Introduction

The eastern United States (U.S.) stands out as one of the most flood-prone region in the U.S. due to various flood generating mechanisms such as heavy precipitation1, snowmelt2, and tropical and extra-tropical cyclones3. In 2023 alone, of the four U.S. flooding events that caused more than a billion-dollar economic loss, three occurred in the eastern U.S4. With flood exposure projected to increase due to climate change and population growth5,6, predicting how different characteristics of this hazard (e.g., magnitude, frequency, duration) are expected to change in the future is crucial for flood preparedness and minimizing associated economic losses and casualties.

To understand and quantify changes in flooding, most of the literature has focused on the magnitude of the observed annual maximum peak discharge7,8,9,10,11,12. However, the use of annual maxima has a major limitation in that it can include values that are too small to be considered as actual flooding (i.e., water out of the riverbanks), potentially complicating the detection of changes13. Analyzing the historical records exceeding a specific flood magnitude or water stage value (i.e., peaks-over-threshold; POT) represents a valuable alternative to address this shortcoming and capture changes in flooding concealed in the annual maximum series. For instance, Mallakpour and Villarini14 demonstrated that utilizing a POT-driven series provides much stronger evidence of an increasing frequency of flood events compared to the trends in annual peak discharge magnitude.

Although there have been efforts to detect trends in POT-driven flood characteristics such as flood frequency and duration14,15,16,17, it is hard to extrapolate these findings for future projections because the observed trends may not persist into the future18,19,20. One approach to address this concern is to first build statistical relationships between flood characteristics and physical drivers responsible for their change21,22,23, and then utilize the projected drivers to assess future changes in flood characteristics19,24,25,26.

Therefore, while the projected changes in the frequency and magnitude of floods have received some attention in the literature, little is known about the projected changes in the duration of this natural hazard at the regional scale. Here, we fill this research gap by applying an attribution-and-projection approach to flood duration at 378 U.S. Geological Survey (USGS) stations across the eastern U.S. The National Weather Service (NWS) classifies flood severity into three levels: minor (i.e., minimal property damage but some public threat), moderate (i.e., some inundation near streams and evacuations of people and/or property transfer), and major (i.e., extensive inundation near streams and significant evacuations of people and/or property transfer)27. We focus on minor and moderate floods because of the limited number of stations and years exceeding the threshold for major floods. We first develop statistical models that enable us to describe the observed changes in the duration of minor and moderate floods; we then leverage this knowledge to assess the future changes in flood durations across the study region for different future scenarios (see Method).

As a first step, we use the seasons to capture different flood processes and attribute the historical changes in flood duration to different physical processes by building binomial regression models for each season (see Method). In terms of predictors, we consider basin- and season-averaged precipitation and temperature, which play an important role in changing multiple flood characteristics (e.g., magnitude22, frequency21, duration28). Besides having been shown to be able to describe well the interannual variability in flood characteristics, these two fundamental climate variables have also the advantage of being available from many global climate models (GCMs), compared to other potentially relevant factors (e.g., soil moisture, evapotranspiration, snowmelt) for which there would be a much more limited GCM availability. Once we develop these season- and location-dependent statistical models, we quantify future changes in the flood duration by using the projected climate predictors under multiple Shared Socioeconomic Pathways (SSPs) (see Method).

Results

Statistical attribution modeling of flood duration

The first step is the development of binomial regression models. There are 378 USGS locations with an established NWS threshold for minor floods, and 161 sites for moderate floods (Supplementary Fig. 1); we decided not to include major floods due to the very limited sample size. As shown in Fig. 1, our statistical attribution models show an overall good performance in capturing the interannual variability in the duration of flooding for all seasons and flood severity levels, with the median correlation coefficients between the observed and modeled flood durations (i.e., the median of the fitted distribution) of ~0.6. When aggregating the seasonal results to the annual scale, these models continue to perform well, particularly across the Coastal Plain. To evaluate the potential role of anthropogenic modifications on these basins (e.g., regulation, urbanization), we stratify the results into reference and non-reference sites29. As shown in Fig. 1, both groups show similar model performances regardless of seasons and flood severity levels, with their differences in median correlation coefficients between observations and statistical model of less than ~0.06. Cross-validation results also show good performance, with the median correlation coefficients of ~0.5 for all seasons and flood severity levels (hatched boxes in Fig. 1). These overall good performances and the limited dependence on basin modifications indicate that our season-averaged climate drivers are the major drivers in controlling the duration of flooding, similar to what was found for flood magnitude22,30,31.

Fig. 1: Performance of statistical attribution models in reproducing the interannual variability in flood duration.
figure 1

Maps and boxplots display the Spearman correlation coefficient between observed and modeled flood durations for four seasonal and annual levels (on the rows) and each flood severity level (on the columns). Hollow circles in the left panel indicate the sites where the correlation coefficient cannot be calculated due to zero modeled values for the whole period. In the boxplots (right panel), in addition to showing the results for all sites (gray boxes), the results are stratified into reference (green boxes) and non-reference (blue boxes) sites. The boxplots also show the correlation coefficient based on cross-validation (CV; hatched boxes). The limits of the box represent the 25th and 75th percentiles, while the line inside of it the median; the limits of the whiskers span the 5th and 95th percentiles.

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To obtain more insights into the different physical mechanisms (using the seasons as proxies), we examine which climate drivers are selected as predictors and how they control the occurrence probability of flooding. For minor flooding (Fig. 2), concurrent precipitation is predominantly selected across the eastern U.S. and has a consistently positive coefficient for all seasons. Lagged precipitation (i.e., precipitation associated with the season prior to the season of interest) exhibits regional variability in its selection across seasons, being mostly selected in the Coastal Plain while rarely elsewhere (e.g., Appalachian regions). In contrast to precipitation, temperature is sparsely selected and shows seasonal differences with a negative impact on the flood occurrence probability in the Coastal Plain during the spring and summer seasons, which represent most of the rainy season. Given that the dominant flood generating process in this region is rainfall in excess of soil moisture storage capacity32,33, warmer temperature can reduce soil moisture by increasing evapotranspiration34, possibly leading to a decrease in the flood occurrence probability. Moderate flooding also shows very similar results (Supplementary Fig. 2).

Fig. 2: Selection of predictors controlling the occurrence probability of seasonal minor flooding across the eastern United States.
figure 2

Maps show the location of sites where each of the four climate predictors is selected: concurrent precipitation and temperature (i.e., basin- and season-averaged precipitation and temperature in the season of interest) and lagged precipitation and temperature (i.e., basin- and season-averaged precipitation and temperature for the season prior to the season of interest). Blue (red) circles indicate the sites where the corresponding predictor positively (negatively) contributes to the occurrence probability of seasonal minor flooding, while the hollow circles represent the sites where the predictor has no contribution to the duration of minor flooding.

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Projected changes in flood durations above given flood severity levels

Before we use the developed models to project flood duration, we need to check how well the climate predictors from GCMs reproduce the observed flood characteristics during the historical period. For 36 GCM candidates (Supplementary Table 1) and at each site, we first obtain the time series of the annual flood durations by using predictors (i.e., basin- and season-averaged precipitation and temperature) extracted from the GCMs as inputs to the developed statistical attribution models; we then fit a nonstationary binomial regression model whose parameter (i.e., occurrence probability of flooding) depends on time to these time series (see Method). Out of 36 GCMs, we select 15 GCMs that can capture the observed annual trend in the occurrence probability of both minor and moderate floods (Supplementary Fig. 3) and use them to compute an ensemble median of the flood duration for historical and future periods.

We assess whether there is a significant shift in the flood duration between the 1985–2014 and 2071–2100 periods under four SSPs (Fig. 3). If we compare the projected shifts over seasons, there is a distinct seasonal difference: for minor flooding (Fig. 3a), winter is the season with the highest percentage of sites where the flood duration is expected to increase, with 18.7–53.3% of sites pointing to an increasing shift depending on the scenario. This is followed by the fall season, showing an increasing shift at 12.6–21.2% of the sites, while the remaining seasons exhibit increasing shifts at less than 16% of sites. The results for decreasing shifts show an opposite seasonal behavior: spring and summer show a decreasing shift at 12.2–26.8% of the locations depending on the scenario, whereas the decreasing shift is limited to 7.1% of sites in fall and winter. For moderate flooding (Fig. 3b), although the percentage of sites with both increasing and decreasing shifts is slightly lower compared to minor flooding, the overall pattern of results is very similar. In the eastern U.S., where the primary flood seasons are winter and spring35,36, flood timing is expected to shift earlier under warning scenarios because of increased rainfall and decreased snowfall under warming scenarios19,37,38. Consistent with this projection, our results suggest that the flood duration is projected to become longer in the winter season.

Fig. 3: Projected shifts in flood duration between the historical (1985–2014) and future (2071–2100) periods for the eastern United States.
figure 3

Barplots display the percentage of sites with a significant shift in the duration of minor (a) and moderate (b) floodings across the eastern United States at the 5% level. In each subplot, the left (right) panels show the results for a significant increasing (decreasing) shift, while the middle panels show the results for no significant shifts. Each row shows results for three different groups (i.e., all, reference, and non-reference sites). In each panel, the redder the bars the higher the emission scenarios (from SSP1-2.6 to SSP5-8.5).

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If we look at the projected shifts across emission scenarios, higher emission scenarios generally result in more sites experiencing a significant shift, especially towards longer flood durations in the winter season for both minor and moderate floods. Consequently, as greenhouse gas emissions increase, the percentage of sites projected to experience longer annual flood duration increases from 26.2% to 47.6% and from 19.3% to 32.3% for minor and moderate floodings, respectively. When stratifying the results into reference and non-reference sites, both groups show very similar behaviors depending on the season and scenario as we described above.

Discussion

In this study, we defined seasonal flood duration as the number of flood days in a season and examined how it could change in the future across the eastern U.S. by applying an attribution-and-projection approach. In the development of statistical models attributing the historical changes in seasonal flood duration to four seasonal climate-related variables, concurrent precipitation was selected as the predictor of seasonal flood duration for almost every site for all seasons, while the other variables showed regional and seasonal variability in their selection (Fig. 2 and S2). These results suggest that seasonal precipitation during the season of interest is the most common and primary climate driver of flooding across the eastern U.S., with the other predictors playing a more muted and regionally variable effect. It is worth noting that the most frequently selected driver does not necessarily represent the one that contributes the most to flood duration, and the use of dominance analysis39,40 can shed light on this aspect.

One limitation of this study is related to the minimum requirements in terms of record lengths to fit the binomial regression model (i.e., if the number of years in which flooding occurred was less than five, we assumed that no flooding is expected to occur in the future). This assumption may have resulted in an underestimation of the percentage of sites with an increasing projected change in seasonal and annual flood durations. Nevertheless, our projections of flood duration point to a future in which floods are expected to last longer, especially in the main flood season (i.e., winter) and under higher emission scenarios. Given that the flood duration is a crucial characteristic of floods, contributing not only to direct economic losses41 but also to indirect and intangible damage such as health-related issues (e.g., contamination, diseases)42, these results underscore the need to make an effort toward climate change mitigation (i.e., reduction in greenhouse gas emissions) as well as adaptation (e.g., raising dikes, detention areas)43.

Although this study focused on the eastern U.S., our attribution-and-projection approach is flexible and applicable to any streamgage as long as there is a discharge/stage threshold for the different flood severity levels, allowing to assess future changes in the duration of this hazard at different spatial scales (e.g., site-specific, regional, continental).

Methods

Seasonal flood durations above given flood severity levels

For U.S. Geological Survey (USGS) streamgages across the eastern U.S., we obtain mean daily discharge series from 1949 to 2019 and screen the stations based on the following criteria: (1) only stations whose basin boundary data (USGS Streamgage NHDPlus Version 1 Basins 2011) are available are considered; (2) a year and each season with less than 10% of missing daily observations are considered; (3) only stations with a minimum of 30 years of observations during the 1980–2019 period are considered. We further classify the stations into reference and non-reference sites according to the Geospatial Attributes of Gages for Evaluating Streamflow, version II (GAGES-II) dataset29 to examine the influence of human disturbance on the duration of flooding. The National Weather Service (NWS) characterizes flood severity into three levels (minor, moderate, and major) and provides their stage and/or discharge thresholds as well as a rating curve. For each station and each flood severity level, we obtain the discharge threshold either directly or by converting the stage threshold using the rating curve. We then count the number of days for which mean daily discharge exceeds the threshold (i.e., flood duration) for four meteorological seasons: fall (September–November), winter (December–February), spring (March–May), and summer (June–August). If there is a single flood event that spans two consecutive seasons, we separate the number of flood days into each corresponding season.

Dominant climate drivers of flood duration

We consider precipitation and temperature as dominant climate drivers of flood duration. To model the time series of seasonal flood durations, we acquire the monthly total precipitation (mm) and monthly mean temperature (°C) from the Parameter-Elevation Regression on Independent Slopes Model (PRISM) dataset44,45, a gridded product at 2.5 arcmin (~4 km) spatial resolution throughout the U.S. After the basin-averaged monthly precipitation and temperature are calculated based on the basin boundary data, we aggregate and average these basin-averaged monthly values to the seasonal scale.

To assess the projected changes in flood durations for the future period, we use precipitation and temperature from global climate models (GCMs) part of the Coupled Model Intercomparison Project Phase 6 (CMIP6)46. We acquire monthly mean precipitation (kg m−2 s−1) and near-surface air temperature (K) for 36 GCMs whose nominal spatial resolutions are no more than 250 km and outputs are available for historical and future periods under SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 (Supplementary Table 1). Once we calculate the basin-averaged monthly total precipitation (mm) and temperature (°C), we conduct empirical quantile mapping47 for each month to remove the biases of each GCM output using the PRISM data as reference. We then aggregate and average the bias-corrected monthly series to the seasonal scale.

Statistical attribution modeling of seasonal flood durations

To develop statistical attribution models to describe the year-to-year changes in seasonal flood durations, we use the Generalized Additive Model in Location, Scale, and Shape (GAMLSS)48 because of its flexibility in modeling the distribution parameters as various functions of explanatory variables. Since the flood duration is defined as the number of days (i.e., discrete variable), we use the binomial distribution to model flood duration. The probability mass function of a binomial distribution can be expressed as follows:

$$P\left(Y=y\left|n,\mu \right.\right)=\frac{n!}{y!\left(n-y\right)!}{\mu }^{y}{\left(1-\mu \right)}^{n-y}({\rm{for}}\,y=0,1,2,\ldots ,n)$$
(1)

where μ is the occurrence probability of flooding and n is the given number of days in a season. To attribute the seasonal flood durations to precipitation and temperature, we use basin- and season-averaged precipitation and temperature in the season of interest (i.e., concurrent season). To incorporate the potential impacts of antecedent conditions, which could be one of the most important factors in flood generation processes33,49, we also include these variables prior to the concurrent season (i.e., lagged season). Using these four climate drivers as covariates, the μ parameter of the binomial distribution is modeled by a logit link function to ensure the range of 0 < μ < 1 as follows:

$$\log \left(\frac{\mu }{1-\mu }\right)={\mu }_{0}+{\mu }_{1}{P}_{{con}}+{\mu }_{2}{T}_{{con}}+{\mu }_{3}{P}_{{lag}}+{\mu }_{4}{T}_{{lag}}$$
(2)

where Pcon (Tcon) is the basin- and season-averaged precipitation (temperature) in the concurrent season, and Plag (Tlag) is the basin- and season-averaged precipitation (temperature) in the lagged season.

For each severity level and season, we develop models only for the stations with at least five years of flood occurrence to ensure the robustness of model fitting. If the number of years in which flooding occurred (i.e., flood duration > 0 days) is less than five, we do not develop models and assume that no flooding occurs. For each station with more than a five-year record, we consider all possible models depending on linear combinations of the four predictors and select the best one using the Schwarz’s Bayesian criterion50. We evaluate the selected model focusing on how well it captures the year-to-year changes in flood durations. To do this, we calculate the Spearman correlation coefficient between observed and modeled seasonal flood durations (i.e., median of the fitted distribution). Additionally, we conduct leave-one-out cross-validation to assess the selected model’s performance toward extrapolation. For a given year, we refit the selected model without the year of data. The fitted model is then used to predict the seasonal flood duration for the excluded year using the predictors for that year. Once we obtain a time series of seasonal flood durations for the period of record by iterating this process for every year, we calculate the Spearman correlation coefficient between observed and cross-validated seasonal and annual flood durations.

Assessment of projected changes in flood durations

By using the bias-corrected GCMs’ basin- and season-averaged drivers as inputs to the binomial regression models whose parameters were estimated using PRISM covariates, we obtain the time series of seasonal flood durations for both historical and future periods. Before investigating how the flood durations are projected to change, we evaluate the suitability of 36 GCMs by comparing the annual trend in the occurrence probability of flooding when using the GCMs and the PRISM over the historical period (1951–2014). For each flood severity level and site, we obtain the time series of annual flood durations from the GCMs and PRISM to fit the nonstationary binomial distribution whose μ parameter has a time covariate (t) as follows:

$$\log \left(\frac{\mu }{1-\mu }\right)={\mu }_{a}+{\mu }_{b}t$$
(3)

By comparing the significance of the trend parameter (μb) fitted from the GCM and PRISM at the 5% significance level, we classify stations into “Match” and “Mismatch” groups as follows:

  • Match group: Both trend parameters fitted from the GCM and PRISM are statistically significant and of the same sign, or they are both not statistically significant.

  • Mismatch group: The trend parameter fitted from the GCM (or PRISM) is not statistically significant, while the one from the PRISM (or GCM) is significant, or both trend parameters fitted from the GCM and PRISM are statistically significant, but of opposite sign.

We then select the GCMs with the percentage of stations within the Match group that is larger than 60% for both minor and moderate floodings. For the selected GCMs, we compute an ensemble median of the seasonal and annual flood durations.

We employ the Student’s t-test to detect increasing (or decreasing) projected shifts in flood durations, with the null hypothesis for the test being that two groups have the same population mean. Therefore, whether the distribution of one group is greater (or smaller) than that of the other group can be tested by using the one-sided test. The significant shift in flood durations between historical (1985–2014) and future (2071–2100) periods is tested by conducting the one-sided Student’s t-test at the 5% level.