Volume 56, Issue 10 e2020WR028096
Research Article
Free Access

How Probable Is Widespread Flooding in the United States?

Manuela I. Brunner

Corresponding Author

Manuela I. Brunner

Research Applications Laboratory, National Center for Atmospheric Research, Boulder, CO, USA

Correspondence to:

M. I. Brunner,

[email protected]

Search for more papers by this author
Simon Papalexiou

Simon Papalexiou

Department of Civil, Geological, and Environmental Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

Search for more papers by this author
Martyn P. Clark

Martyn P. Clark

University of Saskatchewan Coldwater Lab, Canmore, Alberta, Canada

Search for more papers by this author
Eric Gilleland

Eric Gilleland

Research Applications Laboratory, National Center for Atmospheric Research, Boulder, CO, USA

Search for more papers by this author
First published: 14 October 2020
Citations: 14

Abstract

Widespread flooding can cause major damages and substantial recovery costs. Still, estimates of how susceptible a region is to widespread flooding are largely missing mainly because of the sparseness of widespread flood events in records. The aim of this study is to assess the seasonal susceptibility of regions in the United States to widespread flooding using a stochastic streamflow generator, which enables simulating a large number of spatially consistent flood events. Furthermore, we ask which factors influence the strength of regional flood susceptibilities. We show that susceptibilities to widespread flooding vary regionally and seasonally. They are highest in regions where catchments show regimes with a strong seasonality, that is, the Pacific Northwest, the Rocky Mountains, and the Northeast. In contrast, they are low in regions where catchments are characterized by a weak seasonality and intermittent regimes such as the Great Plains. Furthermore, susceptibility is found to be the highest in winter and spring when spatial flood dependencies are strongest because of snowmelt contributions and high soil moisture availability. We conclude that regional flood susceptibilities emerge in river basins with catchments sharing similar streamflow and climatic regimes.

Key Points

  • We assess (seasonal) probabilities of widespread flooding over the United States using a continuous, stochastic streamflow generator
  • The susceptibility to widespread flooding varies seasonally and regionally and is related to the climatic and hydrological regime
  • Regional flood susceptibility is weakened if river basins span regions with different climate and streamflow regimes

1 Introduction

Floods have affected more people worldwide than any other type of disaster in the 21st century (CRED Centre for Research on the Epidemiology of Disasters, 2019). In the United States, economic losses from flood events are estimated to amount to 15 billion USD per year (Swiss Re Institute, 2019) making floods one of the costliest hazards. Costs associated with a flood event can be particularly high if a flood is widespread, that is, if a large area is affected. Whether a flood event is local or widespread likely depends on the strength of spatial dependencies of floods across a region. Brunner, Gilleland, et al. (2020) have shown for the United States that such spatial flood dependencies vary by region and season. Spatial flood dependence across all seasons is high along the entire Pacific coast and the Atlantic coast from the Mid-Atlantic north to New England, in the Rocky Mountains, and on the western slopes of the Appalachian Mountains. It is generally highest in winter and spring and lowest in summer and fall. However, in the Rocky Mountains where snow processes are at play, spatial flood dependencies are low in winter and high in summer.

Despite the potentially high impacts of widespread flood events, we know little about their probabilities of occurrence. This lack of knowledge can be ascribed to two main problems: the sparseness of widespread floods in observed records and the frequent neglect of the spatial dimension of floods in hazard assessments. Regional flood hazard and risk assessments, which consider an exposure and vulnerability component in addition to the hazard component, often focus on individual locations (Vorogushyn et al., 2018). They assume “complete dependence”, that is, that events with the same return period happen jointly at all locations within a river basin and result in inundation areas and impacts with the same return period (e.g., Te Linde et al., 2011; Ward et al., 2013; Winsemius et al., 2013). This assumption is problematic, and large-scale risk analyses should be performed using heterogeneous flood hazard scenarios to estimate regional loss exceedance curves (Thieken et al., 2015).

Stochastic models derived from sufficiently long records can help overcome both problems by enabling generation of long streamflow time series or large sets of flood events if they consider the spatial dependence of flood occurrence across catchments. The latter is crucial to make them useful for the analysis of widespread events and their probabilities. So far, three main modeling approaches have been proposed, which enable consideration of spatial dependencies: (1) indirect, continuous modeling approaches (corresponding to discrete-time models in the stochastic literature) simulating continuous streamflow series by combining a stochastic weather generator with a hydrological model (Winter et al., 2019); (2) indirect, event-based modeling approaches simulating flood events for specific rainfall events generated using spatially dependent intensity-duration-frequency curves allowing for extreme rainfall of different durations at different locations (Le et al., 2019); and (3) direct, event-based approaches enabling the direct generation of flood events by employing spatial extreme value models such as the conditional exceedance model by Heffernan and Tawn (2004) (Diederen et al., 2019; Keef et al., 2013), hierarchical Bayesian models (Yan & Moradkhani, 2015), the multivariate skew-t distribution (Ghizzoni et al., 2010; 2012), or copula-based approaches including pair-copula constructions (Bevacqua et al., 2017; Schulte & Schumann, 2015), Student-t copulas (Ghizzoni et al., 2012), dynamical conditional copulas (Serinaldi & Kilsby, 2017), or the Fisher copula (Brunner, Furrer, & Favre, 2019). All types of approaches have their advantages and disadvantages. The indirect, continuous approach enables explicit consideration of flood triggering antecedent conditions, including soil moisture or snow cover, but includes several uncertainty sources related to both the stochastic precipitation model and the hydrological model. The indirect, event-based approach hinges on the choice of antecedent conditions, which can be crucial in determining actual flood magnitude (Camici et al., 2011). The direct approach only implicitly considers antecedent conditions but avoids including uncertainty sources related to rainfall-runoff transformation.

All of these approaches have previously been used in flood risk assessments. Metin et al. (2020) used an indirect, continuous modeling approach in combination with hydraulic and flood loss models and showed for a case study in the Elbe basin that assuming complete dependence overestimates flood damage on the order of 100% for return periods larger than approximately 200 years. However, they also found that damage is underestimated for small and medium floods with return periods smaller than approximately 50 years. Dyck and Willems (2013) used an indirect, event-based approach to model regional flood losses for a river basin in Belgium. Lamb et al. (2010) employed a direct, event-based approach to estimate exceedance curves of areal damages for a region in northeast England and showed that these damages are overestimated if complete dependence between sites is assumed. Similarly, Quinn et al. (2019) derived loss-exceedance curves for a large set of river basins in the United States using a conditional exceedance model, and Serinaldi and Kilsby (2017) derived aggregated loss curves for a set of large, European river basins using stochastically simulated weekly maxima.

Most of these past studies looking at spatial flood dependencies or regional flood risk either focused on the modeling aspect and the question of how to generate spatially consistent flood events or they estimated regional risk or damage to answer questions such as “how frequently will damages of x Billion dollars occur in a certain region?” Here, we focus on the hazard component of risk, which is independent of a region's damage potential, and ask (1) “how susceptible are different regions in the United States to widespread flooding?” and (2) “which factors influence the strength of this regional susceptibility?” We use a novel stochastic simulation approach, which reliably represents spatial flood dependencies, to simulate a large number of regional flood events going beyond the events contained in observed series. These events are used in two types of regional hazard analyses to derive regional flood hazard estimates for the United States. The first analysis maps regional flood hazard from a river basin perspective and highlights regions with a high susceptibility to widespread flooding. The second analysis uses a local perspective to identify climatic and topographic factors influencing regional flood hazard. While drivers of local flooding (Berghuijs et al., 2016) and spatial flood dependencies (Brunner, Gilleland, et al., 2020) have been investigated in earlier studies, we here identify factors governing regional flood hazard, which may in addition to meteorological and land-surface processes also be influenced by their homogeneity across a region.

Here, we define widespread floods as events where a majority of catchments within a region are jointly affected by an above-threshold event. We employ a novel fourth type of modeling approach, a direct but continuous approach based on PRSim.wave, which is a continuous stochastic streamflow generator recently proposed by Brunner and Gilleland (2020). PRSim.wave enables generating long, continuous, and spatially consistent time series at multiple sites by using phase randomization on a set of wavelet-decomposed streamflow time series. The flood events contained in the simulated series are spatially consistent; however, spatial dependencies are slightly overestimated (observed and simulated F-madograms, which are a measure of extremal dependence, differ by 0.05; Brunner & Gilleland, 2020).

To quantify the susceptibility of a region to widespread flooding, we propose a regional hazard measure, the flood susceptibility index, defined as the probability that a certain percentage of catchments within a region jointly experiences above-threshold events. This measure is different from existing measures such as the regional flood probability proposed by Troutman and Karlinger (2003), which is defined as the probability that at least one site within a region will experience a flood with a specific return period in any given year. We apply the flood susceptibility index to 18 large river basins in the United States to map regional and seasonal susceptibilities to widespread flooding. In addition, we look at such susceptibilities from a local, catchment perspective in order to receive smooth spatial estimates of probabilities for widespread flood events and to establish a link between flood susceptibility and explanatory variables, including catchment and meteorological characteristics. This focus on hazard probabilities, the regional scale, and process understanding distinguishes our study from a previous study on spatially dependent fluvial floods by Quinn et al. (2019), who derived national-scale loss-exceedance curves for the United States using an event-based stochastic model. Using a novel stochastic simulation approach within a regional hazard assessment not only allows us to derive regional hazard estimates potentially valuable for decision making regarding flood management but also to learn about factors influencing regional flood hazard including climatic and topographic factors.

2 Data and Methods

2.1 Data Set

We compute annual and seasonal regional flood hazard for 18 large hydrological regions in the United States from a river basin perspective and from a local perspective using a data set of 671 catchments (Figure 1) with minimal human flow alteration (Catchment Attributes and MEteorology for Large-sample Studies data set CAMELS; Newman et al., 2015). The data set comprises catchments with a wide range of streamflow regimes including intermittent regimes with a weak seasonality mainly located in the Great Plains; regimes governed by winter precipitation showing a strong seasonality, for example, in the Appalachian Mountains; and melt regimes with a spring melt peak mainly located in the Rocky Mountains (Brunner, Newman, et al., 2020). The catchments are almost exclusively small headwater catchments with a very low degree of nestedness which avoids overestimating spatial dependencies. Observed streamflow time series at daily resolution were downloaded for a period of 38 years (1981–2018) from the USGS website (https://waterdata.usgs.gov/nwis) using the R-package dataRetrieval (De Cicco et al., 2018).

Details are in the caption following the image
Eighteen river basins used for the analysis of regional flood hazard from a river basin perspective and the 671 stations in the data set.

The 18 hydrologic regions represent large river basins in the United States and regions with several coastal basins. The subdivision is based on the hydroBASINS data set (Lehner & Grill, 2013), which is based on the Pfaffstetter system (Verdin & Verdin, 1999). We started with the subdivision at Pfaffstetter Level 3 and did some merging and splitting to avoid very small and large basins, respectively. Merging focused on small coastal areas (Pacific Northwest, Texas, Southeast, North Atlantic, and Great Lakes) and splitting on the Mississippi basin (Upper and Lower Missouri, Upper and Lower Mississippi, Ohio, Arkansas, and Red and Ouachita). The 671 catchments in the data set are distributed across the regions with an average number of catchments of 37, a minimum of 7, and a maximum of 101 catchments per region. For most regions, available catchments are spread across the region except for the Rio Grande river basin, where no nearly natural catchments are available in the lower part. For this region, regional flood hazard estimates may therefore not be representative.

2.2 Overview

The regional flood hazard analysis consists of four main steps (Figure 2) described in more detail in the subsequent paragraphs: (1) stochastically simulating spatially consistent, continuous streamflow time series; (2) extracting flood events for individual catchments using a peak-over-threshold approach; (3) determining flood occurrences across all catchments; and (4) regional hazard estimation from a (a) river basin and a (b) local perspective.

Details are in the caption following the image
Illustration of workflow used to derive regional flood hazard estimates: (1) stochastically simulating spatially consistent, continuous streamflow (Q) time series in individual catchments (c1, … , cm); (2) extracting flood events (brown dots) for individual catchments using a peak-over-threshold approach (threshold indicated as red line); (3) determining flood occurrences across all catchments (e1, … , en); and (4) regional hazard estimation from a (a) river basin and a (b) local perspective.

2.3 Stochastic Simulation

We rely on a stochastic streamflow generator because the number of widespread flood events contained in the observed time series is insufficient for a regional hazard assessment. In order to increase the number of available (potentially regional) flood events for the regional frequency analysis, we use the stochastic streamflow generation model PRSim.wave (Phase Randomization Simulation), a direct continuous approach. PRSim.wave was proposed by Brunner and Gilleland (2020) to generate streamflow time series at multiple sites and is based on an earlier version of the model (PRSim), which was originally proposed to simulate streamflow at individual sites (Brunner, Bárdossy, et al., 2019). Both versions of the model are implemented in the R-package PRSim (Brunner & Furrer, 2019). In contrast to other stochastic models used for flood hazard analyses, which usually simulate individual flood events, PRSim simulates continuous streamflow time series. The wavelet-based version of PRSim, PRSim.wave (Brunner & Gilleland, 2020), is applicable to multiple sites, reproduces spatial dependencies between extremes in different catchments, and enables representation of nonstationarities present in the observed time series. However, it does not consider nonstationarities that may arise because of future climate change.

PRSim.wave combines an empirical (nonparametric) spatiotemporal model based on the wavelet transform (Daubechies, 1992; Torrence & Compo, 1998) and phase randomization with the flexible four-parameter kappa distribution (Hosking, 1994). The approach consists of five steps: (1) deriving random phases, (2) fitting of the kappa distribution using L moments, (3) wavelet transform, (4) inverse wavelet transform, and (5) transformation to kappa distribution. Brunner and Gilleland (2020) have shown that PRSim.wave reliably reproduces streamflow characteristics at individual sites including distributional and temporal correlation characteristics for both short- and long-range dependencies (up to the ones present in the observed series). Moreover, they have shown for a large set of 671 catchments, the set also used in this study, that the model reproduces spatial correlation characteristics among multiple sites both for the “normal” part of the streamflow distribution and for extremes including floods. We refer the reader to Brunner and Gilleland (2020) for a more detailed description and evaluation of the model.

PRSim.wave is used, here, to generate urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0001 multivariate and spatially consistent, continuous time series of the same length as the observed series (38 years) consisting of 671 time series each. A sample size of 3,800 years per catchment was found to be sufficient as regional estimates derived from the first and second half of the simulations are almost identical.

2.4 Flood Event Identification

The streamflow series simulated with the stochastic model are used to identify flood events, which are defined, here, as events where streamflow exceeds a certain threshold. Ideally, flood thresholds would be chosen with respect to impacts. However, information on the relationship between threshold and impact is often not available, especially not at a large spatial scale. We therefore use a threshold, which is based on the annual maximum series similar to the approach used by Brunner, Furrer, & Favre, (2019) and by Brunner, Gilleland, et al. (2020). We vary this threshold to extract events more extreme than annual maxima and biannual maxima. Not all of these high-flow events may be associated with inundation or damage.

The flood identification approach consists of two main steps: (1) identifying flood events in individual catchments and (2) determining dates of flood occurrences over all catchments. In the first step, independent POT events are identified in the daily time series of the individual catchments using the uth percentile of the corresponding time series of annual maxima as a threshold, which is varied in a sensitivity analysis described in more detail below (section 2.6). A minimum time lag of 10 days between events is prescribed to ensure independence (Brunner, Gilleland, et al., 2020; Diederen et al., 2019). Using an annual maxima based threshold of u = 20th percentile as used in the main analysis resulted in 57 extracted events per catchment, on average. An annual maxima based threshold compared to a quantile threshold based on daily values results in a more comparable number of events identified across catchments.

In the second step, a data set consisting of the dates of flood occurrences across all catchments is compiled. Independence between events is ensured by retaining only one event within a window of 7 days—a time interval frequently used to separate events in the reinsurance industry (Keef et al., 2013)—by choosing the date when most catchments are affected. This set of over all events is converted into a binary matrix specifying, for each catchment, which of the over all events it is affected by. The entries of the matrix are defined by assigning 1 to catchments that showed a POT event in the window of ±2 days of a specific over all date of occurrence and 0 to those which were not affected by this event. The choice of using a window of 2 days addresses the fact that travel times depend on catchment size and potentially other factors. The full binary matrix is split up into four seasons (winter: December–February; spring: March–May; summer: June–August; and fall: September–November) in order to allow for a season-specific analysis of regional flood hazard.

2.5 Regional Hazard Estimation

Regional flood susceptibilities are estimated from a river basin and a local perspective.

2.5.1 River Basin Perspective

Using the binary, spatial event matrices corresponding to the flood threshold considered, we derive regional flood hazard estimates for each of the 18 regions over all seasons and per season. We try to answer the question “what is the probability of occurrence of an event during which r% of the stations within a region are jointly flooded (i.e., coexperience a peak-over-threshold event at the same time)?” To determine the regional flood susceptibility index, that is, the probability of widespread flooding, for each region, we
  1. determine the available catchments lying within that region;
  2. identify the number of flood events during which r% of the catchments are jointly flooded using the binary flood event matrix; and
  3. compute the susceptibility index as the probability of widespread flooding p derived using the Weibull plotting position (Makkonen, 2006; Weibull, 1938) given by
    urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0002(1)
    where n is the total number of events affecting at least one of the stations in the region and x is the number of events where r% of the stations were affected. We make an example to illustrate the meaning of the flood susceptibility index. Suppose in Step 2 that r% was chosen to be 50% and suppose that the flood events had been identified using a threshold of 1 event per year on average. In that case, an index of, for example, 0.4% would mean that out of 1,000 flood events, four events affect at least 50% of the catchments in the river basin of interest.

The flood susceptibility is on the one hand computed over all seasons using the binary matrix consisting of all simulated events and on the other hand computed per season using the seasonal binary matrices.

2.5.2 Local Perspective

The subdivision of the CONUS into fixed regions (river basins) results in rigid estimate boundaries and somewhat variable station densities across regions. In addition to the river basin perspective analysis, we therefore employ a local perspective approach to derive regional flood estimates. This local perspective approach defines regions from the perspectives of the individual stations in the data set. A catchment's region comprises all the catchments in a radius of d degrees on a geographic grid around the catchment's outlet (see Figure 2, Step 3b, for an illustration). We set urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0003°, corresponding to a radius of approximately 500 km, resulting in similar area sizes as when using the regions based on hydrologic units. For each catchment, we define a region consisting of all catchments within a certain radius. Using the binary, spatial event matrices, we derive regional flood hazard estimates for each of the 671 catchments over all seasons and per season using the same procedure as in the river basin perspective analysis.

2.6 Sensitivity Analysis

The outcome of the regional flood susceptibility analysis is influenced by three main model choices: (1) the flood threshold (u) at individual sites, (2) the areal percentage chosen to define regional events (r), and(3) in case of the local-perspective analysis, the radius (d) chosen to determine regions. We explore the effect of these model choices on regional hazard estimates through a sensitivity analysis.

The effect of threshold selection (u) on regional hazard estimates is explored by using thresholds corresponding to the 10th, 20th, 30th, 40th, and 50th percentile of the annual maximum time series in Step 1 of the event extraction procedure while fixing the areal percentage at 70% and the radius at 5° in the case of the local perspective analysis. A threshold at the 10th percentile of the annual maximum time series corresponds to an event with a return period of 1.1 years while an event at the 50th percentile corresponds to an event with a return period of 2 years.

The effect of the choice of areal percentage on regional estimates is explored by varying r% from 50% to 90% (using 10% increments) while fixing the flood threshold at the 20th percentile and the distance in the local perspective analysis at 5°. Here, a threshold of 70% is said to represent widespread floods affecting the majority of catchments within a region. Clearly, such a threshold choice is subjective, yet we deem these values in accordance with human perception of regional and widespread flooding.

To test the effect of the radius choice (d) on the estimates derived from the local-perspective analysis, the radius size is varied. Radii of 2°, 5°, and 10° corresponding to small, medium, and large regions, respectively, are tested while the threshold and areal percentage are fixed at the 20th percentile and 70%, respectively.

In addition to these three model choices, the outcome of the regional hazard analysis may also be influenced by the sensitivity of the stochastic model to sampling uncertainty. To assess this sensitivity, we fit PRSim.wave not only to the original time series (1981–2018) but also to five resampled time series. These resampled time series are obtained by first resampling 38 years within the range 1981–2018 with replacement and by second composing new series consisting of the daily values of the 38 resampled years. The stochastic model is then set up using each of these resampled time series. Each of the “bootstrapped models” is run urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0004 times to obtain 100 stochastic time series. For each time series, individual and subsequently regional flood events are extracted using the same procedures applied to the time series obtained with the original model. For each of the regional flood events, we determine the percentage of stations affected, that is, the spatial flood extent. The range of the flood extents simulated using the five bootstrapped models is compared to the range of the flood extents simulated using the original model. The sensitivity of the stochastic model to sampling uncertainty is rather small as the range of flood extents obtained with the bootstrapped models is similar to the range obtained using the original model (Figure A1).

2.7 Factors Influencing Regional Flood Susceptibility

To interpret regional differences in the susceptibility to widespread flooding, we compare the local-perspective susceptibility estimates to the degree of spatial dependence as described by the flood connectedness measure introduced by Brunner, Gilleland, et al. (2020). This connectedness measure quantifies the number of catchments with which a specific catchment coexperiences at least 1% of the total number of flood events; that is, a pair of catchments is said to be connected if they are jointly flooded in 1% of the over all flood events.

In addition, we identify factors influencing regional flood susceptibility among (1) the hydrological regime type (Brunner, Newman, et al., 2020), (2) flood characteristics, and (3) physiographical and climatological catchment characteristics in a correlation analysis. Flood characteristics considered are the mean and standard deviation of the date of occurrence and mean magnitude, volume, and duration. Physiographical and climatological catchment characteristics were extracted from the CAMELS data set (Addor et al., 2017) and include latitude, longitude, catchment area, elevation, mean precipitation, mean potential evapotranspiration (ET), aridity (i.e., ratio of mean annual potential ET and mean annual precipitation), snow fraction, mean discharge, baseflow index, runoff ratio (i.e., ratio of mean daily discharge and mean daily precipitation), soil porosity, soil conductivity, sand fraction, silt fraction, soil permeability, and forest cover. For each of these characteristics, we compute the rank-based Kendall's correlation (Kendall, 1937) with over all and seasonal flood susceptibility estimates.

3 Results

3.1 Sensitivity Analysis

The sensitivity of the analysis to method choices is demonstrated by both the river basin and local perspective analyses.

3.1.1 River Basin Perspective

The sensitivity analysis shows that the regional hazard estimates depend both on the flood threshold determined as the uth percentile of the annual maximum time series and the areal percentage threshold r (Figure 3). We group the river basins into three groups according to their flood sensitivity behavior as illustrated by the sensitivity grids in Figure 3. River basins in Group 1 (8, 13, 2, 4, 9, and 14) are susceptible to severe widespread floods (u up to 50th percentile, r = 70%) and located in the western and northeastern United States. River Basin 8, for example, shows relatively high susceptibilities to widespread flooding of >0.45% for most areal coverages and flood thresholds as indicated by the dark red tiles. River basins in Group 2 (17, 10, 5, 12, 18, 7, and 11) are still susceptible to moderate widespread floods (u lower than 50th percentile, r = 70%) as indicated by the dark tiles for lower flood thresholds and areal coverages but lower probabilities, that is, lighter colors, for more severe and widespread events. They are located in the southern United States and also include the Great lakes region and the upper Mississippi and Ohio river basins. In contrast to Groups 1 and 2, river basins in Group 3 (16, 15, 6, 3, and 1) are not prone to widespread flooding but might still experience some floods with a moderate regional extent (50%). River basins in Group 3 comprise the upper part of the Missouri basin, the Southeast, and the Colorado and Columbia river basins.

Details are in the caption following the image
Effect of flood threshold (uth percentile of annual maximum series) and areal percentage threshold on regional flood hazard estimates as represented by the susceptibility index (probability of widespread flooding) for the 18 river basins based on hydrologic units. The darker the color, the higher the susceptibility to widespread flood events. Catchments are grouped into three sensitivity groups showing: (1) severe widespread flooding, (2) moderate widespread flooding, and (3) no widespread flooding.

3.1.2 Local Perspective

The sensitivity of the results toward method choices is confirmed by the local perspective sensitivity analysis (Figure 4). The radius choice has the strongest effect on regional flood susceptibility estimates, followed by the choices of areal percentage and flood threshold. Flood susceptibilities go toward zero for large regions with a radius of 10° and high areal percentages of 90%.

Details are in the caption following the image
Effect of (a) flood threshold (uth percentile of annual maximum series), (b) areal percentage threshold (r), and (c) radius size (d) on local-perspective regional flood hazard estimates as represented by the susceptibility index (probability of widespread flooding) for the 671 regions formed around each catchment. When not involved in the sensitivity analysis u is fixed at the 20th percentile, r at 70%, and d at 2°. The black lines in the boxplots indicate the median; the upper and lower whiskers correspond to 1.5 ∗ RIQ, where RIQ is to the interquartile range.

For the remainder of the analysis, we focus on one flood ( urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0006 th percentile, corresponding to floods with return periods >1.25 years being selected) and one areal percentage threshold (r = 70%), which we use here to define widespread floods. This focus enables discussing spatial and seasonal differences in regional flood hazard in more detail.

3.2 Susceptibility to Widespread Floods

Figure 5 maps regional flood hazard both from a river basin and local perspective. In both cases, the susceptibility to widespread flooding shows high spatial variation. From a river basin perspective (polygons), the propensity for widespread flooding is highest in the coastal basins in the Pacific Northwest, the Sacramento and Klamath basins in California, the Great Basin, Rio Grande, and the North Atlantic region. These findings relate well to the flood risk analysis performed by Quinn et al. (2019), who found that the number of large loss events, which are a result of not only high hazard but also population density, is high in California and the Appalachian Mountains. Widespread flooding is still possible but less likely in the South, in the Upper Mississippi and Ohio river basins, and the Great Lakes region. Widespread flooding is rare in Florida, the Columbia, Missouri, and Colorado river basins.

Details are in the caption following the image
Comparison of river basin and local perspective flood susceptibility estimates [%] (u = 20th percentile, urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0008) for 18 large river basins in the United States (river basin perspective) and the regions formed around the 671 catchments (local perspective). The darker the color, the higher the susceptibility to widespread flooding.

The picture looks slightly different when looking at regional hazard from a local perspective (points). The probability of widespread flooding is still relatively high in the Pacific Northwest, California, the Great basin, and the North Atlantic region and low in the upper part of the Mississippi basin and the Colorado basin. However, there are regions where regional hazard estimates derived from a local perspective clearly differ from those derived from a regional perspective. In the Columbia river basin and the western part of the upper Missouri basin, widespread flooding is more likely when taking a local instead of a regional perspective. These differences between regional and local estimates can be explained by seasonal differences in flood connectedness within a region (Brunner, Gilleland, et al., 2020). In the Columbia river basin, for example, where discrepancies between regional and local estimates are particularly strong, the seasonal strength of flood connectedness in the Cascades and Rocky Mountains is very distinct. Catchments in the Cascades show high spatial dependence in winter while those in the Rocky Mountains show high dependence in spring and summer. If such subregions with seasonally distinct flood behaviors (Brunner, Gilleland, et al., 2020) form a river basin, this results in low probabilities of widespread flooding from a regional perspective. In contrast, the local perspective reflects the fact that floods in catchments in the Cascades often co-occur because of a very expressed flood seasonality, resulting from a concentration of extratropical cyclones in the winter season (Kunkel et al., 2012), and those in the Rocky Mountains also often co-occur because of snowmelt (Brunner, Gilleland, et al., 2020).

3.3 Seasonal Variations in Regional Flood Susceptibilities

The susceptibility to widespread flooding in addition to the perspective and region considered also depends on the season as shown by both the river basin and local perspective analyses (Figures 6 and 7). The river basin perspective analysis shows that over all seasons, widespread flooding is found to be highest in spring (Figure 6). Depending on the region, regional flood susceptibility can, however, also be high in winter (coastal basins in the Pacific Northwest, Sacramento and Klamath river basins in California, the upper and lower Mississippi basins, and the North Atlantic region) and summer (Great Basin and Rio Grande). In contrast, the susceptibility to widespread flooding is low in fall except for the coastal basins in the Pacific Northwest.

Details are in the caption following the image
Seasonal, regional flood susceptibility [%] (u = 20th percentile, urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0009) from a river-basin perspective: (a) over all seasons, (b) winter, (c) spring, (d) summer, and (f) fall. The darker the color, the higher the susceptibility.
Details are in the caption following the image
Seasonal, regional flood susceptibility [%] ( urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0010 percentile, urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0011) from a local perspective ( urn:x-wiley:wrcr:media:wrcr24931:wrcr24931-math-0012): (a) over all seasons, (b) winter, (c) spring, (d) summer, and (f) fall. The darker the color, the higher the susceptibility.

The local-perspective analysis draws a similar and smoother picture than the river basin perspective analysis. It confirms that over all regions, the susceptibility to widespread flooding is highest in spring and winter and weakest in summer and fall. The main difference to the river basin analysis lies in the susceptibilities estimated for the Rocky Mountain region. The susceptibility to widespread flooding is high in the Rocky Mountain region when taking a local perspective while it is low when taking a river basin perspective. The headwater basins in this region contribute to different large river basins, which is why the headwater region is split up when taking a river basin perspective.

The seasonal susceptibility patterns can be related to spatial dependencies in flood occurrence, which describe the degree of flood connectedness for a pair of sites. These dependencies vary by region and season as they are shaped by meteorological and land-surface processes (Brunner, Gilleland, et al., 2020). Brunner, Gilleland, et al. (2020) have shown that spatial dependencies in winter are highest in the Pacific Northwest, in California, and the Appalachian mountains, that is, catchments in these regions coexperience flooding. These high dependencies are reflected by the propensity of these regions for widespread flooding in this season (Figures 6b and 7b). In spring, spatial flood dependencies are overall high resulting in high regional flood susceptibilities during this season. While the high spatial dependencies in the Appalachian region are reflected in the susceptibility to widespread flooding, the Rocky Mountain headwater catchments contribute to different major river basins leading to low susceptibilities to widespread flooding in some surrounding river basins if a river basin perspective is taken (Figure 6c). The high spatial dependencies are, however, reflected if a local perspective is taken (Figure 7c). In summer, spatial flood dependencies are generally low except in the Rocky Mountains and coastal regions in the south affected by tropical cyclones (Kunkel et al., 2012). However, these regionally high dependencies are—because of the above-mentioned topographic boundaries—not reflected in a propensity for widespread flooding unless a local perspective is taken (Figure 7d). Spatial flood dependencies in fall are overall weak except for some regions along the East coast and the Pacific Northwest, which is reflected in the low susceptibility to widespread flooding during this season except for the Pacific Northwest (Figures 6e and 7e).

3.4 Factors Influencing Regional Flood Susceptibility

Based on our local-perspective analysis, we find that the susceptibility of a region around a catchment to widespread flooding is related to the catchment's streamflow regime (Figure 8) and its climate characteristics. Over all seasons, flood susceptibility is highest in regions around catchments with streamflow regimes showing a strong seasonality, that is, New Year's and melt regimes (Figure 8c) in the Pacific Northwest and Rocky Mountains, which also have a strong flood seasonality (Villarini, 2016). In contrast, regional flood susceptibility is low in regions around catchments characterized by regimes with weak seasonality such as intermittent and weak winter regimes. On a seasonal scale, different regimes show high and low regional flood susceptibilities in dependence of their main season of flood occurrence. In winter, susceptibility is high for regions around catchments with a New Year's regime, that is, a streamflow regime characterized by high discharge around the time of the new year, which is mainly found in the Pacific Northwest (Brunner, Newman, et al., 2020). In contrast, susceptibility is close to zero for catchments with a melt regime, where precipitation is accumulated as snow. In spring, regional flood susceptibilities are highest for regions around catchments with a melt or strong winter regime, where snowmelt enhances spatial flood connectedness (Brunner, Gilleland, et al., 2020). In summer, susceptibility is close to zero for catchments of all regime types except for those with a melt regime experiencing frequent flood events in this season (Villarini, 2016). Fall susceptibilities are also close to zero for regions around catchments of most regimes except for regions around catchments with a New Year's regime, which start to be influenced by atmospheric rivers again (Barth et al., 2017; Rutz et al., 2015).

Details are in the caption following the image
Relationship of flood susceptibility with hydrological regime: (a) Map of five hydrological regime types: intermittent regime, weak winter regime, strong winter regime, New Year's regime, and melt regime, (b) median streamflow regime per regime class (color) and variability of regimes within a class (gray), (c) regional flood susceptibility all seasons, (d) winter, (e) spring, (f) summer, and (g) fall. The black lines in the boxplots indicate the median, the upper and lower whiskers correspond to 1.5 ∗ RIQ, where RIQ is to the inter-quartile range.

Regional flood susceptibility is also related to physiographical and climatic characteristics in addition to the regime type where the importance of individual characteristics varies by season (Figure 9). For all seasons, latitude and runoff ratio are the characteristics most strongly correlated with regional flood susceptibility. That is, the higher the runoff ratio of a catchment, the higher is the flood susceptibility for its corresponding region. As discussed above, seasonal regional flood susceptibility is related to the strength of flood connectedness(lowest box). In addition, it is related to other, mainly climatological characteristics. In winter, regions with a high aridity rarely experience widespread floods while catchments with high mean discharge and high flood magnitudes experience widespread floods more frequently. Spring is characterized by overall low correlations. In summer, regional flood susceptibility is most strongly related to the mean flood season, mean flood duration, and aridity. In fall, arid catchments show low regional flood susceptibility while catchments with high mean discharge and high flood magnitudes relate to higher susceptibilities.

Details are in the caption following the image
Correlation of over all and seasonal flood susceptibility with catchment characteristics, flood characteristics, and flood connectedness. Positive and negative correlations are indicated by turquoise and red colors, respectively. The darker the color, the stronger the correlation.

4 Discussion

PRSim.wave, the simulation approach used here, enabled generating a large set of regional flood events with realistic spatial patterns. However, Brunner and Gilleland (2020) showed that this approach slightly overestimates dependence for flood events, which might be translated into a slight overestimation in regional flood risk. It is difficult to quantify the extent of the overestimation because the nonparametric nature of the spatial model component of PRSim.wave precludes a systematic sensitivity analysis. There exist very few alternative modeling strategies for spatial extremes, as modeling spatial dependencies between extremes for a larger data set is very challenging because of a lack of flexible dependence structures applicable in high dimensions (Favre et al., 2018). A parametric alternative modeling strategy for simulating spatial fields is to use parametric spatiotemporal correlation structures and preserve marginal distributions as demonstrated by Papalexiou and Serinaldi (2020) for precipitation, relative humidity, and temperature. However, such a procedure has not yet been applied for simulating spatial streamflow and flooding. Other approaches also exist such as the conditional exceedance model by Heffernan and Tawn (2004). Here, we used PRSim.wave because of its good performance and simple implementation procedure (Brunner & Gilleland, 2020).

Similar to direct, event-based approaches, this direct, continuous approach is easily transferable to other regions with sufficient streamflow observations. The stochastic simulation approach can potentially also be used in combination with a hydraulic model to derive water levels and inundation areas and with information on flood exposure and vulnerability to derive risk in addition to hazard estimates.

We here worked with flood thresholds varying between 1.1 and 2 years. Our regional hazard assessment shows that the probability of widespread flooding is very small already at such low thresholds. Further increasing the thresholds would lead to even smaller regional hazard probabilities. For a specific application, flood thresholds would ideally be chosen with respect to impacts. However, information on the relationship between threshold and impact is often not available, especially not at a large spatial scale. In some cases, for example, the United States, stage-based impact thresholds for certain catchments may be obtained from national agencies (Stern, 2019).

The close relationship between the susceptibility to widespread flooding and the intraregional variability of seasonal, spatial flood dependence indicates that changes in meteorological and land-surface processes governing these dependence patterns and their intraregional variation may also lead to changes in regional flood hazard. These changes may differ by region, as meteorological and land-surface processes may change in a nonhomogeneous way across the United States (Easterling et al., 2017). An assessment of future changes in regional flood hazard would require the use of a modeling chain combining a general circulation model with a hydrological model or a stochastic model incorporating relevant covariates.

Spatial flood dependencies and therefore the probability of widespread flooding may not only be shaped by climate and land-surface processes but also by human flow alteration through reservoir storage or diversions. Such management effects on regional flood hazard were not considered here as we worked with a data set of catchments with nearly natural flows. However, considering such human alterations may change regional hazard estimates as coordinating reservoir operation across catchments may help to alleviate the negative impacts of widespread precipitation events by attenuating peak flows from different subbasins and therefore avoiding the superposition of flood waves (Volpi et al., 2018). Similarly, uncoordinated reservoir management may lead to aggravating widespread events. The focus on natural catchments may, in some regions which are heavily engineered such as the Ohio river basin (Engineers, 2014), lead to susceptibility estimates different from public perception.

5 Conclusions

Our results based on the newly introduced susceptibility index and stochastic simulations derived using a novel continuous approach show that the susceptibility of a region to widespread flooding depends on a few factors including the flood threshold, the region definition, location, and seasonality. Our river basin perspective analysis demonstrates that the susceptibility of large river basins in the United States to widespread flooding is highest in the coastal areas of the Pacific Northwest, the Sacramento and Klamath basins in California, and the North Atlantic region while it is low in the Missouri, Columbia, and Colorado river basins. The susceptibility of a basin to widespread flooding is generally highest in spring when spatial flood dependencies are highest because of high soil moisture availability and snowmelt contributions. Conversely, susceptibility is overall lowest in fall when spatial dependencies in precipitation are not directly translated into high flood dependencies under the influence of land surface effects. Our local-perspective analysis shows that regional flood susceptibilities are closely related to hydrological regimes if river basin boundaries are neglected, that is, if we focus on flexible regions. From such a perspective, highest regional flood susceptibilities are found in regions with strongly seasonal regimes as found in the Rocky Mountains and the Pacific Northwest. At a seasonal scale, regional flood susceptibilities are high in regions with high discharge and flood magnitudes in winter and fall and in snow-influenced regions in spring and summer. Future changes in precipitation and the fraction of snow may therefore seasonally and regionally lead to changes in the susceptibility to widespread flooding.

The comparison of the river basin and local perspective analyses highlights that a region is susceptible to widespread flooding if climatic and hydrological regimes are similar across the whole region (e.g., coastal basins in the Pacific Northwest). In contrast, susceptibility to widespread flooding is low if different parts of a river basin show high connectedness in different seasons. This behavior is illustrated by the Columbia river basin, whose upper part is influenced by snow melt processes in spring and summer while its lower part is dominated by high runoff in winter leading to nonconcurrent extremes in the two different parts of the river basin. We conclude that regional flood susceptibilities are not only governed by meteorological and land-surface processes related to snow and soil moisture—governing factors identified as important for local flooding and spatial flood dependencies in previous studies—but also by the location of topographical boundaries and related to this to the homogeneity of climatic and flood conditions within a region. We suggest that the high susceptibilities to widespread flooding in regions with homogeneous hydroclimatic conditions and their seasonal variations should be considered in decision making.

Acknowledgments

This work was supported by the Swiss National Science Foundation via a PostDoc.Mobility grant (Number P400P2_183844, granted to M. I. B.). We thank the three anonymous reviewers for their thorough assessment and constructive suggestions.

    Appendix A: Sampling Uncertainty Stochastic Model

    Details are in the caption following the image
    Effect of sampling uncertainty on simulated flood extents. Ranges of simulated flood extents obtained by fitting the stochastic model PRsim.wave on the original time series (original) and five resampled time series with replacement (B1–B5). The black lines in the boxplot indicate the median, and the upper and lower whiskers correspond to 1.5 ∗ RIQ, where RIQ is to the interquartile range.

    Data Availability Statement

    The daily discharge time series used in this study are available via the USGS website (https://waterdata.usgs.gov/nwis). The CAMELS catchment attributes can be downloaded online (via https://ral.ucar.edu/solutions/products/camels). The stochastic streamflow simulations, extracted peak-over-threshold events for different thresholds, and an R-script with the essential code needed to extract flood events and compute and visualize regional flood hazard from a river basin and local perspective are provided via HydroShare (Brunner, 2020).