Contemporary and Future Characteristics of  Precipitation Indices in the Kentucky River Basin

Climatic variability can lead to large‐scale alterations in the hydrologic cycle, some of which can be characterized in terms of indices involving precipitation depth, duration and frequency. This study evaluated the spatiotemporal behavior of precipitation indices over the Kentucky River watershed for both the baseline period of 1986–2015 and late‐century time frame of 2070–2099. Historical precipitation data were collected from 16 weather stations in the watershed, while future rainfall time‐series were obtained from an ensemble of 10 Coupled Model Intercomparison Project Phase 5 (CMIP5) global circulation models under two future emission pathways: Representative Concentration Pathways (RCP) 4.5 and 8.5. Annual trends in seven precipitation indices were analyzed: total precipitation on wet days (PRCPTOT), maximum length (in days) of dry and wet periods (CDD and CWD, respectively), number of days with precipitation depth ≥20 mm (R20mm), maximum five‐day precipitation depth (RX5day), simple daily precipitation index (SDII) and standardized precipitation index (SPI, a measure of drought severity). Non‐parametric Mann–Kendall test results indicated significant trends for only ≈11% of the stationindex combinations, corresponding to generally increasing trends in PRCPTOT, CWD, R20mm and RX5day and negative trends for the others. Projected magnitudes for PRCPTOT, CDD, CWD, RX5day and SPI, indices associated with the macroweather regime, demonstrated general consistency with trends previously identified and indicated modest increases in PRCPTOT and CWD, slight decrease in CDD, mixed results for RX5day, and increased non‐drought years in the late century relative to the baseline period. Late‐century projections for the remaining indices (SDII, R20mm) demonstrated behavior counter to trends in the trends identified in the baseline period data, suggesting that these indices—which are more closely linked with the weather regime and daily GCM outputs—were relatively less robust.

The objectives of this study were to: (a) evaluate spatio-temporal magnitudes and trends of historical extreme precipitation indices for a river basin in Kentucky; and (b) compare these findings to projections from GCMs. The specific basin to be studied is the Kentucky River basin, a major tributary of the Ohio River that provides water for nearly 70 municipalities and roughly one-sixth of the Commonwealth's population. Given the relatively recent (2008 and 2012) droughts in Kentucky and the Kentucky River basin [32] and the impacts of drought on ecosystems, agriculture and water management, the findings of this study can be beneficial to policy makers, planners and managers entrusted with ensuring appropriate protection and sustained supplies for the basin's residents.

Study Area
The Kentucky River watershed is centered at approximately 38°41′ N 85°11′ W and encompasses an area of roughly 18,000 km 2 in the north-central part of the state ( Figure 1). Elevations range from 110 m in the northwest to 998 m in the southeast with a mean elevation of 554 m. The length of the main stream of the Kentucky River is 418 km. Mean annual rainfall varies from 1107 to 1308 mm, with the southern portion generally receiving more rainfall than the northern. The major land uses in the watershed are forest (55%) and hay production (25%) with smaller proportions in urban (8%), rangeland (6%), agricultural (2%) and other (4%) land uses. The Kentucky River provides 378,000 m 3 /day water for drinking and other uses [33].

Data Collection and Quality Assessment
Daily precipitation data were obtained from the Global Historical Climatology Network (GHCN) database (http://www.ncdc.noaa.gov/oa/climate/ghcn-daily/) maintained on the National Oceanic and Atmospheric Administration (NOAA) server (https://www.ncdc.noaa.gov/cdo-web/). Sixteen weather stations in the watershed were considered for the selected 30-year period of 1986-2015, subsequently referred to as the baseline period. The 30-year record length, which was near the limit of availability for consistent and near-complete stations in the basin, has a greater potential for bias than longer record lengths but is consistent with historical record lengths used in similar analyses [34][35][36]. Characteristics of the stations are summarized in Table 1, and their locations in relation to elevations, land uses and physiographic regions in the basin are given in Figure 2. The Climatol software package [37] was used to assess relative homogeneity of the data for each station and, had discontinuities been detected, to apply appropriate corrections. No discontinuities were detected in the data, and Climatol was further used to interpolate missing data on the basis of observations at neighboring stations. Sixteen weather stations in the watershed were considered for the selected 30-year period of 1986-2015, subsequently referred to as the baseline period. The 30-year record length, which was near the limit of availability for consistent and near-complete stations in the basin, has a greater potential for bias than longer record lengths but is consistent with historical record lengths used in similar analyses [34][35][36]. Characteristics of the stations are summarized in Table 1, and their locations in relation to elevations, land uses and physiographic regions in the basin are given in Figure 2. The Climatol software package [37] was used to assess relative homogeneity of the data for each station and, had discontinuities been detected, to apply appropriate corrections. No discontinuities were detected in the data, and Climatol was further used to interpolate missing data on the basis of observations at neighboring stations.

Future Climate Data Compilation
This study employed a suite of CMIP5 GCMs to generate daily precipitation data for the period 2070-2099 (subsequently referred to as the late-century period) at a resolution of 0.125°. A total of 10 GCMs (Table 2) were used to incorporate the models' output variability into the study and to reduce the uncertainty associated with choosing any particular model. Subsequent calculations of precipitation indices were based on the means of ensemble output of the GCMs as reported by, for example, Jha et al. [38], Zhang et al. [39] and Venkataraman et al. [40]. Since the focus of this paper is

Future Climate Data Compilation
This study employed a suite of CMIP5 GCMs to generate daily precipitation data for the period 2070-2099 (subsequently referred to as the late-century period) at a resolution of 0.125 • . A total of 10 GCMs (Table 2) were used to incorporate the models' output variability into the study and to reduce the uncertainty associated with choosing any particular model. Subsequent calculations of precipitation indices were based on the means of ensemble output of the GCMs as reported by, for example, Jha et al. [38], Zhang et al. [39] and Venkataraman et al. [40]. Since the focus of this paper is only on extreme precipitation indices, only RCP 4.5 and 8.5 were chosen, as they represent the intermediate and upper range, respectively, of radiative forcings at the end of century. These two emission pathways are considered more realistic in comparison to RCP 2.6.
The bias-corrected and spatially-disaggregated (BCSD) method [41][42][43] was adopted to downscale the GCM results. The BCSD method is a statistical downscaling algorithm that can be considered as consisting of two steps: a bias correction (BC) step and a spatial disaggregation (SD) step. The BC step broadly consists of a comparison of GCM outputs with corresponding observations over a common period. The results of the comparison are used to adjust projections to achieve greater agreement with the historical data and thus a more realistic representation of the spatial domain of interest [44,45]. The SD step involves interpolating the bias-corrected GCM outputs to higher-resolution grids by utilizing the spatial detail provided by observationally-derived datasets. Ning et al. [46] used the BCSD method to analyze projected changes in extreme climatic events over the northeastern United States and provided a detailed description of procedures used for bias correction and spatial disaggregation of GCM outputs. It is to be noted that, as reported by [31], this type of downscaling method does not guarantee close correspondence between short-term (days or weeks) behavior in observations and GCM projections. Additionally, elevation differences are unaccounted for in the interpolation algorithm. Even so, the quantile mapping technique [47] used in BCSD to eliminate bias in daily precipitation data resulted in monthly and annual precipitation predictions that agreed very well with observations [48]. In the present study, only the GCM grid points located nearest to the ground-based weather stations were considered in comparing GCM outputs to historical data.

Extreme Precipitation Indices
Following the joint recommendation of World Metrological Organization Commission for Climatology (CCI), World Climate Research Programme project on Climate Variability and Predictability, several extreme precipitation indices have been used in recent studies to characterize precipitation [58,59]. This study considered six of these indices as relevant to the basin and its potential hydrologic issues in terms of describing depth, duration and intensity for precipitation events up to a moderately extreme nature: 1.
The maximum length of dry periods (CDD, days) 3.
The maximum length of wet periods (CWD days) 4.
Number of days in a year with precipitation ≥20 mm (R20mm, days) 5.
The annual maximum precipitation over five consecutive days (RX5day, mm) 6.
The simple daily precipitation intensity (SDII, mm/day), calculated as PRCPTOT/(number of wet days) The R package Climdex [60] was used to calculate these indices from the daily time series data produced from each GCM, which were subsequently averaged over all GCMs. The final index used in the study was the Standardized Precipitation Index (SPI) [61], which has recently been recommended as a standard drought index by the World Metrological Organization (WMO) [62]. For a given duration, the SPI is calculated as the standard normal deviate of the distribution of cumulative rainfall for that duration; hence, negative values of SPI represent relative drought conditions with drought severity increasing with more negative SPI values (e.g., an SPI ≤ −2 can be considered an extreme drought; Table 3). Following Wang et al. [63], a 12-month duration (ending in December) was used for SPI computations to reflect longer-term conditions using the SPI package in R [64] statistical software. Table 3. Drought classification using the SPI index [61].

Level
Drought Category SPI Values Extreme drought SPI ≤ −2.0

Trend Detection
Prior to trend detection, total annual rainfall was examined for the presence of serial correlation, since serial correlation can adversely affect the quality of trend estimates of the indices such as PRCPTOT and SPI. However, none of stations was found as having significantly serially correlated data.
Trends were estimated at annual scale for the extreme precipitation indices using the nonparametric Mann-Kendall test [65]. The Mann-Kendall test has the advantage of being relatively unaffected by outliers and is not restricted to a particular sample distribution. Trends were spatially interpolated for graphical representation purposes from the point estimates using the surface inverse-distance-weighted (IDW) algorithm in the ArcGIS framework. Interpolation techniques that account for elevation variations have been shown (Xu et al. [66]) to reduce the mean absolute error of daily precipitation interpolations from 7% to 18% relative to inverse distance weighting. Maps derived from the two methods were very similar in major regards; however, the influence of individual stations on the maps was greater for IDW than when altitude was accounted for. While these results were obtained for daily precipitation rather than precipitation indices, the indices might exhibit a similarly high degree of station influence when mapped using the IDW technique.

GCM Performance Evaluation
Performance of the GCMs and ensemble mean in terms of total annual precipitation is indicated in Table 4, in which the mean absolute error (MAE) and normalized standard deviation (NSD) are used as metrics [40,67,68]. Near-unity values of MAE and NSD imply relatively high accuracy and similar variation, respectively, of projections relative to observations. On the basis of both MAE and NSD values, then, the GFDL-ESM2G model can be considered as demonstrating best overall performance ( Table 4). While the performance of the ensemble mean was better than that of any individual model, the ensemble mean was also associated with the lowest NSD, reflecting the damping effect of averaging projections across models. This is indicated in Figure 3, in which the GCM ensemble mean is shown to be very comparable to observations in terms of average magnitude, even if not reflecting the same degree of yearly variation. This comparison argues in favor of the ensemble mean if the interest is primarily in magnitudes (as may apply to studies involving data projections), though the variation in projections might be substantially lower than observed. Figure 4 indicates that, relative to observations, GCM outputs were relatively consistent across models and comparable to observations. Across all GCMs and months, Mean Absolute Error (MAE) [40,67,68] ranged from 0.22 to 14.16 mm. Across all months, MAE was lowest for the HadGEM2-CC (4.16 mm) and highest for the MIROC5 (7.40 mm) GCMs. Across all GCMs, overall performance was best for February (MAE = 1.74 mm) and worst for October (MAE = 10.30 mm). Based on t-tests applied to monthly results, the ensemble mean was in no case significantly (p < 0.05) different from the observed mean, indicating that the ensemble mean successfully reflects observed total monthly precipitation. best for February (MAE = 1.74 mm) and worst for October (MAE = 10.30 mm). Based on t-tests applied to monthly results, the ensemble mean was in no case significantly (p < 0.05) different from the observed mean, indicating that the ensemble mean successfully reflects observed total monthly precipitation.    best for February (MAE = 1.74 mm) and worst for October (MAE = 10.30 mm). Based on t-tests applied to monthly results, the ensemble mean was in no case significantly (p < 0.05) different from the observed mean, indicating that the ensemble mean successfully reflects observed total monthly precipitation.      Table 5 lists the annual mean values of the studied indices along with the trend slope estimates identified from baseline period data, each of which will be discussed individually in the coming subsections. Only a relatively small proportion (≈11%) of the trends were statistically significant (p < 0.05); all stations exhibiting a statistically significant trend for any of the indices were located in the central and northern portions of the basin (Clay station and north). The indices PRCPTOT, CWD and SDII demonstrated significant trends for the highest number of stations (three each), whereas trends in RX5day and SPI were not significant for any of the stations. Significant trends were identified for four of the seven indices for the Clay station, followed by three for the Lexington station.

PRCPTOT
The majority of stations (87.5%) demonstrated an increasing trend in PRCPTOT, suggestive of an overall wetting trend over the baseline period. Trends in PRCPTOT were significant for three of the 16 stations (Clay, Georgetown and Lexington, Table 5  The spatial distribution of PRCPTOT and its trends are given in Figure 5. Late-century projections for RCPs 4.5 and 8.5 are similar in the sense that both indicate modest basin-wide average increases in PRCPTOT (7 mm for RCP 4.5 and 29 mm for RCP 8.5), and except for the extreme southeastern portion (with decreases of 145-165 mm relative to the baseline period), most prominently in the southern portion of the watershed. In some cases, however, the projections are spatially inconsistent with baseline PRCPTOT values ( Figure 5b) and trends (Figure 5a). The Lexington and Georgetown stations, for example, had significantly increasing trends over the baseline period. Late-century projections, however, reflect a decrease (relative to the baseline period) of 8-36 mm for Georgetown and a net change of only −15-13 mm for Lexington. Similarly, the Clay station (which had the highest trend) is unremarkable in RCP 4.5 projections (Figure 5c) and has a lower PRCPTOT than the surrounding area in RCP 8.5 projections (Figure 5d).

CDD and CWD
Magnitudes of trends in CDD and CWD over the baseline period were generally low and significant in only four instances involving three stations (Clay, Frankfort Lock and Gest Lock). Figure 6a indicates generally negative trends in CDD in the northeastern portion of the basin, with (usually weakly) positive trends elsewhere. Figure 6b demonstrates that the northern portion of the basin had relatively higher CDD values than the southern for baseline conditions, a situation expected to persist according to late-century projections (Figure 6c,d). The late-century projections also indicate basin-wide decreases in CDD, with the areal average decreases ranging from two days (RCP 4.5) to three days (RCP 8.5). The projected decreases are generally consistent with trends identified in the baseline period with the possible exception of the west-central portion. The spatial distribution of PRCPTOT and its trends are given in Figure 5. Late-century projections for RCPs 4.5 and 8.5 are similar in the sense that both indicate modest basin-wide average increases in PRCPTOT (7 mm for RCP 4.5 and 29 mm for RCP 8.5), and except for the extreme southeastern portion (with decreases of 145-165 mm relative to the baseline period), most prominently in the southern portion of the watershed. In some cases, however, the projections are spatially inconsistent with baseline PRCPTOT values ( Figure 5b) and trends (Figure 5a). The Lexington and Georgetown stations, for example, had significantly increasing trends over the baseline period. Late-century projections, however, reflect a decrease (relative to the baseline period) of 8-36 mm for Georgetown and a net change of only −15-13 mm for Lexington. Similarly, the Clay station (which had the highest trend) is unremarkable in RCP 4.5 projections (Figure 5c) and has a lower PRCPTOT than the surrounding area in RCP 8.5 projections (Figure 5d).

CDD and CWD
Magnitudes of trends in CDD and CWD over the baseline period were generally low and significant in only four instances involving three stations (Clay, Frankfort Lock and Gest Lock). Figure 6a indicates generally negative trends in CDD in the northeastern portion of the basin, with (usually weakly) positive trends elsewhere. Figure 6b demonstrates that the northern portion of the basin had relatively higher CDD values than the southern for baseline conditions, a situation expected to persist according to late-century projections (Figure 6c,d). The late-century projections also indicate basin-wide decreases in CDD, with the areal average decreases ranging from two days (RCP 4.5) to three days (RCP 8.5). The projected decreases are generally consistent with trends identified in the baseline period with the possible exception of the west-central portion. Findings regarding CWD were generally complementary to those for CDD in that decreases in CDD were accompanied by increases in CWD. Trends in CWD were uniformly positive, strongest in the central and northern portions of the basin (Clay, Frankfort Lock and Gest Lock stations) and weaker elsewhere (Figure 7a). This general result is reflected in the late-century projections ( Figure  7c,d) where, relative to baseline conditions, CWD is anticipated to increase (particularly in the southern portion) throughout the basin. Late-century projections indicate an increase in CWD averaging 3 days across the basin, concentrated primarily in the southern portion for RCP 4.5 and somewhat more uniformly-distributed for RCP 8.5. Similar to the situation of PRCPTOT, the relatively high baseline trend in CWD for the Clay is not reflected in CWD projections (Figure 5c,d). Taken together, the CDD and CWD results suggest basin-wide decreases in runs of dry days along with increases in runs of wet days in the late-century period. Schoof [69] investigated changes in extreme precipitation indices for contiguous US and reported very similar projected changes in CDD and CWD for the time frame of 2066-2095 around the study area.  Findings regarding CWD were generally complementary to those for CDD in that decreases in CDD were accompanied by increases in CWD. Trends in CWD were uniformly positive, strongest in the central and northern portions of the basin (Clay, Frankfort Lock and Gest Lock stations) and weaker elsewhere (Figure 7a). This general result is reflected in the late-century projections (Figure 7c,d) where, relative to baseline conditions, CWD is anticipated to increase (particularly in the southern portion) throughout the basin. Late-century projections indicate an increase in CWD averaging 3 days across the basin, concentrated primarily in the southern portion for RCP 4.5 and somewhat more uniformly-distributed for RCP 8.5. Similar to the situation of PRCPTOT, the relatively high baseline trend in CWD for the Clay is not reflected in CWD projections (Figure 5c,d). Taken together, the CDD and CWD results suggest basin-wide decreases in runs of dry days along with increases in runs of wet days in the late-century period. Schoof [69] investigated changes in extreme precipitation indices for contiguous US and reported very similar projected changes in CDD and CWD for the time frame of 2066-2095 around the study area. Findings regarding CWD were generally complementary to those for CDD in that decreases in CDD were accompanied by increases in CWD. Trends in CWD were uniformly positive, strongest in the central and northern portions of the basin (Clay, Frankfort Lock and Gest Lock stations) and weaker elsewhere (Figure 7a). This general result is reflected in the late-century projections ( Figure  7c,d) where, relative to baseline conditions, CWD is anticipated to increase (particularly in the southern portion) throughout the basin. Late-century projections indicate an increase in CWD averaging 3 days across the basin, concentrated primarily in the southern portion for RCP 4.5 and somewhat more uniformly-distributed for RCP 8.5. Similar to the situation of PRCPTOT, the relatively high baseline trend in CWD for the Clay is not reflected in CWD projections (Figure 5c,d). Taken together, the CDD and CWD results suggest basin-wide decreases in runs of dry days along with increases in runs of wet days in the late-century period. Schoof [69] investigated changes in extreme precipitation indices for contiguous US and reported very similar projected changes in CDD and CWD for the time frame of 2066-2095 around the study area.

R20mm
Two stations (Georgetown and Lexington) indicated significant trends in R20mm (0.27 and 0.25 days/year, respectively); the remainder of the basin was found to have an approximately equal distribution of weakly positive and negative trends (Figure 8a). It is noteworthy that the Georgetown and Lexington stations are nearest in proximity to the most heavily urbanized portion of the basin; Misra et al. [70] suggested a linkage between urbanized areas in the US and increasing trends in indices such as daily maximum rainfall intensity and number of days with heavy precipitation, a finding more recently corroborated by Zilli et al. [71].
Late-century projections reflect basin-wide decreases of 4-5 days in R20mm (Figure 8c,d). Although the Georgetown/Lexington area is, consistent with baseline period trends, in the region of highest projected R20mm, late-century projections indicate decreases for these stations as well.
The results in this case indicate spatial consistency with baseline period analysis, but not trend consistency. This finding is suggestive that, rather than indicating reversal of contemporarily-assessed trends, the GCM projections might be reflecting the issues discussed by Lafon et al. [30]; namely, underestimation of rainfall intensities.

R20mm
Two stations (Georgetown and Lexington) indicated significant trends in R20mm (0.27 and 0.25 days/year, respectively); the remainder of the basin was found to have an approximately equal distribution of weakly positive and negative trends (Figure 8a). It is noteworthy that the Georgetown and Lexington stations are nearest in proximity to the most heavily urbanized portion of the basin; Misra et al. [70] suggested a linkage between urbanized areas in the US and increasing trends in indices such as daily maximum rainfall intensity and number of days with heavy precipitation, a finding more recently corroborated by Zilli et al. [71].
Late-century projections reflect basin-wide decreases of 4-5 days in R20mm (Figure 8c,d). Although the Georgetown/Lexington area is, consistent with baseline period trends, in the region of highest projected R20mm, late-century projections indicate decreases for these stations as well. The results in this case indicate spatial consistency with baseline period analysis, but not trend consistency. This finding is suggestive that, rather than indicating reversal of contemporarilyassessed trends, the GCM projections might be reflecting the issues discussed by Lafon et al. [30]; namely, underestimation of rainfall intensities.

RX5day
Analysis of baseline period data indicated a tendency toward decreasing trends in RX5day in the central portion of the basin and increasing trends elsewhere (Figure 9a). However, no station demonstrated a statistically significant trend in annual maximum five-day rainfall. Consistent with this result, late-century projections indicated modest or very slight changes in RX5day (<7% decrease for RCP 4.5, <1% increase for RCP 8.5) relative to the baseline period (Figure 9b-d). Shifts in the spatial distribution of RX5day across the basin are projected, however, with higher values in the north for the late-century.

RX5day
Analysis of baseline period data indicated a tendency toward decreasing trends in RX5day in the central portion of the basin and increasing trends elsewhere (Figure 9a). However, no station demonstrated a statistically significant trend in annual maximum five-day rainfall. Consistent with this result, late-century projections indicated modest or very slight changes in RX5day (<7% decrease for RCP 4.5, <1% increase for RCP 8.5) relative to the baseline period (Figure 9b-d). Shifts in the spatial distribution of RX5day across the basin are projected, however, with higher values in the north for the late-century.

SDII
Baseline period trends in SDII were mixed; the statistically significant (p < 0.05) trends were negative for two stations (Clay and Frankfort) and positive for the Lexington Station (Figure 10a), and inconsequential overall (Table 5). Projections for RCP 4.5 and 8.5 (Figure 10c,d), however, reflect decreases in SDII throughout the watershed for the late-century period (approximately 3 days for both RCP 4.5 and 8.5). As previously discussed, PRCPTOT was projected to increase (albeit modestly) by late century; this result must therefore necessarily reflect a projected change in annual numbers of wet days. Thus, this finding appears related to results related to CWD, collectively suggesting that either: (a) a currently-weak and mixed trends in SDII (or, more precisely, numbers of wet days) will broadly shift toward the positive direction in the late-century; or (b) the GCM projections contain excessive numbers of wet days.

SDII
Baseline period trends in SDII were mixed; the statistically significant (p < 0.05) trends were negative for two stations (Clay and Frankfort) and positive for the Lexington Station (Figure 10a), and inconsequential overall (Table 5). Projections for RCP 4.5 and 8.5 (Figure 10c,d), however, reflect decreases in SDII throughout the watershed for the late-century period (approximately 3 days for both RCP 4.5 and 8.5). As previously discussed, PRCPTOT was projected to increase (albeit modestly) by late century; this result must therefore necessarily reflect a projected change in annual numbers of wet days. Thus, this finding appears related to results related to CWD, collectively suggesting that either: (a) a currently-weak and mixed trends in SDII (or, more precisely, numbers of wet days) will broadly shift toward the positive direction in the late-century; or (b) the GCM projections contain excessive numbers of wet days.

SDII
Baseline period trends in SDII were mixed; the statistically significant (p < 0.05) trends were negative for two stations (Clay and Frankfort) and positive for the Lexington Station (Figure 10a), and inconsequential overall (Table 5). Projections for RCP 4.5 and 8.5 (Figure 10c,d), however, reflect decreases in SDII throughout the watershed for the late-century period (approximately 3 days for both RCP 4.5 and 8.5). As previously discussed, PRCPTOT was projected to increase (albeit modestly) by late century; this result must therefore necessarily reflect a projected change in annual numbers of wet days. Thus, this finding appears related to results related to CWD, collectively suggesting that either: (a) a currently-weak and mixed trends in SDII (or, more precisely, numbers of wet days) will broadly shift toward the positive direction in the late-century; or (b) the GCM projections contain excessive numbers of wet days.

SPI
While the direction of annual trend in year-ending SPI was in all cases negative, the trend in SPI was not significant (p < 0.05) for any of the 16 stations (Figure 11a). In terms of numerical magnitudes (Table 5), SPI values were quite small relative to drought category ranges (Table 3). Furthermore, as a result of the non-linear relationship between total annual rainfall and SPI, variation in annual rainfall (i.e., PRCPTOT) is amplified during SPI computations; this is evident in the relatively high standard deviations of year-ending SPI (Table 5).

SPI
While the direction of annual trend in year-ending SPI was in all cases negative, the trend in SPI was not significant (p < 0.05) for any of the 16 stations (Figure 11a). In terms of numerical magnitudes (Table 5), SPI values were quite small relative to drought category ranges (Table 3). Furthermore, as a result of the non-linear relationship between total annual rainfall and SPI, variation in annual rainfall (i.e., PRCPTOT) is amplified during SPI computations; this is evident in the relatively high standard deviations of year-ending SPI (Table 5). Relative to baseline SPI values (Figure 11b; zero by definition), both scenarios project increasing average SPI values (i.e., less drought) that demonstrate spatial variation across the watershed ( Figure  11c,d). Projections from RCP 4.5 indicate a late-century basin-wide average SPI of 0.11, whereas RCP 8.5 indicates an average of 0.17. Both of these findings are consistent with the earlier-discussed results regarding PRCPTOT, which is also projected to increase modestly in the late-century. Figure 12 indicates a late-century reapportionment of time spent in non-drought and mild drought conditions. For baseline conditions, approximately 86% of year-ending SPI values were evenly divided between the non-drought and mild drought categories. Late-century projections indicate that the proportion of non-drought and mild drought years will remain similar, but with an increase in non-drought years (to 60%-67%, depending on RCP) and a corresponding decrease in mild drought years. The spatial distribution of average late-century SPI projections is similar for the two RCPs, indicating relatively high values in the central portion of the watershed and lower values in the extreme southeast.
Given the annual duration of SPI computations, the findings of this study argue neither for nor against drought conditions that might arise on a smaller time scale (seasons or months). Depending on the future distribution of rainfall throughout the year, operationally-significant transitions in such shorter-duration droughts are possible. Analysis at a higher time resolution might be beneficial in view of the seasonality of some water demands and the related practical implications on water management. Relative to baseline SPI values (Figure 11b; zero by definition), both scenarios project increasing average SPI values (i.e., less drought) that demonstrate spatial variation across the watershed (Figure 11c,d). Projections from RCP 4.5 indicate a late-century basin-wide average SPI of 0.11, whereas RCP 8.5 indicates an average of 0.17. Both of these findings are consistent with the earlier-discussed results regarding PRCPTOT, which is also projected to increase modestly in the late-century. Figure 12 indicates a late-century reapportionment of time spent in non-drought and mild drought conditions. For baseline conditions, approximately 86% of year-ending SPI values were evenly divided between the non-drought and mild drought categories. Late-century projections indicate that the proportion of non-drought and mild drought years will remain similar, but with an increase in non-drought years (to 60%-67%, depending on RCP) and a corresponding decrease in mild drought years. The spatial distribution of average late-century SPI projections is similar for the two RCPs, indicating relatively high values in the central portion of the watershed and lower values in the extreme southeast.
Given the annual duration of SPI computations, the findings of this study argue neither for nor against drought conditions that might arise on a smaller time scale (seasons or months). Depending on the future distribution of rainfall throughout the year, operationally-significant transitions in such shorter-duration droughts are possible. Analysis at a higher time resolution might be beneficial in view of the seasonality of some water demands and the related practical implications on water management.

Summary and Conclusions
This study used data from 16 GHCN weather stations over the period 1986-2015 (the baseline period) to evaluate spatial variability and trends in precipitation indices for the Kentucky River basin. These findings were then considered alongside projections from 10 CMIP5 GCMs for the period 2070-2099 (late-century period) to assess changes in index magnitudes and spatial distribution as well as consistency with trends identified during the baseline period.
Averaged baseline period findings indicated that the southern portion (with higher elevations and proportion of forest cover) of the basin experienced generally higher PRCPTOT with fewer days separating rainfall events (CDD) and, especially in the extreme southeastern portion, longer runs of days with rainfall ≥1 mm (CWD). The spatial distribution of other indices was generally more uniform; noteworthy variations are more suggestive of microclimate effects (e.g., the Lexington/Georgetown and Clay stations) than systematic spatial trends. Trends in the indices over the baseline period were significant for only about 11% of the station-index combinations, all in the central and (to a lesser degree) northern portions of the basin, which are generally dominated by pasture/hay and urban land uses. Trends in PRCPTOT were among the most consistent, demonstrating increasing values (up to 15.68 mm/year) for all but two of the 16 stations and significant for three stations in the north-central portion of the basin. The Lexington and Georgetown stations, both in close proximity to the most heavily urbanized portion of the basin and separated by only about 50 km, had significant trends in R20mm, indicative of an increasing number of heavy rainfall events over the baseline period. Trends for remaining indices were directionally and spatially mixed to a higher degree, demonstrating less apparent relation to elevation or land use. The Clay station, in particular, was associated with inconsistent (relative to neighboring stations) results, perhaps related to its location near a physiographic region boundary (in the transition between Eastern Coal Fields and Outer Bluegrass, also transitional between dominant land uses), its relatively low elevation within the Kentucky River valley, or both.
Late-century projections for PRCPTOT, CDD, CWD, RX5day and SPI were, in the spatial aggregate, consistent with the trends identified on the basis of baseline data. These projections indicate modest (<2.5%) increases in total precipitation on wet (>1 mm) days with decreases (by 2-3 days) in maximum runs of dry days and increases (approximately three days) in maximum runs of wet days. Maximum five-day precipitation (RX5day) projections demonstrated more sensitivity to

Summary and Conclusions
This study used data from 16 GHCN weather stations over the period 1986-2015 (the baseline period) to evaluate spatial variability and trends in precipitation indices for the Kentucky River basin. These findings were then considered alongside projections from 10 CMIP5 GCMs for the period 2070-2099 (late-century period) to assess changes in index magnitudes and spatial distribution as well as consistency with trends identified during the baseline period.
Averaged baseline period findings indicated that the southern portion (with higher elevations and proportion of forest cover) of the basin experienced generally higher PRCPTOT with fewer days separating rainfall events (CDD) and, especially in the extreme southeastern portion, longer runs of days with rainfall ≥1 mm (CWD). The spatial distribution of other indices was generally more uniform; noteworthy variations are more suggestive of microclimate effects (e.g., the Lexington/Georgetown and Clay stations) than systematic spatial trends. Trends in the indices over the baseline period were significant for only about 11% of the station-index combinations, all in the central and (to a lesser degree) northern portions of the basin, which are generally dominated by pasture/hay and urban land uses. Trends in PRCPTOT were among the most consistent, demonstrating increasing values (up to 15.68 mm/year) for all but two of the 16 stations and significant for three stations in the north-central portion of the basin. The Lexington and Georgetown stations, both in close proximity to the most heavily urbanized portion of the basin and separated by only about 50 km, had significant trends in R20mm, indicative of an increasing number of heavy rainfall events over the baseline period. Trends for remaining indices were directionally and spatially mixed to a higher degree, demonstrating less apparent relation to elevation or land use. The Clay station, in particular, was associated with inconsistent (relative to neighboring stations) results, perhaps related to its location near a physiographic region boundary (in the transition between Eastern Coal Fields and Outer Bluegrass, also transitional between dominant land uses), its relatively low elevation within the Kentucky River valley, or both.
Late-century projections for PRCPTOT, CDD, CWD, RX5day and SPI were, in the spatial aggregate, consistent with the trends identified on the basis of baseline data. These projections indicate modest (<2.5%) increases in total precipitation on wet (>1 mm) days with decreases (by 2-3 days) in maximum runs of dry days and increases (approximately three days) in maximum runs of wet days. Maximum five-day precipitation (RX5day) projections demonstrated more sensitivity to the RCP, ranging from a roughly 7% decrease for RCP 4.5 to a 1% increase for RCP 8.5. Both RCPs project that on the basis of watershed-wide average SPI values, non-drought years will be more-common in the late-century, with mild drought years becoming less common; the proportion of years with more intense drought conditions (moderate, severe or extreme) is projected to remain essentially unchanged from the baseline period. Additional analysis based on a higher level of temporal disaggregation of projections will be required to support water resource management planning and operations that are based on smaller time durations (e.g., semi-annually or seasonally).
It may be noted that the above indices are associated with the "macroweather" (Lovejoy [72]) regime, considered as 5-10 days to 10-30 years. In other words, they are less vulnerable to the challenges of shorter-duration (i.e., the "weather" regime) GCM projections and could have been expected to be of relatively high fidelity. While this appears to have been the overall case, anomalous results occasionally surfaced in the spatial domain. The apparent microclimates in the vicinities of the Lexington/Georgetown and Clay stations, for example, were not evidenced as expected in the projections. This phenomenon is likely an outcome of the GCM output downscaling algorithm and/or the mapping algorithm, especially given the distance and elevation difference between the Clay station and its neighbors.
In the cases of the remaining indices (R20mm and SDII), late-century projections sometimes stood in contrast to trends identified during the baseline period. The significant baseline period trends in R20mm, for example, were in the positive direction; projections from both RCPs, however, indicate basin-wide decreases in the late-century period. Similarly, an overall negligible trend was identified for SDII during the baseline period; however, basin-wide decreases were projected for the late-century, including stations for which the SDII trend was statistically significant (p < 0.05) and positive. Unlike the previous five indices, R20mm and SDII are highly associated with the "weather" regime with R20mm being a sum individual, not-necessarily-consecutive days and SDII being a function of a similar sum. To a relatively high degree, therefore, the robustness of these indices is dependent on that of daily GCM outputs. For this study, ensemble GCM projections appear to have more wet days, containing fewer instances of moderately severe rainfall, than anticipated on the strength of baseline data analysis. This, in turn, suggests opportunity in terms of improvements to appropriate internal model structure and/or supplementary output processing algorithms.
The inconsistencies between baseline period trends and late-century projections are cautionary; at a minimum, they suggest limitations in reconciling analyses on relatively small temporal and spatial scales to GCM projections, even when those projections are bias-corrected and spatially downscaled. It seems possible that this study's findings with regard to baseline period conditions and trends reflect relatively large influences of small-scale variables such as elevation and land cover, whose relative importance diminishes in the context of relatively low-resolution GCM projections. While scale-and timeframe-related anomalies need not be irreconcilable, their occurrence can represent challenges to those charged with applying low-resolution projections to smaller scales of decision-making and effective management.