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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
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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. 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 http://wharton.upenn.edu/riskcenter .
A new approach to spatially explicit flood loss characterization
via hazard simulation
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December 18, 2014
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Jeffrey Czajkowski1,3 , Luciana K. Cunha2,3 , Erwann Michel-Kerjan1 , James A. Smith2,3
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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
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Corresponding author: Jeffrey Czajkowski, The Wharton School, University of Pennsylvania, Huntsman Hall, Suite 500, 3730
Walnut Street, Philadelphia, PA, 19104, USA; jczaj@wharton.upenn.edu; +(1) 215 898-8047
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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.
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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
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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.
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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).
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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.
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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.
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Methods for the Local Characterization of Flooding
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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.
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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).
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We characterize the DRB flood hazard through observed and simulated streamflow data.
Each method presents advantages and limitations (see M1 for further details). Observed
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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.
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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).
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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.
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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
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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,
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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.
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Summary of flood characterization and losses from four major events
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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.
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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).
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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.
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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
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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.
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Linking local flood hazard to flood loss
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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.
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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,
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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.)
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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.
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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.
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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
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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
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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.
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Novelty and Value of the Proposed Approach
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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.
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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. However, such an
approach provides a unique, reliable and computationally efficient way to spatially characterize
floods in ungauged and/or poorly gauged regions.
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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 will
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(41).
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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.
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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.
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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.
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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
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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
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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.”
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376
The Horton number indicates the degree of stream branching (27) 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.
17
377
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