Flood loss footprint characterization via hazard simulation

Transcription

1 Flood loss footprint characterization via hazard simulation Jeffrey Czajkowski Wharton Risk Center University of Pennsylvania Luciana K. Cunha Department of Civil and Environmental Engineering, Princeton University Erwann Michel-Kerjan Wharton Risk Center University of Pennsylvania James A. Smith Department of Civil and Environmental Engineering, Princeton University April 2015 Working Paper # Risk Management and Decision Processes Center The Wharton School, University of Pennsylvania 3730 Walnut Street, Jon Huntsman Hall, Suite 500 Philadelphia, PA, USA Phone: Fax: wharton.upenn.edu/riskcenter

2 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. Natural disasters, technological hazards, and national and international security issues (e.g., terrorism risk insurance markets, protection of critical infrastructure, global security) are among the extreme events that are the focus of the Center s research. The Risk Center s neutrality allows it to undertake large-scale projects in conjunction with other researchers and organizations in the public and private sectors. Building on the disciplines of economics, decision sciences, finance, insurance, marketing and psychology, the Center supports and undertakes field and experimental studies of risk and uncertainty to better understand how individuals and organizations make choices under conditions of risk and uncertainty. Risk Center research also investigates the effectiveness of strategies such as risk communication, information sharing, incentive systems, insurance, regulation and public-private collaborations at a national and international scale. 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

3 Flood loss footprint characterization via hazard simulation Jeffrey Czajkowski 1,3, Luciana K. Cunha 2,3, Erwann Michel-Kerjan 1, James A. Smith 2,3 1 Wharton Risk Management and Decision Processes Center, 3730 Walnut Street, Philadelphia, PA USA 2 Department of Civil and Environmental Engineering, Princeton University, E413 Engineering Quad, Princeton, NJ USA 3 Willis Research Network, 51 Lime Street, London, EC3M 7DQ, UK Corresponding author address: Jeffrey Czajkowski, The Wharton School, University of Pennsylvania, Huntsman Hall, Suite 500, 3730 Walnut Street, Philadelphia, PA 19104, USA; jczaj@wharton.upenn.edu; Tel.: +(1)

4 ABSTRACT Among all natural disasters, floods have historically been the primary cause of human and economic losses around the world. Improving flood risk management requires a multi-scale characterization of the hazard and associated losses --- the flood loss footprint. But this 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 simulated FPR is then shown to be a key statistical predictor for associated flood losses, based on insurance claims. Importantly, because it is based on a simulation procedure that utilizes generally readily available physically-based data, our flood simulation approach may be broadly utilized, even for ungauged and poorly gauged basins, thus providing the necessary information for public and private sector actors to effectively reduce flood loss and save lives. 2

5 1. Introduction 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 (in 2012 and 2014) and the US (2011, 2012) 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) ; that is, the flood loss footprint. Current significant annual economic damage and human losses caused by riverine floods, combined with projected increases in flood intensity and frequency 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. Ideally, floods would be characterized by detailed maps of inundated areas, depths and duration. Even though detailed hydraulic models have improved in recent years, they still have significant limitations for operational use over large areas with spatial resolution similar to the one applied in this work (unit catchment area on the order of 1 km 2 ). Limitations include high implementation cost, excessive computational time, and large data requirements (6,7,8,9). The most efficient hydraulic models can be applied globally if relatively coarse calculation units are defined (unit catchment area on the order of 500 km 2 ) (8). 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). 2. Novelty and Value of the Proposed Approach To overcome these issues, we propose a novel and interdisciplinary methodology that links flood hazard (here represented by the normalized spatial characterization of flood intensity) to flood impacts (here represented by the number of insured flood claims incurred), and allows us to better understand relationships between them. We introduce a computationally efficient multiscale 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 the simulated flood hazard and the actual insured flood claims. 3

6 The significant contribution of our proposed methodology is that it has the potential to be applied to any region of the world, since it requires only data that is generally available worldwide (14,15,16). As in any model application, the accuracy of the results depends on the accuracy and resolution of the key input data or suitable proxies. For example, radar rainfall datasets are not available in many countries. In this case, precipitation datasets provided by remote sensing, which present larger errors, and coarse spatial and temporal resolution, would have to be used. Nevertheless, the methodology present in this study is especially valuable for the regions for which almost no data is available and flood hazard is rarely quantified. 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 because it is easily and quickly computed. 3. Methods for the Local Characterization of Flooding 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. 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, inasmuch as an accurate simulation of the impact of dams on floods requires precise information about the dams location, surface areas, volumes, operating purposes and rules, information which is usually not readily available. Moreover, dam operations during extreme floods are usually defined in real time by multiple stakeholders, and do not follow static operation rules. We address this issue by applying a filter to estimate the outflow from the dams. The delay rate is defined by two factors: type of reservoir (controlled or not controlled) and the purpose of the reservoir (e.g., water supply, flood control). 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). We characterize the DRB flood hazard through observed and simulated streamflow data. Each method presents advantages and limitations (see M1 for further discussion). Observed streamflow is typically measured at specific points in the river network by stream gauges. To obtain a spatially continuous representation of observed FPR, we first normalize the peak flow of each gauge using its individual 10-year flood peak from the historical record. We then estimate FPR for each link in the river network by interpolating the 72 observed values using the 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 4

7 sparse nature of stream gauging networks in many settings limits the utility of data-driven approaches to characterize the spatial extent of flooding. 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). 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. In CUENCAS, the terrain is discretized into hillslope and link that allows the simulation of flood processes close to the scale they occur in nature. By defining parameters that are directly linked to measurable physical properties we avoid the need for calibration. 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. These datasets are widely available from satellite remote sensing systems. For the Delaware River Basin model implementation we used 4 km x 4 km, hourly Stage IV rainfall maps (30), climatological potential evapotranspiration values provided by the MOD16 product (31), topographic characterization provided by the 30 m x 30 m National Elevation Dataset, soil parameters provided by the 10 m x 10 m Gridded Soil Survey Geographic (gssurgo) (32), and hydraulic geometry parameters estimated based on USGS hydraulic measurements (as described by Cunha, 2012 (33) ). To remove streamflow dependency on drainage area, and to allow the spatial visualization of flood intensity, we utilize the normalized flood peak ratio (FPR) approach (19). For each gauge, the FPR is the event flood peak divided by the 10-year flood peak flow value from the historical record. We use the 10-year flood peak since we believe this value can be accurately estimated using relatively short time series (20-30 years). When historical data is not available, this value can be estimated using regionalization (22, 34). 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 5

8 characterize flood data (35,36) and flood losses (11) over large regions. A required step to apply this methodology is to estimate regional values for the 10-year 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. (37) and estimate the FPRs that correspond to each of the National Weather Service (NWS) flood categories action, minor, 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. 4. Summary of Flood Characterization and Losses from Four Major Events We investigate four recent (2004, 2005, 2006 and 2011) extreme flood events in the Delaware River Basin. Smith et al. (38) 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. The associated loss data are the actual insurance claims incurred for these four events by the US National Flood Insurance Program (NFIP). In the United States, 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 (39,40). We benefit from a unique access to its entire portfolio from 2000 to 2012 as well as individual policy claim data. For each of these four events and resulting flooding, 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). 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 5,241 (for the 2004 event) to 9,729 (for 2005, 2006 and 2011 events) NFIP policies-in-force 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 number of claims. 1 For further description of these categories see 6

9 5. Flood Hazard Simulation 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 high correlation coefficients for almost all gauges (see extended data Figure 6); the model provides better streamflow estimates than the average (Nash-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. However, the effect of the reservoirs decreases as basin scale increases and the model accurately simulates flow across multiple scales (see extended data Figure 7). 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 thus potentially the fundamental control of flooding by the river network is not adequately captured. 6. Linking Local Flood Hazard to Flood Loss 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 and exposure-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. In addition to the observed and simulated 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. To characterize 7

10 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. The size of the river indicates the type of flood the area is more susceptible to. For example, flash floods are common in small rivers that present fast response to rainfall. Large rivers are more susceptible to floods caused by rainfall events with long duration (see M3). We also control for other relevant exposure 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. It could be that unobserved state-oriented policies related to land-use, zoning, storm water, etc. impact the number of claims incurred per flood event therefore 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. For statistical power purposes we pool the data from all four storms; as these are different types of flooding events we also control for any unobserved event-specific fixed effects through event dummy variables (one for each storm; 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.) 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). As we incorporate the FPRs in two distinct ways we present four different models: model 1 utilizes the observed maximum FPR continuous value; model 2 utilizes the simulated maximum FPR continuous value; model 3 utilizes observed maximum FPR discretized NWS classifications; and model 4 utilizes the simulated maximum FPR discretized NWS classifications. 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 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. Models 1 and 3 confirm that the number of claims increases with observed maximum FPR (statistically significant at 1 and 5 percent levels), as expected. Czajkowski et al. (11) found similar results in the relationship between number of claims and observed FPR for 23 states impacted by 8

11 Hurricane Ivan. What we can do, though, is quantify this effect. 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. 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 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. The novelty of this work is again in the explicit quantification of these relationships using a method that does not solely rely in observed data. 7. Conclusions and Future Research 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. 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 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( ) = 1.81 times the expected number of claims for tract with value that is less than NWS major flood. 9

12 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 (41,42,43). Regional flood frequency estimates can be obtained based on empirical and modeling approaches (e.g., Viglione et al. (44), Guo et al. (34) ). The simulated FPR depends on the accuracy of the input and forcing data. For example, where radar rainfall datasets are not available, precipitation datasets provided by remote sensing would have to be used. Or the statistical relationships developed here between simulated flood hazard and insured flood claims could be used to generate a proxy of the flood loss footprint where flood claim data can be difficult to obtain in other parts of the world, or where there is no insurance data (local parameters such as construction type and housing cost would have to be considered as well, of course). However, our approach provides a unique, reliable and computationally efficient way to spatially characterize floods in ungauged and/or poorly gauged regions. Our findings highlight the technological capabilities that can lead to a better integrated risk assessment of extreme riverine floods in a more precise and timely manner. This capacity should be of tremendous value to a number of public and private sector stakeholders dealing with flood disaster preparedness and loss estimation/forecasting and financial indemnification of victims of floods around the world: scientific forecasters, emergency teams, engineers and urban planners, local and national governments as well as residence and building owners and their insurers, when flood insurance is available (45). 10

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15 37 Villarini, G., R. Goska, J.A. Smith, and G.A. Vecchi, North Atlantic tropical cyclones and U.S. flooding, Bulletin of the American Meteorological Society, 95(9), , Smith, J.A., M.L. Baeck, G. Villarini, and W.F. Krajewski, 2010: The hydrology and hydrometeorology of flooding in the Delaware River Basin, Journal of Hydrometeorology, 11(4), Michel-Kerjan, E. (2010) Catastrophe economics: The National Flood Insurance Program. Journal of Economic Perspectives 24(4): Michel-Kerjan, E. and Kunreuther H (2011) Redesigning flood insurance. Science 333: Batjes, N. H., 1997: A world dataset of derived soil properties by FAO UNESCO soil unit for global modelling. Soil Use and Management, 13, 9 16, doi: /j tb00550.x. 42 Batjes, N. H., 2009: Harmonized soil profile data for applications at global and continental scales: updates to the WISE database. Soil Use and Management, 25, , doi: /j x. 43 Kerr, Y.H., Waldteufel, P., Richaume, P., Wigneron, J.-P., Ferrazzoli, P., Mahmoodi, A., Al Bitar, A., Cabot, F., Gruhier, C., Juglea, S.E., Leroux, D.; Mialon, A., Delwart, S., "The SMOS Soil Moisture Retrieval Algorithm, Geoscience and Remote Sensing, IEEE Transactions, 50 (5), 1384,1403, May Viglione, A., R. Merz, J. L. Salinas, and G. Blöschl (2013), Flood frequency hydrology: 3. A Bayesian analysis, Water Resour. Res., 49, doi: /2011wr Aerts, J. Botzen, W. Emanuel, K. Lin, N., de Moel, H. and E. Michel-Kerjan (2014). Evaluating Flood Resilience Strategies for Costal Megacities, Science, Vol. 344:

16 Tables Negative binomial model for the count of flood claims Model (1) Model (2) Model (3) Model (4) Extra tropical *** *** Convective Ivan NJ * -0.30* NY -0.85*** -0.56*** -0.63*** -0.54** Housing Units NFIP Policies 0.03*** 0.02*** 0.03*** 0.02*** Number Pixels Percentage River -0.06*** -0.08*** -0.07*** -0.08*** Horton One -0.88*** *** Horton Two Horton Three Horton Five ** -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 0.56*** ObsMax_Action ObsMax_Minor -0.42** ObsMax_Moderate -0.58*** SimMax_Action -0.91*** SimMax_Minor SimMax_Moderate -0.67*** constant -0.85*** -0.89** Ln alpha 0.77*** 0.75*** 0.83*** 0.76*** N Log likelihood LR chi Prob > chi 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 14

17 Figures 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 identified in the water bodies and wetlands database. 15

18 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. 16

19 Figure 3. NWS Characterized Flood Peak Ratios and Percent of Total Claims 17

20 Flood loss footprint characterization via hazard simulation Supplemental Material Methods. 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. 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. The most efficient hydraulic models can be applied globally if relatively coarse calculation units are defined (e.g., Yamazaki et al (4) unit catchment area is on the order of 500 km 2 ). Whereas our study unit catchment area on the order of 1 km 2. Flood depth stemming from a hydraulic model would require a rating curve or detailed cross section for each river link. Rating curves are available only for gauged locations. Also, using just flood depth does not provide information about how the specific studied event compares to historical events, or how the flood in a subwatershed compares to the flood in a neighboring watershed. 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 (1,5). Todate, there is no modeling framework that can simulate floods across multiple scales and over large areas in a timely manner. 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 (6,7). On the other hand, observed streamflow data provides a direct measure of the magnitude of floods (8,9), 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 (10,11), 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 (12,13), 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. 18

21 Remote sensing instruments on airplanes are another means to successfully measure flood inundated area, however, as described by Di Baldassarre and Uhlenbrook (2012) (14), 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 (15). M2. Peak flow scales as a power law of drainage area, Q(A) = A θ, where A is drainage area, is the intercept, and θ the exponent (16, 17, 18, 19). We estimated the scale relationships for 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 (20; 21; is unavailable, regional flood frequency estimates can be obtained using regionalization 22;23,24). 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 5 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). 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 tract, 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 the 2005 event and June 25 to July 05 for the 2006 event). There are approximately 783,000 housing units in the basin from 2010 census tract data (approximately 693,000 for Ivan from 2000 census tract data). Combined with the 9,729 (for 2005, 2006 and 2011 events) NFIP policies-in-force (5,241 for 2004 event, 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 (25,26,9). As the dependent variable 19

22 in our multivariate analysis is the number of NFIP flood insurance claims occurring in an impacted census tract, which is a non-negative count (including zero value observations), we specifically utilize a zero-inflated negative binomial (ZINB) count model estimation (9). A ZINB specification allows for over-dispersion 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 (27). 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, 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. 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 (28) 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. The Horton number indicates the degree of stream branching (29) that is directly related to the basin size. Horton order equal to 1 (0 otherwise) indicates an unbranched tributary (a small creek), Horton order equal to two (0 otherwise) indicates the confluence of two or more first orders. The Delaware River at Trenton has a Horton order of seven. The size of the river indicates the type of flood the area is more susceptible to. For example, flash floods are common in small rivers that present fast response to rainfall. Large rivers are more susceptible to floods caused by rainfall events with long duration. 20

23 Methods References 1 Hodges, B.R. (2013) Challenges in continental river dynamics, Environmental Modelling & Software, 50: Wagener, T., and Coauthors, 2010: The future of hydrology: An evolving science for a changing world. Water Resour. Res, 46, n/a n/a, doi: /2009wr Sivapalan, M., and Coauthors, 2003: IAHS Decade on Predictions in Ungauged Basins (PUB), : Shaping an exciting future for the hydrological sciences. Hydrological Sciences Journal, 48, , doi: /hysj Yamazaki, D., G. A. M. de Almeida, and P. D. Bates, 2013: Improving computational efficiency in global river models by implementing the local inertial flow equation and a vector-based river network map. Water Resour. Res, 49, , doi: /wrcr Dottori, F., G. Di Baldassarre, and E. Todini (2013), Detailed data is welcome, but with a pinch of salt: Accuracy, precision, and uncertainty in flood inundation modeling, Water Resour. Res., 49, , doi: /wrcr Tapiador, F. J., and Coauthors, 2012: Global precipitation measurement: Methods, datasets and applications. Atmospheric Research, , 70 97, doi: /j.atmosres Sapiano, M. R. P., and P. A. Arkin, 2009: An Intercomparison and Validation of High-Resolution Satellite Precipitation Estimates with 3-Hourly Gauge Data. J. Hydrometeor, 10, , doi: /2008jhm Villarini, G., and J. A. Smith, 2010: Flood peak distributions for the eastern United States. Water Resour. Res, 46, W06504, doi: /2009wr Czajkowski, J., Villarini, G., Michel-Kerjan, E., Smith, J.A., Determining Tropical Cyclone Inland Flooding Loss on a Large-Scale through a New Flood Peak Ratio-based Methodology, Environmental Research Letters, 8(4): Di Baldassarre, G., and A. Montanari, 2009: Uncertainty in river discharge observations: a quantitative analysis. Hydrol. Earth Syst. Sci, 13, , doi: /hess Dottori, F., M. L. V. Martina, and E. Todini, 2009: A dynamic rating curve approach to indirect discharge measurement. Hydrol. Earth Syst. Sci, 13, , doi: /hess Beighley, E., McCollum, J, Assessing Global Flood Hazards: Engineering and Insurance Applications. Presentation at 3rd International Workshop on Global Flood Monitoring & Modelling, University of Maryland College Park, MD, USA. 13 Dell, M., B. Jones, and B. Olken (2013). What do we learn from the weather? The new climateeconomy literature. Journal of Economic Literature, 52(3), Di Baldassarre, G. and Uhlenbrook, S. (2012), Is the current flood of data enough? A treatise on research needs for the improvement of flood modelling. Hydrol. Process., 26: doi: /hyp Alsdorf, D., E. Rodriguez, and D. Lettenmaier, 2007: Measuring Surface Water From Space. Rev. Geophys, 45, RG Gupta, V. K., R. Mantilla, B. M. Troutman, D. Dawdy, W. F. Krajewski, Generalizing a nonlinear geophysical flood theory to medium-sized river networks, Geophys. Res. Lett., 37, L11402, doi: /2009gl Mandapaka, P. V., W. F. Krajewski, R. Mantilla, and V. K. Gupta, 2009: Dissecting the effect of rainfall variability on the statistical structure of peak flows. Advances in Water Resources, 32, , doi: /j.advwatres Ayalew, T. B., W. F. Krajewski, R. Mantilla, and S. J. Small, 2014: Exploring the effects of hillslope-channel link dynamics and excess rainfall properties on the scaling structure of peakdischarge. Advances in Water Resources, 64, 9 20, doi: /j.advwatres Smith, J. A., G. Villarini, and M. L. Baeck, 2011: Mixture Distributions and the Hydroclimatology of Extreme Rainfall and Flooding in the Eastern United States. J. Hydrometeor, 12, , doi: /2010jhm

24 20 Chokmani, K., and T. B. M. J. Ouarda, Physiographical space-based kriging for regional flood frequency estimation at ungauged sites, Water Resour. Res., 40, W12514, doi: /2003wr Viglione, A., R. Merz, J. L. Salinas, and G. Blöschl (2013), Flood frequency hydrology: 3. A Bayesian analysis, Water Resour. Res., 49, doi: /2011wr Booker, D.J., R.A. Woods, Comparing and combining physically-based and empiricallybased approaches for estimating the hydrology of ungauged catchments, Journal of Hydrology, 508: Nguyen, C.C., E. Gaume, O. Payrastre, Regional flood frequency analyses involving extraordinary flood events at ungauged sites: further developments and validations, Journal of Hydrology, 508: , ISSN Guo, J., H-Y Li, L. R. Leung, S. Guo, P. Liu, M. Sivapalan, Links between flood frequency and annual water balance behaviors: A basis for similarity and regionalization, Water Resources Research, 2014, 50, Dixon, L, Clancy N, Seabury SA, Overton A (2006) The National Flood Insurance Program s Market Penetration Rate: Estimates and Policy Implications. Santa Monica, CA: RAND Corporation. 26 Michel-Kerjan E, Lemoyne de Forges S, Kunreuther H (2012) Policy tenure under the U.S. National Flood Insurance Program. Risk Analysis 32(4): Long JS, Freese J. (2006) Regression models for categorical dependent variables using Stata. Stata Press Publication, College Station, TX 28 Caldwell, D. B. (2012). Definitions and General Terminology. Operations and Services Hydrologic Services Program, National Weather Service Manual December 4. (accessed April 26, 2015.) 29 Shreve, R. L., Statistical law of stream numbers, J. Geol., 74, 17-37,

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33 Extended Data Figure 6: Model validation. Correlation coefficient from the comparison of observed and simulated hydrographs for the 2004, 2005, 2006, and 2011 events. Sites are color coded based on the tributaries of the Delaware River, coded according to the USGS hydrological units (see Figure 1).. 31

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35 Extended Data Figure 7: Selected simulated (blue for simulation with dam and light blue without dam) and observed (black) hydrographs for We show three hydrographs for gauges located downstream for reservoirs (Connorsville dam, Bear Swamp, and Betzville Dam), and hydrographs for multiple drainage areas (3.3, 433.2, 751.1, , and km 2 ) to demonstrate the ability of the model to accurately simulate flow across scales. Yellow, orange, and red lines represent the 2, 10 and 100-year return period. 33