Spatial distribution of socio-demographic and housing-based factors in relation to flash and slow-rise flooding hazards in the U.S

Previous studies have drawn attention to racial and socioeconomic disparities in exposures associated with flood events at varying spatial scales, but most of these studies have not differentiated flood risk. Assessing flood risk without differentiating floods by their characteristics (e.g. duration and intensity of precipitation leading to flooding) may lead to less accurate estimates of the most vulnerable locations and populations. In this study, we compare the spatial patterning of social vulnerability, types of housing, and housing tenure (i.e. rented vs. owned) between two specific flood types used operationally by the National Weather Service—flash floods and slow-rise floods—in the floodplains across the Contiguous United States (CONUS). We synthesized several datasets, including established distributions of flood hazards and flooding characteristics, indicators of socioeconomic status, social vulnerability, and housing characteristics, and used generalized estimating equations to examine the proportion of socially vulnerable populations and housing types and tenure residing in the flash and slow-rise flood extents. Our statistical findings show that the proportion of the slow-rise flooded area in the floodplains is significantly greater in tracts characterized by higher percentages of socially vulnerable. However, the results could not confirm the hypothesis that they are exposed considerably more than less vulnerable in the flash flooded floodplains. Considering housing-occupancy vulnerability, the percentage of renter-occupancies are greater in the flash flood floodplains compared to slow-rise, especially in areas with high rainfall accumulation producing storms (e.g. in the Southeast). This assessment contributes insights into how specific flood types could impact different populations and housing tenure across the CONUS and informs strategies to support urban and rural community resilience and planning at local and state levels.


Introduction
Flooding is among the most catastrophic natural disasters, contributing to national burdens on social, economic, and health systems in the United States [1,2]. Moreover, future flood exposure [3] and disaster probability [4] are projected to increase over the contiguous United States (CONUS) due to changing climatic conditions [5][6][7] and population growth scenarios [8][9][10], thus posing more significant risks and damage to economic and human systems. Assessing flood risk requires a comprehensive understanding of the links between multiple spatially dependent variables, including characteristics of the precipitation causing the floods, geographic extent of flooded areas, exposed populations within the flooded areas, and the underlying social vulnerability of the people.
A growing body of research has investigated associations between spatial distributions of social vulnerability 4 and exposures to pre-and post-flood hazards [11][12][13][14][15][16][17]. Most studies suggest that lowincome households, racial and ethnic minorities [18][19][20], as well as households that rent [21][22][23], may be more vulnerable to adverse outcomes associated with flooding. Often, people with the least capacity to prepare, respond, and recover from flooding events also tend to live where their exposure to such events is greater [23,24]. Nevertheless, in other contexts, socioeconomically-advantaged populations may experience greater exposure to flooding [25], mainly in coastal regions, where locational and environmental benefits such as the attraction of waterfront amenities [26] are contrasted with high-impact weather events like hurricanes that often produce significant coastal flooding.
However, despite recent progress in understanding how flooding impacts populations across the U.S., studies on flooding as it relates to issues of environmental justice still have not revealed clear patterns of disproportionate exposure for socially disadvantaged populations [27]. More nuanced insight into social vulnerability and flooding patterns is needed to improve the development and implementation of context-specific guidance around harm prevention and reduction. A better understanding of the intersection of flooding risk and housing type and tenure may be one way to address currently conflicting findings in the scientific literature. Specifically, we still do not understand whether strong relationships exist between housing types (i.e. single-family, multi-family, and mobile homes) and housing tenure (e.g. renter versus owner occupancy status) and their vulnerability to floods of different types, particularly across large scales in the United States.
In addition, floods in the U.S. occur across a wide spectrum of atmospheric and hydrologic processes that have not adequately been accounted for in previous research. For example, the National Weather Service uses two primary flood definitions in operational decision-making 5 : (1) Flash floods that 'occur within a short time period after a rain event-generally 6 h or less,' and (2) slow-rise (river) floods that are 'caused by a gradual increase in water level of a river or creek.' Differentiating floods by type, as shown in this study, may be another way to address currently conflicting findings in the scientific literature. For example, floods can manifest as large regional 4 In defining social vulnerability throughout this study, we use the following, well-established definition: 'the characteristics of a person or group and their situation that influence their capacity to anticipate, cope with, resist, and recover from the impact of a natural hazard' [26,33,[39][40][41][42]. 5 www.weather.gov/ffc/floods. river floods over long periods of time, local shortduration flash floods, coastal storm surges, and urban drainage overflow [28]. The associated characteristics of different flood types within distinct hydrologic regimes likewise vary and may influence their impact on surrounding communities [29]. For instance, flash floods are distinctive for their rapid onset and extremely high-water flow over short durations.
In contrast, slow-rise floods (also called fluvial or river floods) occur due to slowly increasing river flows that eventually leave the channel banks. In both examples, the impact on homes in surrounding communities is significant but different, as property losses are commonly lower in flash floods [30] than in slowrise floods [31,32]. Thus, assessing the spatial patterns of impacted communities by specific flood types and how they intersect with patterns of social vulnerability, housing types, and housing tenure within those affected communities is critical to identifying where, when, and for whom to distribute resources for protection against flooding.
This study employs flood hazard maps, spatial socioeconomic and housing data, and flood characteristics to examine the following questions: (i) To what extent are socioeconomic-disadvantaged populations vulnerable to flash or slow-rise floods? (ii) To what extent are housing types and tenure (i.e. rentervs. owner-occupied housing) associated with exposure to flash or slow-rise floods? We hypothesized that increased socioeconomic vulnerability would be associated with greater exposure to floods and that these associations would be different for flash versus slow-rise flood zones. We further hypothesized that mobile housing and renter-occupied housing would be more strongly associated with exposure to flash and slow-rise floods than owner-occupied housing. We used generalized estimating equations to assess associations of social vulnerability and housing type and tenure with distributions of exposure to flash and slow-rise flood risks. We used geospatial analyses to investigate where flooding characteristics of flash and slow-rise floods intersect with indicators of socially vulnerability and housing in the flood extents across the CONUS. Results from this analysis could inform whether housing tenure and flood type warrant greater consideration in the context of residential flood management decision-making.

Data sources
Our analysis involves synthesizing several datasets, including established distributions of flood hazards, flood type characteristics (e.g. rainfall accumulation and cumulative flood episodes), housing characteristics (e.g. housing type, occupant tenure), and indicators of socioeconomic status and social vulnerability (table 1). All data were publicly available at the census tract level or higher spatial resolution for a national-scale analysis across the continental United States (CONUS). We conducted a spatial analysis at the census tract level because it is conventionally understood to correspond to a neighborhood scale [33] and reveals geographic patterns of potential population vulnerability to the disaster that can be used in the mitigation, preparedness, response, and recovery [34].

Flood hazard map and boundaries
We used the fluvial and pluvial flooding boundaries of the 100 year recurrence interval flood developed and validated in Wing et al [35] because they are contiguous, high resolution, and exhibit accuracy to local studies carried out by U.S. government agencies. In addition, it is essential for flood risk map used for insurance and management activities in the U.S. The area inundated by the 100 year recurrence interval flood represents an area with a 1% or greater probability of being flooded each year. The flooding boundaries were developed by using a twodimensional hydrodynamic model of the CONUS with a 30 m digital elevation area [35]. The flooding data were validated against the Federal Emergency Management Agency Special Flood Hazard Area maps and included flooding in catchments larger than 50 km [2,35].

Flood-type characteristics
To classify floods by type, we used the flood database developed and published by Dougherty and Rasmussen [36], who created a flood-producing storm database by merging storm reports with streamflow-indicated floods and rainfall data. This database is limited by the availability of multiple high-resolution data types, with multi-sensor rainfall data available since 2002 and streamflow-indicated floods from Shen et al [37] only existing up to 2013. Thus, the data coverage is 2002-2013, over which time period storms that specifically produce flash and slow-rise floods are documented.
Flash flood events were defined as the 'rapid and extreme flow of high water into a normally dry area, or rapid water level rise in stream or creek above a predetermined flood level, beginning within six hours of the causative event.' Slow-rise events were defined as 'the inundation of a normally dry area caused by an increased water level in an established watercourse, or ponding of water, generally occurring more than six hours after the causative event and posing a threat to life or property [38].' These definitions do not specify a criterion for damage or inundation because they are primarily used for storm-reporting purposes, as established by the National Weather Service, and are widely used by the atmospheric and hydrologic science communities.
We extracted two flooding characteristics for both flood types from the database: (i) average annual rainfall accumulation (i.e. the average flood-producing storm rainfall in millimeters), and (ii) cumulative flood episodes (i.e. the cumulative annual number of flooding events). The rainfall accumulation was derived from the 4 km, hourly, Stage-IV precipitation dataset [39] over a ±5 • latitude/longitude grid box around the geographic centroid of flood reports from the National Center for Environmental Information database from 2002 to 2013 [36]. Using these two flood characteristics together, we can gain insight into how different localities have experienced flash and slow-rise floods between 2002 and 2013.

Socio-demographic and housing data
Housing and socioeconomic variables were from the 2009 to 2013 ACS 5 year estimates from the U.S. Census Bureau website (www.census.gov/programssurveys/acs). Our housing variables included median  housing age (in years), housing tenure (owner or renter-occupied housing units), and housing types by structure (single-family, multi-family, and mobile homes). In addition, we selected socioeconomic variables (table 2) that indicate different household deprivation domains, such as income, employment, housing, household characteristics, transportation, and demographics [19]. These variables are commonly used in distributive environmental justice research to evaluate socioeconomic variability in health outcomes and social vulnerability to natural hazards [26,33,[40][41][42][43].

Data processing
Data in this study are synthesized and processed in several steps using ArcGIS Pro. First, we overlaid the raster grid of flood characteristic data (e.g. annual average rainfall accumulation distribution between 2002 and 2013 across the CONUS; figure S1) with flood hazard map boundaries and counties' census tract boundaries in CONUS. Second, we counted the total number of pixels with non-zero flood depth values within each tract, calculated the total area covered by these pixels, and divided it by the land area of the tract to derive the proportion of the tract area flooded. Third, we intersected the resulting flood hazard map layer containing the flooding characteristics with the averaged 2009-2013 census tract socioeconomic, housing types, and occupancy tenure dataset inside the floodplain. Finally, we extracted the census tracts that lay partially or entirely within the flooding boundaries and experienced at least one flood episode between 2002 and 2013.
To derive the proportions of housing and sociodemographic variables in the floodplains per census tract, we assumed that each neighborhood's socioeconomic and demographic conditions were uniformly distributed [26,44]. Based on this assumption, each tract's percentage of the independent variables was multiplied by the census tract floodplain area to estimate the proportions in the floodplains per census tract. (i.e. census tract flood extent). The total number of census tracts in the floodplains that had experienced at least one flash and slow-rise flood was 20 833 and 20 970, respectively. Henceforth, 'area' in this study indicates the flooded floodplain area. Table 2 shows the descriptive statistics of the resulting datasets.

Exploratory geospatial analysis
Here, we used two commonly used quantitative approaches to assess the social vulnerability to floods. The first approach is an integration analysis, which involves overlaying geospatial layers of flood hazard and social vulnerability indicators to determine where high levels of each coincide [45,46]. The second employs the construction and mapping of indices to identify which dimensions of social vulnerability dominate flood-prone areas [47,48]. We combined both methods to explore the spatial clustering of statistically significant variables from the generalized estimating equations (GEEs) model output. Combining geospatial instruments and statistical methods to assess floods and vulnerability in the affected areas has been beneficial for improving flood incidence visualization and quickly distinguishing vulnerable areas [49].
A flowchart showing the roadmap of the dataset and methods is shown in figure S2 in the supplemental material. First, we constructed a social vulnerability index (SoVI) with the ten socioeconomic variables (listed in table 2) based on the SoVI algorithm of Cutter et al [18], further explained in section 2.3.2. Second, we used the hotspot analysis, also known as Getis-Ord Gi * analysis, to detect significant hotspots of flooding characteristics, SoVI, and housing variables across the CONUS. For a spot to be considered a hotspot (or coldspot), the location must have a high, positive Z-score surrounded by other high, positive Z-score values (or a low, negative Z-score surrounded by other low, negative Z-score values) [26,50]. Third, we utilized two-way crosstabulation (an integration analysis) and a dasymetric mapping technique to identify the coincidence of detected hotspots or coldspots of flooding characteristics with the SoVI and housing variables inside the flood extents.
And lastly, we used the local Moran's I to evaluate spatial autocorrelation of SoVI and housing indicators across the flood extents in the floodplains. Moran's I is a measure of spatial autocorrelation, ranging from −1 (completely dispersed in space) to +1 (perfectly correlated in space), and can be interpreted similarly to a correlation coefficient [50][51][52][53][54]. This represents a measure of how different or similar a SoVI or housing indicator is compared to neighboring census tracts. Specifically, it evaluates whether census tracts with similar social vulnerability and housing indicators rankings tend to be grouped closer or spread farther apart. However, it cannot provide causal mechanisms that produce spatial clusters but can illuminate local patterns across census tracts [51]. Further guidance and details on these techniques are available in any software that can perform geospatial analysis (e.g. ArcGIS, Python, and R programming).

Social vulnerability index (SoVI)
Guided by the approach developed by Cutter et al [18], the ten variables listed in table 2 were used to construct SoVI. However, using these variables to develop an indicator of social vulnerability may not comprehensively capture vulnerability conditions of a particular area at a local level. Still, such indices provide a useful estimate of baseline vulnerability applicable for comparative purposes across different locations or time scales [48,55]. For example, an index (in this case, the SoVI) can establish baseline vulnerability and be tracked over time, which is vital for policymakers in disaster risk reduction.
The SoVI algorithm uses principal components analysis (PCA) to reduce a large set of variables to a smaller group of latent factors and then sums the factors into an index. Prior to the PCA, the variables are standardized to a mean of 0 and a standard deviation of 1 (z-score). Seven indicators have a positive relationship with social vulnerability, indicating that they increase in value with increasing vulnerability. We did not drop the variables but inverted the signs of the three negative indicators to maintain consistency with other prior environmental justice studies that have indicated these population groups were significantly exposed to environmental hazards [11,[40][41][42] (table 3). Varimax rotation is used to simplify the structure of the dimensions to produce more independence among the factors [50]. Based on the Kaiser criterion, we extracted four components with eigenvalues of 1.0 [43,56], and a minimum loading score of 0.30, and together represent 60% of the total variance of the socioeconomic variables. The first four components explained the 22%, 15%, 13%, and 10% of the overall variance.
Lastly, we used an additive model to produce a SoVI score on all four component scores (factor loadings) for each tract. The additive model was chosen because it does not make a priori assumptions about factor importance in the overall sum, although that's not realistic [18]. This approach was assumed as a suitable option because there was no defensible method of assigning weights to the variables. Hence, each factor was viewed as having an equal contribution to the tract's overall vulnerability. We defined the SoVI as a relative measure of the overall social vulnerability for each tract; and the statistical summary is shown in table 2. We classified census tracts with SoVI greater than 1 standard deviation as highly vulnerable, while the least vulnerable are those with less than −1 standard deviation from the mean (figure S3).

Generalized estimating equations
We used GEEs, a multivariable technique appropriate for exploring the geographic clustering of neighborhoods, to predict the flash or slow-rise flood extent and estimate statistically valid inferences on potential associations with hypothesized SoVI and housing variables. Data for flash and slow-rise floods were analyzed separately, with results for each examined comparatively to explore differences and similarities. Our continuous dependent variable was the census tract flood extent. This variable has been modeled in previous studies [15,23,33,52]. It was appropriate for our study because we are interested in the distribution of social, housing, and economic vulnerabilities in areas susceptible to flash or slow-rise floods in the floodplains. GEEs have been used in prior studies on neighborhood inequalities in flooding [15,17,23,33,42], and further details (i.e. assumptions, advantages, and limitations) are described in supplemental materials B1. In summary, we defined clusters of census tracts based on the median decade of housing age (1939 or earlier; 1940-1949; 1950-1959; 1960-1969; 1970-1979; 1980-1989; 1990-1999; 2000 or later). Using a median decade of housing to define clusters has been documented to match the developmental formation of the census tract [15,57].
We explored normal and Gamma distributions with the log and identity link function using an exchangeable correlation structure for a total of 4 model specifications for each flood type. We used the quasi-likelihood under the independence model criterion (QIC) to evaluate model fit, where the lowest values indicate better fit [15,57,58]. We selected the normal distribution with log link and exchangeable correlation structure in the GEEs models for the final model because the dependent variable has a nonnormal distribution and the lowest QIC. And lastly, we used variable inflation coefficients to test for multicollinearity, and there was no indication of multicollinearity in the models since all variable inflation coefficients were below 5.0. A detailed explanation of model development was reported in supplemental material B2. Tables 4 and 5 show the results from the GEE models exploring the statistical associations between the flood extent, housing, and social vulnerability indicators in the floodplains. Model 2 specifications produced the best model result for flash and slow-rise flood extents based on the lower values for the QIC. Numbers in the Exp (Beta) column are the elasticity. Therefore, they can be interpreted as the percentage change in the proportion of tract flooded area for every unit increase of the independent variables (after subtracting one and multiplying by 100).

Flash floods
Compared to single-family homes, mobile homes were associated with a 19% increase in flash flood extents, indicating that single-family homes have a significant presence in flash flood events (β = 0.171). In addition, median household income is negatively associated with flash flood extent, indicating that lower income was associated with areas with a greater percentage of flash flood area after adjusting for other variables (β = − 0.185, 95% CI = 0.074-0.253).
Compared to owner-occupancy, in census tracts characterized by higher percentages of renteroccupancy, the proportion of flash flooded areas is significantly greater; and they were associated with 19% greater presence in the flood extent (p < 0.003). As for flooding characteristics, a unit increase in the amount of rainfall accumulation producing flash floods was associated with a 27% increase in the flash flood extent (β = 0.240, p = 0.006). In contrast, the number of flood episodes shows a positive relationship with flash flood extent, but at a statistically non-significant level.

Slow-rise flood
Unlike flash floods, the GEE result shows that the proportion of slow-rise flooded extent is significantly greater in tracts inhabited by higher percentages of socially vulnerable populations (p < 0.01).

Flash floods
Hotspots of rainfall accumulation producing flash floods were clustered along the Mississippi River corridor, partly along the Pacific Northwest (border of Northern California and Oregon), and the Mid-Atlantic regions ( figure 1(a)-red). Coldspots (i.e. low rainfall accumulation producing flash floods) were clustered in the Midwest, Rocky Mountain, and Northeast regions ( figure 1(a)-blue). Hotspots of flash flood episodes were clustered in the Ohio River valley and Mississippi River ( figure 1(b)red), while the coldspots were clustered in other regions of the CONUS.

Slow-rise floods
On the other hand, compared to flash floods, rainfall accumulation producing slow-rise floods (figure 2(a)-red) were clustered in the Northeast, Midwest, Pacific Northwest, and the lower Southeast along the Gulf coast. Coldspots were in other regions of the CONUS (figure 2(a)-blue). Hotspots of slowrise flood episodes were clustered (figure 2(b)-red) in the Northeast, Ohio River valley, and upper Midwest.

Flooding characteristics, socio-vulnerability, and housing indicators
Here, we examine the coincidence of detected hotspots or coldspots of rainfall accumulation, SoVI, and housing indicators with the rainfall accumulation producing flash and slow-rise storms in the floodplains across the CONUS. We present and discuss the results for rainfall accumulation because of its statistical significance in the GEE results. It is also an essential factor that determines the severity of flooding. Figures 3 and 4, described below, are presented with the county-level resolution because counties are wellestablished administrative units with similar political and governmental functions [59]. County-level analyses can also be easily related to social, economic, and housing data available at the census tract level.

Social vulnerability index (SoVI)
Socially vulnerable populations were clustered in areas that experienced high amounts of rainfall accumulation producing flash floods ( figure 3(a)). By contrast, populations in the Southwest and Northwest plains with either high (figure 3(a)-blue) or low (figure 3(a)-green) social vulnerability were clustered in areas that experienced low amounts of rainfall accumulation producing flash floods. Compared with slow-rise floods ( figure 3(b)), smaller clusters of high socially vulnerable (red) were located in areas that experienced high amounts of rainfall accumulation producing slow-rise floods, e.g. in Florida, North Georgia, New York, Massachusetts, Vermont, and New Hampshire. In other words, these clusters are habitable areas in the floodplains that experienced significantly higher rainfall accumulation during the slow-rise flood-producing storms.
The spatial pattern above shows the national trend of the socially vulnerable in areas prone to flash and slow-rise flood-producing storms. However, we observed an interesting and distinct geospatial pattern using local Moran's I to examine the detected hotspots at a more granular level (figure 4). For example, along the Mississippi corridor, we observed both high socially vulnerable and less vulnerable (HLblue and LL-green) inhabit neighboring areas susceptible to high rainfall accumulation producing flash floods in the flood extents ( figure 4(a)-inlet). This spatial pattern gives a possible explanation for the GEE empirical analysis for flash flood extents, in which socially vulnerable had a positive relationship at a statistically non-significant level (p = 0.076), an indication that both high and low socially vulnerable could have a similar level of exposure inside the flood extents.
In contrast, we observed a local spatial pattern in which socially vulnerable (HH-red) were more noticeable in the flood extents of areas prone to high rainfall accumulation producing slow-rise floods, e.g. in Florida, North Georgia, New York, Massachusetts, Vermont (figure 4(b)-inlet). This pattern could support a relationship shown in the GEE analysis, in which the socially vulnerable exhibit significant exposure in hotspots of slow-rise floods (p = 0.026). Figure 5(a) shows the national trend of housing tenure coinciding with the rainfall accumulation producing flash flood extents. High renter-occupancy (red) was considerably exposed to high rainfall, producing flash floods in parts of the Pacific Northwest, Texas, and the South, except in Arkansas and Alabama (orange), where owner-occupied were clustered in the flood extents. In the upper Midwest, owneroccupancies inhabit areas that experience less rainfall accumulation (green). High renter occupancies are in the low rainfall accumulation producing flash floods in the Southwest and Great plains (blue).

Renter-occupancy households
Like flash floods, significant clusters of rentersoccupancy households inhabit areas prone to high rainfall accumulation producing slow-rise floods (red) in the Pacific Northwest and lower Southeast region along the gulf coast ( figure 5(b)). Conversely, more owner-occupied households were clustered in areas with high rainfall producing slow-rise floods (orange) in the Mid-Atlantic region and part of the Midwest. Using local Moran's I to investigate the local spatial patterns in these hotspots county level boundaries, but the data are presented for areas that experienced the flood type. Red and blue colors indicate hotspots and coldspots, respectively (i.e. statistically significant clustered areas that experienced similar high or low amounts of rainfall accumulation producing storms, respectively). Confidence limits of 99%, 95%, and 90% refer to percent likelihood that the identified clusters did not occur by chance, respectively. Grey areas indicate where flash flood producing storms occurred but were not spatially clustered (i.e. not statistically significant clusters by our analysis), and the white areas on the map indicate places where no storm data were recorded. shows county level boundaries, but the data are presented for areas that experienced the flood type. Red and blue colors indicate hotspots and coldspots, respectively (i.e. statistically significant clustered areas that experienced similar high or low amounts of rainfall accumulation producing storms, respectively). Confidence limits of 99%, 95%, and 90% refer to percent likelihood that the identified clusters did not occur by chance, respectively. Grey areas indicate where flash flood producing storms occurred but were not spatially clustered (i.e. not statistically significant clusters by our analysis), and the white areas on the map indicate places where no storm data were recorded.   high and low values, respectively. High and low extremes indicate the variable greater than one standard deviation and less than one standard deviation, respectively. The grey areas are not statistically significant, and the white indicates places that did not experience the storm.
in the Southeast, we observed that neighboring clusters of renter-occupied inhabit areas with high rainfall-producing flash floods (figure 6(a)-red) than slow-rise floods (figure 6(b)-red). This spatial pattern can be linked with the results shown in the GEE analysis that more renters have greater exposure to flash floods risks (β = 0.177; 95% CI = 0.139-0.206) than slow-rise floods (β = 0.131; 95% CI = 0.116-0.330).
The renter occupancies clustered in the areas with high rainfall producing flash and slow-rise floods were households with low-income earnings (figure C1, blue and green), especially in the U.S. South ( figure C1(a)). In contrast, high-income homeowners reside in areas with similar flooding characteristics in Mid-Atlantic and East coast (orange). Interestingly, we observed that high-income renters (red) are vulnerable to flash and slow-rise floods in South Texas and South Florida (e.g. in Broward and Palm Beach counties), respectively ( figure C1(b)). The spatial pattern and clustering of high-income affluent residents living in these hotspots along the waterfronts and beaches close to the coast could be in exchange for the locational, environmental, and financial benefits, especially when the associated benefits are high [11,26].

Mobile homes
Mobile homes associated with low-income households have been reportedly overrepresented in floodplains, particularly in rural areas [60]. Our result showed that high proportions of mobile homes residents (red) in the Southeast region inhabit areas prone to high rainfall accumulation producing flash floods ( figure C2(a)). In addition, mobile home clusters were in areas susceptible to high rainfall producing slow-rise floods (red) in the Pacific Northwest and the Southeast along the gulf coast (e.g. South Texas, Louisiana, Mississippi, North Carolina, and Florida) ( figure C2(b)). This pattern supports the existing knowledge that mobile home siting is often found in floodplains, making residents in mobile homes in these locations more susceptible to both flash and slow-rise flood risks [61,62].

Discussion
This study adds to the rapidly evolving understanding of how the impacts of flooding are distributed among the U.S. population. In addition, it contributes to understanding how social vulnerability interacts with flooding hazards, distinguishing between two different flood types with the potential for other downstream health, economic, and asset impacts. Our objective is to determine whether the socially vulnerable and renters' exposures to flash floods were distributed more inequitably to flash flood risks than to slow-rise. Our GEE statistical result did not confirm the hypothesis that the average proportion of flash-flooded area in the floodplains is significantly greater in tracts characterized by higher percentages of socially vulnerable. However, this result is substantiated by the geospatial pattern observed in the Southeast, along the Mississippi River corridor (figure 4(a)), where both socially vulnerable and less vulnerable inhabit areas with high amounts of rainfall producing flash floods. The local spatial pattern shows that the socially vulnerable is just as likely to have similar exposure as the less socially vulnerable during flash flood events in these floodplain areas (p = 0.076). Using population estimates at the census tract could strengthen our inference, but this variable was not included in this study. Densely populated areas are at high risk for flash floods. The construction of buildings, highways, driveways, and parking lots increases runoff by reducing the amount of rain absorbed by the ground. This runoff increases the flash flood potential, and both socially vulnerable and less vulnerable might inhabit areas with these built environment features.
Our result differs from some popular findings in EJ literature that the socially vulnerable have greater exposure than the less vulnerable during flash flooding events. However, it aligns with empirical analysis and field data findings from a recent study in South Carolina [63], in which many socially vulnerable in the rural areas and less vulnerable neighborhoods in the middle-to upper-income areas of the city and suburbs incurred significant damage to their homes. In addition, results from slow-rise flooding are similar to the popular findings that have reported that the socially vulnerable are significantly exposed to flooding risks (p < 0.05), especially during Hurricanes Harvey [15,23,33], Katrina [64]. Hurricanes have the flooding characteristics of slow-rise floodspersist for longer, and are caused by mesoscale convective systems [36,64].
As for housing occupancy, low renter occupancies were substantially overrepresented and more vulnerable to both flood types than more economically affluent homeowners. Specifically, renter occupancies have 12% greater exposure to flash flooding risks than slow-rise. Again, the spatial pattern is more noticeable in the U.S. South for flash and slow-rise floods, except in a few areas on the East coast and along the coastal lines of Nueces (in Texas), Broward and Palm Beach counties in Florida, where high-income renters were associated with high slow-rise flood producing storms.
Several vulnerability studies of river flooding generalize flooding as river-related events, but specific mitigation, planning, and response are required for different flood types. The duration of precipitation and the amount of rainfall accumulation producing the flood should be considered when examining housing and social vulnerability. Classifying socioeconomic position or housing tenure and type may further inform how flood prevention and mitigation response resources are allocated on a local scale to mitigate disaster impacts and unjust environmental outcomes. This study shows that our spatial vulnerability assessment approach can identify areas and communities vulnerable to specific flood types. However, our analysis cannot distinguish whether the most susceptible renter-occupancy are renter-single family or renter-mixed family homes (e.g. high-rises, townhomes) due to the lack of data to investigate further into the tenure structure of vulnerability.
It should be noted that the social vulnerability indicators examined in this study neither include the consequences of the unequal exposures shown during the flash and slow-rise floods nor the indicators of resilience, risk perception, and coping capacity in the analysis. However, prior studies investigating flood recovery experiences for vulnerable populations have reported that areas with a high representation of the socially vulnerable are less likely to receive financial assistance from the different government agencies [65,66]. Considering that future forecast and storm predictions show that climate change is expected to intensify flood risks in these locations susceptible to high rainfall accumulation producing storms [67], our results inform regions where resources for damage prevention (e.g. site of an appropriate level of stormwater infrastructure in lowincome neighborhoods prone to slow-rise floods) and damage response (e.g. individual assistance and loans for home repairs to renter-occupied homes) should go, but currently do not. Future research can examine the question by investigating the number of people affected in the floodplain, not the extent or proportion of disparities (as shown in this study). Such a future pursuit may shed additional light on how disaster prevention and response resources can be distributed uniquely by different flood types.
The analyses of this study are limited in several ways that may be addressed in future research. The first limitation is that the study assumed that socioeconomic and demographic conditions were uniformly distributed in each census tract, which is a common approach but imperfect because such situations are often unevenly distributed throughout census tracts (e.g. urban vs. suburban vs. rural areas in the same census tract). Second, the study could not investigate the interactions between housing type and tenure, which could help differentiate residents by the nature of their vulnerability. Additionally, the study could not distinguish between households living on different levels of multi-family housing, which could affect their exposure to flood risk. Future studies could include datasets that distinguish between renters and owners of single and multi-family homes, stratified by those living on the ground level versus higher levels in the housing complexes.

Conclusion
Unlike previous studies of sociospatial inequalities that have made analytical distinctions based on coastal and inland flooding [11] or without distinguishing flood type [14,68], our study systematically distinguishes distributive inequalities in flash flood risks exposure compared to slow-rise inequalities in flash flood risks exposure compared to slowrise floods in the floodplains across the CONUS. It is essential because distinguishing between these two flood types in terms of their flooding characteristics, such as the amount of rainfall accumulation and duration of precipitation within those affected communities, is critical to identifying where, when, and for whom to distribute resources for protection against flooding.
In terms of scientific implications, previous studies have shown that the socially vulnerable are significantly affected during flooding events. We found that the socially vulnerable have significantly greater risks in areas with high rainfall producing slow-rise floods. However, the socially vulnerable are likely to have as much exposure as the less socially vulnerable in some areas with high rainfall accumulation producing flash floods floodplains. On the other hand, the average proportion of renter-occupancies has significantly greater exposure than owner-occupancies in floodplains susceptible to high rainfall producing flash floods than slow-rise floods. Our result does not suggest that these inequalities are strongly characterized by housing or socioeconomic disparities because these areas had high levels of flooding regardless of these explanatory variables. Instead, our assessment provides empirical evidence showing the inequalities and environmental injustice associated with residences in floodplains that are susceptible to flash and slow-rise floods across the CONUS. We intend for our findings to contribute insight into how specific flood types could impact different populations and housing tenures across the CONUS and inform strategies to support urban and rural community resilience and planning at local and state levels.

Data availability statements
No new data were created or analysed in this study.

Acknowledgments
The Colorado Water Center funded this research.

Compliance with ethical standards
Conflicts of interest: The authors declare no competing financial interests.