United States floods within the context of atmospheric moisture sources and pathways

Non-stationarity in flood event magnitudes and timing due to the changing hydrologic regime under climate variation has a key role in water resources management (Jain & Lall 2000, 2001). A reliable estimation of flood frequency and magnitude to anticipate future extremes is vital for life security and property protection. Thus, precise knowledge about the nature of flood variability will contribute to improving strategies for future water resource management and flood risk mitigation. Almost three decades after the publication date of the B17-B ‘Guidelines for determining flood flow frequency: Hydrology Subcommittee Bulletin 17B’ framework by the Interagency Advisory Committee on Water Data, in March 1982, Stedinger & Griffis (2008) recommended the use of the expected moment algorithm (EMA) to address the limitations of the adapted statistical framework in B17-B. Subsequently, B17-C ‘Guidelines for determining flood flow frequency – Bulletin 17C’ (England et al. 2018), the updated version of B17-B, improved the statistical framework and used EMA to deal with uncertainties in historical information, zero and low floods, interval data, and confidence limits. To this end, B17-C is still limited in addressing the flood variability within the context of climatic variability and change, as the committee group listed this objective in the framework's future studies.

Numerous studies on the dynamic risk of floods have attempted to modulate the changes in flood risks. For example, modification of the mathematical model of the Log-Pearson Type III distribution (LP3) to account for co-variate (e.g., time, SST, etc.) has been used to improve flood risk estimation (Jain & Lall 2000; Kashelikar & Griffis 2008; Stedinger & Griffis 2011; Gurrapu et al. 2023; Maimone & Adams 2023; Masoumi et al. 2024; Reinders & Munoz 2024; Yalcin 2024). Conversely, Aljoda & Jain (2021) showed moderate co-variability between climate indices and streamflow merits attention, in particular related to high-frequency atmospheric phenomena, such as atmospheric rivers (ARs) – a key moisture delivery mechanism for the US West Coast (Ralph et al. 2006; Dettinger 2011; Dettinger et al. 2011; Neiman et al. 2011; Ralph & Dettinger 2012; Corringham et al. 2019, 2022; Rhoades et al. 2021).

On the other hand, flood frequency analysis in different regions of the US often contains annual floods generated by distinctive different hydrologic and hydroclimatic processes (Waylen & Woo 1982; Webb & Betancourt 1990; Hirschboeck 1991; Berghuijs et al. 2016). As such, a fundamental assumption, i.e., the statistical treatment of flood records based on considering the events as independent, identically distributed variables (i.i.d.), which considers floods time series as time sampling of random homogeneous events (as in B17-B and B17-C) does not apply in regions of mixed population flood events. Among the different flood-generating mechanisms, ARs are responsible for large, regional-scale floods (Ralph et al. 2006; Dettinger 2011; Neiman et al. 2011; Lavers & Villarini 2013; Barth et al. 2017).

Recent changes in the seasonality and magnitude of extreme precipitation in North America critically impact societal vulnerability, infrastructure design, planning, and adaptation (Pryor & Schoof 2008; Pal et al. 2013; Mallakpour & Villarini 2017; Marelle et al. 2018; Aljoda & Dhakal 2023; Dhakal et al. 2023, 2015; Henny et al. 2023). A crucial scientific task is to understand the recent changes in extreme events statistics (frequency and magnitude) and to link these changes to large-scale atmospheric phenomena (i.e., ARs) (Aljoda & Dhakal 2024). This study examined the role of AR and their moisture trajectories and sources on the heterogeneous flooding events of annual maximum flows (AMFs) in the US and their impact on the magnitude and frequency estimates used for the design of flood structures. Three research foci related to the nature and variability of AMF events across the US are:

• To develop a methodology for robust curvilinear estimation of AR events based on a principal curve-based approach, thus integrating the axes of maximal integrated water vapor transport (IVT) variation and time progression over the event lifecycle.

• To characterize the place-based mixed population of AMF by delineating the constituent remote atmospheric moisture sources, thus enabling climate-informed partitioning of the flood record for risk analyses and estimation of hydroclimatic non-stationarity.

• Systematically apply the new methodology to a US-scale assessment of AMFs to understand their regionality and develop new modalities for flood frequency estimation in a changing climate.

A comprehensive statistical framework with three phases of analysis is introduced to achieve these goals. Phase I: attributes the AMF records to their generating mechanisms and shows the major processes. Phase II: identify the moisture tracks and sources and investigate their impacts on flooding frequency and magnitude. Phase III: quantify the nature of flood variability based on moisture sources variation. The remainder of this paper is organized as follows. Section 2 shows the original contribution of this work to the literature of flood frequency analysis. Section 3 describes the data and methods used. Section 4 explains the three phases of analysis in more detail in the methods section. This is followed by a review and discussion of the results of this research article. Finally, Section 5 concludes the paper.

During the last decade of the 20th century, developments in the understanding of atmospheric moisture pathways led to the recognization of large-scale moisture delivery as a precursor to floods (Hirschboeck 1991). After ARs were introduced in the literature by Zhu & Newell (1998), scientists studied the links between ARs, precipitation, and floods (Ralph et al. 2006; Neiman et al. 2008). Since 2010, studies have started to look at the variability in floods from a hydroclimatic and meteorological perspective (e.g., Lavers et al. 2011, 2012; Dettinger 2011; Lavers & Villarini 2013; Berghuijs et al. 2016; Lu & Lall 2016; Barth et al. 2017; Konrad & Dettinger 2017; Dickinson et al. 2019; Brunner et al. 2020) to address the variability of flooding risks. This work introduces a new methodology to explain the nature of flood variability compared with recent studies on flood risk in the literature, as summarized in Table 1.

The shape index of ARs provided by the Global ARs Database (https://ucla.box.com/ARcatalog) was used to determine which ARs are associated with flood events (AMF records). This dataset detects ARs based on IVT intensity, direction, and geometry (Guan & Waliser 2015, 2019; Guan et al. 2018). Their criteria to detect AR are: (a) IVT intensity at each grid cell must be greater than max (85th percentile, 100 kg m⁻¹ s⁻¹), whichever is larger; (b) mean IVT over the AR should be within 45° of AR shape orientation and with an appreciable poleward component (i.e., 50 kg m⁻¹ s⁻¹); (c) AR length must be greater than 2,000 km and the length/width ratio greater than 2; and (d) as the refinement for less well-structured ARs, requirement (a) is repeated for up to five times, each time with an increase of 2.5 in the IVT percentile threshold if requirements (b) and (c) fail. The shape index is a unique number that is given to each observed AR at each 6-h time-step to distinguish between several ARs available over the globe. This dataset is an NCEP/NCAR reanalysis product available in a 6-h global scale with resolution. The NCEP/NCAR 6-h IVT time series (1948–2015) from the AR catalog provided by Jonathan Rutz (https://www.inscc.utah.edu/∼rutz/ar_catalogs/) is used to eliminate the grid points of AR with IVT < 250 kg m⁻¹ s⁻¹ from the determined polygon of AR shape. Finally, to determine the flood-generating mechanism of each event, we obtain daily time series of the surface air temperature (SAT), precipitation rate (PR), and water equivalent of accumulated snow depth (WEASD) from the NCEP/NCAR reanalysis data provided by the National Oceanic and Atmospheric Administration (NOAA) Physical Sciences Laboratory (PSL) (https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html). These variables are available globally with different resolutions for 1948–2020.

As the scope of this research work is to study the role of ARs and oceanic moisture sources in the context of flood frequency and magnitude across the US by performing at-site hydroclimatic analysis, it is impractical to show numerous plots that demonstrate the same results for different locations within the study area. Therefore, the study area is divided into regions to generalize the facts from a regional perspective. However, we select representative basins in the regional analysis to avoid the visual complexity of showing all the regional results in a single plot. The hydrologic and climate regions are two standard methods to divide the US into sub-regions. The USGS split the conterminous US into 18 geographical regions based on the drainage area of a major river, such as the Missouri region, or a series of rivers, such as the Texas Gulf region (see Figure 1 and Supplementary Table S1 for region locations and names). The second method of division is the US climate regions. Karl & Koss (1984) performed temporal and spatial climatological analyses on statewide temperature and precipitation data to subdivide the coterminous US into nine climate regions (Figure 1). Consequently, scientists in NOAA – National Centers for Environmental Information have identified nine climatically consistent areas within the contiguous US (https://www.ncdc.noaa.gov/monitoring-references/maps/us-climate-regions.php) and used them for climate monitoring and providing data for the public services and private sectors. Since this study focuses on the impact of large-scale atmospheric patterns on floods, we select the climate region division as the spatial scale to perform the analysis.

The analysis in this study is divided into three separate phases. Phase I of the analysis is to determine the flood mechanism of each AMF event. The next phase of the analysis is to determine the moisture major axis (trajectories) and sources for a group of events identified in Phase I and apply the flood frequency analysis to these events in the third phase of the analysis.

Finally, the Phase III analysis is performed by applying the LP3 distribution to the results of Phase II to investigate the role of ARs and their sources in the flood frequency and magnitude. The LP3 distribution is a widely accepted tool for flood frequency analysis due to its ability to handle skewed, heavy-tailed data, commonly seen in peak flood events. By applying a log transformation, it stabilizes variance and provides more accurate estimates for extreme floods. Although LP3 traditionally assumes stationarity, recent studies (such as Jain & Lall 2000; Kashelikar & Griffis 2008; Stedinger & Griffis 2011; Gurrapu et al. 2023; Maimone & Adams 2023; Masoumi et al. 2024; Reinders & Munoz 2024; Yalcin 2024) have shown that it remains effective in non-stationary contexts when combined with modern methods like trend analysis and time-varying parameter models. Bulletin 17-C continues to recommend the use of LP3 for flood frequency analysis due to its robustness and flexibility, especially with enhancements like maximum likelihood estimation (MLE) and Bayesian methods for non-stationary conditions (England et al. 2018). This adaptability makes LP3 particularly suitable for analyzing floods driven by ARs, which often produce extreme, skewed data. When ARs are considered as covariates, LP3's flexibility allows it to accurately capture both the frequency and magnitude of these events, especially in regions like the US West Coast, where ARs are a major factor in flood risk (Barth et al. 2017, 2019).

Since physical processes other than ARs also generate rainstorms, the rain days are separated throughout the year between AR and non-AR-rain day categories. To determine which rain process is more frequent across the study area, the method counts the non-AR-Days during the year which have rain (PR > 1 mm) as well as the AR-Days at each grid cell. Figure 6(c) shows the long-term median for the annual number of days with and without ARs. Most of the rainy days in the western US are caused by ARs, and the number of AR-Days is much higher than non-AR-Days (Figure 6(c)). Furthermore, the coastal areas of the western US have an average or high number of AR-Days through the year compared with the mid-west and southwest regions wherein fewer wet days occur. Most of the wet days in the eastern and central parts of the US are due to the non-AR processes. In general, the 60-year median of the annual number of wet days in the eastern half of the US is significantly high compared with the western half (Figure 6(c)).

These findings diverge from some studies (e.g., Lavers & Villarini 2013; Barth et al. 2017). A basin is affected by AR if its major axis is within a specific distance at any side to the stream gauge location. As such, a flood can be attributed to an AR, although the AR is out of the watershed boundaries, or a peak of discharge can be attributed to a non-AR-generated process due to a lack of AR detection. Conversely, the present study's methodology to examine the AR's impacts on floods intersects the AR and basin boundaries to relate both events. As a result, our approach provides relatively robust and accurate percentage estimates of AMF-AR-related events across the contiguous US.

The investigation of ARs impacts on flood magnitude is performed on an at-site scale. To examine the AR effects on the river discharge, we analyzed the AMFs for the nine climate regions separately. Supplementary Figure S2 shows the AMF quantiles for the AR and non-AR-generated events. The boxplots demonstrate the impacts of ARs on the AMF across different quantiles. The peak discharge flows in the nine regions gauges are clearly influenced by ARs as there is an increase in the medians and interquartile range of the AMF-AR events. The upper quantiles of AMF-AR events in the selected stream gauges of the Northeast, Northwest, and West climate regions are increased compared with the AMF-non-AR events. Further, the AMF interquartiles in arid and semi-arid regions such as the South, Southwest, and West are significantly larger due to the ARs impacts. However, there are none or modest impacts of ARs on the lower quantiles of AMFs across the nine regions. As a result, although studies in the literature (e.g., Ralph et al. 2006; Lavers & Villarini 2013; Barth et al. 2017) showed that ARs are a major cause of the largest floods in different regions, the type of analysis presented here concluded that ARs have effects on small and large floods.

The risk in flood frequency and magnitude under the impacts of ARs is also measured by the ratio of the 100-year flood of AMF-AR to AMF-non-AR by using LP3 estimates. The distribution is performed when there are at least 10 events in each group to minimize the level of uncertainty in the 100-year flood estimation. A ratio greater than 1.1 means that ARs are responsible for causing the large floods while a ratio less than 0.9 indicates that other flood-generating mechanisms control the large AMFs. However, the interval 0.9–1.1 is considered even effects, and ratios are not determined for catchments observing homogeneous or weak mixed population floods.

In comparison, the estimation of moisture source contribution to AMF-AR events in the representative basins is closely matching those for the regions in many cases (Figure 10). For instance, both estimations in Figure 10(d) and 10(h) show that the sub-tropical Pacific Ocean is the main source of moisture in the region. However, the single basin-based estimation of source contribution occasionally under- or overestimates the regional contribution of the moisture source. As such, the single basin-based estimation overestimates the contribution of the extratropical Pacific Ocean moisture in the Southwest and underestimates the contribution of sub-tropical Pacific Ocean moisture in the West North Central region (Figure 10(g) and 10(i)). To this end, although the estimation of the source contribution may not reflect the actual response of the majority of basins in the region due to an insufficient number of detected AMF-AR events in the record of the representative basin, the results of estimations confirm the major sources for each climate region.

Supplementary Figures S3–S11 show the LP3 flood frequency curves for the AMF events in populations of: (a) mixed events, (b) non-AR-generated events, (c) AR-generated events, and sort the latter based on the main sources of moisture, (d) Pacific AR-generated events, (e) Atlantic AR-generated events, (f) Caribbean Sea and Gulf of Mexico AR-generated events, and (g) local-AR-generated events for the nine representative basins. A threshold of five AMF events is assigned to apply the LP3 on the data points. In the Central region representative basin, the flood frequency curve of the mixed population events (Supplementary Figure S3(a)) shows that floods are dominated by ARs at varying degrees. Further, the fitted LP3 curve shows a poor fit in the right-hand tail of the distribution. However, the separation of events based on non-AR and AR generating floods (Supplementary Figure S3(b) and S3(c)) helps to have a better fit to the AMF-non-AR events although this raises the level of uncertainty due to the lack of data points. Therefore, there was little to no improvement in the fit of the distribution line for the AMF-AR events. Yet, the AR-source-based separation for the AR generating floods population (Supplementary Figure S3(d), S3(f), and S3(g)) show the improved flood frequency curves among the AR-generated population of the Pacific Ocean, Caribbean Sea and Gulf of Mexico, and local moisture. The LP3 fit line for the mixed population in the East North Central representative (Supplementary Figure S4) underestimated the large AR floods. As such, the AR-source-based separation of AMF-AR events improves the fit line in the upper tail. However, the flood frequency curve overestimates the non-AR events. Although the LP3 fit line for mixed population events in the Northeast representative basin (Supplementary Figure S5) preserves the overall data distribution, separating the events provides a more precise fit, particularly for cases with a sufficient number of events, such as AMF-AR and AMF events driven by ARs originating from the Caribbean Sea and the Gulf of Mexico. As almost all AMF events in the Northwest representative station are generated by ARs and most of them are from the Pacific Ocean, the three flood frequency curves in Supplementary Figure S6 have properly fitted the data points. In the South region representative, the AMF-AR events dominate both tails in the distribution (Supplementary Figure S7). While the LP3 distribution of the mixed population events observed poor fit, the events separation improves the distribution fit line for the AMF-non-AR and AMF-AR events such as the events generated by the effects of the Caribbean Sea and Gulf of Mexico. In the Southeast region representative, the flood frequency curve has a poor fit to the mixed population event (Supplementary Figure S8). Although the events separation improves the AMF-non-AR observations fit line, the distribution shows a poor fit in the right-hand tail. On the other hand, the source-based separation of the AMF-AR events improves the distribution fit for large floods. Contrary to all other region representatives, the Southwest region representative basin is dominated by the AMF-non-AR events at varying degrees (Supplementary Figure S9). The LP3 distribution shows a poor fit to the mixed population events. However, the events separation does not improve neither the AMF-non-AR events as they may come from different flooding mechanisms (Supplementary Figure S1) nor the AMF-AR events due to insufficient number of events. In the West region representative basin, although the AMF events are evenly generated in the mixed population (Supplementary Figure S10), the right-hand tail of the LP3 distribution is dominated by the AMF-AR-generated events. The distribution of the mixed population shows a good fit for the data points as most of the flood events are very close in their magnitudes. Furthermore, the events separation improves the flood frequency curve of the AMF-AR events as most events are caused by the Pacific Ocean moisture. However, the LP3 distribution fit overestimates the AMF-non-AR events. Last, the representative basin of the West North Central Climate region shows a poor fit in the upper tail of the heterogeneous events distribution (Supplementary Figure S11). Although the events separation indicates underestimated LP3 fit to the non-AR-generated floods, the upper tail of the distribution is improved to fit the flood events caused by ARs that affected the basin and their sources.

All in all, eight of nine basins have their largest flood events over 60 years and are generated by ARs no matter what their sources are. But the Southwest representative basin which is the least impacted by ARs has its third largest flood over the entire record caused by ARs. Further, although the events separation is biased in the fit line of the AMF-non-AR events distribution in some cases as they may be caused by different flood-generating processes, the flood frequency curves of the floods generated by ARs and their sources are improved to fit the data.

To examine the impacts of ARs and their sources on the flood magnitude, we perform the LP3 distribution on the AMF events to calculate the 100-year flood which is typically used for the design of flood structures. The impact of ARs on flood magnitude is determined by calculating the ratios of the 100-year flood of the AMF-AR and AMF-AR-source-based (Pacific Ocean, Atlantic Ocean, Caribbean Sea and Gulf of Mexico, and Local) events to the 100-year flood estimated from the AMF-non-AR events. For statistical confidence of the results, we resample the actual AMF time series 1,000 times and split them into subgroups based on their flood-generating processes. Then, the 100-year floods for each population are calculated to find the required ratios to construct their PDF estimates. As a result, the further the actual ratio of a selected population deviates from one in the PDF, the greater the confidence in its accuracy.

Supplementary Figure S12 shows the ratio of the 100-year flood from AMF-AR and their sources to the 100-year flood of the AMF-non-AR events, and the PDF of the ratios calculated from the resampled actual time series of the AMF events for the nine climate region representative basins. Table 5 lists the ratios of the 100-year flood estimated from the real floods generated by ARs and their sources to those generated by non-AR, as well as in which quantile is the actual ratio located with regard to the ratios from resampled events in the nine representative basins. As a result, all basins have at least one actual ratio greater than one which ensures the impact of ARs and their sources on the flood magnitude (Supplementary Figure S12 and Table 5). As such, the magnitude of a 100-year flood estimated from the AMF-AR population is 50% larger than the 100-year flood of the AMF-non-AR events in the representative basin of the Central region. While the impact of ARs originating in the Atlantic Ocean on the 100-year flood of the East North Central region representative is four times larger than the magnitude of the 100-year flood estimated from the AMF-non-AR population. In the same manner, the ARs of the Caribbean Sea and Gulf of Mexico and the local moisture double the magnitude of the 100-year flood in the Northeast representative basin. Furthermore, the ARs of the Caribbean Sea and Gulf of Mexico increase the 100-year flood magnitude by 350% in the South representative basin. The most impacted ARs on the 100-year flood in the Southeast representative basin is the local moisture which increases the magnitude to 600%, while the moisture of the Pacific Ocean rises the 100-year flood by 183% in the Southwest representative basin. In addition, the Pacific also levels the magnitude of 100-year flood up to 345 and 298% in the West and West North Central representative basins, respectively. However, ratios for the Northwest representative cannot be calculated since all the annual floods in the records are generated by ARs.

This study examined the role of ARs, their moisture trajectories, and sources in generating heterogeneous AMF across the US. We focused on the impact of AR-induced floods on the magnitude and frequency estimates used in the design of flood structures. Flood frequency analyses often reveal that annual floods in various regions of the country result from distinct hydrologic and hydroclimatic processes (Waylen & Woo 1982; Webb & Betancourt 1990; Hirschboeck 1991; Berghuijs et al. 2016), with ARs playing a major role in regional-scale flood generation.

The classification of 623 USGS stream gauges over the period 1956–2015 into five main flood agents (Snowmelt, Local rain, Local rain on snow, AR-rain, and AR-rain on snow) provided insights into the key drivers of flood events. Our results demonstrated that ARs are a significant contributor to floods across vast regions of the US, particularly in the western half of the country. ARs contributed to approximately 73% of the AMF events, with notable impacts across several climate regions. This underscores the critical role of ARs in flood frequency and magnitude, which varies across regions, as demonstrated by our results for different flood quantiles.

The new statistical framework developed in this study, which uses a WPC approach to track AR-induced flood events, allowed for the integration of moisture source trajectories. This methodology enabled us to identify and visualize the curvilinear pathways of ARs that contribute to floods, as well as quantify the percentage contributions of moisture sources. While this approach provided a more accurate representation of ARs' roles in flood frequency, earlier studies that used simpler methods, such as a single point AR index, may have overestimated ARs' influence.

By partitioning AMF events based on AR moisture sources, this study was able to improve the fit of the LP3 distribution, particularly in regions where ARs were the dominant source of flood-inducing moisture. This partitioning allowed for a more accurate flood frequency analysis by accounting for the specific characteristics of AR-generated floods. However, separating mixed population floods into AR and non-AR sources did not enhance the LP3 fit in all cases, except in regions where a single moisture source, like ARs, overwhelmingly dominated, such as the Northwest.

While this study has contributed to a better understanding of AR-generated floods, several areas for improvement and future research remain. First, further refinement of the partitioning technique or the exploration of alternative statistical models may be necessary to better capture the complexity of mixed population floods in regions where multiple flood mechanisms interact. For instance, hybrid approaches that integrate non-parametric or machine learning techniques with traditional flood frequency methods could be investigated.

Additionally, the use of more recent, higher-resolution datasets, such as ERA-5 and MERRA-2, could be explored to update the analysis and examine how changes in AR characteristics due to climate change may affect future flood risks. Extending the time period and using these improved datasets could help refine flood frequency estimates and better capture shifts in atmospheric patterns, including potential increases in AR frequency and intensity.

Moreover, future research could also examine the role of other large-scale atmospheric phenomena, such as tropical cyclones and convective systems, in flood generation. This would provide a more comprehensive understanding of flood risks in regions not dominated by ARs, such as the Southeast and Gulf Coast areas. In addition, testing the relationship between AMF and AR events and climate change indices – such as inter-annual, decadal, and centennial scales – could help clarify the role of long-term climate variability. Analyzing how indices like the El Niño–Southern Oscillation (ENSO) or the Pacific Decadal Oscillation (PDO) influence AR-related floods would provide deeper insights into the broader climatic drivers of flood risks.

Finally, applying the findings from this study in practical contexts, such as water resource management, floodplain mapping, and infrastructure design, is a critical next step. By incorporating AR-source-based flood frequency analysis into flood risk assessments, stormwater infrastructure, and climate adaptation strategies, future work could provide tangible benefits for flood mitigation and resilience planning. This would ensure that flood structure designs are based on the most accurate and up-to-date understanding of flood risk variability, ultimately improving public.

This research received no external funding.

All relevant data are available from an online repository or repositories: https://www.sciencebase.gov/catalog/item/59692a64e4b0d1f9f05fbd39; https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html; https://dataverse.ucla.edu/dataset.xhtml?persistentId=doi:10.25346/S6/YO15ON; https://www.inscc.utah.edu/~rutz/ar_catalogs/

The authors declare there is no conflict.