1. Introduction
Conventional planning estimates of extreme rainfall frequency and magnitude have utilized the stationary climate assumption in extreme precipitation calculations (Hershfield 1961; Bonnin et al. 2006; Perica et al. 2013, 2018). However, the nonstationarity produced by climate change has been increasingly shown to be an important consideration for extreme precipitation analysis (Kunkel et al. 2013; Westra et al. 2014; Paciorek et al. 2018). Even the present-day frequency and intensity of extreme precipitation events are underestimated in a stationary analysis in the presence of an upward trend in precipitation and recent heavier rain-producing storms (Wright et al. 2019; Vu and Mishra 2019). Consequently, there has been considerable effort in recent years to develop actionable projections of intensity, duration, and frequency (IDF) of extreme rainfall for use in planning (Martel et al. 2021; Yan et al. 2021; Schlef et al. 2023).
Extreme precipitation risk is particularly relevant for the Gulf Coast and southeastern regions of the United States. Most of the top 100 largest area-averaged, multiday precipitation events for the period 1949–2018 occurred in the southeastern United States (Kunkel and Champion 2019). Furthermore, the Gulf Coast and southeastern regions of the United States have some of the largest and most significant trends in extreme rainfall according to a range of aggregation methods and statistical tests (Kunkel et al. 2013; Wu 2015; Wright et al. 2019; Kunkel et al. 2020). Some of the largest rainfall events in U.S. history have occurred in recent years along the Gulf Coast and southeastern coast, such as Hurricane Harvey (van der Wiel et al. 2017; Paerl et al. 2019; Case et al. 2021; Mazurek and Schumacher 2023). This recent history of extreme rainfall may have made some existing IDF analyses obsolete, especially in North and South Carolina where the existing National Oceanic and Atmospheric Administration (NOAA) analysis used data up to the year 2000.
Extreme rainfall projections often rely upon climate model output. For example, Mascioli et al. (2016) found positive trends in winter and spring extreme precipitation over much of the central and eastern United States, and Janssen et al. (2014) found a positive trend in extreme precipitation day frequency in the United States in phase 5 of the Coupled Model Intercomparison Project (CMIP5) simulations. However, precipitation simulations in global climate models have well-known shortcomings arising from coarse model resolution. For example, light precipitation frequency tends to be overestimated while extreme precipitation frequency is usually underestimated, and precipitation seasonality can be challenging to capture (Dai 2006; Mehran et al. 2014; Janssen et al. 2014; Asadieh and Krakauer 2015; van der Wiel et al. 2016). On a global scale, the observed annual maximum daily precipitation has increased faster than in most CMIP5 climate models (Asadieh and Krakauer 2015). Dynamical downscaling using convection-permitting simulations is showing promise in reducing model biases in extreme precipitation (Cannon and Innocenti 2019; Kendon et al. 2023). Alternatively or in addition, statistical downscaling is commonly used, which introduces stationary assumptions regarding the relationship between model-simulated conditions and occurrences of extreme precipitation.
Observation-based studies for the United States have shown a range of trend estimates at various levels of significance for different lengths of data records and aggregation magnitudes, with statistically significant trends found in durations from minutes to a few days (Kunkel et al. 2013) and generally larger trends in the eastern United States than the western United States (Kunkel et al. 2013; Wu 2015; Wright et al. 2019; Kunkel et al. 2020). Janssen et al. (2014) found that the trend in the frequency of extreme precipitation event days in the United States was larger in observations than in CMIP5 models. Station-based approaches find a preponderance of positive trends in the southern and southeastern United States, but relatively few trends attain statistical significance at individual stations (Villarini et al. 2013; Dhakal and Tharu 2018; McKitrick and Christy 2019; Brown et al. 2020). The challenge is that annual 1-day extreme precipitation indices at the local scale exhibit much greater natural variability compared to annual precipitation (Martel et al. 2018).
The variety and uncertainty of results may motivate a reliance upon the basic thermodynamic principle that maximum water content in the atmosphere increases by roughly 7% °C−1 (Clausius–Clapeyron scaling). However, there does not appear to be any Clausius–Clapeyron regime: larger intensities have larger fractional increases than smaller intensities, with no detected plateau in the rate of increase (Pendergrass and Hartmann 2014; Wu 2015; Feng et al. 2019; Giorgi et al. 2019; Martel et al. 2021), and shorter durations likewise have larger fractional increases than longer durations (Kao and Ganguly 2011; Martel et al. 2021; Emmanouil et al. 2022).
For quantification of nonstationarity, observed and modeled trends are complementary. The initial plan for nonstationary IDF analysis for the United States by NOAA contemplates fitting a nonstationary model to the historical record but estimating future trends entirely from (downscaled) climate model output (Perica et al. 2022), which implies that past trends would not inform estimates of future trends. Observed trends are (mostly) real, but they are confounded by natural variability. For historical trend information to usefully inform estimates of future trends, it should be precise enough that uncertainties are not substantially larger than model-based uncertainties, taking all sources of uncertainty into account (Lehner et al. 2020).
One avenue for improvement in observation-based trend estimates is in the specification of the statistical model. All of the studies of observed extreme precipitation trends in the United States discussed above used time as a covariate. But climate change is not linear in time; a better-specified statistical model would represent climate-driven precipitation changes as an appropriate function of climate parameters, and there are many viable candidates for covariates (Ouarda et al. 2019; Roderick et al. 2020; Vinnarasi and Dhanya 2022). Also, seldom considered explicitly is the choice of dependent variable. The thermodynamic expectation based on Clausius–Clapeyron is that a linear rate of climate change (as measured, for example, by magnitude of temperature change) should be associated with an exponential increase in precipitation intensity.
A second avenue for improvement lies in the historical record itself. Climate change has been fastest from the final quarter of the twentieth century to present, with less overall change prior to that. With time as a covariate, historical data prior to 1950 have little value, as it extends the period of record to an interval over which an overall linear temporal trend model would be inappropriate. With a climate-related covariate, it pays to extend the historical record as far back as possible, as it improves the accuracy of the estimation of the baseline from which the nonconstant trend arises.
A third avenue for improvement is in the spatial aggregation of data for climate trends. Spatial aggregation of distribution parameters is common in regional frequency analysis (Hosking and Wallis 1997), and studies of trends in the United States have typically aggregated station-based information over multistate regions. The NOAA plans (Perica et al. 2022) contemplate estimating all parameters, including nonstationary components, over the same spatial footprint. It is not clear how large a spatial footprint is necessary for adequate reduction of trend uncertainty, or whether a larger footprint would mask climate-driven spatial variations in trends.
Recent work on extreme event attribution of Hurricane Harvey’s rainfall illustrates the potential importance of these issues. Risser and Wehner (2017) used historical trends over southeast Texas for the period 1950–2016 and found a best estimate of climate change’s impact on intensity of 24%–38%. In contrast, van Oldenborgh et al. (2017) found changes of 18%–19% for a longer period and for a precipitation metric that ought to be changing more rapidly, not less. Though there are many differences between the methods of the two studies, we find below that a major contributing factor in this discrepancy appears to be the choice of spatial footprint.
This work examines extreme precipitation across the Gulf Coast and southeast coast of the United States with the goal of improving upon existing local extreme precipitation understanding through each of these three avenues for improvement: choice of the statistical model, extended periods of record, and investigation of spatial variability of trends. As a secondary objective, we consider the impact of rainfall events over the past 1–2 decades on stationary and nonstationary return values.
The remainder of this paper is organized as follows: section 2 discusses the data and methods used for the analyses. In particular, the method for extending the period of record is discussed in section 2a, the choice of statistical model is discussed in sections 2c and 2d, and techniques for spatial aggregation are discussed in sections 2b and 2e. Section 3 compares the stationary analysis of our data to the NOAA Atlas 14 IDF values presently in effect (Bonnin et al. 2006; Perica et al. 2013, 2018). The nonstationary results are presented in section 4. An analysis of the impact of recent storms is discussed in section 5. Final conclusions and a brief discussion of future work are given in section 6.
2. Data and methods
a. County composite construction
Daily precipitation data from the period 1890–2019 were acquired from stations located in a geographical area encompassing the Gulf Coast and southeastern coast of the United States, bounded roughly by 26°N, 35°N, 100°W, and 75°W, from the Applied Climate Information System (ACIS) database, which is maintained by NOAA’s regional climate centers. Most of these data have undergone quality control as a part of the Global Historical Climate Network–Daily (GHCN-Daily) database (Menne et al. 2012). Only 1%–2% of values flagged within GHCN-Daily are valid observations that have been flagged erroneously (Menne et al. 2012). Daily data are much more widespread than hourly data and include much longer periods of record, making them well suited for quantifying systematic long-term trends.
Before further assessing the quality of the station data, composite county time series of annual block maximum precipitation were created. The concept and motivation are similar to that of the Threaded Extremes (ThreadEX) dataset for population centers (Owen et al. 2006): to create place-specific records of meteorological extremes with as long a record length as possible. In addition, compositing here is intended to obtain spatially comprehensive independent data with the assumption that stations were within a similar meteorological setting to sample similar statistical precipitation distributions. This assumption should not introduce an overall bias (Keim et al. 2005) because mountainous areas such as western North Carolina and northwestern Arkansas are avoided. Counties have an average size of 1860 km2, which should be a small enough area to prevent any large climatological variations in precipitation distributions between stations. Nonetheless, spurious trends are possible within individual composite time series.
Maximizing the record length is intended to improve the estimation of climate-related trends by anchoring those trends in a longer period of slow change. Among the resulting county composite time series, about half include data prior to 1910. Note that record length is improved at both ends, as the number of long-term climate stations in the Cooperative Observer Network has declined in recent years (Fiebrich 2009; Daly et al. 2021) even as nontraditional measurement networks such as the Community Collaborative Rain, Hail, and Snow (CoCoRaHS) network have proliferated (Reges et al. 2016; Goble et al. 2020). Using counties as the geographical domain for aggregation has the benefit of being easily understood by data users and takes advantage of the tendency of the Cooperative Observer Network to have at least one active observer in each county.
Developing county composites also has the benefit of keeping the number of stations relatively constant through time across space. There was a substantial expansion of the Cooperative Observer Program in the mid-twentieth century, and recent years have seen a large but spatially inhomogeneous increase in observers for the Collaborative Community Rain, Hail, and Snow network. A relatively constant number of stations means that recent years are not overrepresented in the analysis dataset.
Unlike ThreadEX, compositing here is performed objectively and priority is given to long-term stations rather than currently active stations. To create the county composites, stations within a county with no more than 9 missing days for a given year were identified. If only one station met that criterion, then that station’s data were utilized for that year’s block maximum. If more than one station met that criterion, then the station with the longest period of record was used. In cases where no stations met the missing day threshold, that year’s block maximum for the county would be set to missing. County composites were discarded if they had fewer than 30 years of block maxima.
Additional quality control attempted to eliminate any flawed extreme precipitation values that were not caught in the original GHCN-Daily algorithms. Spatial outliers were flagged, original observer forms, radar data, and other nearby reports were checked, and outliers were eliminated if these additional data supported suspicions. Through this quality control process, 37 data points were removed out of a total of 60 flagged points and 66 113 block maxima values overall.
b. Substate pooling
Aggregating precipitation station data yields more signal in trend estimates of extreme rainfall and a better estimate of higher-order moments (Martins and Stedinger 2000; Fischer and Knutti 2016; Kunkel et al. 2020). To take advantage of aggregation while retaining as much spatial structure as possible, counties were pooled together to create substate regions of approximately 10 counties each and 20 000 km2 in area across the entire region of analysis (Fig. 1). More (fewer) counties are contained in a single region in states with smaller (larger) counties, such as Georgia (Texas).
The pooled multicounty regions used in this study.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
Pooled regions were defined subjectively based on the following three constraints or preferences: 1) pooled regions may not cross state boundaries; 2) pooled regions should share similar geographic qualities that may affect extreme precipitation, such as distance from the coast and presence of significant orographic features; and 3) pooled regions should be compact. The state boundary constraint preserves easy interpretation of pooled regions by local stakeholders. The other two considerations were motivated by the assumption that extreme rainfall at all stations within a pooled region ought to be similarly affected by climate change, given that different extreme-rainfall-producing processes (tropical cyclones, mesoscale convective systems, etc.) may respond differently to climate change. Figure 1 depicts the pooled regions across the states used in this study.
c. Stationary and nonstationary statistical model framework
Zero nonstationary parameters: ξ = β0; ln(α) = β1; κ = β2; p instead of ln(p) is used as the dependent variable since the ln() transform is unnecessary with a stationary model.
One nonstationary parameter: ξ = β0 + β1c(t); ln(α) = β2; κ = β3.
Two nonstationary parameters: ξ = β0 + β1c(t); ln(α) = β2 + β3c(t); κ = β4.
Here, p is the annual block maximum precipitation; ξ, α, and κ are the location, scale, and shape parameters; and c(t) is the time-dependent covariate, to be specified below. The model parameters βi were determined through the maximum likelihood estimation (MLE) method rather than L-moments due to its ability to evaluate nonstationary extreme value distributions (Martins and Stedinger 2000). We did not apply a prior constraint on κ (El Adlouni et al. 2007) because we found that the pooled sample sizes were sufficiently large to make such a constraint unnecessary. For analysis of pooled data, statistical fits were performed collectively on all county composite data within each pooled region as a single population.
The Python interface to the climextRemes package (Paciorek et al. 2018) was used to perform the MLE. The initial optimization method was Nelder–Mead; the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method was attempted if Nelder–Mead failed to converge. Failure of both methods was very rare for the county composites and nonexistent for the pooled data. Confidence intervals for return values in any given year are based on 1000-member bootstraps. The 1000 alternative time series are created by drawing with replacement observations from random years, with a given draw including all pooled stations from the same random year to preserve spatial dependencies. The stationary or nonstationary statistical fits are estimated for each alternative time series, and the 95% confidence interval is the width that encompasses 95% of the fits.
The data used in this analysis correspond to once-daily observations of accumulated precipitation. This timing constraint leads to lower 1-day precipitation maxima in general than what would be observed if the 24-h period were allowed to start at an optimal time of day. To correct for this, following Perica et al. (2018), the daily totals are multiplied by 1.11 prior to return period analysis.
d. Selection of model order and covariate for composite and pooled data
In their simplest form, models of nonstationarity assume some sort of linear relationship with time. However, the climate has historically not changed at a constant rate, and the statistical model should use a time-dependent covariate that reflects physical understanding of the magnitude of the climate change effect over time. As a driver of nonstationarity, the change in water vapor holding capacity in the atmosphere, or the thermodynamic response, has been predicted to be the main driver of changes in extreme precipitation in the northern mid- to high latitudes (Pfahl et al. 2017). As such, temperature is a logical choice. But which temperature? The temperature most closely related to extreme precipitation intensity is the temperature of the free troposphere at the time the extreme precipitation is taking place. This is imperfectly linked to coincident surface temperature and even more poorly linked to seasonal or annual average local surface temperature.
Local or regional temperatures are affected by a variety of climate modes and phenomena, each of which may have a different influence on extreme precipitation. Phenomena known to affect temperature and precipitation in the region include land–atmosphere coupling (Hoerling et al. 2013; Santanello et al. 2013), El Niño and Atlantic multidecadal variability (McCabe et al. 2004), and Gulf of Mexico temperatures (Groisman et al. 2012). Choosing a temperature covariate that is affected by other modes means that part of the resulting diagnosed relationship will be associated with weather patterns driven by that mode of variability rather than by climate change (Westra et al. 2013).
These considerations make global mean surface temperature (GMST) a practical proxy option for a covariate (Westra et al. 2013; O’Gorman 2015; Pendergrass et al. 2015; Sanderson et al. 2019; Sun et al. 2021), especially for single-day or longer accumulations (Vinnarasi and Dhanya 2022). Here, we test CMIP5-simulated GMST, using historical plus RCP8.5 CMIP5 simulation output (one member per model) from the Koninklijk Nederlands Meteorologisch Instituut (KNMI) Climate Explorer. The RCP8.5 projections apply to less than a decade of the historical observation period, and over that time, all scenarios have similar mean global temperatures, so the choice of scenario is here based on the largest available number of simulations. We choose CMIP5 over CMIP6 because several CMIP6 models seem to have unrealistic amplitudes of GMST change (Zelinka et al. 2020; Hausfather et al. 2022). Of local relevance, van der Wiel et al. (2017) tested both Gulf of Mexico sea surface temperature and GMST as covariates for extreme precipitation along the Gulf Coast; both showed similar sensitivities, but uncertainty was greater with Gulf of Mexico sea surface temperature due to the noisier temperature record.
CO2 forcing can be used as another covariate (Risser and Wehner 2017); changes in the natural log of atmospheric CO2 concentrations are approximately proportional to forcing changes associated with CO2 (Myhre et al. 1998). Using CO2 forcing avoids long-term natural variability and the GMST fluctuations associated with volcanic eruptions, which will affect precipitation differently from greenhouse gases or even climate change (Mascioli et al. 2016), but it is less directly associated with extreme precipitation changes. Total forcing is a possible alternative, but aerosol forcing is likely to have a qualitatively different effect on precipitation than greenhouse gas forcing (Lin et al. 2016), and the proportional influences are expected to change in the future in favor of greenhouse gas forcing.
A covariate more directly related to moisture, such as dewpoint temperature or precipitable water, may be even better than temperature (Roderick et al. 2020; Kunkel et al. 2020; Kim et al. 2022). However, the same local versus global issues arise as with GMST, and global-scale surface temperature analyses are available for a much longer period of record for model validation than dewpoint or precipitable water.
To further inform the choice of statistical model and covariate, we apply the Akaike information criterion (AIC) and Bayes information criterion (BIC) to models with year, CMIP5 GMST, and ln(CO2) as covariates. Both metrics evaluate the trade-off between goodness of fit and number of parameters, with a larger number of model parameters risking overfitting. BIC penalizes the number of parameters to a greater extent than AIC. For both, lower numbers are more desirable. Differences between models are more relevant than absolute magnitudes, so for each population and dependent variable, we subtract the corresponding stationary model value. Negative values for a nonstationary model imply that it is better than a stationary model at representing the data. We average AIC and BIC values across all composite stations or pooled regions. The results are shown in Table 1.
Information criterion analysis, multiple covariates. AIC and BIC differences relative to stationary model fits, according to dependent variable (block maximum precipitation or logarithm of block maximum precipitation) and population. Comp. = county composite stations. DV = dependent variable. GMST = modeled global mean surface temperature derived from historical climate model ensembles. Year, GMST, and ln(CO2) are the candidate covariates. The scores for the chosen models are bolded.
For all populations and criteria, nonstationary models of the logarithm of precipitation provide a greater improvement over the stationary case than nonstationary models of precipitation itself, consistent with our expectation based on the Clausius–Clapeyron relationship between extreme precipitation and climate change. For the county composites, models with a nonstationary location parameter are equivalent to a stationary model according to AIC but are less appropriate according to BIC. For the pooled regions, both nonstationary location and scale parameters are a more suitable model choice than one with a nonstationary location parameter alone according to AIC, while for BIC, a nonstationary scale parameter is not worth the extra degree of freedom. In all cases, the three covariates are roughly equivalent, with a slight preference for ln(CO2). With little objective reason to choose a particular covariate, we prefer CMIP5 GMST because it is a more comprehensive measure of climate change than CO2 concentration alone, because it, like CO2, is physically connected to extreme precipitation changes, and because it is directly amenable to future projections through the use of global warming levels (Hausfather et al. 2022).
We next compare CMIP5 GMST to observed GMST from Berkeley Earth (Rohde and Hausfather 2020). The goodness of fit is much better with Berkeley Earth than with CMIP5. However, Berkeley Earth conflates climate change and natural variability, which affect extreme precipitation in different ways. We hypothesize that the better fit with observed GMST lies in the strong correlations between El Niño and GMST and between El Niño and southern U.S. precipitation, in which case El Niño would be a confounder. To minimize the influence of this potentially confounding factor while preserving any direct climate change signal, we also test smoothed observed GMST (Philip et al. 2020). Table 2 shows that there is essentially no difference in fit between smoothed observed GMST and CMIP5 GMST, lending support to our hypothesis. Because CMIP5 GMST can be readily extrapolated through climate model projections, we use CMIP5 GMST rather than smoothed Berkeley Earth GMST in the analyses that follow.
Information criterion analysis, GMST. AIC and BIC differences relative to stationary model fits, according to the version of global mean surface temperature (GMST) used as a covariate. Comp. = county composite stations; DV = dependent variable. The scores for chosen models are bolded.
Based on these considerations, the models chosen for the nonstationary analysis were as follows:
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A GEV fit to the logarithm of precipitation with the location parameter covarying with the CMIP5 mean model surface temperatures for county composites.
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A GEV fit to the logarithm of precipitation with the location and scale parameters covarying with the CMIP5 mean model surface temperatures for pooled regions.
Based on the AIC and BIC results, the county composite trends may have considerable statistical noise. The pooled region trends should be more statistically constrained at shorter return periods but may be more noisy for the longer return periods at the tail of the GEV distribution where the scale parameter has greater influence.
e. Representation of trend magnitudes
An example of a set of pooled block maxima and their stationary and nonstationary fits is shown in Fig. 2. The pooled region shown is North Carolina Region 4, along the southern North Carolina coast. This region experienced one of the largest historical trends of any region analyzed. The fits are represented as the expected 2- and 100-yr return values (annual exceedance probability of 0.5 and 0.01, respectively), along with 95% confidence intervals based on 1000 bootstrap samples. A second example (Fig. 3) shows a region (Alabama Region 4) that has experienced a negative trend in 100-yr return values, although its 2-yr return value trend is slightly positive. The dips and wiggles in both nonstationary fits are mostly due to the effect of volcanic activity on the covariate, GMST.
Pooled annual 24-h block maxima for the southeast North Carolina pooled region, scaled by 1.11 to adjust for constrained daily time of observation (Perica et al. 2018), along with stationary GEV estimate of the 100-yr return value (yellow) and nonstationary estimates of the 2-yr return value (blue) and 100-yr return value (reddish-brown). Shading represents 95% confidence intervals. Large dots correspond to reference values for quantifying the magnitude of the trend; see text for details.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
As in Fig. 2, but for the west-central Alabama pooled region.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
The extreme rainfall nonstationarity is quantified as the percent change in expected precipitation return values between 1980 and 2020. In Figs. 2 and 3, this corresponds to the difference in value of the two dark red dots. Over this period, climate change was roughly linear, so this period is useful for temporal characterization of the modeled ongoing trend. In addition, the year 1980 corresponds to the average year across all pooled regions in which the nonstationary return values equal the results of a stationary analysis using the same dataset. So this metric can also be interpreted as the difference between present-day (2020) stationary and nonstationary values. In other words, in this analysis, the stationary estimates of extreme rainfall apply to the climate as it existed several decades ago (Wright et al. 2019; Vu and Mishra 2019). Note that this result is also dependent on the period of record of the data; a stationary analysis relying mostly on more recent data would be less dated but would still lag the actual climate. Because the difference in CMIP5 GMST between 1980 and 2020 is 0.85 K, these 1980–2020 differences can be directly converted to a rate of change per degree of global warming by multiplying by 1/0.85 = 1.17.
f. Gaussian process model and representation of uncertainty
Because the pooled trends still exhibit considerable spatial noise regarding trend magnitudes and even signs, we use an additional statistical model (a spatial Gaussian process model) to the pooled trends themselves rather than to the precipitation data. This enables to obtain a larger-scale aggregated estimate of the extreme precipitation trends across the region, including statistical uncertainty. To apply a Gaussian process model, the individual pooled region trends are assigned to the geographical centroids of each region and projected onto a Lambert conic conformal projection with reference latitudes at 33° and 45°N. The Gaussian process model takes into account spatial covariance of the trend estimates at the pooled regions, which is present in part because block maxima in neighboring pooled regions are generated by some of the same extreme weather events. Though the model produces a complete spatial pattern of trends, we are concerned only with the mean trend and its uncertainty. We report 95% confidence intervals for the domain-wide and subdomain aggregated trends. The Gaussian process model estimation is carried out using the “likfit” function in the geoR package in R, with the Matern covariance model and default parameter settings except without a fixed kappa. A Gaussian process model assumes that each data point is the product of a stochastic process with normally distributed output and covariance with neighboring points a function of spatial separation. The pooled trend data appear consistent with that assumption except for two exceptionally large trends in North Carolina; it is not known whether this represents a violation of the Gaussian assumption or reflects an underlying uptick in climate change effects there.
For the most part, we do not report statistical uncertainties for the composite or pooled region fits. This is because we think it is more useful to view the local trends as representations of the observed effect of the combination of climate change and natural variability. We do not think it is meaningful to single out those local trends that are statistically significant. That subset will tend to be at locations where natural variability and climate change both produced a same-signed trend, thereby yielding a biased estimate of the climate change trend. Instead, we use the spatial Gaussian process model to further aggregate across natural variability and produce a more representative estimate of the underlying trend, with associated 95% confidence intervals.
3. Stationary analysis and comparison with NOAA Atlas 14
To benchmark the methods described here, a stationary GEV analysis was performed to compare with the NOAA Atlas 14 analyses. Return values were first calculated from the block maxima in the county composites for 2- and 100-yr return periods.
The 2- and 100-yr composite stationary 1-day duration return values are plotted in Fig. 4. Higher return values exist along the immediate Gulf Coast. The 2-yr return values are spatially more coherent than the 100-yr return values. This reflects the fact that return values toward the middle of the cumulative GEV distribution are more robust than those at the tails. Pooling by region is sufficient to produce spatially coherent return value estimates even at the longer return periods using these methods, which is apparent in the systematic reduction in return values with distance inland (Fig. 5). Locally higher return values in northwestern South Carolina, northern Georgia, and south-central Texas are apparently the result of topographic effects in those areas from the southern Appalachians and the Edwards Plateau.
County composite 1-day rainfall amounts (in. and mm) from the quality-controlled full dataset under a stationary model for (a) a 2-yr return period and (b) a 100-yr return period. Counties with a gray “x” had fewer than 30 years of block maxima available.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
Pooled area 1-day rainfall amounts (in. and mm) from the quality-controlled full dataset under a stationary model for (a) a 2-yr return period and (b) a 100-yr return period.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
Overall, the stationary return value pattern calculated using the methods outlined here appears to be consistent with the prior stationary estimates of NOAA Atlas 14 (Fig. 6), with similar spatial variations of return values with distance from the coast. Differences may arise with NOAA Atlas 14 for three reasons. First, different methods of GEV estimation and aggregation are employed. Second, different but largely overlapping sets of stations are utilized, although our analysis creates county composites rather than retaining stations individually. Our analysis was designed to optimize the nonstationary analyses shown below, while the NOAA Atlas 14 analysis is designed to perform well under an assumption of stationarity. Third, our county composite input data will tend to have data more evenly distributed across the decades than the NOAA Atlas 14 analyses, whose underlying data include many stations that began operation in the 1940s and 1950s. One consequence of this last difference is that, in the presence of an upward trend of observed extreme precipitation, our stationary analysis should produce smaller return values than NOAA Atlas 14.
Averaged area 1-day rainfall amounts (in. and mm) from the NOAA Atlas 14 Volume 2 (North and South Carolina), Volume 9 (Alabama, Arkansas, Georgia, Louisiana, Florida, and Mississippi), and Volume 11 (Texas) datasets under a stationary model for (a) a 2-yr return period and (b) a 100-yr return period. Data end years for each volume were 2000, 2011, and 2019, respectively.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
For a more direct comparison with NOAA Atlas 14 stationary estimates, Fig. 7 shows the differences between NOAA Atlas 14 and our own stationary analyses, with our analyses using data truncated in the same year as the corresponding NOAA Atlas 14 analysis. For North and South Carolina, the latest data are from 2000; for Texas, the latest data are from 2017; and for all other states, the latest data are from 2011. The predominantly negative values in Fig. 7 are consistent with the expectation of smaller return values from our analysis; typical differences are around 3%–5%, with greater variability in the differences with the larger return period (Fig. 7b). The largest differences between the stationary estimates occur in southeast Florida where our return values are much larger than those of NOAA Atlas 14; we speculate that this is caused by the strong near-coast gradient in extreme precipitation frequency (Perica et al. 2013). Our analysis uses primarily the stations with the longest period of record, which in southern Florida tend to be concentrated along the coast.
Percentage difference in pooled region 1-day rainfall amounts between our calculated stationary return values and the NOAA Atlas 14 values shown in Fig. 5 for (a) a 2-yr return period and (b) a 100-yr return period. The comparison is made between analyses with the same data time cutoffs as mentioned in Fig. 6; e.g., the North Carolina and South Carolina differences reflect the differences between our calculated return values using the dataset cutoff in 2000 and the NOAA Atlas 14 Volume 2 values which also used data through 2000.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
4. Nonstationary analysis
The nonstationary analysis of block maxima rainfall, as described in section 2, allowed for an examination of the trends in extreme rainfall across the area of study. Figure 8 depicts the 100-yr county composite trend patterns. Because only the location parameter is nonstationary for the county composite analysis, the 2- and 100-yr trends are identical when expressed as a percentage difference. The trends vary from ∼−30% to ∼+70% across the area of study. Larger positive trends are found across Louisiana, Mississippi, East Texas, and coastal North Carolina. However, there are also numerous county composites with negative trends throughout this area. Georgia, for example, reflects this juxtaposition well with several negative trends interspersed among positive trends; record lengths can be much shorter in Georgia due to the smaller county sizes from which to draw composites from individual stations, which can leave more noise in the trend estimates. We interpret the county-to-county trend noise in general as being due to the limited number of samples of extreme precipitation events in each county.
Percentage changes in nonstationary composite station estimates of expected 1-day return values between 1980 and 2020 for the 100-yr return period.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
Coherent spatial patterns within 1-day duration trends across the area of study become more apparent in the pooled regions. Pooled trends for the 2- and 100-yr 1-day duration precipitation return values are shown in Fig. 9. The trends for the 2-yr return period show less spatial variability than the 100-yr return period trends because they are less affected by event outliers. However, both figures show large intensity increases in East Texas and Louisiana as well as North Carolina and little to no increase in southern Texas, southern Florida, and parts of Alabama, Georgia, and South Carolina.
Percentage changes in nonstationary pooled station estimates of expected 1-day return values between 1980 and 2020 for (a) a 2-yr return period and (b) a 100-yr return period.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
These pooled trends are real in the sense that they reflect the historical record of extreme precipitation throughout the area. A few of the largest trends are even statistically significant at the 95% confidence level. However, more relevant to society is whether these trends should be expected to continue into the future. Although a formal attribution analysis (e.g., Kirchmeier-Young and Zhang 2020; Huang et al. 2021) is beyond the scope of this paper, we consider two issues: whether the overall intensification trend should be expected to continue and whether the spatial pattern of trends should be expected to continue.
To address the first question, we apply a spatial Gaussian process model (GPM) to the pooled trends shown in Fig. 9, assigning each pooled trend to the center of its region for the purpose of spatial statistical analysis. The resulting estimates of the mean trends are shown in Fig. 10. Focusing for now on the trends using data through 2019, both the 2- and 100-yr return value trends are statistically significant at the 95% confidence level, with magnitudes of about 9% (3%–15%) for 2-yr return values and 16% (4%–28%) for 100-yr return values, meaning that a trend is detected at this spatial scale. More importantly, these trend magnitudes are consistent with both physics-based and model-based estimates of the expected rate of intensification of extreme precipitation. On a much larger regional scale, Kirchmeier-Young and Zhang (2020) attributed a similar magnitude trend to anthropogenic influences, so we conclude that this observed overall trend is predominantly a manifestation of anthropogenic climate change and thus should be expected to continue.
Mean trend estimates and their respective 95% confidence intervals using all pooled trends, the Gulf Coast pooled trends, and the southeast pooled trends. Colors for the mean trend and confidence interval markers correspond to the different ending years of each subset dataset.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
A trend is detectable over even smaller areas. The GPM analysis is repeated for only Gulf Coast states (Texas, Arkansas, Louisiana, Mississippi, Alabama, and western Florida) and only southeast states (Georgia, South Carolina, and North Carolina). Results are also shown in Fig. 10. The Gulf Coast area is large enough (and spatial variability small enough) that the extreme precipitation trend is detectable over this smaller region, but a trend is not detectable at the 95% confidence interval over the southeastern United States. Of course, this does not mean that no trend is present; the observed subregion trend is compatible with the study region trend estimate.
As for the regional variations, we have but one realization of the climate record, and it is difficult to tell from observations alone whether the trend patterns seen in Fig. 9 are forced or free. However, large climate model ensembles, whether multimodel or single model, consistently fail to produce large spatial variations of extreme precipitation trends in the southern or southeastern United States (Lopez-Cantu et al. 2020; Coelho et al. 2022). It therefore seems likely that the observed large spatial variations in extreme rainfall trends are due to natural variability, including weather randomness, rather than being forced by climate change, so that the spatial pattern of the trends should not be expected to continue.
5. Impact of recent storms
The larger trends in Fig. 9 appear to coincide with the locations of recent notable extreme precipitation events such as Hurricane Harvey and Hurricane Florence (Martinaitis et al. 2021). To assess the extent to which recent weather events have impacted the stationary and trend estimates of extreme precipitation since NOAA Atlas 14, we truncate our rainfall data at 2000 (the Atlas 14 data cutoff for North and South Carolina) and 2011 (the Atlas 14 data cutoff for most of the rest of the study area) and repeat our analyses. Differences between the stationary return value estimates from the data through 2011 and 2019 for 100-yr return values of 1-day duration precipitation are shown in Fig. 11a. Notably, in the pooled estimates, there are several regions with positive differences (2019 values are higher when there is a positive difference). Locations in southeastern Texas and the coasts of the Carolinas specifically highlight the potential influence of recent storms such as Hurricane Harvey and Hurricane Florence that have impacted these regions. From Arkansas to Florida, which for the most part avoided exceptional widespread rainfall during the past decade, differences are generally small.
Differences in pooled region stationary estimates of 1-day 100-yr return values (in. and mm) from (a) datasets ending in 2011 and 2019 and (b) datasets ending in 2000 and 2019.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
With the data record truncated to 2000, the differences between the stationary estimates are magnified (Fig. 11b). Some more negative differences (2019 values are lower) are apparent with this shorter dataset. In eastern portions of North and South Carolina, the inclusion of data after the local NOAA Atlas 14 analysis increases the return value of the 100-yr amount by 1–1.5 in. (20–40 mm). Amplified differences even in the stationary return values emphasize the importance of updating extreme precipitation estimates for planners.
Recent storms influence the trends in the nonstationary extreme precipitation as well. Figure 12 displays the percentage changes between the trend estimates from data ending in different years. Impacts from the recent events have similar signs between the trends and stationary estimates, as expected. The 100-yr return period or smaller spatial scale precipitation estimates specifically are much more influenced by event outliers as they affect the tails of the probability distribution more than the center of the distribution.
Percentage differences in nonstationary trend estimates of 1-day 100-yr return values using data ending in (a) 2011 and 2019 and (b) 2000 and 2019.
Citation: Journal of Hydrometeorology 25, 5; 10.1175/JHM-D-22-0157.1
Larger differences in the trends exist between the full dataset and the dataset that ends in 2000. The much smaller extreme precipitation trend in eastern North Carolina with the full dataset than with data ending in 2000 is apparently a reflection of the influence on trend analysis of heavy rainfall near the end of the twentieth century such as Hurricane Floyd. Nonstationary trend estimates, as well as the stationary estimates discussed earlier in this section, can be vastly different when using shorter periods of record. Nonetheless, region-wide trends for the most part continue to be detectable even with the shorter periods (Fig. 10).
6. Discussion and conclusions
To our knowledge, this is the first study to quantify nonstationary historic 1% return frequency 1-day precipitation trends with their confidence intervals along the Gulf Coast and southeastern coast. The 100-yr return value change from 1980 to 2020 was 16% ± 12% (95% confidence interval) aggregated over the entire study region and 12% ± 8% across the Gulf Coast region specifically. The estimated trend in the smaller southeastern region was larger but not statistically significant. These changes correspond to a rate of increase of 19% ± 14% K−1 for the study region and 14% ± 10% K−1 for the Gulf Coast. Changes in the less extreme 2-yr return values were smaller: 11% ± 7% K−1 for the study region and 9% ± 8% K−1 for the Gulf Coast. The ability to translate historic trends into future projections provides a valuable complement to model-based projections of future precipitation intensity.
The positive trends across the Gulf Coast and southeastern coast of the United States do broadly align with prior studies, even studies that aggregated stations to a larger level. Kunkel et al. (2020) estimated a 4% per decade trend in 2-yr 1-day return values in the southeastern United States. Wu (2015) found a 30-yr change of about 8% in the 100-yr 1-day return values over a similar area. Sun et al. (2021) found statistically significant numbers of stations with annual maximum precipitation increases in central and eastern North America but did not estimate the aggregated trends. Likewise, Villarini et al. (2013) identified the presence of trends but did not compute the magnitude of those trends. Wright et al. (2019) identified trends in regional numbers of design value exceedances but did not translate these into extreme precipitation amount trend values.
The specific pattern of trends also sheds some light onto apparently conflicting prior studies. For example, McKitrick and Christy (2019) analyzed very long period-of-record data for a handful of stations in the southeastern United States and found that positive trends for extreme precipitation were only found at some stations and a region-wide positive trend depended on extreme precipitation in 2015–17. The majority of these stations happen to be located in those parts of Mississippi, Alabama, Georgia, and northern Florida where the historic trends are relatively weak and nonexistent (Fig. 9), and none of them are in the parts of Texas, Louisiana, and North Carolina with the largest trends. Conversely, the large trend in extreme precipitation in southeast Texas found by Risser and Wehner (2017) in their analysis of Hurricane Harvey and the analysis by Fagnant et al. (2020) over an even smaller region around Houston were both focused on a subregion of the Gulf Coast with a particularly large historical trend. Our expectation is that the large trend there is due in part to natural variability and should not be expected to continue at a similar rate in the future.
The analyses also illustrate two shortcomings in conventional extreme precipitation analyses. First, stationary analyses from two decades ago for North and South Carolina underestimate the stationary risk that would be assessed by including more recent data, including recent landfalling hurricanes. Second, any stationary analysis is an underestimate of the present-day extreme precipitation risk, let alone the future extreme precipitation risk, no matter how up-to-date the data.
Future work can improve upon and add to the insights gleaned from this study. Given the large inland decrease of precipitation, there may be value in aggregating the pooled areas into coastal, near-coastal, and inland regions to compare how the extreme rainfall trends and associated patterns change spatially. It may also be worth considering the seasonality of these trends, i.e., determining the trend estimates for spring, summer, fall, and winter. Differences in trends between seasons could potentially provide information on the drivers of these trends. It would be useful to know whether an index storm approach has a significant effect on the pooled region statistics and trends, including local confidence intervals, and whether the methods employed here to produce long data records are optimal or produce significantly improved trend estimates at the local level. Also, it may be beneficial to include additional covariates for phenomena such as El Niño so that the statistical model captures major causes of variability and better represents the overall extreme precipitation time series. This would come at the cost of additional model complexity, though, and exploring that option is beyond the scope of this paper. Finally, much of the extreme precipitation along the southern and southeastern coasts derive from landfalling tropical cyclones, whose precipitation has different spatiotemporal statistical characteristics than other extreme rainfall events. Extreme precipitation separately from tropical cyclones may have benefits not just for stationary characterization (Miniussi et al. 2020) but for nonstationary analysis and projection.
Similar nonstationary extreme rainfall analysis approaches could be applied elsewhere. However, additional care would need to be taken in areas of complex topography in creating composite stations and pooled regions because of large differences in precipitation climatology over relatively small areas. In addition, the Gaussian process model for aggregating trend estimates geographically might need additional spatial covariates that would allow for how climate-driven extreme rainfall trends may depend on topographic slope angle and storm type.
Acknowledgments.
This research was funded in part by the Harris County Flood Control District and by the National Oceanic and Atmospheric Administration under Contract 1332KP21FNEEN0010. We thank Mikyoung Jun and Lingling Chen for helpful statistical discussion and code for the Gaussian process modeling.
Data availability statement.
The quality-controlled 1-day block maxima rainfall data for the county composites in each pooled region referenced in this study can be found at https://dataverse.tdl.org/dataset.xhtml?persistentId=doi:10.18738/T8/GP4SPQ. The stationary and nonstationary return values from the GEV models for each county composite and pooled region can also be found at https://dataverse.tdl.org/dataset.xhtml?persistentId=doi:10.18738/T8/0ESMAS. These datasets are contained within the Texas A&M University Dataverse Repository under the larger Texas Data Repository. Analysis software is available from the corresponding author upon request.
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