This report documents the development of projected DDF curves for precipitation for the State of Florida, for the periods 2020–59 and 2050–89. Hereinafter, precipitation will be implied when referring to DDF curves. As part of this study, an ensemble method was used to determine median change factors for precipitation depths as well as intermodel variability at locations throughout Florida. Change factors were determined for durations of 1, 3, and 7 days, and return periods of 5, 10, 25, 50, 100, 200, and 500 years. The 7-day duration was included to capture potential future changes in precipitation at the multiday timescale, such as high precipitation caused by stalling storms. Change factors were computed from DDF curves fit to precipitation data from six downscaled climate datasets for two 40-year periods representing future projected climate for the periods 2020–59 (centered on 2040) or 2050–89 (centered on 2070), and historical (retrospective) climate for 1966–2005 for the study area. Change factors were derived from four datasets that downscale models from the Coupled Model Intercomparison Project Phase 5 (CMIP5; Taylor and others, 2012):

Change factors were also derived from two datasets that downscale models from the Coupled Model Intercomparison Project Phase 6 (CMIP6; Eyring and others, 2016):

The CMIP6 historical simulations end in 2014; however, the common historical period 1966–2005 was used as the reference period for change factor computation for both CMIP5 and CMIP6 downscaled climate datasets. In summary, a total of six downscaled datasets (CORDEX, LOCA, MACA, JupiterWRF, LOCA2, and NEX-GDDP) were used to compute change factors.

Perica and others (2013) derived historical DDF curves from historical observations at meteorological stations in Florida, which are published in NOAA Atlas 14. The DDF curves based on partial-duration series (PDS) from NOAA can be multiplied by the change factors derived in this study to determine potential future extreme precipitation depths for events of a given duration and return period for time periods centered on 2040 and 2070.

In describing our processing and analysis, the definitions of several terms are important to clarify. In this report, the term “reanalysis” is used to refer to dynamical climate model simulations that are based on observed boundary conditions and are meant to match observed weather as precisely as possible. General circulation models (GCMs) broadly refer to global-scale dynamical climate models that are coupled atmosphere-ocean general circulation models or Earth systems models, such as used in CMIP5 and CMIP6 studies. The term “historical observations” is used to refer to weather observations used in statistical downscaling. The term “historical simulations” is used to refer to GCM and associated downscaled models that are tuned to preindustrial conditions (around 1850 or 1750 depending on reference; see Schurer and others, 2017, for a discussion) and possibly to more recent historical conditions (Mauritsen and others, 2012; Hourdin and others, 2017) but are otherwise not constrained to precisely match daily weather conditions from 1850 to the present. The term “future projections” refers to those by GCMs and associated downscaled models of future climate that assume a specific GHG emission scenario or concentration trajectory.

Three observational precipitation datasets were used in this study to define a baseline for historical conditions for comparing DDF curves fitted to precipitation output from downscaled climate datasets for the historical period and for evaluating the performance of climate models in reproducing historical climate extreme indices. The observational datasets include NOAA Atlas 14 (Perica and others, 2013), which provides data at the location of weather stations, and datasets that interpolate weather-station observations to grid points: the Parameter-elevation Regressions on Independent Slopes Model (PRISM; Daly and others, 2008, 2021) and the SFWMD’s Precipitation “Super-grid” (SFWMD, 2005).

Various efforts to downscale global climate predictions to local and regional scales have been initiated by climate research groups in the United States and abroad. In this study, historical and future projections of precipitation based on statistical, dynamical, and hybrid downscaling of GCMs were used to develop future DDF curves for Florida. The GCMs were developed as part of the World Climate Research Programme’s CMIP5 and CMIP6. The CMIP5 model data are a concatenation of historical (retrospective) GCM simulations covering the period 1850–2005 and future projections for the period 2006–2100 (Lawrence Livermore National Laboratory, 2022a). The CMIP6 historical simulation period is 1950–2014, and future projections encompass the period 2015–2100 (Lawrence Livermore National Laboratory, 2022b). Taylor and others (2012) provide an overview of the CMIP5 experimental design and Eyring and others (2016) for CMIP6. Notably, the historical CMIP5 and CMIP6 model simulations are not intended to reproduce the precise sequence of historical climate variability. GCMs are often run starting with different initial conditions to create an ensemble of possible trajectories for the historical and future climates that may result because of changes in natural variability (unforced or internal variability, also called climate noise in Taylor and others, 2012). The use of ensembles helps separate the climate change “signal” from the climate noise. Often, only one ensemble member is used for downscaling, which limits the range of events that are downscaled. Table 2 lists the number of ensemble members downscaled by each downscaled climate dataset by emission scenario. The particular ensemble members downscaled for each GCM by each of the downscaled climate datasets used in this study are listed in the data release associated with this report (Irizarry-Ortiz and Haider, 2023).

The CMIP5 future projections are based on four different representative concentration pathways (RCPs) corresponding to low (RCP2.6), medium-low (RCP4.5), medium-high (RCP6.0), and high (RCP8.5) year 2100 total radiative forcing values with respect to the preindustrial period (circa 1750; Intergovernmental Panel on Climate Change [IPCC], 2013; van Vuuren and others, 2011). The number next to the RCP label indicates the approximate increase in total radiative forcing at the end of the century (2100), in watts per meter squared, caused by GHG emissions. RCP2.6 represents a scenario of stringent climate policies to reduce GHG emissions, and the radiative forcing increase at 2100 from GHG emissions is 2.6 watts per meter squared. RCPs with higher numbers are the result of higher emissions and result in larger changes in global temperatures. RCP8.5 represents future conditions that could result from limited or no climate change mitigation, is a worst-case scenario (Hausfather and Peters, 2020), and is considered low likelihood by the IPCC (2021a); the two middle scenarios are roughly equally spaced between the low and high scenarios (Terando and others, 2020). Similar to the historical simulations, the CMIP5 future projections are also not intended to simulate the precise sequence of actual future variations in climate and may not capture the exact timing of future shifts in natural cycles. Terando and others (2020) recommend that, whenever feasible, the entire range of RCP-based scenarios be considered when assessing potential future effects; however, the choice of scenarios is limited by their availability in downscaled climate datasets. For CMIP5, only RCP4.5 and RCP8.5 are available in most downscaled climate datasets.

The CMIP6 projection scenarios are described by Eyring and others (2016) and Riahi and others (2017) and are based on the concept of shared socioeconomic pathways (SSPs), which have been developed by the energy modeling community. Updated versions of the four CMIP5 RCP scenarios are available in CMIP6 and are called SSP1-2.6, SSP2-4.5, SSP4-6.0, and SSP5-8.5, with each of these having a similar change in 2100 radiative forcing levels as their CMIP5 RCP counterparts and representing low, medium-low, medium, and high emissions scenarios, respectively. The first number next to the SSP label indicates different levels of challenges to mitigation and adaptation resulting from different potential future socioeconomic trends, as described by Riahi and others (2017), and the number after the dash indicates the approximate increase in total radiative forcing at the end of the century (2100), in watts per meter squared, caused by GHG emissions. Despite the 2100 radiative forcing being similar between a CMIP6 SSP scenario and its CMIP5 RCP counterpart, the pathways of emissions, GHG mix, and land uses vary over time between the RCP and corresponding SSP scenario. Figure 1.28 of the IPCC’s sixth assessment report (IPCC, 2021a) shows a comparison of the range of fossil fuel and industrial carbon dioxide (CO₂) emissions across IPCC assessments that include the RCP and SSP scenarios.

Effective radiative forcing at the end of the 21st century is slightly higher in the CMIP6 SSP than in the equivalently named CMIP5 RCP scenario (fig. 3 of Fredriksen and others, 2023). The IPCC (2023, p. 9) states with medium confidence that “the overall radiative forcing tends to be higher for the SSPs compared to the RCPs with the same level.” For this reason, results from CMIP5 and CMIP6 may not be directly comparable. The use of different GCMs or different versions of GCM models in the two CMIPs also precludes a direct comparison. CMIP6 also includes four additional SSPs representing intermediate levels of forcing between the four original scenarios such as the medium-to-high scenario SSP3-7.0. The CMIP6 model data are a concatenation of historical (retrospective) GCM simulations covering the period 1850–2014 and future projections for the period from 2015 to at least 2100. A description of the GCMs downscaled by the different downscaled climate datasets evaluated in this study can be found in the data release associated with this report (Irizarry-Ortiz and Haider, 2023).

Many GCMs are unable to simulate extremes well because of their coarse spatial resolution and their inability to capture subgrid-scale physics (Misra and others, 2011). Statistical and dynamical downscaling are two methods used to generate high-resolution (about 50-km grid spacing or less) climate projections based on coarse-resolution fields simulated by GCMs. In statistical downscaling, coarse-resolution fields (typically about 100-km grid spacing or greater) simulated by GCMs are used as predictors of high-resolution meteorological variables (Wilby and Wigley, 1997; Wilby and others, 1998). Historical observations are used to train and bias-correct the statistical-downscaling methods. Such methods are largely empirical and are based on the inherent assumption that the methods will perform equally well in the future as in the historical training period (Nover and others, 2016). In dynamical downscaling, a regional climate model (RCM) is forced by coarse-resolution boundary and initial conditions from a coarse-resolution GCM. Like a GCM, an RCM solves the physical equations, but over a limited area and discretized at finer temporal and spatial resolutions than the source GCM output. This method results in more physically based downscaling than that of statistical methods. Dynamical downscaling is more time and computer-resource-intensive than statistical downscaling, however, so RCM resolutions on the order of tens of kilometers are typically used to downscale long-term simulations. Because of modeling limitations, output from RCMs is also often bias-corrected to observations. Lastly, hybrid approaches that combine features of statistical and dynamical downscaling have been developed. These approaches combine the ability of dynamical techniques to capture the physics of the precipitation process with a reduction in computational requirements for downscaling a single or multiple GCMs (see, for example, Walton and others, 2015; Madaus and others, 2020). Irizarry-Ortiz and others (2022) discuss downscaling methods in more detail.

Extreme value theory (EVT) is a branch of statistics that deals with the stochastic behavior of extreme and rare events found in the tails of probability distributions and includes events that are unusually large or small. The extreme events modeled in EVT are beyond the central tendency and most frequent range of variation of the variable at hand and include the estimation of events that are more extreme than any that have already been observed (Coles, 2001). The probability of occurrence of a climate or weather variable can be described by a probability distribution function. The upper tail of the probability distribution, representing the larger values of extreme precipitation, might change under future conditions. EVT provides a class of models that make it possible to extrapolate from observed or modeled extremes to unobserved or unmodeled extremes (Coles, 2001).

EVT has developed under two main approaches. In the classical block maxima (or minima) approach (Fisher and Tippett, 1928; Jenkinson, 1955; Coles, 2001), the probability distribution of maxima (minima) over a given block of time, typically a year, is modeled. This is herein referred to as the “annual maxima approach.” The second approach, called peaks-over-threshold (POT), consists of extracting from a continuous record the peak values that exceed (or fall below) a particular threshold and modeling their distribution (Davison and Smith, 1990; Irizarry-Ortiz and others, 2022). The timeseries of threshold exceedances derived from the POT approach is a PDS. Both extreme value approaches can be implemented under stationary and nonstationary frameworks. Stationarity implies that, given any subset of variables, their joint distribution stays the same through time, which is the approach taken here. In this study, first-order stationarity was validated using the Mann-Kendall nonparametric trend test with a significance level (alpha) of 0.05. In contrast, nonstationary processes have characteristics that change systematically through time, for example, as seasonal effects or in the form of trends (Coles, 2001). These changes are reflected as changes in their probability distribution through time. Irizarry-Ortiz and others (2022) provide a detailed discussion of the annual maxima and POT approaches. The POT approach was used in this study and will be discussed hereafter in the context of the stationary framework.

ARFs are used in stormwater infrastructure design to convert point precipitation for a given duration and return period into areal precipitation over a given area for the same duration and return period (Pavlovic and others, 2016). Typically, the area of interest is a watershed. ARFs are also useful when comparing simulated precipitation between datasets with different resolutions. As demonstrated by Chen and Knutson (2008), precipitation output from climate models should be interpreted as areal means rather than as point values, and their use and analysis should remain consistent with that interpretation. Otherwise, large differences in precipitation fields among datasets with different resolutions may be misinterpreted as bias. If the comparison is performed at consistent spatial scales, the true bias may be smaller or even of a different sign. In the computation of DDF change factors, described in the “Multiplicative Quantile Delta Mapping” section, current and future ARFs are assumed to be constant so that they would cancel out; however, ARFs are still useful when assessing model performance by comparing modeled extremes against observed extremes.

To evaluate the performance of modeled precipitation extremes from datasets of various resolutions by comparison against observational datasets for a chosen historical period in this study, grid-cell (areal) scale DDF curves were divided by ARFs to approximate station-scale (point-scale) DDF curves. The model-derived station-scale DDF curves for the historical period can then be compared to station-scale DDF curves from NOAA Atlas 14 volume 9 (Perica and others, 2013) or other sources. Because the station data used in developing the NOAA Atlas 14 DDF curves may include data for the period 1840–2008, depending on the station, all the precipitation data available from the historical period (1950–2005) of the downscaled climate datasets were used for this comparison. The two sets of historical DDF curves may not be completely comparable because of the differences inherent in the data and methods used to develop them, which include (1) different periods of record, and (2) different methods for DDF curve-fitting (regional frequency analysis on annual maximum series for NOAA Atlas 14 versus constrained maximum likelihood [CML] for the downscaled climate model datasets as discussed in Irizarry-Ortiz and others, 2022). Therefore, some differences between the two are to be expected.

Irizarry-Ortiz and others (2022) discuss known sources of ARF data and methods. In their study, geographically fixed-area ARF curves for climate regions across the State of Florida (fig. 5) were used to account for differences in spatial scale when comparing the model-derived station-scale DDF curves for the historical period to station-scale DDF curves from NOAA Atlas 14 volume 9 (Perica and others, 2013). Figure 6 shows the mean ARFs developed by Irizarry-Ortiz and others (2022) for 1-, 3-, and 7-day durations by ARF region (fig. 5). Also shown are error bars representing the mean ARF for each ARF region plus and minus one standard deviation of the grid-cell values within each ARF region. As expected, the mean ARF increases with increasing duration and its variability decreases. Overall, ARF values decrease from north to south Florida, and ARF values tend to be lower on the west coast of south Florida than on the east coast. As shown in figure 6, the ARF correction is close to 1 for most datasets, except for the CORDEX models and in particular for the coarser NAM-44i models.

Quantile mapping or CDF-matching methods (Panofsky and Brier, 1968) are often applied to bias-correct precipitation time series from climate model simulations, but the methods can similarly be used to bias-correct annual maximum series of precipitation or DDF curves. They can also be used as a form of statistical downscaling that attempts to bridge the scale mismatch between the model grid-cell estimates and the point observations. In this study, a MQDM approach (Wang and others, 2013; Cannon and others, 2015) is used to bias-correct projected future DDF curves. MQDM, as opposed to its additive version, is better suited to correcting variables such as precipitation where preserving relative changes is important to respect the Clausius-Clapeyron relation (Wallace and Hobbs, 2006), which relates the amount of atmospheric moisture to temperature changes. Lanzante and others (2021) confirmed the superiority of MQDM over its additive version by means of a “perfect model” experiment. The MQDM method is described in more detail by Irizarry-Ortiz and others (2022), and only the most relevant version of the equation is included in this manuscript:x^m,p adj.=Fm,p adj.−1F=Fo,h−1F⋅Fm,p−1F/Fm,h−1F,(1)where

The annual nonexceedance probability for the model projections in the future projection period (F= Fm,px^m,p) is related to the return period by the following relation:F= 1 − P = 1 − 1/T,(2)where

The term Fm,p−1F/Fm,h−1F in equation 1 is the change factor for the particular nonexceedance probability (or return period), and duration. The assumption is that the relative change between historical and future projected conditions can be indicative of future changes in DDF curves even if the models are biased. The ultimate goal of this study is to obtain change factors from the historical period (1966–2005) to the future projection periods (2020–59 and 2050–89) across the locations of NOAA Atlas 14 stations in Florida. These change factors could then be applied to the PDS-based DDF curves from NOAA Atlas 14 to obtain future projected DDF curves.

NOAA Atlas 14 stations in the Florida Keys (08-2418, 08-4570, 08-5035, and 08-8841, defined in Irizarry-Ortiz and Haider, 2023) are inactive in most downscaled model grids (fig. 3). In such cases, data from the closest mainland grid cells to these four stations were used for developing DDF curves at these four locations. Although the NEX-GDDP dataset extends to the Florida Keys, the technical note for the dataset (Thrasher and others, 2021) warns that because of a lack of validation of its training dataset (GMFD) over oceans, downscaled values over small island areas might not be realistic. Therefore, change factors developed for these four locations in the Florida Keys are highly uncertain and should be used with caution.

The following is a description of the analytical steps used to derive change factors based on CORDEX, LOCA, MACA, LOCA2, and NEX-GDDP downscaled climate datasets (fig. 4). For each dataset, the closest grid cells to each of the 242 NOAA Atlas 14 stations in Florida were identified for each model. For each of these grid cells, rolling sums of daily precipitation were computed using R package RcppRoll (Ushey, 2018) to obtain the cumulative 3- and 7-day precipitation totals. This process was repeated for each climate model run for historical and future projection periods for each RCP or SSP scenario in each dataset. It is expected that all extreme values might be downward-biased because of their being constrained to a clock-based interval (that is, a consistent daily timestep). Therefore, rolling sums for the durations of interest were multiplied by correction factors (table 1; Perica and others, 2013) to convert constrained precipitation totals to unconstrained precipitation totals for each duration, that is, to the maximum precipitation for any time period of the given duration. Checks were made to ensure that the selected exceedances for each duration were larger than for shorter durations overall by comparing their CDFs.

The POT approach was used to fit the generalized Pareto (GP) probability distribution (Pickands, 1975; Leadbetter and others, 1983; Davison and Smith, 1990; Coles, 2001; Katz and others, 2002) to exceedances above a high threshold (fig. 4), as described by Irizarry-Ortiz and others (2022). In this study, thresholds were defined for every location (grid cell) on the basis of a percentile of the precipitation totals for each duration that would result in 2–3 exceedances per year (λ) for each duration after declustering; the chosen percentiles were 99th, 98th, and 97th for 1-, 3-, and 7-day durations, respectively. The runs declustering method in the extRemes package from R (Gilleland and Katz, 2016) was used with run lengths equal to the duration in days, plus 1 day (fig. 4). That is, run lengths of 2, 4, and 8 days were chosen for 1-, 3-, and 7-day durations, respectively. Our choice of run length for the 1-day event is similar to that of NOAA (2022a), which found that dependent events in the time series of exceedances do not affect the precipitation frequency estimates substantially and that declustering the daily exceedances using a 1-day separation period between exceedance events would be adequate. The run length is the number of threshold deficits to be considered as starting a new cluster. These run lengths were chosen to exclude neighboring (clustering) rolling-sum precipitation values that include the same high-precipitation days.

The extRemes package from R (Gilleland and Katz, 2016) was used to compute the interval-based extremal index of the exceedances declustered by the runs declustering method with prespecified run lengths. The objective of this exercise was to confirm that the exceedances declustered on the basis of prespecified run lengths were reasonably independent. A cutoff value of 0.7 for the interval-based extremal index, θ, was assumed to be indicative of adequate tail independence. Additional statistical tests, such as the lag-1 Kendall autocorrelation coefficient (KACF; Durbin, 1960) and the Mann-Kendall trend test (MK; Mann, 1945; Kendall, 1970), were employed to determine whether precipitation excesses above a chosen threshold met the basic assumptions for POT, namely that the declustered excesses were independent and identically distributed. The GP was then fit to cluster maxima, hence the POT approach.

The GP was fitted one duration at a time using the traditional maximum likelihood (ML) approach and for all durations at once using the CML approach (Irizarry-Ortiz and others, 2022) at each model grid cell where a NOAA Atlas 14 station is located (fig. 4). In the CML approach, the GP shape and scale parameters are simulated as linear functions of duration and constraints are added to ensure that return levels for a given duration are larger than those for a shorter duration. The CML approach requires fitting two fewer parameters than the traditional ML approach (Irizarry-Ortiz and others, 2022). The resulting GP fits based on the CML approach are used to derive DDF curves by using the quantile function of the GP for each duration and converting the return periods of interest into nonexceedance probabilities. The tradeoff between model fit and parameter parsimony in the CML approach compared to the traditional ML approach is quantified by means of the Akaike Information Criterion (AIC; Akaike, 1973). In addition, a bootstrapping approach was used to determine goodness of fit (GOF) for the GP distribution (fig. 4) using the tests defined in Irizarry-Ortiz and others (2022): Kolmogorov-Smirnov, Anderson-Darling, Cramér-von Mises, the Pearson product moment correlation coefficient on probability-probability plots, and the Pearson product moment correlation coefficient on quantile-quantile plots. In addition to the GOF statistics described above, two other methods were used to determine whether the GP distribution is a reasonable distribution to model exceedances above a high threshold, as in Irizarry-Ortiz and others (2022). First, the gamlss R package (Rigby and Stasinopoulos, 2005) was used to fit all the available probability distributions in the package that can model real positive values. Second, an L-moment ratio diagram (Hosking, 1990; Vogel and Fennessey, 1993) was used to determine whether the excesses above the selected threshold at each location follow a GP distribution.

The resulting DDF curves apply at the grid-cell scale and are divided by appropriate ARFs to obtain station-scale values for both historical and future projection periods. Assuming the historical ARF applies to the future projection period, the ARF would cancel out in the computation of change factors; however, the ARF allows for comparison of the station-scale DDF curves fitted to simulated historical precipitation data as part of this study against the NOAA Atlas 14 PDS-based DDF curves that were fitted to historical observations of precipitation. Finally, the MQDM method (eq. 1) was used to compute change factors as the ratio of the future projected DDF precipitation depth to the historical DDF precipitation depth for each station grid cell in each downscaled climate dataset.

Model culling refers to the process by which some models are eliminated from further analysis, and the remaining subset of climate models (referred to as “best” models, hereafter) are selected to inform future changes in impact-relevant climate variables (such as used by Infanti and others, 2020). The “best” models are determined by a series of performance measures of relevance to the region and variables of interest. The performance measures are typically based on how well the models reproduce historical observations at weather stations or in comparison to observational gridded products in the region of interest. For this study, precipitation extremes and their return periods in Florida are of the utmost importance to meet the study objective. The use of the word “best” within quotes is to emphasize that these models are the ones that best reproduce historical observations for the limited set of performance measures evaluated, but we do not imply that these models would necessarily perform best in simulating all aspects of the historical or future climate or result in the most accurate change factors.

The Expert Team on Climate Change Detection and Indices (ETCCDI; further information available at http://etccdi.pacificclimate.org/list_27_indices.shtml) has defined climate extremes indices on the basis of daily precipitation data. The original ETCCDI indices and variations thereof (Zhang and others, 2011) have been used by many researchers worldwide to assess the performance of GCMs and downscaled climate products (see, for example, Donat and others, 2013; Sillmann and others, 2013a, b; Srivastava and others, 2020). Several ETCCDI precipitation extreme indices were selected to quantify model performance, as documented in table 3. The ETCCDI precipitation extreme indices were supplemented with additional indices of relevance to this study, as listed in table 3. Preliminary evaluation of precipitation extreme indices for the various downscaled climate datasets used in this study showed correlation between some of the indices, and only a small number of models remained when model culling was based on all the indices listed in table 3. To include as many models as possible to inform the potential range of change factors, a decision was made to only use four precipitation extremes indices in selecting the “best” models (fig. 4). These selected indices consist of annual maxima of consecutive precipitation for durations of 1, 3, 5, and 7 days, and are the most relevant to the estimation of precipitation extremes.

Two reference observational datasets were used to evaluate historical precipitation extremes indices in this study: the SFWMD “Super-grid” and PRISM. Various studies have found that the model performance in capturing climate extremes indices varies depending on the reference dataset chosen (Gleckler and others, 2008; Sillmann and others, 2013a, b; Donat and others, 2014; Wang and others, 2020). The SFWMD “Super-grid” and PRISM observational datasets were chosen for validation of precipitation extreme indices instead of the gridded observational precipitation datasets used in bias correction of the downscaled datasets (Livneh, Daymet, gridMET, Livneh unsplit, and GMFD). As discussed by Irizarry-Ortiz and others (2022), PRISM was chosen on the basis of Behnke and others (2016), who identified it as one of the best performing datasets at capturing daily precipitation statistics and most climate extremes indices at meteorological stations in Florida, whereas the SFWMD “Super-grid” dataset was developed by the SFWMD to cover nearly the entire SFWMD and with a long enough record to allow for analysis of trends (SFWMD, 2005). In this study, the common 25-year historical period between PRISM and the downscaled datasets (1981–2005) was chosen as the base period for computation of percentiles in the percentile-based indices and for calculation and performance evaluation of the precipitation extremes indices.

The precipitation extremes indices were calculated using Python code developed by Gibson (2021). The Python code relies on Python bindings (Max Planck Institute for Meteorology, 2022b) to CDO. The CDO utility remapnn (Max Planck Institute for Meteorology, 2022c) was used to remap the climate indices computed for the downscaled climate datasets to the grids of the PRISM and SFWMD ”Super-grid” datasets using nearest-neighbor interpolation. This interpolation method was used so as not to add information to the downscaled climate datasets that was not already there. In essence, the assumption was made that the grid-cell values from the downscaled climate datasets represent mean values over the grid cell (see Chen and Knutson, 2008), and the node value was assigned to all PRISM and SFWMD “Super-grid” locations having their centroid within a model grid cell. Although the resolution of the indices may be the same for the reference and downscaled datasets after remapping, differences in climate indices are to be expected because of differences in the native scale of each dataset and the order of steps followed in remapping (that is, climate index computation first, followed by remapping, or vice versa). Climate indices for the reference datasets represent the approximately 4- or 3.2-km spatial mean of daily station precipitation that was used for each PRISM or SFWMD “Super-grid” cell, respectively. In contrast, climate indices for CORDEX, for example, were calculated from the 25- to 50-km daily precipitation simulated for each CORDEX grid cell and then assigned to all PRISM or SFWMD “Super-grid” cells located within the area of the CORDEX grid cell.

To summarize the spatial pattern match of each climate index in the downscaled datasets to the reference dataset, various performance measures from Gleckler and others (2008), Sillmann and others (2013a), and Srivastava and others (2020) were used. These performance measures were evaluated separately for five distinct climate regions in Florida (fig. 2). The climate regions were defined as the NOAA (2011) U.S. Climate Divisions for the State of Florida, with Florida climate divisions 5, 6, and 7 merged into a single region named “south Florida” hereafter. Guttman and Quayle (1996) explain the history behind U.S. climate divisions.

The root-mean-square error (RMSE) statistic is used to summarize the performance of each model in capturing the climatology (long-term mean for 1981–2005) of each index calculated from the reference dataset at the model resolution:RMSEm,I=1C∑c=1CIm,c¯−Io,c¯2,(3)where

The best models will have a small RMSEm,I. The relative performance of a model in simulating the climatological mean of the reference observational dataset can be computed by normalizing the RMSEm,I as follows:NRMSEm,I=RMSEm,I−RMSEmed,IRMSEmed,I,(4)where

The median is used for normalization to avoid undue influence by outlier models having unusually large errors. The best models will have a large negative NRMSEm,I, indicating that the model performs better than most models. A large positive NRMSEm,I indicates that the model performs worse than most models. To quantify the overall performance of a model in simulating the climatological mean of all indices, the Model Climatology Index (MCI) from Srivastava and others (2020) was used, but it was modified to use the mean of the NRMSEm,I values over all indices for a particular model as opposed to the median.

In addition to the spatial pattern in the climatological mean, it is important to quantify how different models capture the spatial pattern of the interannual variability of each climate index from gridded observations. For this purpose, the interannual variability skill score (IVSS; Chen and others, 2011; Jiang and others, 2015) was used, which is defined asIVSSm,I=1C∑c=1CσI,m,cσI,o,c−σI,o,cσI,m,c2,(5)where

The best models will have a small IVSSm,I. The relative performance of a model in simulating the interquartile range of the reference observational dataset can be computed by normalizing the IVSSm,I as follows:NIVSSm,I=IVSSm,I−IVSSmed,IIVSSmed,I,(6)where

The best models will have a large negative NIVSSm,I, indicating that the model performs better than most models. A large positive NIVSSm,I indicates that the model performs worse than most models. To quantify the overall performance of a model in simulating the interannual variability of all indices, the Model Variability Index (MVI) from Srivastava and others (2020) was used but was modified to use the mean of the NIVSSm,I values over all indices for a particular model as opposed to the median. Lastly, the MCI and MVI for each model were plotted as a scatterplot, with the best performing models having the largest negative MCI and MVIs.

In this report, only results considering all models are presented; however, the list of best models and results, such as change factor quantiles considering only best models, are included in the data release associated with this report (Irizarry-Ortiz and Haider, 2023).

Extreme precipitation events were identified as those exceeding the 99th, 98th, and 97th percentiles of precipitation for 1-, 3-, and 7-day durations, respectively. After declustering the precipitation exceedances using run lengths equal to the duration plus 1 day, it was determined that more than 95 percent of the grid cells had an extremal index (as calculated from the intervals method of Ferro, 2003; and Ferro and Segers, 2003) of 0.7 or greater in all periods, durations, and models in all downscaled climate datasets. The inverse of the extremal index provides an estimate of the mean cluster size (Moloney and others, 2019); therefore, an extremal index of 0.7 would correspond to mean cluster size of 1.4. This increases confidence that the declustering was adequate for the great majority of cells. This approach was applied to the CORDEX, LOCA, MACA, LOCA2, and NEX-GDDP downscaled climate datasets. After declustering, the CML approach was used to fit the GP distribution to declustered precipitation excesses for durations of 1, 3, and 7 days, for the periods 2050–89 and 1966–2005 at every grid cell closest to each of the 242 NOAA Atlas 14 stations in Florida.

As discussed by Winsberg (2020) and Irizarry-Ortiz and others (2022), the historical monthly frequency distribution of extreme precipitation is bimodal over most of the State, peaking in June and September. Winsberg (2020) explained the June peak as resulting from the Intertropical Convergence Zone moving north and having more influence on the local weather and the September peak as resulting from the greater frequency of tropical storms reaching the State during that month, which corresponds to the peak of the Atlantic hurricane season. Figures 13–15 show the median change in the annual cycle of the mean monthly number of declustered threshold exceedance events from the historical period (1966–2005) to the future periods (2020–59 and 2050–89) for durations of 1, 3, and 7 days, as simulated in each downscaled climate dataset for the climate regions shown in figure 2. The percentile-based historical threshold is used to define the number of exceedance events for both the historical and future periods. For example, the 99th percentile value chosen as the threshold to define extreme 1-day events in the historical period (fig. 13) corresponds to about 3.6 extreme precipitation events per year on average. Those 3.6 extreme events in an average year have an associated annual cycle (Winsberg, 2020) with less than one extreme event happening per month on average (see Irizarry-Ortiz and others, 2022). Therefore, figure 13 shows the median changes across models in the mean monthly number of exceedances of the threshold value defined by the 99th percentile of the historical data. Figures 14–15 can be interpreted in a similar manner to the above explanation for figure 13; however, they correspond to 3- and 7-day extreme events defined as those exceeding the 98th and 97th percentiles, respectively. Note that in fitting the GP distribution, different percentile-based thresholds are used for the historical and future periods. When the percentile-based historical threshold is used to define exceedance events for the historical and future periods, as in figures 13–15, the median change in the annual number of threshold exceedance events from the historical to the future periods is generally positive for most datasets, climate regions, durations, and periods. This means that an increase in the number of extreme events is projected, especially for the northernmost climate regions and for the latter period 2050–89.

Overall, the median change in the number of future exceedance events for all durations (figs. 13–15) follows a similar seasonal pattern as the projected median changes to the mean annual cycle of precipitation (fig. 12). The similarity in seasonal changes between overall precipitation and the number of future exceedance events is more evident for the 7-day duration (fig. 15), whereas changes for 1- and 3-day durations are more erratic, although a seasonal pattern can still be discerned. The number of future exceedance events is generally projected to increase during the dry season, particularly during the transitional months for the longer durations, and decrease during the wet season, especially in the south. The annual number of future exceedance events is projected to increase the most according to the CORDEX and NEX-GDDP datasets and the least according to the LOCA and MACA datasets. The annual number of future exceedance events is projected to increase the most in the northern climate regions and less so further south because of decreases in the number of events during the wet season in the south, particularly in the period 2050–89.

The AIC is used to quantify goodness of fit. For each grid-cell location corresponding to NOAA Atlas 14 stations in every downscaled model, the change in AIC (ΔAIC) was calculated with respect to the traditional maximum likelihood (ML) model. It was found that more than 95 percent of grid cells have ΔAIC values below 2 and 7, which according to Burnham and Anderson (2002) and Burnham and others (2011), respectively, indicates that there is substantial evidence and support for the (simpler) CML model compared to the traditional ML model. A relatively small percentage of cells (< 0.2 percent) exceeds the ΔAIC threshold of 7 units.

The figure 16 bar graphs indicate the percentage of model grid cells with p-values less than 0.05 for the lag-1 KACF and the MK trend test on excess values in the historical (1966–2005) and future projection (2020–59 and 2050–89) periods. The null hypothesis that precipitation-excess data are not autocorrelated is measured by the KACF, whereas the null hypothesis that it does not exhibit monotonic trends is quantified by the MK test. The nominal rate line in figure 16 represents the expected percentage of rejections of the null hypothesis when it is true, which is the significance level or expected nominal value of 5 percent. Also shown in this figure is the 95-percent prediction interval for the significance level under multiple comparison testing and under the assumptions that the data are uncorrelated and that the number of false rejections of the null hypotheses follows a binomial distribution, as in Serinaldi and Kilsby (2014). The percentage of rejections of the null hypothesis of no autocorrelation and no trend are close to the nominal value for most periods and durations. The main exception is CORDEX for which the null hypothesis is rejected more often than the nominal rate for MK tests in the historical period and the future period 2050–89. Another exception is MACA for which the null hypothesis rejection rate is slightly larger than the nominal rate for the 3- and 7-day MK tests in the historical period, and for the 1- and 3-day MK tests in the future period 2050–89. The 1- and 7-day MK tests for LOCA in the future period 2050–89 also have rejection rates slightly larger than the nominal rate. The 7-day KACF test for MACA and the 1- and 7-day KACF tests for the NEX-GDDP in the historical period also indicate a rejection rate slightly larger than expected. The maximum rejection rate obtained for the MK tests is 7 percent, which is comparable to the 7- to 8-percent rejection rates corresponding to the 98th percentile-based threshold chosen by Serinaldi and Kilsby (2014) in fitting the GP to rainfall observations for the period 1970–2011. On the basis of these results, we conclude that it is acceptable to use a stationary approach in fitting the GP for these two 40-year periods.

Figure 17 shows bar graphs indicating the percentage of model grid cells for which the null hypothesis that the historical (1966–2005) and the future projected (2020–59 and 2050–89) precipitation-excess data follow a GP distribution is rejected at the 0.05 significance level for each duration in each downscaled climate dataset. The p-values are bootstrapped on the basis of the CML assumption, as discussed in appendix 3 of Irizarry-Ortiz and others (2022). Results are only shown for the model grid cells closest to the 242 NOAA Atlas 14 stations used in this study. The figure shows a nominal rate of 5 percent and a 95-percent prediction interval for the significance level. Overall, CORDEX tends to perform worse for the 1-day duration compared to the other datasets, especially in the future periods, with rejection rates much higher than the nominal rate of 5 percent expected by chance if all data follow a GP distribution. For the 1-day duration, only MACA and NEX-GDDP in the historical period consistently show rejection rates below or close to 5 percent across all GOF tests. LOCA tends to perform worse than the other datasets for 3- and 7-day durations, with higher rejection rates than the chosen nominal rate of 5 percent. Limited GOF testing based on the traditional ML approach with bootstrapping indicates a similar percentage of rejections, indicating that the performance deterioration when using CML does not have a large influence on the high test rejection rates for the GOF statistics and that, in fact, the raw excess data do not always seem to follow a GP distribution.

Figures 18 and 19 show L-moment ratio diagrams for precipitation excesses in the historical (1966–2005) and future projection (2020–59 and 2050–89) periods for CMIP5 and CMIP6 downscaled climate datasets, respectively. JupiterWRF is only included in the 1-day panel in figure 18 because 3- and 7-day durations were not evaluated for this dataset. The empirical L-moment ratios for all datasets shown in figure 18 tend to follow the GP line shown in the figure. As the duration increases, the cloud of points shifts slightly from the portion of the GP curve to the upper right of the exponential (“EXP”) point, which corresponds to positive shape parameters, to the portion of the GP curve to the lower left of the exponential point, which corresponds to negative shape parameters. This shift reflects a general decline in shape parameters with increasing duration. In figure 18, some LOCA points show lower L-skew and L-kurtosis, especially for the 1-day duration, indicating a tendency for lower GP shape parameters and lower extremes in all periods. There is also a slight tendency for higher L-kurtosis in the future projection periods than in the historical period, indicating a tendency for higher GP shape parameters and higher extremes in the future. A portion of the cloud of points to the left of the exponential point tends to be located somewhat below the GP curve.

The cloud of points for NEX-GDDP (fig. 19) is much more compact around lower L-skew and L-kurtosis values than for the other datasets, which implies lower shape parameter values. This finding indicates that this dataset has smaller extreme precipitation values than the other datasets and, as will be shown, underestimates extreme precipitation. The lower extreme precipitation in NEX-GDDP might be the combined result of the use of GMFD for training and bias correction and the BCSD downscaling method, which is much simpler than analog-based methods used in LOCA and MACA. For example, Avila-Diaz and others (2020) found that GMFD substantially underestimates daily and multiday extremes in Brazil compared to other datasets of similar spatial resolution. The BCSD method combines the observed historical daily spatial climatology of precipitation with relative changes at each timestep simulated by a GCM. Therefore, interannual variability in extremes mainly reflects that of the GCM as opposed to originating from analogue historical days as in other methods, which may also limit the variability in extremes.

Figures 18 and 19 also show more points farther to the upper right of the GP curve in the future projection periods compared to the historical period, reflecting an overall tendency for larger shape parameters and larger extremes in the future.

The bar charts in figure 20 show the percentage of model grid cells for which a given probability distribution is one of the five best fitting probability distributions among the tested distributions according to the AIC, which include all the available functions for positive real numbers in the gamlss R package. The selection of the best fitting probability distributions was performed using the fitDist function in gamlss, which uses the AIC to balance GOF with distribution parsimony. In this figure, the first four bars (EXP, PARETO2, PARETO2o, and GP) correspond to different parameterizations of the GP and the exponential distribution, which is the special case of the GP having a shape parameter of zero. The bars for the remaining distributions are ordered from higher to lower percentage. The GP is an adequate distribution for most locations, durations, periods, and datasets; however, various parameterizations of the Weibull distribution are also among the best fitting distributions. The GP with an exponent different from zero (that is, PARETO2, PARETO2o, and GP in fig. 20) appears to be less adequate for NEX-GDDP, whereas the GP with an exponent of zero (EXP in fig. 20) and the various parameterizations of the Weibull distribution appear to be more adequate. This reflects the lower L-skew and L-kurtosis values for NEX-GDDP shown in figure 19.

Using global precipitation data, Serinaldi and Kilsby (2014) show that nonzero precipitation (that is, equivalent to a POT approach with a threshold of zero) tends to follow a Weibull distribution, and they reference studies showing a progressive shift from GP to Weibull as the threshold is decreased. This finding indicates it is possible that the selected constant percentile-based threshold for each duration may be too low at some locations (that is, the asymptotic conditions for the GP are not being met), resulting in more rejections of the null hypothesis of a GP distribution than the expected nominal value of 5 percent (significance level). Figures 18 and 19 show, however, that the empirical L-moment ratios are generally in better alignment with the GP curve than with the Weibull curve. In fact, the deviation of the cloud of points from the GP curve in the region below the exponential point is away from the Weibull distribution rather than toward it. Therefore, the GP distribution has more support than the Weibull distribution. Although the generalized Gamma and generalized Beta Type 2 distributions have more parameters, they are not among the best fitting distributions according to the AIC (fig. 20). In other words, the improvement in fit is not sufficient to justify the higher number of parameters in these distributions.

The overall percentage difference of the model-derived station-scale DDF depths for the entire historical period available in the downscaled climate datasets (1950–2005) were analyzed relative to the partial-duration series (PDS)-based DDF depths from NOAA Atlas 14 volume 9 (Perica and others, 2013). The percentage differences (fig. 21) are calculated from the mean DDF depths at all 242 NOAA Atlas 14 stations in Florida, except for JupiterWRF where the difference is only based on the 171 stations in central and south Florida included on its grid (fig. 3G). The DDF depths from NOAA Atlas 14 volume 9 are based on statistical fits to precipitation observations within the period 1840–2008, depending on the station. Although different methods and periods of record are used in DDF fitting for the downscaled climate datasets compared to NOAA Atlas 14 volume 9, it is still informative to evaluate their overall differences. From figure 21, it is evident that the JupiterWRF dataset has the lowest absolute difference from observed DDF depths for the 1-day duration, on the order of less than 10 percent, followed by CORDEX-Daymet with median differences of about −12 to −21 percent, and CORDEX-gridMET with median differences of about −21 to −25 percent. LOCA and MACA-gridMET perform poorer than most datasets for the 1-day duration, with median differences in the range of −33 to −36 percent. The poor daily performance for LOCA might be a result (at least in part) of deficiencies in its training dataset (Livneh and others, 2015) mentioned earlier in this report. LOCA2, which uses Livneh unsplit for training, has lower negative biases than LOCA, especially for the 1-day duration (about −20 percent). NEX-GDDP performs poorer than all the other datasets and underestimates extremes, with median 1-day differences ranging from −61 to −75 percent. This underestimation of extremes is evident in the L-moment diagrams (figs. 18–19), where NEX-GDDP has lower L-skew and L-kurtosis than the other datasets.

Although the MACA-Livneh dataset uses the Livneh and others (2013) dataset for training, it did not show differences as large as those for LOCA, with differences in the range of −26 to −28 percent for the 1-day duration (fig. 21), indicating that the differences in LOCA may also be due to the downscaling method used. Two different versions of the Livneh dataset (Livneh and others, 2013, 2015) and two different periods are used in bias correcting LOCA and MACA, which may also explain some of the differences. MACA-gridMET has median 1-day differences of about −33 to −35 percent, close to those of LOCA, but larger negative differences than in MACA-Livneh. MACA-gridMET models always show negative differences, whereas some MACA-Livneh models show positive differences for the 7-day duration.

Overall, the longer return periods show more negative differences (with the exception of CORDEX and JupiterWRF for the 1-day duration) and the differences are more variable across models than for the shorter return periods (fig. 21). The negative differences generally decrease with increasing duration for most datasets but remain quite large for NEX-GDDP. For the 7-day duration, some MACA-Livneh, LOCA2, and CORDEX-Daymet models even exhibit positive differences. Overall, the range of negative differences increases with increasing duration. Although CORDEX starts with the smallest 1-day negative difference with respect to observations, its percentage difference does not improve with increasing duration quite as much as those for the other datasets, indicating that the RCMs and (or) the bias-correction scheme may be inadequate in simulating multiday extreme events. Overall, the CORDEX-Daymet negative differences are smaller than in CORDEX-gridMET by 4–9 percent, depending on duration and return period.

The differences between extremes fitted to observations and those derived from the downscaled climate datasets might result from a combination of factors, some of which have been mentioned previously. These factors include the following, among others:

The percentage difference was computed between (1) station-scale precipitation depths obtained by fitting the GP distribution with CML to precipitation depths from the datasets used to bias-correct each downscaled climate dataset and (2) the PDS-based DDF depths from NOAA Atlas 14 for 1840–2008 (fig. 22). The periods of record and native resolutions for each bias-correction dataset vary by downscaled climate dataset, as described in each applicable subsection of the “Downscaled Climate Datasets” section. The precipitation data were obtained for the closest grid cell to each of the 242 NOAA Atlas 14 stations at the native resolution of each bias-correction dataset. The ARF values corresponding to these resolutions are very close to 1 with the exception of GMFD for which ARF values range from 0.89 to 0.98, depending on region and duration (fig. 6). Comparison of figure 22 with the median percentage difference in precipitation depths across models for each downscaled climate dataset in figure 21 indicates similar magnitudes and patterns of change with respect to changes in duration and often with respect to changes in return period. These similarities indicate that the overall percentage difference of the model-derived station-scale DDF depths for the historical period (1950–2005) compared to the PDS-based DDF depths from NOAA Atlas 14 volume 9 is largely a result of the bias-correction datasets not being able to capture the localized station-based DDF depths from NOAA Atlas 14. Daily biases were found to be the lowest for Livneh unsplit (used in LOCA2), followed by Daymet (used in CORDEX), which has the highest resolution of the bias-correction datasets (1 km). Despite daily biases being the lowest for Livneh unsplit, Ensor and Robeson (2008) found that Livneh unsplit slightly mutes extremes as a result of the gridding process. Ullrich (2023) also found that Livneh unsplit and LOCA2 exhibit larger values for most quantiles near the observing stations used in their development, especially in the southeastern United States. Therefore, extreme events at Livneh unsplit grid cells where NOAA Atlas 14 stations are located but that were not used in the interpolation to develop Livneh unsplit are expected to underestimate the NOAA Atlas 14 extremes to some degree.

The improvement of Livneh unsplit at capturing daily extremes compared to the original Livneh datasets is also evident in figure 22. The GMFD dataset used in developing the NEX-GDDP downscaled climate dataset is by far the most biased, especially for the 1-day duration. The large biases in GMFD are partially attributed to its much coarser resolution compared to the other datasets. However, Avila-Diaz and others (2020) found that GMFD substantially underestimates climate indices related to extreme precipitation, such as RX1day, RX5day, and R95p (table 3), in Brazil compared to other datasets of similar spatial resolution, such as the fifth European Centre for Medium Range Weather Forecasts Reanalysis—ERA5 (Hersbach and others, 2020). Irizarry-Ortiz and others (2022) show that differences in the periods of record and DDF-fitting methodologies only account for a small portion of the bias in the model-derived station-scale DDF depths compared to the PDS-based DDF depths from NOAA Atlas 14 volume 9.

Initially, the best models were selected by evaluating the MCI and MVI criteria from Srivastava and others (2020) over the period 1981–2005 and considering all the precipitation extremes indices listed in table 3. This process resulted in a very small subset of best models. Given the desire to include as many models as possible to inform the potential range of change factors, a decision was made to only use four precipitation extremes indices in selecting best models, namely the annual maxima of precipitation for durations of 1, 3, 5, and 7 consecutive days. Irizarry-Ortiz and Haider (2023) include tables listing the best models for each climate region according to the MCI and MVI when each downscaled climate dataset (CORDEX, LOCA, MACA, LOCA2, and NEX-GDDP) is evaluated on its own for the four precipitation extremes indices chosen. Tables listing best models when all the CMIP5 datasets are evaluated together are also included in Irizarry-Ortiz and Haider (2023). In this case, the median RMSE and IVSS are defined on the basis of all the models in all the downscaled climate datasets. A model was considered to be among the best if it had a negative MCI and a negative MVI when compared to either the PRISM or SFWMD “Super-grid” observational datasets. Because of the small sample size, all models were considered the best models for the JupiterWRF dataset. As in Irizarry-Ortiz and others (2022), few LOCA models were considered best when all CMIP5 downscaled climate datasets were evaluated together. The CMIP6 datasets were not compared against each other because only models from LOCA2 would have been considered best on the basis of the poor performance of NEX-GDDP, as discussed below.

The median RMSE of the climatology of extreme precipitation indices across the different models in each downscaled climate dataset evaluated against PRISM (fig. 23) indicates that the CMIP6 NEX-GDDP performs poorer than the remaining datasets for the great majority of the indices (11–13 out of 15, depending on the climate region). Some exceptions are cumulative dry days (CDD), annual total wet day precipitation (PRCPTOT), simple daily intensity index (SDII), and annual count of days with precipitation greater than or equal to 1 mm (R1mm) for the northernmost climate regions for which NEX-GDDP performs similar to the other datasets. The poorer performance found for NEX-GDDP is consistent with findings by Avila-Diaz and others (2020) over Brazil where GMFD, the training and bias-correction dataset used in NEX-GDDP, was found to substantially underestimate extreme precipitation. The improvement from LOCA to LOCA2 caused by the switch from the Livneh and others (2015) to the Livneh unsplit (Pierce and others, 2021) dataset is also evident in figure 23. In general, the climatological performance of the datasets worsens toward the south for cumulative dry days (CDD), number of heavy precipitation days (R10mm), and PRCPTOT as quantified by the median RMSE. In contrast, the performance for the SDII improves toward the south. The performance for the maximum 1-day and multiday precipitation-depth indices (RX1day, RX3day, RX5day, and RX7day), as well as for the annual total precipitation from very wet and extremely wet days in inches and percentage (R95p, R95pTOT, R99p, and R99pTOT), is best for the north, north-central, and south-central Florida climate regions. Figure 24 shows the median IVSS across models in each downscaled climate dataset evaluated against the PRISM observational dataset. The poorer performance of NEX-GDDP in terms of IVSS is evident for the RX1day, RX3day, RX5day, and RX7day indices and in the southernmost climate regions, consistent with previous findings of low interannual variability in extremes for this dataset (fig. 19).

In this report, only results considering all models are presented; however, the list of best models and results, such as change factor quantiles at individual stations only considering best models, are included in the data release associated with this report (Irizarry-Ortiz and Haider, 2023).

Change factors for DDF precipitation depths for the periods 2020–59 and 2050–89 with respect to the period 1966–2005 were computed for all model grid cells associated with NOAA Atlas 14 stations in the State of Florida from all CMIP5 and CMIP6 downscaled climate datasets evaluated as part of this study. The change factor data are available in the data release associated with this report (Irizarry-Ortiz and Haider, 2023). Figures 25–26 show median change factors for all climate regions shown in figure 2, considering all models and all RCP and SSP scenarios, for the periods centered on 2040 and 2070, respectively. In these figures, the term “all datasets” refers to the median considering all CMIP5 and CMIP6 datasets. Median change factors and their range generally increase with increasing return period and are similar across durations for all climate regions in the two future periods. The increase in change factors with return period is consistent with Lopez-Cantu and others (2020), who found that at the continental scale, high-end daily extremes generally increase more than low-end extremes, as determined by evaluating various downscaled climate datasets for the period 2044–99 with respect to 1951–2005. That is, the largest historical precipitation events get larger under future conditions. The exception is JupiterWRF for which 1-day change factors do not vary much with return period. The IPCC (2021b, p. 15) also states that “There will be an increasing occurrence of some extreme events unprecedented in the observational record with additional global warming, even at 1.5 °C of global warming. Projected percentage changes in frequency are higher for rarer events (high confidence).”

Median change factors across all CMIP5 and CMIP6 datasets range between 1.04 and 1.18 for the period 2020–59 and between 1.05 and 1.23 for the period 2050–89, depending on duration and return period. When considering all RCPs and SSPs (figs. 25–26), median change factors from the LOCA, LOCA2, and JupiterWRF datasets (1-day duration only) are usually the lowest, followed by those from the NEX-GDDP, CORDEX, and MACA datasets. One exception is the median change factors from CORDEX being slightly larger than those from MACA for the 5- and 10-year, 7-day event in south Florida for the period 2050–89 (fig. 26). Overall, the median change factors are found to increase from 2020–59 to 2050–89 with the exception of MACA in the south Florida climate region where they decrease slightly in the latter period, especially for the 7-day duration. It is possible that this result is tied to the reduction in precipitation projected during summer for most MACA models in this region in the latter period (fig. 9). The median change factors also do not increase much for LOCA from 2020–59 to 2050–89, especially in the south Florida climate region. As a result of the lower median change factors projected by LOCA for the two periods in the south Florida climate region, this region has the largest range of change factors, especially for the 1-day duration.

With the exception of the longer return periods for the northwest Florida climate region, NEX-GDDP results in somewhat higher median change factors than LOCA2, especially in the north and south Florida climate regions for both periods (figs. 25–26). LOCA2 generally results in very similar though slightly higher change factors than LOCA in the north-central, south-central, and south Florida climate regions, and lower median change factors in the northwest and north Florida climate regions compared to LOCA for the period 2050–89 (fig. 26). The differences between LOCA and LOCA2 median change factors are even smaller for the earlier period 2020–59, with the exception of the north-central Florida climate region where the differences are slightly larger than in the latter period (fig. 25).

Median change factors were computed for all datasets, climate regions, and models, but only considering RCP4.5 and RCP8.5 and SSP2-4.5 and SSP5-8.5, which correspond to medium-low and high emission levels and are more directly comparable (figs. 27–28). As mentioned previously, although each RCP and its corresponding SSP attain about the same radiative forcing in the year 2100, the emissions pathways may differ. Comparison of figures 25 and 26 with 27 and 28 indicates slightly higher median change factors when only the medium-low and high emissions scenarios are considered. Median change factors considering all CMIP5 and CMIP6 datasets but only the medium-low and high emissions scenarios range between 1.05 and 1.21 for the period 2020–59 and between 1.06 and 1.27 for the period 2050–89.

Figures 29 and 30 show the median change factors by RCP/SSP for all datasets, climate regions, and models. Notably, the number of ensemble members downscaled by each dataset varies by RCP/SSP (table 2), which confounds the comparison of change factors across RCP/SSP in some datasets. A steep increase in median change factors with increasing return period is evident for the MACA and CORDEX datasets in the two periods. In the period 2020–59, the median change factors are generally lower in RCP8.5 than in RCP4.5 for MACA and CORDEX (with the exception of CORDEX in the south Florida climate region), whereas the opposite is generally the case for the latter period, 2050–89 (fig. 30). For MACA, this is the case even for return periods shorter than the 40-year period used in DDF fitting (5–25 years), which indicates that the higher change factors in RCP4.5 are not simply an artifact of extrapolation caused by distribution fitting for longer return periods, but that they are a feature of the bulk of the exceedance data used in DDF fitting. For the period 2050–89, the median MACA change factors in RCP8.5 are much higher than those of RCP4.5 in the northwest Florida climate region. Median change factors for RCP4.5 and RCP8.5 from CORDEX also deviate substantially for the northwest and north-central Florida climate regions in the latter period (fig. 30). CORDEX downscales 14 models under RCP4.5 and 54 under RCP8.5 (table 2); therefore, comparisons across RCPs are imbalanced for CORDEX. When the same 14 models are compared across RCPs, CORDEX generally has higher change factors under RCP8.5 than RCP4.5. LOCA has higher median change factors for RCP8.5 than RCP4.5 in the latter period (fig. 30); however, the differences between RCPs are smaller and RCP4.5 change factors are often higher than RCP8.5 change factors in the earlier period.

Median change factors from NEX-GDDP tend to stay flat or even decline with return period for most durations and SSPs in the northwest Florida climate region, especially in the earlier period, and in the northwest, north, and south-central Florida climate regions for the 1-day duration in the latter period (fig. 30). This may be related to the GMFD training and bias-correction dataset and the BCSD method used in NEX-GDDP resulting in too little interannual variability in extremes, with high historical extremes not well captured (figs. 19 and 21), an issue that may be amplified in the future projections. In the latter period, median change factors from NEX-GDDP tend to be highest under SSP2-4.5 and lowest under SSP3-7.0 in the north-central, south-central, and south Florida climate regions, especially for the 7-day duration. In the northwest and north Florida climate regions, median change factors from NEX-GDDP for the latter period (fig. 30) mostly increase or change little with increasing emissions (SSP level); however, SSP3-7.0 has the highest change factors for the 7-day duration in the northwest Florida climate region. NEX-GDDP downscales a smaller number of models and ensemble members under SSP3-7.0 (table 2); therefore, comparisons across SSPs are imbalanced for NEX-GDDP; however, the previously discussed variation in change factors with SSP remains very similar when only the GCM and ensemble member combinations with data available for all four SSPs downscaled by NEX-GDDP are considered.

Median change factors from LOCA2 generally increase with return period (figs. 29–30). In both periods, SSP3-7.0 generally has the lowest median change factors in LOCA2, with the exception of the north-central Florida climate region in the earlier period and the northwest Florida climate region in the latter period. The differences between SSPs are somewhat reduced when only the GCM and ensemble member combinations available for all three SSPs downscaled by the LOCA2 dataset are considered.

Figures 31–34 show maps of median change factors for the 1-day, 100-year event from each CMIP5 and CMIP6 downscaled climate dataset in the two periods of interest. In addition, maps of median change factors considering all datasets available for each CMIP version are provided. For CMIP6, maps are also provided that include only the SSP2-4.5 and SSP5-8.5 scenarios. The spatial patterns of median change factors are quite different across the different datasets. MACA clearly projects the highest change factors in both periods (figs. 31 and 33). CORDEX projects areas of higher change factors in southeast Florida, western south-central Florida, north Florida, and portions of northwest Florida in the earlier period. In the latter period, the highest median change factors projected by CORDEX are in western central Florida. Isolated stations in south Florida have median change factors less than 1 in LOCA in both periods. In the latter period, LOCA projects higher median change factors at some stations in north-central and north Florida. JupiterWRF also projects change factors smaller than 1 at isolated stations in south and central Florida. When all CMIP5 datasets are considered together, the lowest median change factors are generally concentrated in south-central and south Florida.

NEX-GDDP projects the highest median change factors in the urbanized areas of southeast Florida and near Lake Okeechobee (figs. 32 and 34). As in LOCA, isolated south Florida stations have median change factors less than 1 in LOCA2, especially in the earlier period. In the latter period, the highest median projected change factors are in central Florida. When all CMIP6 datasets are considered, there is little spatial variation in median change factors throughout the State in the earlier period and some isolated stations with higher values in central and south Florida in the latter period. These patterns do not change substantially when only SSP2-4.5 and SSP5-8.5 are considered.

For the entire continental United States, Lopez-Cantu and others (2020) found that, despite being the least biased overall compared to observed extremes, the MACA-gridMET multimember mean change factors (for the period 2044–99 with respect to 1951–2005) are also considerably larger than for the other datasets evaluated, which include Bias-Corrected Constructed Analog (BCCA) version 2, LOCA, and CORDEX without bias correction (called CORDEXnoBC hereafter). They found that BCCA version 2 results in the lowest change factors for the continental United States, followed by LOCA, low-resolution CORDEXnoBC models, high-resolution CORDEXnoBC models, and MACA-gridMET models. Furthermore, Lopez-Cantu and others (2020) found that the downscaled climate datasets somewhat preserve the pattern of the change signal in the native GCM change factors; however, the magnitude of the signal is reduced in BCCA version 2 and increased in MACA-gridMET. For the southeastern United States, using the CanESM2 GCM as an example, they found for RCP4.5 that LOCA and low-resolution CORDEXnoBC models tend to preserve the GCM change signal the best, whereas MACA-gridMET amplifies the change signal, especially for longer return periods, consistent with our findings. High-resolution CORDEXnoBC models were found to amplify the change signal more evenly across return periods. Their findings were similar for RCP8.5, but they found that LOCA tends to mute the change signal, whereas its amplification in MACA-gridMET and the high-resolution CORDEXnoBC models is slightly lower than in RCP4.5.

As in Irizarry-Ortiz and others (2022), isolated outlier change factors as high as 8–10 are estimated for individual stations, especially by MACA. When these very high change factors are multiplied by NOAA Atlas 14 DDF curves, the resulting future projected DDF values can be as high as 100 in. or more over 3- to 7-day durations and return periods beyond 100 years. These values exceed the record high precipitation accumulations recorded around the globe in the last decade, as discussed in Irizarry-Ortiz and others (2022). Some recent examples of extreme precipitation events in or near Florida include Hurricane Irma in 2017 with rainfall totals of 10–15 in. across the peninsula and a maximum of 21.7 in. within St. Lucie County (NOAA, 2017). Hurricane Dorian in 2019 produced storm-total rainfall of 22.8 in. at a location in the Bahamas (NOAA, 2020a). Hurricane Eta brought more than 14 in. of rainfall to south Florida, with a localized total of 20.7 in. for November 2020 (NOAA, 2020b). Hurricane Ian produced rainfall totals of 10–20 in. over central and eastern Florida in September 2022, causing major flooding that in some areas took months to recede. The highest rainfall associated with Hurricane Ian was about 27 in. within Grove City, Florida (NOAA, 2022b). A rapid-attribution modeling study by Reed and Wehner (2023) found that 3-day accumulated rainfall from Hurricane Ian was 18 percent higher because of climate change, which is much higher than would be expected because of the Clausius-Clapeyron relation. Close to 26 in. of rainfall was recorded over 24 hours at the Fort Lauderdale-Hollywood International Airport on April 13, 2023, with the majority of the rainfall occurring over a 6- to 12-hour period (Florida Climate Center, 2023) and causing significant flooding. The April 2023 event was associated with a warm front moving north into south Florida and was classified as a 12-hour, 1,000-year event according to NOAA (2023). Over 20 in. of rainfall was recorded over a 72-hour period on June 11–13, 2024, in south Florida with some locations receiving over 27 in. of rainfall (Florida Climate Center, 2024). Areas in southwestern and southeastern Florida received the most rainfall, and hourly and daily rainfall records were broken during the event. A shift toward more frequent extremes, especially for rarer events, was documented in the IPCC’s fifth assessment report (Collins and others, 2013) and further validated in a contributed section of their sixth assessment report (IPCC, 2021b). Attribution studies have determined that climate change has increased the likelihood and (or) intensity of these historical events. (See Reed and others [2020] for Hurricane Dorian, and Reed and Wehner [2023] for Hurricane Ian.)

Evidence of record-breaking precipitation extremes and their links to climate change, as referenced above, has been accumulating over the last few decades; however, given that the very high change factors computed here were generated by statistical downscaling or bias-corrected dynamical downscaling, the confidence in them is not as high as it would be if they had been generated by a purely physically based model. In addition, the highest change factors are associated with very long return periods, which are much longer than the number of years of data used in DDF fitting and are highly uncertain. High shape parameters of the GP distribution were fit especially for MACA because of isolated very large 1-day and multiday extremes, as discussed in Irizarry-Ortiz and others (2022). The quasi-stationary approach used in this study, whereby DDF curves are fit for a limited future 40-year projection period using local data, may also contribute in that it is possible that these very extreme precipitation events only happen once in a much longer period than the 40 years analyzed. These events, however, appear to be much more common in MACA than in the other downscaled climate datasets and may be, at least in part, a result of the downscaling method.

Wootten (2018) shows how subtle decisions performed in the process of statistical downscaling, such as tail adjustment, trace adjustment, and interpolation, can affect the accuracy of the prediction and increase the uncertainty in future projections, especially for extremes and event occurrence. Wang and others (2020) found that MACA projects significant increases in the 20-year daily event in New England compared to LOCA for which the projected changes are inconclusive over most of the area. In LOCA, model consensus is lacking over most of the region, but where models agree, the projected changes have a smaller magnitude than in MACA. Their finding is generally consistent with this study’s findings for Florida. Wang and others (2020) note that projected changes in the mean annual maximum daily event are quite close between MACA-Livneh and MACA-gridMET but differ significantly between LOCA and MACA-Livneh. As a result, they conclude that differences in the projected changes are primarily caused by differences in the downscaling method, rather than by differences in the observational data used in training; however, LOCA and MACA used two different versions of the Livneh dataset for bias correction, which somewhat complicates the comparison.

The factors identified as potentially contributing to biases in DDF curves for the historical period, in addition to other factors such as scenario uncertainty and natural variability, contribute to the total uncertainty in derived change factors, as discussed in Irizarry-Ortiz and others (2022). Because of the large uncertainties in the derived change factors and associated future DDF curves, methods for decision making under deep uncertainty could be used to increase flexibility in the planning process. These methods are documented by Marchau and others (2019) and include decision scaling, robust decision making, and dynamic adaptive policy pathways, among others. Flexibility in the phasing and design of various flood control adaptation measures could reduce long-term costs while considering the evolution in climate science as well as local and global changes in climate and sea-level rise with consideration for potential tipping points. Research gaps and recommendations have also been outlined by Florida International University’s Sea Level Solutions Center (Florida International University, 2021).