Results and Discussion

We find a significant, positive relationship between monthly precipitation and flood damages, with a 1-SD increase in the monthly precipitation anomaly corresponding to a >3-fold increase in flood damages (Fig. 1B). Variation in monthly, state-level precipitation (after accounting for state-month and state-year fixed effects) explains 21% of the observed variation in monthly flood damages. The log-linear response suggests exponential growth in flood damages for a given increase in monthly precipitation, and we find a similar shape and magnitude of response using either a quadratic or nonparametric binned model (Fig. 1B). We also show that the presence of reporting errors in the data (such as missing damages) is unlikely to cause an overestimation of the effect of precipitation on flood damage (SI Appendix, Text and Fig. S1).

Although months with flood damages occur at a range of precipitation anomalies, the largest damages primarily occur at precipitation anomalies >2 SDs (Fig. 1B). As expected, the slope of the relationship is flatter across negative monthly precipitation anomalies when using a nonlinear functional form. Smaller flood damages do occur during months with negative statewide precipitation anomalies (Fig. 1B), possibly due to lagged effects from snowmelt, precipitation in adjacent states, or short-duration and/or localized precipitation during months that are relatively dry at the state-month scale. (We include additional models to test for some of these effects, as described below.)

Given the range of temporal and spatial scales at which flooding occurs, we compare our primary monthly, state-level regression model with regression models that use shorter- or longer-duration precipitation, or precipitation over large watersheds that span multiple states. Monthly maximum 5-d precipitation has a positive effect on monthly flood damages, but the effect is smaller compared with that of total monthly precipitation (Fig. 1C). Using a lagged precipitation model, we find that precipitation in previous months has a positive effect on flood damages (SI Appendix, Fig. S2A) but that these effects are much smaller than the effect of the current-month precipitation. Further, although there are additional effects from precipitation that occurs out-of-state (SI Appendix, Fig. S3), these effects are small compared with that of within-state precipitation. Combined, these analyses indicate that results based on the state-month regression are consistent with models that account for the effects of shorter- or longer-duration precipitation, or large-scale flooding processes.

We do find regional differences in the magnitude of the effect of monthly precipitation on flood damages (Fig. 1C), reflecting both regional differences in the conditions creating flood hazards (e.g., the type of weather events associated with extreme precipitation, and the primary flooding processes) and regionally specific patterns of exposure and vulnerability (e.g., patterns of land use and development). Additionally, some regions show seasonal variations in the effect of precipitation on flood damages (Fig. 1D). For example, there are smaller effects of precipitation on flood damages during the winter (December through February) season in the Northern Rockies, Upper Midwest, and Northeast regions. This result could reflect the fact that these cold regions receive snow in the winter, which would not have the same immediate impact on flooding as rain during warmer seasons. We use the regional, monthly regression model (Fig. 1C) as our primary model for later analyses, but we test the sensitivity of our results to these seasonal effects (see Fig. 3B).

We use our regression model results as a framework to understand the effect of historical precipitation changes on flood damages. Because monthly total and maximum 5-d precipitation have a similar effect on monthly flood damages (Fig. 1C), and because previous studies have detected changes in short-duration (e.g., daily or 5-d) precipitation extremes (5, 28), we analyze trends in both monthly total (Fig. 2A) and maximum 5-d precipitation (Fig. 2B). Further, given existing evidence that trends in extreme precipitation are larger and sometimes of opposite sign compared with trends in mean precipitation (29), we calculate trends at multiple quantiles within the distributions of monthly total and maximum 5-d precipitation. This approach allows us to distinguish between changes in the wettest months (which are associated with the largest flood damages; Fig. 1B) and changes in the median or drier months.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 2.

Observed trends in monthly total and maximum 5-d precipitation. (A) Observed 1928-to-2017 trends in the 50th, 75th, and 95th percentiles of monthly precipitation, measured in SDs per decade. Trends are calculated on a 2.5 × 2.5° grid using quantile regression and the PRISM monthly precipitation product. (B) Same as A, but for monthly maximum 5-d precipitation. Trends are calculated on a 2.5 × 2.5° grid using quantile regression and the Climdex HadEX3 monthly Rx5day product.

Fig. 2 shows trends in the 50th, 75th, and 95th percentiles of the monthly total and maximum 5-d precipitation distributions from 1928 to 2017. These analyses confirm that historical precipitation trends are not uniform across the distribution, with the 95th percentile exhibiting the largest trends. The spatial pattern of changes in monthly precipitation is very similar to that of monthly maximum 5-d precipitation. Most of the northwestern, central, and eastern United States have seen increases in median (50th percentile) monthly precipitation, whereas the Southwest has experienced decreases in median monthly precipitation. This spatial pattern is very similar to reported changes in annual mean precipitation over the United States, which results from changes that vary by region and season, including increases in fall precipitation in the Southeast, Northeast, and Great Plains and decreases in spring precipitation in the Southwest (29).

Precipitation during the wettest months (i.e., the 95th percentile) has increased across most of the country, even in some areas where median monthly precipitation is decreasing (Fig. 2). This pattern is also true for monthly maximum 5-d precipitation, and is consistent with previously identified increases in short-duration (e.g., daily or 5-d) precipitation extremes (29). The largest increases in the 95th percentile have occurred in the Midwest and Northeast.

Based on the regional regression coefficients, expected state-level flood damages have increased by an average of 35, 50, and 70% for precipitation at the 50th, 75th, and 95th percentiles, respectively (SI Appendix, Text and Fig. S4). In some states, we calculate that damages from the wettest 5% of months are now more than three times what would be expected in the absence of the observed precipitation changes (SI Appendix, Fig. S4).

Removing the historical quantile-specific monthly precipitation trends in each state allows us to estimate the effect of state-level precipitation changes on cumulative national-level damages (Fig. 3A and Methods). We find that precipitation changes have contributed 36% ($73 billion) of the 1988-to-2017 cumulative US flood damages. Uncertainty in the regional regression coefficients (Fig. 1C) and observed precipitation trends (SI Appendix, Figs. S4 and S5) yields a 95% confidence range of 20 to 46% (39 to $91 billion) contributed by state-level precipitation trends.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 3.

Cumulative damages due to historical precipitation change. (A) Cumulative observed flood damages (gray) and estimated portion due to historical precipitation change (green) from 1988 to 2017. Error bars show the 95% CI for cumulative damages in 2017 (based on precipitation trends from 1928 to 2017). (B) Impact of historical precipitation change on cumulative flood damages in 2017 using various regression model specifications. From left to right, the models are the regional model (same as A), the regional-seasonal model (Fig. 1D), a regional model with lagged precipitation (SI Appendix, Fig. S2A), a linear model (Fig. 1B), and a quadratic model (Fig. 1B). (C) Sensitivity of cumulative damages from precipitation change to starting year of precipitation trend calculation. All estimates use the same regional regression model used in A.

Our results are robust to using alternative regression models that account for lagged and seasonal effects (Fig. 3B), and to calculating precipitation trends over different time periods (Fig. 3C). They are also robust to using different assumptions about possible unreported damages (SI Appendix, Fig. S6); further, the fact that the historical flood damage values are likely underestimated and/or unreported in earlier years (1) would cause the effect of precipitation on damages to be underestimated, and thus make our estimate of the contribution of historical precipitation change conservative (SI Appendix, Text and Fig. S1A).

There are limitations to using the state-month as the unit of analysis, because flooding can occur on shorter or longer timescales, and over smaller or larger areas. However, we find that our primary regression model yields a similar (although slightly lower) estimate of the contribution of historical precipitation change compared with versions of the model that include effects of precipitation over longer timescales (Fig. 3B) or larger spatial scales (SI Appendix, Fig. S3). The strong similarity between historical trends in monthly total and monthly maximum 5-d precipitation (Fig. 2), as well as similarity in their effect on damages (Fig. 1C), indicate that an analysis based on 5-d precipitation would yield a similar estimated contribution of historical precipitation change. Together, these sensitivity analyses suggest that our primary estimate of the contribution of historical precipitation trends to total US flood damages is both robust and conservative.

Prior studies have attributed increases in short-duration precipitation extremes over the United States to anthropogenic climate forcing by comparing historical trends with climate model simulations (10, 30), isolating forced changes from those driven by modes of natural climate variability (31⇓⇓–34), or calculating the probability of extreme events (i.e., “risk ratio”) with and without anthropogenic climate forcing (9, 35, 36). While the general circulation models that comprise the Coupled Model Intercomparison Project (CMIP5) ensemble show a thermodynamic response to warming (37, 38) (Figs. 4 and 5), they do not explicitly resolve the precipitation processes that cause flood damages (such as severe thunderstorms and tropical cyclones), and may underestimate the magnitude of extreme precipitation change (10, 28, 29, 31). Given the large uncertainties in modeled precipitation trends, particularly at the spatial scale of individual events, we do not use our regression analysis to explicitly separate the contributions of forced climate change and unforced climate variability to cumulative flood damages.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 4.

Change in probability of exceeding early industrial baseline precipitation thresholds during the recent historical period, simulated by the CMIP5 global climate model ensemble. (A) Probability of exceeding the early industrial baseline (1860 to 1920) 50th, 75th, 95th, and 99th percentile monthly precipitation thresholds during the recent historical period (1988 to 2017). Probabilities are shown as a ratio relative to the probability during the baseline period, and are based on a 24-model ensemble (SI Appendix). Solid colors indicate strong model agreement (following the IPCC AR5 definition, when ≥66% of models agree with the direction of change shown on the map). Black stippling indicates <66% of models agree with the direction of change shown. (B) Same as A but for monthly maximum 5-d precipitation.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 5.

Projected changes in monthly total and maximum 5-d precipitation. (A) Projected change in the 50th, 95th, and 99th percentiles of monthly precipitation by 2081 to 2100 for RCP2.6. Changes are relative to the recent historical (1988 to 2017) period. Maps show the mean change across a 17-model ensemble (Methods). Solid colors indicate strong model agreement (following the IPCC AR5 definition, when ≥66% of models agree with the direction of change shown on the map). Black stippling indicates <66% of models agree with the direction of change shown. (B) Same as A but for RCP8.5. (C) Same as A but for monthly maximum 5-d precipitation. (D) Same as B but for monthly maximum 5-d precipitation.

However, we do use the CMIP5 global climate model simulations to assess changes in the probability of monthly total and maximum 5-d precipitation thresholds over the recent historical period (1988 to 2017) compared with an early-industrial baseline (1860 to 1920; SI Appendix, Text). The probability of exceeding the baseline 50th and 75th percentiles of monthly precipitation has increased slightly across the central and eastern United States in the recent historical period, and decreased slightly across the Southwest (Fig. 4). In contrast, the probability of exceeding the baseline 95th or 99th percentiles has increased across most of the United States, especially for monthly maximum 5-d precipitation (Fig. 4). This analysis suggests that anthropogenic climate forcing has increased the frequency of extreme monthly precipitation, with the ensemble mean response (Fig. 4) showing many similarities to the observations (Fig. 2). However, despite the mean wetting in response to anthropogenic forcing, there is some disagreement across models on the direction of change over the recent historical period, particularly at the higher-percentile thresholds (Fig. 4). We must therefore conclude that the estimated flood damages due to precipitation change (Fig. 3) represent the combined effects of anthropogenic forcing and natural variability, and cannot be entirely attributed to anthropogenic climate change.

To understand the implications of additional global warming for the cost of future flood damages, we evaluate future precipitation change in the “high-” (RCP8.5) and “low-” (RCP2.6) emissions scenarios analyzed in the assessment of impacts, adaptation, and vulnerability in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report [IPCC AR5 (16)]. In both scenarios, the 95th and 99th percentiles of monthly total and maximum 5-d precipitation are projected to increase across most of the United States by midcentury (2046 to 2065) relative to the recent historical period (SI Appendix, Fig. S7). Under the high-emissions scenario (RCP8.5), there is strong model agreement that the wettest months (both in total precipitation and maximum 5-d precipitation) will continue to intensify through the end of the century (Fig. 5). In some parts of the northeastern and western United States, the 99th percentile of monthly maximum 5-d precipitation is projected to increase by more than 1 SD (Fig. 5B). Combined with our regression model, these analyses suggest that—absent changes in exposure or vulnerability—future global warming is very likely to increase the costs of flooding, but that those increases could be greatly reduced under a low-emissions scenario consistent with the UN Paris Agreement.

Overall, our findings are consistent with prior conclusions that flood damages are sensitive to variations in weather (39⇓–41), and that climate change has likely increased historical damages from flooding and/or tropical cyclones (42, 43). While some studies have not found an impact of climate change on historical flood damages (20, 21), this contrast may be explained by different methodology, including 1) the scale of the analysis (for example, country-year in previous studies vs. state-month in our study); 2) our use of fixed effects to isolate precipitation variation from the many other time-invariant and time-varying factors that might also affect flood damages (such as variations in exposure and vulnerability); and 3) our use of precipitation trends at different percentiles of the distribution to isolate trends affecting the wettest months (in which damages are most likely to occur).