Introduction

The immediate effects of wildfire—loss of life, destruction of property, interruption of critical services, and poor air quality1,2,3—can be devastating. Wildfire is also known to enhance susceptibility to flash floods and debris flows triggered by short-duration, high-intensity rainfall in steep and severely burned terrain4,5. Postfire debris flows, which are fueled by the entrainment of sediment on hillslopes and in channels, exhibit notably more destructive power than flash floods owing to amplification of flow depth, discharge, and shear stress6 that is imparted by the most dangerous constituents (mud, boulders, and downed trees) of these gravity- and fluid-driven mass movements (Fig. 1b). They can be triggered by 15-min rainfall intensities7 with recurrence intervals as low as one year8 in the first two years after fire9. Major postfire debris flows, which have caused substantial damage or loss of life, have been initiated by relatively low rainfall intensities and by rainfall intensities greatly exceeding the baseline triggering thresholds10,11. Studies have projected that extreme precipitation at sub-daily periods will scale at or above the Clausius-Clapeyron (CC) relationship12,13,14,15, which states that the moisture-holding capacity in the atmosphere increases at a rate of approximately 7% per degree Celsius. Some observational and climate projection studies note substantial “super-CC” scaling at up to double the expected rate of intensification following the CC relation12,15,16,17. Although projections of rainfall intensification vary across different durations, spatial extents, regional climates, and storm characteristics12,18,19,20,21, there is substantial evidence that the short-duration (<1 h) rainfall conducive to postfire debris flows will continue to intensify, and perhaps at a higher rate than long-duration (≥1 h) rainfall14,15.

Fig. 1: Annual frequency of rainfall threshold exceedances for burned areas across the American Southwest where postfire debris flows have been a concern in the last decade, including the 2018 Montecito debris-flow event.
figure 1

a State-specific bar plots reflect the mean annual frequency of simulated 15-min rainfall intensity threshold exceedances associated with 175 burned areas across the American Southwest (Supplementary Fig. 1). Vertical black lines indicate standard error of the mean. We calculated these exceedance statistics for burned areas where, between 2014 and 2022, the U.S. Geological Survey (USGS) issued rainfall thresholds as part of emergency assessments of postfire debris-flow hazards. Shaded relief map provided by Environmental Systems Research Institute83. State boundaries provided by U.S. Census Bureau84. b Photograph shows the effects of postfire debris-flow inundation associated with the 9 January 2018 Montecito debris-flow event, which occurred in southern California. Photograph taken by Jeffrey A. Coe, USGS.

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Postfire debris flows have been documented throughout the American Southwest, including areas dominated by warm-season (June–September) and cool-season (October–May) rainfall22. Most of the postfire debris flows that have been observed in coastal areas of the Southwest (e.g., southern California) have occurred during the cool season. During this time, cool-season precipitation in the western United States is primarily dominated by extratropical cyclone/frontal systems, which may host mesoscale convective features, such as narrow cold frontal rainbands that are capable of producing intense rainfall that meets or exceeds postfire debris-flow triggering thresholds23,24,25. These storms may also feature atmospheric rivers, although the presence, absence, or strength of an atmospheric river is not a reliable predictor of whether short-duration, high-intensity rainfall conducive to postfire debris flows will occur23,26. Most of the postfire debris flows that have been documented in the interior Southwest (i.e., Arizona, Colorado, New Mexico) have been associated with warm season (June–September) convection during the North American Monsoon27,28,29. Decaying tropical systems, which typically arrive in the Southwest during the transition between the warm and cool seasons, have also triggered postfire debris flows30.

As wildfire activity increases throughout the western United States31, so too has the demand for the emergency assessment of postfire debris-flow hazards32, including areas where our understanding of postfire debris-flow initiation is limited, such as in the Cascade ranges spanning northern California, Oregon, Washington, and British Columbia33. This demand, coupled with recent observations of postfire debris flows in regions where they were previously undocumented26,34, highlights a need to understand how rainfall intensification driven by climate change may heighten our exposure to this hazard. Despite progress in recognizing the potential effect of rainfall intensification on postfire debris flows35,36, we have not yet developed an approach to quantify how the frequency, magnitude, and seasonality of rainfall capable of triggering postfire debris flows could evolve. Here, we provide this information by tracking rainfall threshold exceedance metrics across dynamically downscaled (3.75-km horizontal grid spacing), convection-permitting simulations of short-duration (15-min) rainfall37 for historical (1990–2005) versus late 21st-century (2085–2100) climate scenarios. Our approach enables a physics-based representation of the meteorological phenomena often associated with postfire debris flows (convective rainfall), honors the timescale of postfire debris-flow triggering rainfall (low recurrence interval, sub-hourly duration), and resolves these characteristics at a spatial scale that is suitable for long-term hazard planning.

Results

We refer to our climate simulation output as WRF-BCC (Weather Research and Forecasting Model-Bias Corrected Community Earth System Model), the simulation epochs as HIST (historical; 1990–2005) and FUT (future; 2085–2100), and the future emissions scenarios as RCP (Representative Concentration Pathway) 4.5 and 8.5. We characterize trends in 15-min rainfall intensity (I15 [mm per hour]) threshold exceedance for 175 burned areas across the American Southwest (Fig. 1a), as well as for mountainous terrain throughout California and Colorado (Figs. 2 and 3), for three WRF-BCC simulation scenarios: (1) HIST, (2) FUT4.5, and (3) FUT8.5. We provide more detailed descriptions of the climate simulations and thresholds in the “Methods” section, which follows the ”Discussion” section.

Fig. 2: Annual frequency of rainfall threshold exceedances for mountainous terrain throughout the State of California.
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State of California with an overlay of scatter plots that reflect 15-min rainfall intensity threshold (equivalent to a one-year recurrence interval under the present climate) exceedances in mountainous terrain for the WRF-BCC HIST, FUT4.5, and FUT8.5 simulation scenarios. Several areas are labeled for reference, including “KLM” (Klamath Mountains), “NCR” (Northern Coast Ranges), “Sierra Nevada” (SNV), “SCR” (Southern Coast Ranges), “TRV” (Transverse Ranges), and “PNR” (Peninsular Ranges). State boundaries provided by U.S. Census Bureau84.

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Fig. 3: Annual frequency of rainfall threshold exceedances for mountainous terrain throughout the State of Colorado.
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State of Colorado with an overlay of scatter plots that reflect 15-min rainfall intensity threshold (equivalent to a one-year recurrence interval under the present climate) exceedances in mountainous terrain for the HIST, FUT4.5, and FUT8.5 simulation scenarios. Several areas are labeled for reference, including “FRG” (Front Range), “SWA” (Swatch Range), “SJM” (San Juan Mountains), and “SDC” (Sangre de Cristo Mountains). State boundaries provided by U.S. Census Bureau84.

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Frequency of rainfall threshold exceedance

The WRF-BCC simulations project a rise in the frequency of above-threshold rainfall across the American Southwest. Specifically, we observe a significant (p < 0.05) increase in the mean annual frequency of I15 threshold exceedance for FUT4.5 and FUT8.5 across 175 burned areas in Arizona, California, Colorado, Nevada, New Mexico, and Utah (Fig. 1a) where the U.S. Geological Survey (USGS) issued rainfall thresholds as part of emergency assessments of postfire debris-flow hazards32. These 15-min rainfall thresholds were calculated with an empirical debris-flow likelihood model22,38 that is routinely applied to areas of concern in the western United States where the control of short-duration rainfall on the hazard has been measured directly26,39,40. Across these burned areas, FUT4.5 projects a mean exceedance two times that of HIST (1.4 versus 0.7 exceedances per year), while the mean exceedance rate for FUT8.5 is more than four times that of HIST (3.1 versus 0.7 exceedances per year). USGS-assessed burned areas in California show the greatest increases in threshold exceedance (2.3 and 6.5 times higher than HIST for FUT4.5 and FUT8.5, respectively), while increases in threshold exceedance in neighboring Nevada (1.3 and 1.8 times higher than HIST for FUT4.5 and FUT8.5, respectively) and Arizona (1.5 times higher than HIST for both FUT4.5 and FUT8.5) are the lowest. Increases in exceedance rates for New Mexico, Colorado, and Utah fall in-between, with mean exceedance rates 1.6–2.2 times greater than HIST for FUT4.5 and 2.2–2.4 times greater than HIST for FUT8.5 (Fig. 1a).

Our statewide analyses of I15 threshold exceedance in mountainous terrain, for which we evaluate spatially variable thresholds equivalent to a one-year recurrence interval41, indicate that the future frequency of I15 threshold exceedance will not be spatially uniform (Figs. 2, 3). For example, FUT8.5 projects substantial increases (>6 exceedances per year versus ≤1.5 in HIST) in California throughout the Sierra Nevada, Northern Coast Ranges, and Klamath Mountains, with notable increases (>1.5–6 exceedances per year versus ≤1.5 in HIST) in the Peninsular, Transverse, and Southern Coast Ranges (Fig. 2). Rainfall intensification is less apparent (many cases < 1.5 exceedances per year) for the mountainous terrain of the Mojave and Colorado Deserts in southeastern California. This finding is consistent with others who have also projected greater changes in rainfall intensification for northern California than in southern California18,42,43. Increases in the frequency of threshold exceedance are not as apparent in Colorado (Fig. 3) compared to California (Fig. 2). For example, FUT8.5 projects that limited areas in the San Juan Mountains of southwestern Colorado will experience substantial (>6 exceedances per year) increases in the frequency of threshold exceedance; however, there are notable (>1.5–6 exceedances per year) increases in the frequency of threshold exceedance in the Front Range, Sangre de Cristo Mountains, and Sawatch Range of central and southern Colorado. Rises in above-threshold exceedance projected by FUT4.5 and FUT8.5 are similar in their spatial distribution across California and Colorado, but the FUT4.5 exceedance rates are generally lower than FUT8.5 (Figs. 2, 3).

Magnitude and seasonality of rainfall threshold exceedance

Similar to the marked rise in the mean annual frequency of threshold exceedance, we also observe a significant (p < 0.05) increase in the mean I15 threshold exceedance ratio for FUT4.5 and FUT8.5 across burned areas in the Southwest as compared to HIST (Fig. 4a). The exceedance ratio is calculated by dividing the simulated I15 by the I15 threshold. The exceedance ratio is equal to one when the simulated I15 is equal to the I15 threshold and it is more than one when the simulated I15 is greater than the I15 threshold. Given that the volume of debris flows scales with rainfall intensity44, this result indicates that larger and potentially more destructive debris flows may become more common. Specifically, FUT8.5 projects higher percent increases in mean exceedance ratios than FUT4.5 for our burned area analyses (FUT4.5 = +4% and FUT8.5 = +12%) and our statewide mountainous terrain analyses (California FUT4.5 = +2% and FUT8.5 = +5%; Colorado FUT4.5 = +4% and FUT8.5 = +9%). Our results also indicate that trends in the magnitude of threshold exceedance will not necessarily follow those associated with the frequency of threshold exceedance. For example, Colorado may experience increases in the mean annual frequency of threshold exceedance that are less severe than California (Figs. 2, 3), but Colorado is projected to experience greater increases in mean threshold exceedance ratios than California (Fig. 4a).

Fig. 4: Summary of rainfall threshold exceedance ratios and seasonality of rainfall threshold exceedances for California, Colorado, and the American Southwest.
figure 4

a Box and whisker plots that track changes in the exceedance ratio of 15-minute rainfall intensity thresholds for the HIST, FUT4.5, and FUT8.5 simulation scenarios for mountainous terrain throughout California and Colorado (Figs. 2, 3, Supplementary Fig. 1), as well as for 175 burned areas across the American Southwest (i.e., Arizona, California, Colorado, Nevada, New Mexico, and Utah) where the U.S. Geological Survey issued rainfall thresholds as part of emergency assessments of postfire debris-flow hazards between 2014 and 2022 (Fig. 1a, Supplementary Fig. 1). The boxes in a are bound by the first and third quartile, with the median indicated by a line, and the whiskers extend from the boxes to the farthest data point within 1.5 times the inter-quartile range. The bar plots illustrate differences in the seasonality of rainfall threshold exceedance for mountainous terrain throughout b California and c Colorado.

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The overall distribution of cool- versus warm-season threshold exceedance appears largely unaffected across mountainous terrain in California and Colorado under a changing climate (Fig. 4b, c). WRF-BCC projects that California will continue to be dominated by cool-season (October–May) exceedances (HIST = 85%, FUT 4.5 = 93%, and FUT8.5 = 96%) and that Colorado will continue to be dominated by warm-season (June–September) exceedances (HIST = 87%, FUT 4.5 = 78%, and FUT8.5 = 76%). However, there are some shifts at the meteorological season scale. In California, for example, the December–January–February (DJF) season experiences an increase (+24%) in the mean proportion of exceedances in FUT8.5 compared to HIST. The March–April–May (MAM) and September–October–November (SON) seasons, on the other hand, experience decreases in the mean proportion of exceedance (−8%) in FUT8.5 compared to HIST. This pattern is consistent with other studies that have noted a “sharpening” of the precipitation season in California to the core winter months45, as well as the intensification of atmospheric river storms and sub-daily intensities within them17. The Klamath Mountains and Sierra Nevada are areas of California that are projected to experience some of the greatest increases in the frequency of exceedances (Fig. 2) and typically experience snowfall in the DJF season. The increase in the mean proportion of exceedances during the DJF season may be associated with the projected transition to more precipitation falling as rain under a warming climate46. The snow-to-rain transition could also be reflected in the slight increase in the mean proportion of exceedances in Colorado during DJF and SON (+1%) in FUT8.5 compared to HIST. We observe negligible change in Colorado for the MAM season (−0.2%) in FUT8.5 compared to HIST. California and Colorado are projected to experience decreases in the mean proportion of exceedances during the June–July–August (JJA) season (−8% and −2%, respectively) in FUT8.5 compared to HIST. These shifts in threshold exceedance frequency during the JJA season and the early SON season are likely associated with projected changes in the frequency and intensity of the North American Monsoon and decaying tropical systems impacting the Southwest47,48,49.

Discussion

We find that rainfall intensification driven by climate change is projected to amplify known triggering conditions for postfire debris flows in the American Southwest. This amplification is reflected by significant increases in the frequency (Fig. 1a) and magnitude (Fig. 4a) of short-duration rainfall intensity threshold exceedances for burned areas in the Southwest where postfire debris flows have been a concern in the past, as well as across mountainous terrain in California and Colorado that are potentially susceptible to the hazard (Figs. 2, 3). An increased frequency of exceedance indicates that we may expect more opportunities for sufficiently intense rainfall to initiate debris flows before postfire soil-hydraulic recovery and/or vegetation regrowth can reduce susceptibility to flash floods and runoff-generated debris flows39,50,51,52,53. Temporal changes in sediment sourcing (e.g., gradual entrainment from hillslopes, mass failure of the channel bed, and shallow landsliding) have been observed to fuel multiple postfire debris flows over the course of a rainy season in the first year after fire40,54. Therefore, rainfall intensification could result in more postfire debris flows for settings that are not sediment supply limited. An increased magnitude of exceedance means that we may also expect enhanced mobilization of sediment and other dangerous debris, which would result in greater inundation depths and runout distances along developed valley bottoms, floodplains, and fan surfaces44,55. Therefore, rainfall intensification may result in more damaging postfire debris flows such as those associated with the 2018 Montecito debris-flow event in Santa Barbara County, California11 (Fig. 1b). Although our focus is on debris flows generated by excessive surface-water runoff soon after the fire, the trends in rainfall intensification that we report in this study may also be problematic for steep, unburned areas in the American Southwest that generally lack vegetation and are also prone to runoff-generated debris flows56. However, our results are not applicable to debris flows generated by landslides, for which the simulated triggering conditions have been shown to be sensitive to the antecedent soil saturation51.

Climate-enhanced postfire debris-flow likelihood and magnitude have been recognized for southern California35. Our analyses, which expand on this work, have implications for hazard planning across the American Southwest. For example, the ratio of rainfall threshold exceedance for FUT4.5 or FUT8.5 to HIST (Fig. 1a) could be used as a scaling factor for each state to broadly assess to what extent rainfall intensification could affect the frequency of threshold exceedance in areas where postfire debris flows have been a concern in the past (e.g., RCP4.5/HIST = 2.3 for California versus 1.6 for Colorado). The relatively high spatial resolution of our results (Figs. 2, 3) could also facilitate more localized planning. For example, we show that the intensification of short-duration rainfall could be more severe in mountainous areas, such as northern California (Fig. 2). This includes areas where communities, emergency managers, and weather forecasters may be less accustomed to contending with postfire debris, flows (relative to those in southern California), in part because the hazard has only recently been systematically documented26,34. Therefore, this study highlights increased hazard potential and the benefits of prefire planning, education, and outreach for postfire hazards36.

We use the first available projections of 15-min rainfall for 15-year periods at 3.75-km grid spacing in the American Southwest. We observe rainfall intensification at the sub-hourly timescale, consistent with studies of hourly precipitation intensification that include the Southwest14,17,18,57. However, we recognize that representing convective processes associated with short-duration, high-intensity rainfall in climate models is challenging58,59,60. Due to the computational constraints associated with producing simulations at such fine spatiotemporal scales, our results are limited to downscaling a single general circulation model (GCM) realization with a single WRF configuration. Additional studies could corroborate our findings as outputs at similarly high spatial and temporal resolutions become available from various modeling efforts with other GCM inputs, downscaling model cores, and physics parameterizations. Future research could also assess changes in the meteorological characteristics (e.g., storm types) driving over-threshold rainfall events (including extreme mesoscale and synoptic atmospheric features) within the context of projected changes to fire behavior. Such analyses would provide a more in-depth explanation of the intra-seasonal changes we observe and provide insight for forecasting high-intensity rainfall and postfire debris flows where rainfall intensification and increased fire activity may geographically overlap under a changing climate.

We assess the short-duration rainfall characteristics that most commonly trigger debris flows in the first two years after wildfire in the western United States. Short-duration, high-intensity rainfall produces excessive surface-water runoff that can rapidly amplify stream power and mobilize debris, particularly in low-order catchments where the time-to-concentration is short7. Our analyses of burned areas rely on short-duration rainfall thresholds calculated for recent wildfires using an empirical model that was trained on debris-flow observations from southern California and has been tested against hundreds of debris-flow observations across Arizona, Colorado, Idaho, Montana, New Mexico, and Utah22,38. Our statewide analyses rely on the known recurrence interval of the short-duration rainfall intensities associated with these same debris-flow observations8; therefore, our analyses could be extended beyond California and Colorado as part of a future study. The control of short-duration rainfall on debris-flow triggering soon after fire has also proven valid for the highly destructive debris flows that followed recent megafires (>100,000 acres) in central and northern California26,34. However, we refrain from expanding our analyses to the Pacific Northwest, where the effect of short-duration rainfall on debris-flow generation after wildfire is considerably more uncertain61 and short-duration precipitation frequency data for the present climate41 is unavailable (Supplementary Fig. 1). The recent wave of very large, high-severity wildfires in the Pacific Northwest62 underscores the value of field-verified inventories of debris-flow occurrence to support the refinement of conceptual models for the conditions that trigger postfire debris flows in this area and short-duration precipitation frequency data that can be used to support climate analyses like those we present here.

Topographic steepness, soil burn severity, and soil erodibility are important factors that influence susceptibility to postfire debris flows22,38. We implicitly account for these factors in our analyses of burned areas where postfire debris flows have been a concern in the recent past; however, our statewide analyses of mountainous terrain do not consider future fire behavior or changes in sediment availability. Increased wildfire activity is projected across our study area in the mid-to-late 21st century and is generally expected to enhance soil erosion across many watersheds in the western United States63, although there is spatial variability in these wildfire projections64,65,66. Furthermore, changes to ecological succession/transition that are expected to accompany climate change67 may affect regional burn severity and recovery characteristics. We prioritize a focus on changes in rainfall because previous work has indicated that future debris-flow activity will be more sensitive to rainfall intensification than increases in fire frequency and severity, at least for areas dominated by shrubland vegetation35. We also recognize that regional variability in soil and rock properties and their connection to sediment availability is an important susceptibility factor. Loose, unconsolidated materials lining channels and mantling hillslopes are thought to contribute to postfire debris-flow susceptibility across a wide range of geologic conditions68, but these kinds of deposits have not yet been systematically identified at the spatial scales that we explore for this study. Therefore, while our statewide rainfall threshold exceedance maps (Figs. 2, 3) identify where we may expect an amplification of rainfall conditions that are conducive to triggering postfire debris flows, more work would be helpful to identify regional factors that could affect debris-flow susceptibility.

Methods

Climate data

We analyzed a set of convection-permitting (3.75-km horizontal grid spacing) climate simulations that were dynamically downscaled using the Weather Research and Forecasting-Advanced Research WRF model (WRF-ARW) Version 4.1.269. Initial and lateral boundary conditions for WRF-ARW were taken from the bias-corrected70 output from Phase 5 of the Coupled Model Intercomparison Project (CMIP5)71 version of the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM)72,73. Bias correction prior to dynamic downscaling improves regional simulation performance, particularly for temperature and precipitation74,75.

For climate comparisons, we examined three, 15-year epochs: (1) a historical period (HIST) spanning 1 October 1990–30 September 2005 and (2,3) a late-21st century period (FUT) spanning 1 October 2085–30 September 2100 under Representative Concentration Pathway (RCP) 4.5 (FUT4.5) and 8.5 (FUT8.5). RCP 4.5 and RCP 8.5 characterize intermediate and pessimistic future emissions scenarios, respectively. The simulations used spectral nudging every six hours, an approach where regional climate models are driven by select spatial scales associated with the general circulation model76, to maintain consistency of synoptic-scale features between the general circulation model (GCM) and the higher-resolution WRF-ARW domain at the boundaries77,78. Mesoscale phenomena are not nudged and are, therefore, allowed to dynamically evolve within the model domain. This simulation dataset, which we refer to as WRF-BCC, is one of the only available with archived 15-min rainfall over multiple climate epochs, thus permitting our novel analysis of short-duration rainfall in a climate change framework.

A comparison of WRF-BCC HIST precipitation data was performed37 against the Parameter-elevation Regressions on the Independent Slopes Model (PRISM)79 and a gridded precipitation observation ensemble dataset80 (originates from over 12,000 unique surface stations) that accounts for observational uncertainty resulting from issues like gage undercatch, complex terrain, and low station density. WRF-BCC HIST and PRISM showed 0.91 Pearson’s r correlation for average annual and monthly precipitation, with a bias smaller than at least one ensemble member of observations. A broad dry bias was noted in the southeast, east, and northeast United States, whereas WRF-BCC HIST simulations were found to have a wet bias in most of the Northern Plains and Intermountain West during DJF when compared to observations. Overall, the biases are not statistically significant at the 90% significance level using a Mann–Whitney U test for the medians, and it is plausible that some of the wet bias in the high elevations of the Intermountain West is due to a lack of reliable observations.

Rainfall thresholds

Our analyses focus on two spatial subsets of the WRF-BCC simulation output: (1) 175 burned areas across the Southwest (i.e., Arizona, California, Colorado, Nevada, New Mexico, and Utah) where the USGS conducted emergency assessments of postfire debris-flow hazards32 between 2014 and 2022, and (2) mountainous terrain81 throughout California and Colorado (Fig. 5a, Supplementary Fig. 1). Each USGS hazard assessment includes an estimate of the 15-min rainfall intensity (I15) needed to generate postfire debris flows. These rainfall thresholds are based on a logistic regression22,38 that predicts the statistical likelihood (i.e., a value ranging from 0 to 1) of postfire debris flows based on the topographic slope, soil burn severity, and soil erodibility along stream segments and at drainage basin outlets. The rainfall thresholds that we used were calculated for a likelihood of 0.5, a value that has been widely applied to estimate debris-flow triggering conditions in the western United States32. This likelihood-based rainfall threshold approach has been shown to generally perform as well, and in some cases better than, preexisting regional rainfall thresholds in Arizona, Colorado, Montana, and New Mexico38, and has also performed similarly well in areas with no preexisting regional thresholds34.

Fig. 5: Conceptual overview of the methodology for tracking rainfall threshold exceedances.
figure 5

a For our analyses of U.S. Geological Survey (USGS)-assessed fires, we selected the Weather Research and Forecasting Model-Bias Corrected Community Earth System Model (WRF-BCC) cells in the American Southwest (i.e., Arizona, California, Colorado, Nevada, New Mexico, and Utah) within burn perimeters where, between 2014 and 2022, the USGS issued rainfall thresholds as part of an emergency assessment of postfire debris-flow hazards (Supplementary Fig. 1). For our statewide analyses, we selected the WRF-BCC cells that intersected mountainous terrain throughout the State of California and Colorado and applied a 10-km buffer. Mountainous terrain map provided by USGS81. State boundaries provided by U.S. Census Bureau84. b For each WRF-BCC cell that we selected for our assessment-based analyses, we developed log-linear fits to predict the recurrence intervals (RIs) of local 15-minute rainfall rates. We used these expressions to convert USGS rainfall thresholds (e.g., dashed blue arrow) to rainfall RI thresholds (e.g., dashed orange arrow). We assume 15-min rainfall RI thresholds equal to one year (under the present climate) for our statewide analyses. c We then conducted a rainfall intensity-duration-frequency analysis for each WRF-BCC cell and used power fits to convert rainfall RI thresholds to WRF-BCC rainfall thresholds (dashed gray arrow). d Finally, we tracked WRF-BCC rainfall threshold exceedances (e.g., orange bar) for the historical (HIST, 1990–2005) and late 21st-century RCP 4.5/8.5 (FUT, 2085–2100) scenarios.

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To ensure consistency between our two types of threshold analyses, we conducted a rainfall intensity-duration-frequency (IDF) analysis for each WRF-BCC HIST grid cell-of-interest (e.g., Fig. 5a) using a partial-duration series approach82. For our statewide analyses, we assumed spatially variable I15 thresholds that are equivalent to the one-year rainfall recurrence interval8 for HIST. For our burned area analyses, we used the median of the USGS-based I15 thresholds32 that were calculated among drainage basin outlets (a metric commonly distributed for hazard guidance) for each fire and converted the I15 thresholds into rainfall recurrence intervals using National Oceanic and Atmospheric Administration (NOAA) Atlas 14 precipitation frequency data41 (Fig. 5b). We used NOAA Atlas 14 precipitation data to calculate the recurrence interval of the USGS-based I15 thresholds because we found that WRF-BCC HIST could underestimate the frequency of short-duration, high-intensity rainfall relative to estimates from NOAA. The median recurrence interval associated with the USGS-based I15 thresholds (1.6 years) is similar to the return period that we used for our statewide threshold analyses (1 year) and consistent with previous research8. We then used the IDF analyses to convert the recurrence intervals into equivalent WRF-BCC I15 thresholds (Fig. 5c). We only retained WRF-BCC I15 thresholds for our analyses if the log-linear and power fit that we used to calculate rainfall recurrence intervals (Fig. 5b) and rainfall thresholds (Fig. 5c) resulted in a coefficient of determination (R2) ≥ 0.9.

We identified three straightforward metrics to characterize future trends in the frequency, magnitude, and seasonality of postfire debris-flow triggering conditions with the WRF-BCC simulation output: (1) the mean annual I15 threshold exceedance rate, (2) the mean I15 threshold exceedance ratio, and (3) the mean seasonality of I15 threshold exceedance. To calculate these metrics for a given WRF-BCC grid cell with the associated HIST, FUT4.5, and FUT8.5 simulation timeseries, we tallied each I15 exceedance (Fig. 5d), computed the ratio of the simulated I15 to the I15 threshold for each exceedance, and organized the exceedances into monthly bins and seasonal breaks (i.e., October–May, cool season; June–September, warm season).