Predicting flood damage probability across the conterminous United States

Floods are the leading cause of losses in the United States, with billions of dollars incurred every year in the form of government outlays, property damages, and agriculture losses, as well as significant loss of life. The Federal Emergency Management Agency (FEMA) oversees the development of Flood Insurance Rate Maps (FIRMs), which delineate the 100 year floodplain and identify areas that have a 1% annual chance of flooding or a 26% chance of flooding at least once during a 30 year mortgage (Holmes and Dinicola 2010). However, FEMA-constructed FIRMs are often outdated (e.g. the majority of FIRMs are 5–15 years old; ASFPM 2020), spatially incomplete (only 61% of the conterminous United States [CONUS] has been mapped; ASFPM 2020), and represent a dichotomous hazard condition (i.e. 'inside' or 'outside') rather than a continuous surface of flood risk. FEMA recently instituted a new risk rating methodology—Risk Rating 2.0—to incorporate spatially varying flood risk information (e.g. flood frequency, distance to water) for properties across the nation (FEMA 2021). However, Risk Rating 2.0 is only reflected in a property's flood insurance premium, and the 100 year floodplain boundary is still the primary metric against which floodplain management (e.g. elevated buildings) and flood insurance requirements are set (CRS 2021). As a result, development directly adjacent to the floodplain may still be exposed to flooding, while also being built to a lower standard (Patterson and Doyle 2009, Blessing et al 2017). Overly simplified, incomplete, and inaccurate flood maps have led to disparities between locations designated as high risk and where damage has occurred (e.g. Brody et al 2014, Blessing et al 2017). Given that climate and land use are dynamic across space and time, outdated maps will invariably exacerbate risk.

Completing and updating flood hazard maps for the nation is time consuming (computationally intensive hydraulic modeling; FEMA 2019) and resource intensive ($3.2–$11.8 billion to complete and $107–$480 million to maintain annually; ASFPM 2020). New cost-effective methods are needed to rapidly assess flood damage probability (FDP) across the nation and update information across areas experiencing environmental change (e.g. land-cover and climate change). Machine learning (ML) offers an effective and computationally efficient alternative to model FDP over large spatial domains and at moderate resolution. Several studies have employed various ML algorithms to model the spatial distribution of flood susceptibility, damage, and inundation. For example, Woznicki et al (2019) used random forest (RF) classification to develop a spatially complete 100 year floodplain map of the CONUS (i.e. the Environmental Protection Agency [EPA] 100 year floodplain). Alipour et al (2020) used RF to predict flash flood damage across the Southeast United States. Recent studies have leveraged RF and National Flood Insurance Program (NFIP) claims to predict the probability of flooding (Mobley et al 2021) or the number of insurance claims from past flood events (Yang et al 2021a). Numerous other studies have employed support vector machines, classification and regression trees, maximum entropy, RFs, and artificial neural networks to map flood susceptibility (Tehrany et al 2014, Wang et al 2015, Lee et al 2017, Zhao et al 2018, Choubin et al 2019, Mobley et al 2019). These studies typically take advantage of various geospatial datasets (e.g. land cover, elevation, climate, soil characteristics) and flood inventory databases representing a sample of flood events to generate spatially explicit estimates of flood susceptibility at unsampled locations for the study area of interest.

Here we present a proof of concept for rapid prediction of FDP using only open-source data and ML methods. Our modeling framework (figure 1) provides the opportunity to fill in gaps of unreported or unaccounted flood damage, identify unexpected damage, and rapidly update estimates of FDP as new information becomes available. In this study, we investigate the following questions to understand the underlying drivers of FDP in the U.S. and provide the first-ever spatially explicit estimate at scale: (a) Where are flood damage events frequently observed and how often are they reported outside of the FEMA 100 year floodplain? (b) What environmental and land cover characteristics are most correlated with flood damage? and (c) Can we accurately predict the spatial distribution of flood damage and identify where FDP is the highest? We define 'flood damage probability (FDP)' as the likelihood of any given location to be impacted by monetary damage, injuries, loss of life, or disruptions to the economy due to excessive rainfall and overflowing water bodies (i.e. flash or riverine flood) in a 14 year period (NOAA NWS 2019). This definition assumes stationary climate and land use conditions. Here, 'FDP' differs from 'flood susceptibility' and 'flood probability' in that it accounts for the likelihood that floods have directly impacted people, the economy, and the built environment (i.e. the likelihood that a location experienced damage due to flooding, rather than only flooding).

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We developed RF (Breiman 2001) models to estimate the probability of flood damage for each 100 m pixel in the CONUS, as well as spatial estimates of standard errors (SE) for four selected cities. Our modeling framework (figure 1) consisted of training RF models using an occurrence dataset (i.e. presence and pseudo-absence, assigned a value of 1 and 0 respectively) and a suite of geospatial predictors. Independent RF models were developed and their parameters (e.g. sample fraction, minimum node size) optimized for each 2-digit hydrologic unit code (HUC-2) watershed (figure S1 available online at stacks.iop.org/ERL/17/034006/mmedia) to account for spatial variability of climatic and physiographic conditions. Training presence data consisted of geolocations of 71 434 reported flood damage events (flash or riverine; NOAA Storm Events database; NOAA NWS 2018, 2019) occurring between December 2006 and May 2020 (i.e. 14 years of data; figure 2) to serve as a sample of locations that have experienced flood damage. Coastal (i.e. storm surge, tidal) and lakeshore flood event types and reports prior to December 2006 were not included in this study because records lack precise location information. We analyzed the presence data by identifying spatial bias of the reported events.

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RF requires at least two response classes, so we generated pseudo-absence data points (i.e. non-flood-damaged points) to serve as a proxy for locations where flood damage has not been reported (Mobley et al 2021; for a detailed description of the response variable, see section 1.3 in the supplementary materials). Pseudo-absence data points were randomly sampled across the landscape based on the following criteria: (a) equal number as presence points per watershed, (b) equal number as presences per land cover class, (c) excluded from a combined 100 year floodplain (figure S1; table 1), and (d) excluded from grid cells with presence points. Given that the pseudo-absence sampling technique can significantly influence the model, we conducted a robust sensitivity analysis for one HUC-2 watershed to determine the appropriate pseudo-absence to presence (PA:P) ratio for sampling criteria 'a' and 'b' (figure S2; Barbet-Massin et al 2012). We also explored different model (predictor) resolutions because there is not an indication of the extent of event damage in the database. The final sampling scheme was selected based on model performance (i.e. total error rate, false positive rate, false negative rate, and area under the curve [AUC]) and used a PA:P ratio of 1:1 and a spatial resolution of 100 m (see supplementary materials section 1.3.2 for further details regarding the selection of the PA:P ratio and spatial resolution).

Initially, we evaluated 13 predictors for their ability to estimate FDP. We eliminated the 'slope' and 'average annual maximum 1 day precipitation' predictors due to their high correlation with topographic wetness index and average annual maximum 3 day precipitation, respectively. The final subset of 11 predictor variables (table 1) used to train the RF models included hydrologic characteristics, topographic surface derivatives, flood severity, climate, soils, and socio-economic exposure (figures S3 and S4). All variables were resampled to 100 m resolution. We applied each RF model to map the probability and presence of flood damage at unsampled locations (i.e. for each 100 m pixel) across the CONUS and to generate SE estimates for four selected cities. Commission/omission error minimizer thresholds (minimizes the difference between false positive and false negative error rates) were used to convert flood damage probabilities to binary presence and absence of flood damage (Václavík and Meentemeyer 2009). We assessed model accuracy using 4-fold cross-validation (CV; i.e. training data consists of 75% of the dataset; CV accounts for spatial bias in the training dataset), AUC, and total error rate. Total error rates (i.e. [fp + fn]/[tp + fp + fn + tn], where fp = false positive, fn = false negative, tp = true positive, tn = true negative) were calculated within each land cover class and within each 100 year floodplain class by converting FDP predictions to binary presence/absence using the commission/omission error minimizer thresholds calibrated for each HUC-2 watershed model. A detailed methodological description of the modeling workflow (figure 1) can be found in supplementary information section 1.

3.1. Observed distribution

Our analysis of the locations of the reported flood damage events with regard to land cover and the FEMA 100 year floodplain revealed that there were numerous damage events reported across the built environment and outside of FEMA delineated high-risk areas. With regard to land cover class, we found that most reported events were located in developed (29.6%) or agricultural (28.1%) areas (figure 3(a)). Developed and agricultural classes make up 3.6% and 23.6% of CONUS land surface, respectively. The distribution of flood damage events normalized by land cover class area (points in class i/total km² of class i; figure 3(c)) revealed that developed areas had the highest proportion of events (0.072 reported flood events per km² of developed land). Developed land was followed by planted/cultivated (0.011), forest (0.008), wetlands/water (0.006), barren (0.004), then herbaceous/shrubland (0.003). For the FEMA 100 year floodplain, a majority of the reported flood damage events were located either outside (68.3%) of the floodplain or in unmapped (16.2%) areas of the CONUS (figure 3(b)). The distribution of flood damage events normalized by floodplain class area (number of points in class i/total km² of class i; figure 3(d)) revealed a greater proportion of reported events inside the floodplain (0.021), followed by areas outside of the floodplain (0.011), and unmapped areas (0.004).

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3.2. Predicted distribution and damage probability

3.2.1. Model performance

The aggregated models performed well at the CONUS scale, with an average AUC of 0.750 (first quartile = 0.726; third quartile = 0.802), indicating that our models were able to successfully distinguish between presences and pseudo-absences (i.e. flood-damaged and non-flood-damaged points). Model performance varied by environmental conditions (table S1). Analysis of total error rate by land cover class revealed lower error rates across wetlands/water (mean = 0.158; standard deviation [S.D.] = 0.056) and barren (mean = 0.299; S.D. = 0.211) areas, while forest had the highest error rates (mean = 0.346; S.D. = 0.045). Error rates for the 100 year floodplain were much higher outside of the mapped floodplain (mean = 0.347; S.D. = 0.018) than inside of the floodplain (mean = 0.000; S.D. = 0.000).

3.2.2. Underlying drivers of FDP

The relative importance of each predictor was generally consistent across each HUC-2 watershed model (18 total in the CONUS; figures 4 and 5; table S2). Proximity to streams was the most important predictor for 33% of the models (average rank across HUC-2s of 2.7). Other important variables included elevation (average rank = 2.7), average annual maximum 3 day precipitation (average rank = 3.4), the combined 100 year floodplain (i.e. 'inside' or 'outside'; average rank = 5.2), and height above the nearest drainage (average rank = 5.6). Predictors of moderate importance included urban road density (average rank = 5.8), profile curvature (average rank = 6.3), and topographic wetness index (average rank = 6.7). Potential channelization, percent hydric soils, and land cover displayed low relative importance, with average ranks greater than 8. Some HUC-2 watershed models displayed differences in variable importance (figure 5; table S2). For example, average annual maximum 3 day precipitation was ranked second in importance for the Missouri watershed, while it was ranked fourth in importance for the Lower Mississippi watershed. Percent hydric soils was ranked higher for the Lower Mississippi watershed (ranked fifth) than for the Missouri watershed (ranked eleventh). Urban road density was also more important in the Lower Mississippi watershed (ranked second) than the Missouri watershed (ranked sixth).

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Partial dependence plots (PDPs) are useful for interpreting the relationship between a predictor and the response variable for black box methods, such as RF (Friedman 2001). Development of PDPs for four selected watersheds allowed us to visualize the relationship between the five most important continuous predictors (i.e. elevation, proximity to streams, average annual maximum 3 day precipitation, height above the nearest drainage, and urban road density) and FDP (figure 6; see figures S5–S9 for PDPs of remaining predictors and watersheds). Across the four watersheds, FDP generally: (a) decreased with higher elevations, (b) was higher in close proximity to streams, (c) increased with higher average annual maximum 3 day precipitation, (d) decreased with greater elevations above the nearest drainage, and (e) increased with greater urban road density. While these are the general patterns, some watersheds display a unique relationship between the predictor and the response. For example, the South Atlantic-Gulf watershed has an increase in FDP between an elevation of 0 m and 500 m before plateauing. Also, FDP decreases between average annual maximum 3 day precipitation values of 130 mm and 200 mm for the Texas-Gulf watershed.

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3.2.3. Spatial variation, distribution, and uncertainty of predicted FDP

Predictions of FDP (figure 7) ranged from 0 to 1, where values close to 0 represent low FDP and values close to 1 represent high FDP over a 14 year period. Across the CONUS, flood damage probabilities are much higher inside of the combined 100 year floodplain (mean = 0.961; S.D. = 0.087) than outside of the 100 year floodplain (mean = 0.392; S.D. = 0.155). In addition, potential exposure to flood damage is prevalent across both inland and coastal areas.

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Applying the error minimizer threshold (see supplementary information equation (1)) to the FDP estimates predicted the presence of flood damage at approximately 2626 613 km² of land area (figure S10). Comparing the areas of predicted damage for each land cover class to the respective total area of the class revealed that wetlands (61%) had the highest proportion of predicted damage (i.e. 61% of pixels classified as wetlands throughout the CONUS exceeded the error minimizer threshold, as generated for each HUC-2 watershed; figure S11(a)). The wetland land cover class was followed by developed (42%), planted/cultivated (38%), forest (32%), barren (29%), and herbaceous/shrubland (28%). Our analysis also revealed that areas inside of the FEMA floodplain had the highest proportion of predicted damage (99%), followed by areas outside of the floodplain (31%), then unmapped areas (28%; figure S9(b)).

To better understand uncertainty associated with predicted FDP, we modeled the spatial distribution of SE for four selected cities (i.e. Charleston, South Carolina; Omaha, Nebraska; Houston, Texas; Salt Lake City, Utah; figure 8) that represent a range of environmental contexts. Across the four selected cities, SE ranged from 0.0 to 0.26, in which values close to 0 and 0.26 represent low and high average variability, respectively (for a detailed description of estimated SE see supplementary section 1.1.2). Overall, SE appear to follow topographic characteristics. For example, SE are low in close proximity to rivers in Charleston, downtown Houston (Buffalo Bayou), and Omaha (Missouri River). There are pockets of high SE in the downtown sections of each city. High SE are also prevalent in some mountainous areas surrounding Salt Lake City.

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3.2.4. Regional patterns in FDP

Differential risk patterns emerge when comparing average FDP across different regions (figure 9). Across the nine census divisions in the CONUS, we found that FDP was the highest across the East South Central (mean = 0.518; S.D. = 0.223), West South Central (mean = 0.501; S.D. = 0.263), South Atlantic (mean = 0.498; S.D. = 0.260), and West North Central (mean = 0.470; S.D. = 0.224) divisions (table S3). The five states/districts with the highest average FDP were Louisiana (mean = 0.662; S.D. = 0.320), Missouri (mean = 0.615; S.D. = 0.192), the District of Columbia (mean = 0.604; S.D. = 0.174), Florida (mean = 0.599; S.D. = 0.344), and Mississippi (mean = 0.574; S.D. = 0.251; table S4). Numerous counties across Florida (e.g. Monroe, Collier, Franklin), Louisiana (e.g. Cameron, St. Bernard, Concordia), and Mississippi (e.g. Issaquena Sharkey, Leflore) displayed FDPs greater than 0.790 (figure 9; table S4). North Carolina had three counties (Dare, Hyde, and Tyrrell) within the highest 30 counties for FDP. Tennessee and Virginia each had one county (Lake and Poquoson) in the highest 30.

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In the absence of reliable flood hazard information, risky decisions will continue to be made, affecting assets and lives. Therefore, we present a modeling framework to estimate a continuous surface of FDP for each 100 m pixel in the CONUS. This proof of concept for rapid prediction of FDP using only open-source data is the first study of its kind to analyze the underlying drivers and spatial distribution of FDP across the CONUS. Our approach is computationally efficient, replicable, and can be easily updated in response to changing environmental conditions. Our results support previous findings (e.g. Blessing et al 2017), which show that a large portion of flood loss is reported in areas classified as 'of minimal flood hazard' (i.e. outside of the FEMA 100 year floodplain). Our study expands upon previous research by determining whether these findings are consistent across the entire CONUS at a moderately fine spatial grain. We found 84.5% of the total reported damage events between 2006 and 2020 to be located outside of the FEMA delineated high-risk zones or in an unmapped area of the CONUS (figure 3), suggesting that FEMA flood hazard mapping is not capturing the full extent of flood damage exposure. Such a large percentage may be partially attributed to limitations (i.e. unrecorded return periods for the reported damage events) and potential bias (i.e. flood damage is more likely to be reported in locations where it affects people and the built environment) associated with the training dataset. The NOAA Storm Events database records damage reported after any flood frequency (e.g. 100 year, 500 year flood, etc), whereas the FEMA floodplain only represents the 100 year return period. However, a high presence of reported events in areas of minimal hazard or in unmapped areas suggest that communities throughout the nation are susceptible to localized flooding that current management policies fail to consider, leading residents and developers to continue risky development decisions that may lead to subsequent damages. We reiterate the calls of previous researchers for up-to-date and spatially complete flood hazard maps that characterize a continuous surface of flood risk probability.

The variable importance analysis and PDPs provide valuable insight regarding the important predictors and their respective relationship to FDP. Proximity to streams was the most important predictor for 33% of the models and proximity to streams and elevation had the highest average variable importance rank (average rank = 2.7), suggesting that these variables are underlying drivers of flood damage across many different geographic contexts. The PDP analysis reveals the topographic characteristics associated with areas more vulnerable to flood damage, which could be used to inform land use (e.g. development) and flood damage mitigation policies. While the distinct drivers of and their relationships to FDP were generally consistent across the HUC-2 watershed models, we found some differences that are attributed to environmental variation (e.g. land use, topography, climate) between watersheds. For example, the general increase in FDP with higher elevations for the South Atlantic-Gulf watershed could be due to the presence of large cities at higher elevations. Building the RF models at the HUC-2 watershed scale and implementing the explanatory analysis allowed us to uncover and capture these variations across different spatial domains.

Our CONUS-scale estimates of FDP show great variability in potential exposure to damage across the landscape. The probability map is useful for decision-making purposes (e.g. guiding land use regulations), as it provides a measure of confidence in flood damage occurrence. Our map of the presence of flood damage (i.e. flood damage occurrence in a 14 year period; figure S10), on the other hand, delineates locations with modeled probabilities greater than a calculated threshold. While the presence map does not provide any measure of confidence, it can be tailored to specific needs (e.g. preference of false positives over false negatives) by changing the threshold used (Pearson 2009). Specifically, we used a threshold that minimized the difference between false positive (predicting flood damage where there is none) and false negative (not recognizing flood damage) error rates, which predicted a total damage land area of approximately 2626 613 km² (figure S10). By contrast, the total land area within the mapped FEMA 100 year floodplain is approximately 572 209 km² (Woznicki et al 2019). The difference in area (2054 404 km²) is attributed to a combination of factors: (a) RF model coverage in areas unmapped by FEMA, (b) false positives, (c) choice of threshold, (d) potential underestimation of exposure by FEMA, and (e) various flood frequencies captured in the NOAA database (e.g. 100 year, 500 year flood, etc), while the FEMA floodplain only represents the 100 year flood. Overall, it appears that the models overestimated FDP, particularly in Southwestern portions of the CONUS. While this result is counterintuitive from a climatology perspective, 'dry' states can nonetheless experience damaging flash flooding, even if the return frequencies of the individual events are low. Moreover, communities across dry areas may not have adapted to reduce their relative exposure to flood hazards in the way 'wet' or coastal states have. To further investigate uncertainty in predicted results, we generated spatially explicit SE for four selected cities. While it was not computationally feasible to produce SE for the entire CONUS, we showed that standard error maps can be useful for identifying locations with greater uncertainty. Knowledge of uncertainty is imperative for developing meaningful and cost-effective solutions in decision-making contexts (Reckhow 1994).

Consistent with other studies, our results show flood damages often reported outside of areas managed to mitigate flood damages, such as the 100 year floodplain boundary (Brody et al 2014, Blessing et al 2017). This suggests that estimates of place-specific likelihood of flood damage can help policy makers, developers, and residents make more informed planning decisions. Overall, our study developed a computationally efficient and open-source approach to estimating FDP across large spatial scales and at moderate resolution, with all of the watershed models completing the training, 4-fold cross validation, and prediction in an average of 5.55 h (first quartile: 3.21; third quartile: 6.66; using 8 cores and an average of 23 GB of RAM per watershed). Because of the efficiency of the approach, the model could be used to update estimates on a frequent basis as more flood damage reports are added to the NOAA Storm Events database and as many regions of the country continue to experience rapid environmental change (e.g. land-cover and climate change).

Our study provided an initial proof of concept for rapid prediction of FDP across large spatial scales using only open-source data and ML methods, however, the current approach has some limitations. First, the results are limited by the comprehensiveness, including any biases, of the observation dataset (i.e. the NOAA Storm Events database). See sections 2, 3.1, and supplementary 1.6 for detail on spatial bias. For example, observations of flood damage only contain flash or riverine flood events. Observations of coastal flooding (storm surge and tide effects) lack the location accuracy (i.e. exact latitude and longitude; NOAA NWS 2018) required by the approach. As a result, flood damage probabilities are lower than expected along coastlines (figure 7). Importantly, both the extent to which the available presence (i.e. reported flood damage events) data match the environmental context and the type of absence data used (i.e. true-absences or pseudo-absence) can impact the results (Václavík and Meentemeyer 2009, 2012). We addressed possible bias by refining the pseudo-absence sampling scheme based on our analysis of the spatial distribution of reported events and by accounting for spatial sorting bias in cross validation (supplementary materials section 1.6, model evaluation).

Another limitation is the way exposure and flood hazard are represented in the model. Exposure predictors are land use/land cover and urban road density, while flood hazard predictors are average annual maximum 3 day precipitation and the 100 year floodplain boundary. These are geospatial predictors used in similar model approaches and environmental contexts (Wang et al 2015, Giovannettone et al 2018, Choubin et al 2019, Mobley et al 2019, Woznicki et al 2019, Chen et al 2020). Future work could benefit from exploring or creating high-resolution (e.g. parcel level) open-source datasets that better capture socio-economic exposure and vulnerability, which may only be applicable for smaller study areas. While it could be possible to incorporate multiple flood severity predictors to capture the frequency, intensity, and duration of rainfall associated with different hydrometeorological extremes, flood severity predictors are likely to be highly correlated with one another. In the case of purely predictive RF models, highly correlated predictors do not present any issues. However, in our study, we are also interested in building an explanatory model, and variable importance measures can be biased whenever predictors are highly correlated (Strobl et al 2007, 2008). Future work could employ dynamic modeling frameworks that more precisely incorporate the spatio-temporal extent and depth of rainfall, runoff, and flooding during an event. This framework could be used in near and long-term forecasting applications of FDP, particularly as projections show that flood damages are likely to increase through the 21st century (Wobus et al 2017, Wing et al 2018, Swain et al 2020). The release of new flood inundation archives (Tellman et al 2021, Yang et al 2021b) based on remotely sensed imagery represent promising developments that could form the necessary observational basis for such a dynamic modeling framework.

Lastly, our study assumed stationary climate and land use conditions. This assumption may be violated given anthropogenic influences on both climate and land cover. The use of 2016 NLCD data could have impacted the results because the underlying land use could have changed during the time period of data used in our study (December 2006–May 2020). A temporally dynamic modeling framework could be developed to better capture changes in land use and climate across space and time and to better relate flood damage events and predictions to environmental change.

The authors gratefully acknowledge financial support by the U.S. Geological Survey Southeast Climate Adaptation Science Center (Award Number G19AC00083) and the North Carolina State University Sea Grant program (Award Number R/MG-2011). The authors thank John Vogler and the Landscape Dynamics group from the Center for Geospatial Analytics for their valuable comments to help improve the manuscript. We acknowledge the computing resources provided on Henry2, a high-performance computing (HPC) cluster operated by North Carolina State University. We also thank Lisa Lowe for their assistance with optimization, which was provided through the Office of Information Technology HPC services at NC State University. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5066/P954TTQN. Data will be available from 28 February 2022.

E L C: conceptualization, methodology, software, formal analysis, writing—original draft, writing—review & editing, funding acquisition. G M S: conceptualization, writing—review & editing, supervision, funding acquisition, A T: methodology, writing—review & editing. C C S: methodology, writing—review & editing. H M: methodology, writing—review & editing. A S: writing—review & editing. R K M: conceptualization, writing—review & editing, supervision, funding acquisition. All authors have read and agreed to the submitted version of the manuscript.