood hydrology and hydrometeorology and showed that floods in the Delaware River are produced by a diverse collection of flood-generating mechanisms. The 2004 and 2011 events were caused by extreme rainfall from hurricanes Ivan and Irene, respectively. The 2005 event was caused by a winter–spring extratropical system that combined snowmelt, saturated soils, and heavy rainfall over a period of approximately twenty-four hours. The 2006 flood was the product of a series of mesoscale convective systems that were associated with a trough-ridge system over the eastern US. 126 127 128 129 130 131 132 133 134 The associated loss data are the actual insurance claims incurred for these four events by the US National Flood Insurance Program (NFIP). In the US, coverage for flood damage resulting from rising water is explicitly excluded in homeowners’ insurance policies, but such coverage has been available since 1968 through the federally managed NFIP. Thus, the NFIP is the primary source of residential flood insurance in the US(34,35), and we benefit from a unique access to its entire portfolio from 2000 to 2012 as well as individual policy claim data from 1978. For each of these events, we determine the total number of residential flood claims incurred and the number of NFIP policies in-force in the Delaware River Basin at the census tract level (Extended Data Table 1). 135 136 137 138 139 140 141 142 143 144 On average across all four events, 30 percent of our composite DRB census tracts incurred at least one residential flood claim, with 4,919 total claims incurred in the DRB across all four events. The total damage (building and contents) for those events was approximately $161 million, with a storm-weighted average damage per claim of approximately $20,500. These claims were generated from the 9,729 NFIP policies-in-force (5,241 for Ivan) in the basin. Given the relatively low flood insurance penetration in the basin (see M3 and Extended Data Figure 2 for a map of NFIP policies by census tract), the number of claims and associated losses can be considered a lower-bound estimate of the actual (insured and uninsured) DRB flood losses incurred for these events. But since the vast majority of flood insurance in the US is obtained through the NFIP, our data is a good representation of the insured flood loss amounts. 145 146 147 148 149 150 The dense stream-gauge network of the DRB allows us to assess our simulated peak flow methodology by comparing observed and simulated hydrographs, as well as peak flows for the locations for which streamflow data are available. Even in a complex drainage basin, with pronounced heterogeneities in rainfall due to orographic precipitation mechanisms, the comparison of simulated and observed discharge resulted in correlation coefficients larger than 0.8 for all active gauges; the model provides better streamflow estimates than the average (Nash1 For further description of these categories see http://www.crh.noaa.gov/arx/?n=flooddefinitions 4 151 152 153 154 155 156 157 158 159 160 161 Sutcliffe coefficient of efficiency larger than 0) for 72%, 75%, 90%, and 81% of the active gauges for the 2004, 2005, 2006, and 2011 events. The model underperformed for sites located immediately downstream from reservoirs since we adopted a simplified model to estimate reservoir outflow, but the decline in performance was located a short distance downstream of reservoirs. In Figure 2 we present maps of observed and simulated FPR for the 2004 event overlaid by census tracts that presented at least one claim for the specific event. Maps for the remaining events (2005, 2006, and 2011) are shown in Extended Data, Figures 3 to 5. The apparent weaknesses of the data-driven approach are visible in the maps, even with the dense stream-gauging network of the Delaware River. The data-driven approach has a clear area of influence around a stream gauging station and potentially the fundamental control of flooding by the river network is not adequately captured. 162 Linking local flood hazard to flood loss 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 In order to explicitly determine the relationship between flood hazard and residential flood losses, we conduct a multivariate regression analysis at the DRB census tract level on the number of flood claims incurred in each tract as a function of a vector of relevant flood hazard, exposure, and vulnerability explanatory variables with a primary focus on the simulated and observed FPRs. We incorporate the FPRs in two distinct ways: first, as the maximum FPR value achieved in each census tract; and second, in order to provide further relative context to these continuous FPR values, we discretize the maximum FPR into the “action,” “minor flood,” “moderate flood,” and “major flood” – high water level terminology categories used by the NWS. Figure 3 illustrates the simple bivariate relationship between simulated and observed FPRs and flood claims with the FPRs grouped by their associated NWS category. Clearly, FPRs classified as a major flood (> 1.08) are associated with the vast majority of the flood claims in the DRB for these studied events. But claims were also incurred for action, minor, and moderate FRPs, and this bivariate view of the data does not account for any other hazard or exposure characteristics potentially leading to a flood claim. These other aspects of the data will be formally controlled for in the regression analysis. 178 179 180 181 182 183 184 185 186 187 188 189 In addition to the FPRs, we added into the regression model controls for other flood hazard characteristics including the size of the census tract (“number pixels” where each pixel is 90 x 90 meters), the density of the river network in the track (“percentage river”), and dummy variables along a scale from one to seven that indicate the size of the river inside each tract. To characterize the size of the river in each tract we use the Horton system of river ordering. We attribute to each tract the largest Horton order. Horton four, the median river size on the seven point scale is the omitted category. We also control for other relevant exposure and associated vulnerability factors including the number of housing units and the number of flood insurance policies-in-force in each census tract. All else being equal, as these flood hazard and exposure factors increase, one would expect a larger count of flood insurance claims. We control for any space invariant unobserved heterogeneity between the three states in the DRB through a fixed effect estimation via state dummy variables (PA, NY, and NJ), with PA the omitted category, 5 190 191 192 193 and for any unobserved event-specific fixed effects through event dummy variables (“extrop,” “cnvctv,” “ivan,” “irene”), with Irene being the omitted category. (See the Methods section M3 for a description of the statistical analyses employed. A complete list and description of the variables used in the models is provided in Extended Data Table 2.) 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 Table 1 presents the results where we model the count of claims for the 1,435 census tracts with at least one NFIP policy-in-force (full-model results are presented in Extended Data Table 3). For all four models we run the likelihood ratio chi-squared test which indicates that each of the models is statistically significant at the 1 percent level. We also see that the number of NFIP policies-in-force and the size of the river (Horton order six and seven) – are consistently statistically significant at the 1 percent level and positive drivers of flood claims for an average census tract in the DRB. Claims increase with the size of the river since floods in larger rivers tend to affect larger areas than floods in small creeks. Therefore, areas closer to a larger river such as the main Delaware stream, are more susceptible to damaging floods. The major negative driver of flood claims for an average census tract when the tract is located in NY State (as compared to one in PA or NJ). This is expected since the DRB in NY is comprised mainly of forested areas, with very low population density. From the inflated portion of the Negative Binomial (NB) model (Extended Data Table 3) we see that the larger the percentage of river (drainage density) in a tract, the less likely it is to observe zero claims. Drainage density is intrinsically linked to the region topography. Likewise, the more NFIP policies-in-force, the less likely it is to observe zero claims. 210 211 212 213 214 215 216 217 218 219 220 Models 1 and 3 show that the number of claims increase with observed maximum FPR (statistically significant at 1 and 5 percent levels). Czajkowski et al.(11) found similar results in the relationship between number of claims and observed FPR for 23 states impacted by Hurricane Ivan. From model 1, if a census tract were to increase its observed maximum FPR by one unit, the expected number of claims from an event would increase by a factor of 1.81 while holding all other variables in the model constant. From model 3, census tracts experiencing flood peak ratios classified as action, minor, or moderate have expected number of claims that are 72 percent , 66 percent and 56 percent lower than the ones expected for tracts experiencing major flood peak ratio while holding all other variables in the model constant.2 As expected, from the inflated portion of the model (Extended Data Table 3), a higher observed FPR value is not a statistically significant driver of a less likely zero-flood claim occurrence. 221 222 223 224 225 Most notably, though, from the Table 1 results is that simulated FPR coefficient values in models 2 and 4 produce very similar results to the observed flood peak coefficient values in models 1 and 3. This result demonstrates the validity of the simulated FPR obtained based on a parsimonious multi-scale hydrological model. For both simulated and observed flood peak values we see statistical significance at the 1 percent level for continuous (and similar coefficient 2 Separate estimation not shown using dummy variable for simulatedmax_major = 1, 0 otherwise indicate census tract experiencing a simulated flood peak ratio classified as major have exp(.5963917) = 1.81 times the expected number of claims for tract with value that is less than NWS major flood 6 226 227 228 229 230 magnitudes of 0.59 and 0.57), and categorized FPR (based on NWS flood categories). All four models capture about 17 percent of the overall count of claim variation in the data. Lastly, we see from the inflate portion of models 2 and 4 (Extended Data Table 3) that larger simulated FPR values are statistically significant drivers of a lower likelihood of observing a zero-flood claim for an average census tract. 231 Novelty and Value of the Proposed Approach 232 233 234 235 236 237 238 239 240 Previous research has shown that observed FPRs can be used to spatially characterize flood events(19) and are key statistical drivers of the number of flood claims incurred for riverine flooding from tropical cyclones (TC) in the eastern US(11). In this study we again confirm these findings, and more importantly, we propose a methodology that does not solely rely on observed streamflow data. Observed streamflow data are not readily available in satisfactory density for flood hazard characterization in most areas of the world, especially in some of the regions with the highest vulnerability to floods(12,13). To demonstrate the sensitivity of estimated flood intensity on gauge density, we present in Extended Data Figure 6 observed FPR values for the 2006 flood event based on different number of gauges. 241 242 243 244 245 246 247 248 249 250 Results presented in this study show that simulated FPR estimated from a physically based hydrological model predicts the number of flood claims in the Delaware River for major flood events, as well as the observed FPR obtained from a unique dense stream-gauging network. The simulated FPR method for flood hazard characterization can be applied to any region of the world using routinely available remote sensing data sets for digital elevation models(15), rainfall(14), land cover(16), and soil properties(36,37,38). Regional flood frequency estimates can be obtained based on empirical and modeling approaches (e.g., Viglione et al.(39), Guo et al.(40)). The simulated FPR depends on the accuracy of the input and forcing data. 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Evaluating Flood Resilience Strategies for Costal Megacities, Science, Vol. 344: 473-475. 260 10 261 Tables Negative binomial model for the count of flood claims Model (1) Model (2) Model (3) Model (4) Extra tropical 2005 -0.78*** -0.02 -0.67*** -0.09 Convective 2006 -0.19 0.18 -0.15 0.11 Ivan 2004 -0.01 -0.13 -0.11 0.02 NJ -0.08 -0.26 -0.34* -0.30* NY -0.85*** -0.56*** -0.63*** -0.54** Housing Units 0.00 0.00 0.00 -0.00 NFIP Policies 0.03*** 0.02*** 0.03*** 0.02*** Number Pixels -0.00 0.00 0.00 0.00 Percentage River -0.06*** -0.08*** -0.07*** -0.08*** Horton One -0.88*** -0.52 -0.93*** -0.43 Horton Two -0.05 0.29 -0.13 0.36 Horton Three 0.00 0.25 0.13 0.23 Horton Five -0.30 -0.47** -0.44** -0.51** Horton Six 1.21*** 0.86*** 1.08*** 0.98*** Horton Seven 1.53*** 1.27*** 1.42*** 1.25*** Observed Max FPR 0.59*** Simulated Max FPR ObsMax_Action -0.33 ObsMax_Minor -0.42** ObsMax_Moderate -0.58*** SimMax_Action -0.91*** SimMax_Minor -0.33 SimMax_Moderate -0.67*** constant -0.85*** -0.89** 0.09 0.09 Ln alpha 0.77*** 0.75*** 0.83*** 0.76*** N Log likelihood 262 263 264 265 266 267 268 0.56*** 1435 1435 1435 1435 -1841.3 -1847.5 -1854.9 -1847.8 LR chi2 541.4 493.0 514.3 492.2 Prob > chi2 0.00 0.00 0.00 0.00 Table 1. Estimated coefficients from count model portion of zero-inflated negative binominal model for 1,435 census tracts with at least one NFIP policy-in-force where: model 1 observed maximum FPR continuous value; model 2 simulated maximum FPR continuous value; model 3 observed maximum FPR discretized NWS classification (major flood is the omitted category); and model 4 simulated maximum FPR discretized NWS classification (major flood is the omitted category). Standard errors are not reported. The log-transformed alpha parameter of the NB distribution captures any overdispersion in the model. * p<.1; ** p<.05; *** p<.01 11 269 Figures 270 271 272 273 274 275 Figure 1: Map of the DRB showing the USGS hydrological units (HUC08) boundaries, the river network, and the location of the USGS streamflow gauges and reservoirs. The reservoirs purposes are defined as: C: Flood control and storm water management, S: water supply, H: Hydroelectric, R: Recreation, F: Fish and wildlife pond, and O: Other. WWet refers to reservoirs identify in the water bodies and wetlands database. 276 12 277 278 279 Figure 2: Simulated (a) and observed (b) peak flow ratio for the 2004 event. See Extended Data Figures 3 to 5 for 2005, 2006, and 2011 events. 280 13 281 282 Figure 3. NWS Characterized Flood Peak Ratios and Percent of Total Claims 14 283 Methods. 284 285 286 287 288 289 290 291 M1. Mathematical models provide spatially explicit estimates of flood magnitude based on the simulation of the dominant physics processes that control floods. However, as an indirect estimate, model results are susceptible to uncertainties in the input datasets (e.g. rainfall), model structure, and parameterization. We can classify flood simulation models as: (1) hydrologic models, (2) hydraulic models, and (3) coupled hydrologic and hydraulic models. Hydrological models estimate streamflow across the river network by transforming rainfall into runoff and propagating the flow through the river network(1). Hydraulic models focus on simulating flow transport in the river channel, and provides as output flood inundation and depth. 292 293 294 295 296 297 298 299 300 301 The application of hydrological and hydraulic models over large areas is usually limited by data availability. Traditional hydrological models require historical hydro-meteorological data (rainfall and streamflow) for parameter calibration(2,3). Hydraulic models required detailed information about the geometry of river and floodplain (channel slope, geometry and roughness), and observed inundation data for model calibration and validation. These datasets are rarely available, especially over large areas. Moreover, computational efficiency is still a limitation when using the spatial resolution required for the simulation of small river (on the order of few meters), and attempting to simulate a basin as large as the DRB(1,4). To-date, there is no modeling framework that can simulate floods across multiple scales and over large areas in a timely manner. 302 303 304 305 306 307 308 309 310 311 312 313 In lieu of mathematical models, rainfall observations are often used to characterize flood events, even though they neglect the physical processes that occur over land and the built environment that control/modify flood generation. The advantage is that rainfall information is available worldwide through remote sensing datasets(5,6). On the other hand, observed streamflow data provides a direct measure of the magnitude of floods(7,8), intrinsically accounting for rainfall-runoff and flow transports. But a primary source of analysis error is in the measurement itself, which is especially uncertain during extreme flood events(9,10), and complicated by highly controlled reservoir and dam environments. A further disadvantage of observed streamflow data is that many regions of the world are ungauged (11,12), and even gauged regions do not have the required gauge density for a spatially explicit characterization of flood magnitudes (3). Data interpolation methods play a crucial role in the spatial characterization of floods in less densely gauged areas, often subjectively so. 314 315 316 317 Remote sensing instruments on airplanes are another means to successfully measure flood inundated area, however, as described by (13), these technologies are still costly and cannot be used in an operational way, especially over large areas. Remote sensing instruments on satellites are limited to large rivers (14). 318 319 320 M2. Peak flow scales as a power law of drainage area, Q A ∝ A , where A is drainage area, ∝ is the intercept, and θ the exponent (15, 16, 17, 18). We estimated the scale relationships for 15 321 322 323 324 325 326 327 10-year floods using USGS annual peak flow data for gauges in the Delaware River with at least 20 years of data. We use the methods described in Bulletin 17B (IACWD 1982) to quality control annual peak flow data, fit the parameters of the Log-Pearson10 type III distribution, and estimate peak flow for a 10-year return period. We then estimate the exponent and coefficient of the power law relation between drainage area and peak flow with different return periods. When historical data is unavailable, regional flood frequency estimates can be obtained using empirically-based or modeling-based approaches (19, 20; 21; 22;23). 328 329 330 331 332 333 334 335 336 337 338 M3. In order to ultimately associate flood hazard to residential flood losses, we combine the FPRs with the spatial structure of residential flood insurance losses as represented by NFIP flood insurance claim observations in the impacted DE River Basin area. Residential equates to single-family, two to four family, and other residential structures. Non-residential (i.e., primarily commercial) structures covered by the NFIP, less than five percent of the total insured portfolio, are excluded from this analysis. The NFIP portfolio does not contain individual residential location (street address), therefore we aggregate NFIP policies and claims incurred at the US census tract level, the lowest level of geographic identification in the NFIP dataset. Since we are focused on analyzing riverine flood losses, we exclude all claims explicitly due to “tidal water overflow” as classified by the NFIP (i.e., storm surge losses). 339 340 341 342 343 344 We use the 2000 US Census tract to evaluate the 2004 event, and the 2010 US Census tract to evaluate the 2005, 2006, and 2011 events. A total of 346 census tracts comprise the DE River Basin for the 2000 Census tracts, and 401 for the 2010 Census tract. Hurricane Ivan and Irene claims are identified by unique catastrophe numbers in the NFIP claims database. To identify the claims related to the 2005 and 2006 events we pull claims from the date range of each event (March 27 to April 15 for 2005 event and June 25 to July 05 for 2006 event). 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 Of the approximately 783,000 housing units (approximately 693,000 for Ivan) in the basin from 2010 census tract data, this represents a relatively small implied NFIP market penetration (i.e., policies-in-force divided by the number of housing units). However, individual census tract implied NFIP market penetration amounts ranged up to 20 percent. Low flood insurance penetration rates are a chronic issue in the United States, especially in inland areas and in many countries around the world (24,25,8). As the dependent variable in our multivariate analysis is the number of NFIP flood insurance claims occurring in an impacted census tract, which is a nonnegative count (including zero value observations), we specifically utilize a zero-inflated negative binomial (ZINB) count model estimation (8). A ZINB specification allows for overdispersion resulting from an excessive number of zeroes by splitting the estimation process in two: 1) estimating a probit model to predict the probability that zero claims take place in a given tract (i.e., the inflation portion of model); and 2) estimating a negative binomial (NB) model to predict the count of claims in a given tract (26). Vuong test results comparing the ZINB to the non-zero-inflated NB specification indicate strong support of the ZINB over the NB. Additional tests conducted strongly support the choice of the ZINB model over zero-inflated Poisson, NB, 16 360 361 362 363 and Poisson estimations. For the inflated portion of the ZINB model, which estimates the probability of zero flood claims occurring in any one census tract, we include variables that control for the number of housing units, the number of NFIP policies in-force, the percentage of the census tract that is river, and observed or simulated continuous FPR. 364 365 366 367 368 369 By using the 25th and 75th percentiles as reference points (see Extended Data Figure 1 boxplots) we can define FPRs that correspond to the NWS flood categorization (refer to Caldwell, D. B., 2012 for class definition): FPRs lower than 0.51 correspond to “action”; FPRs greater than 0.51 and less than or equal to 0.78 correspond to “minor flood”; FPRs greater than 0.78 and less than or equal to 1.08 correspond to “moderate flood”; and FPRs greater than 1.08 correspond to “major flood.” 370 371 372 373 374 375 376 The Horton number indicates the degree of stream branching (27) that is directly related to the basin size. 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