Changes in Extremes of Temperature , Precipitation , and Runoff in California ’ s Central Valley During 1949 – 2010

This study presents a comprehensive trend analysis of precipitation, temperature, and runoff extremes in the Central Valley of California from an operational perspective. California is prone to those extremes of which any changes could have long-lasting adverse impacts on the society, economy, and environment of the State. Available long-term operational datasets of 176 forecasting basins in six forecasting groups and inflow to 12 major water supply reservoirs are employed. A suite of nine precipitation indices and nine temperature indices derived from historical (water year 1949–2010) six-hourly precipitation and temperature data for these basins are investigated, along with nine indices based on daily unimpaired inflow to those 12 reservoirs in a slightly shorter period. Those indices include daily maximum precipitation, temperature, runoff, snowmelt, and others that are critical in informing decision making in water resources management. The non-parametric Mann-Kendall trend test is applied with a trend-free pre-whitening procedure in identifying trends in these indices. Changes in empirical probability distributions of individual study indices in two equal sub-periods are also investigated. The results show decreasing number of cold nights, increasing number of warm nights, increasing maximum temperature, and increasing annual mean minimum temperature at about 60% of the study area. Changes in cold extremes are generally more pronounced than their counterparts in warm extremes, contributing to decreasing diurnal temperature ranges. In general, the driest and coldest Tulare forecasting group observes the most consistent changes among all six groups. Analysis of probability distributions of temperature indices in two sub-periods yields similar results. In contrast, changes in precipitation extremes are less consistent spatially and less significant in terms of change rate. Only four indices exhibit statistically significant changes in less than 10% of the study area. On the regional scale, only the American forecasting group shows significant decreasing trends in two indices including maximum six-hourly precipitation and simple daily intensity index. On the other hand, runoff exhibits strong resilience to the changes noticed in temperature and precipitation extremes. Only the most southern reservoir (Lake Isabella) shows significant earlier peak timing of snowmelt. Additional analysis on runoff indices using different trend analysis methods and different analysis periods also indicates limited changes in these runoff indices. Overall, these findings are meaningful in guiding reservoir operations and water resources planning and management practices.


Introduction
Climatic and weather-induced hazards including excessive heat, flooding, and drought are often economically, environmentally, and societally disruptive [1][2][3].Previous studies have suggested that such hazards are typically caused by changes in the frequency and intensity rather than the mean of hydro-climatic variables including precipitation, temperature, and runoff [4,5].Changes in these variables are projected to intensify in both magnitude and occurrence frequency in the future [6][7][8][9].In light of those observations and projections, numerous studies have been dedicated to investigating the (often evolving) spatial and temporal characteristics of observed hydroclimatic extremes in areas prone to these extremes including the State of California [10][11][12][13][14][15][16][17], with the general goal being to (1) gain insights on their past behavior so that they can be better predicted in the future; and (2) inform the development of corresponding mitigation and adaptation strategies.
As the home to over 37 million people [18] and an important economy in the world, California predominantly relies on a relatively small number of big storms in the winter in the Central Valley to meet its increasing and often competing water demand during the spring and early summer [19].A year having fewer or greater than average of such events can be particularly dry or wet.The State is thus prone to hydroclimatic extremes, with the most recent examples being water year 2015 (record high temperature and record low snowpack observed across the State) [20] and water year 2017 (record high precipitation in the Northern Sierra).Any changes to precipitation, temperature and runoff events, particularly extremes, could have long-lasting adverse impacts on the society, economy, and environment of the State.Understanding the variability and trends in these extremes is the foremost step in better predicting their future occurrence and behavior.This is particularly important in the Central Valley which serves as a major water supply source for the State.The Central Valley also accommodates the majority of the State's complex water storage and transfer system including the Central Valley Project (CVP) and State Water Project (SWP).On average, these two projects collectively provide water to about two thirds of Californians and about 15,000 km 2 of farmland across the State annually [21].
A number of previous studies have looked at the changes in hydroclimatic extremes in areas covering California [22][23][24][25][26].The data used were typically at monthly or coarser resolution either focusing on climatic (precipitation and temperature) extremes or hydrologic (runoff) extremes.Those studies may be more meaningful in guiding long-term planning practice rather than real-time operations (e.g., providing flow forecasting to inform decisions for a short-term reservoir release schedule).The latter requires the analysis to be focused on an operational dataset (used to train or run the operational models) at temporal (sub-daily) and spatial (at forecasting basin) scales meaningful to short-term operations.Additionally, those studies generally employed the traditional linear regression approach that requires the residuals of the fitted regression line be normally distributed.This assumption is often difficult to be satisfied.Similar studies have also been conducted in regions out of California [27,28].To our knowledge, no studies have been conducted to assess the changes in both climatic and hydrologic extremes in California, (1) at the spatial scale directly relevant to real-time water management operations; (2) using operational datasets; and (3) via a trend analysis approach other than the traditional linear regression method.
This study provides a comprehensive trend analysis of precipitation and temperature extremes for 176 major operational forecasting basins in six different forecasting groups as well as runoff extremes at 12 major water supply reservoirs in California's Central Valley.Operational long-term six-hourly precipitation and temperature along with daily inflow data for those study basins and reservoirs are used for this purpose.The study adopts a non-parametric rank-based Mann-Kendall test method with a trend-free pre-whitening procedure which requires fewer assumptions than the linear regression method.Additionally, this study investigates changes in empirical probability distributions of individual study metrics in two equal sub-periods via the two-sample Kolmogorov-Smirnov test.The study aims to address the following questions: (1) what are the direction (increasing, decreasing, or no change), rate of change, and spatial coverage of the changes in those precipitation, temperature, and runoff extremes; and (2) what are the scientific and practical implications of these changes?
The smallest reservoirs include Englebright Reservoir in the Feather-Yuba region (FYU) and Lake Success in the Tulare region (TUL) (Table 2).In terms of total annual runoff, Shasta Lake receives the largest amount on both seasonal (April-July) and annual scales, while Lake Success observes the least amount on both temporal scales.The ratio of April-July runoff over annual runoff, however, generally increases from north to south, with the exception being Lake Success which is located in the foothills (Figure 1) and is thus less impacted by snow.This indicates the increasing dominance of snow contribution to the annual runoff in the southern Sierra watersheds.Those watersheds are typically located in higher elevations (Figure 1) and thus more impacted by snow.For most reservoirs, the data record period is water year 1961-2010.For Englebright and Don Pedro, however, the data is only available in a slightly shorter period (Table 2).receives the largest amount on both seasonal (April-July) and annual scales, while Lake Success observes the least amount on both temporal scales.The ratio of April-July runoff over annual runoff, however, generally increases from north to south, with the exception being Lake Success which is located in the foothills (Figure 1) and is thus less impacted by snow.This indicates the increasing dominance of snow contribution to the annual runoff in the southern Sierra watersheds.Those watersheds are typically located in higher elevations (Figure 1) and thus more impacted by snow.For most reservoirs, the data record period is water year 1961-2010.For Englebright and Don Pedro, however, the data is only available in a slightly shorter period (Table 2).

Study Indices
The indices investigated in this study include nine indices for each variable of temperature, precipitation, and runoff (Table 3).The temperature and precipitation indices are fairly standard indices defined by the World Meteorological Organization Commission for Climatology and the Expert Team on Climate Change Detection, Monitoring, and Indices (ETCCDMI) [31].They have been widely applied in analyzing extreme events worldwide [12,14,15,17,[32][33][34][35].The runoff indices selected are typically used as operational metrics in guiding reservoir operations and water supply planning practices [36].The snowmelt related indices (S1D, S3D, S5D, and SP) are determined from

Study Indices
The indices investigated in this study include nine indices for each variable of temperature, precipitation, and runoff (Table 3).The temperature and precipitation indices are fairly standard indices defined by the World Meteorological Organization Commission for Climatology and the Expert Team on Climate Change Detection, Monitoring, and Indices (ETCCDMI) [31].They have been widely applied in analyzing extreme events worldwide [12,14,15,17,[32][33][34][35].The runoff indices selected are typically used as operational metrics in guiding reservoir operations and water supply planning practices [36].The snowmelt related indices (S1D, S3D, S5D, and SP) are determined from runoff observations from April-July which is typically deemed as the major snowmelt period in California.The timing of the center of mass of the annual runoff (QC) is calculated as a flow-weighted timing following [37,38]: where t i (i = 1, 2, 3, . . ., n; n = 365 for normal years and 366 for leap years) is timing in days since the start of the water year; q i is the corresponding runoff observation for day i.

Trend Analysis
There are generally two types of trend analysis methods, parametric and non-parametric [39,40], commonly applied in climatic and hydrological trend analysis.Compared to parametric methods (e.g., linear regression), the non-parametric approaches require fewer assumptions including not requiring the study data to be normally distributed.The assumptions on data distribution are often not satisfied due to a range of issues including missing data.As such, the non-parametric methods are considered more robust than the parametric ones [40].Among the non-parametric methods, the Mann-Kendall test (MKT) [41,42] is likely the most widely used, particularly in the field of hydrology and climatology [43].This study employs the MKT in assessing the significance of a trend.In this approach, the sign of each possible pair of observations is first identified, followed by the calculation of the corresponding test statistic δ.The null hypothesis (H 0 ) assumes no significant monotonic trend in the observations while the alternative hypothesis suggests otherwise.The null hypothesis is rejected when |z| > z 1−α/2 , where z 1−α/2 is the probability of the standard normal distribution at a significance level of α.In this study, α is set as 0.05 unless otherwise noted.The corresponding z 1−α/2 equals 1.96 in this case.The non-parametric Theil-Sen approach (TSA) [44,45] is used in the study to identify the slope of significant trends determined via the MKT.The slope values (vector S) of all data pairs in the study time series are first determined: where n is the length of the time series; x i and x j are time series values at time i and j, respectively, with i > j.The median of S is the Sen's estimate on the slope.A positive (negative) slope value indicates an increasing (decreasing) trend.A detailed explanation on the TSA method can be found at [43].
Previous research [46][47][48] suggested that the presence of positive serial correlation (which is common in hydroclimatic observations including temperature and runoff measurements) increases the probability of false rejection of the null hypothesis of no trends.[43,49] proposed a trend-free pre-whitening procedure (TFPW) to address the serial correlation issue.The general steps include, first, de-trending the original time series which has a significant trend (determined via the MKT with a significance level of 0.05); removing a lag-one auto-regressive process from the de-trended time series to produce a new time series; adding the trend in the original time series to the new time series, yielding a pre-whitened time series which is then used in the trend analysis.The readers are referred to [49] for technical details on the TFPW procedure.

Distribution Pattern
In addition to the trends across the entire study period, changes in empirical probability distributions of individual study indices in two equal sub-periods of the study period are also investigated.Specifically, the study period of a specific index (e.g., 1949-2010 for R10) is divided into two halves (e.g., 1949-1979 and 1980-2010).The general idea is to evaluate if there are any pronounced shifts in the statistical characteristics (e.g., median, probability distribution) of the study indices in two different phases of the study period.Two equal sub-periods (e.g., two halves of the study period) are often adopted as a common practice [30].The empirical probability distribution functions (PDFs) of the index in these two sub-periods are derived and compared with each other.Following [32], a two-sample Kolmogorov-Smirnov test is applied to test if the index values in two sub-periods come from a same distribution (null hypothesis) or different distributions (alternative hypothesis).Specifically, the test compares the cumulative distribution functions (CDFs) of two samples in those two sub-periods, respectively.The test outputs a p-value corresponding to a critical value of the maximum absolute difference between these two CDFs.The alternative hypothesis is favored if the p-value is less than a preset significance level (0.05 in this case).More details on this method are available in [32,50].

Temperature Indices
A variety of basins show significant trends for each of the nine temperature indices, ranging from 41 basins (for number of warm days (TX90)) to 136 basins (for annual mean minimum temperature (TNM)) out of the 176 study basins (Figure 3a).The trends in three indices including number of cold days (TX10), number of cold nights (TN10), and mean diurnal temperature range (DTR) are mostly negative, indicative of decreasing number of cold days, cold nights, and decreasing daily temperature range for those basins.For warm days (TX90), about half of the basins (22 out of 41) showing significant changing tendency have increasing trends.For the remaining five indices, the trends are generally positive, suggesting that the number of warm nights (TN90), six-hourly maximum (TX6h) and minimum (TN6h) temperature, and annual mean maximum (TXM) and minimum (TNM) temperature are all increasing for those basins that exhibit significant trends.The relationship between these trend slopes and basin elevations is moderate for the number of cold days (TX10, with a Pearson's correlation coefficient at 0.53 and p = 0.002) and minimum six-hourly temperature (TN6h, with a correlation coefficient at 0.57 and p = 0), indicating basins in higher elevations have a relatively stronger increasing trend in these two indices.For other indices, the correlation is generally not strong (Figure 3a), neither is the relationship between these trend slopes and the geographic location (latitude and longitude) of the study basins (not shown).It is worth noting that there are a few basins showing increasing trends in cold days (TX10) and diurnal temperature range (DTR) as well as decreasing warm nights (TN90) and annual mean maximum temperature (TXM).However, these basins only account for a very small percentage of the entire study area (1.3% for TX10, 1.9% for TN90, 1.6% for TXM, and 1.7% for DTR).Nevertheless, the inconsistent responses across different basins to the changing climate highlight the complex geographic conditions of these basins (Tables A1-A6).Looking at the overall percentage of area showing significant trend (Figure 3b), slightly above 60% of the total area of the 176 study basins exhibits increasing trend for number of warm nights (TN90), maximum six-hourly temperature (TX6h), and annual mean minimum temperature (TNM).There is roughly 60% of the total area showing decreasing trend in the number of cold nights (TN10).About half of the area observes increasing minimum six-hourly temperature (TN6h), while the basins showing a smaller daily diurnal temperature ranges also accounts for about half of the total area.For the remaining indices, the area with either increasing or decreasing trend accounts for less than one third of the total area.minimum (TNM) temperature are all increasing for those basins that exhibit significant trends.The relationship between these trend slopes and basin elevations is moderate for the number of cold days (TX10, with a Pearson's correlation coefficient at 0.53 and p = 0.002) and minimum six-hourly temperature (TN6h, with a correlation coefficient at 0.57 and p = 0), indicating basins in higher elevations have a relatively stronger increasing trend in these two indices.For other indices, the correlation is generally not strong (Figure 3a), neither is the relationship between these trend slopes and the geographic location (latitude and longitude) of the study basins (not shown).It is worth noting that there are a few basins showing increasing trends in cold days (TX10) and diurnal temperature range (DTR) as well as decreasing warm nights (TN90) and annual mean maximum temperature (TXM).However, these basins only account for a very small percentage of the entire study area (1.3% for TX10, 1.9% for TN90, 1.6% for TXM, and 1.7% for DTR).Nevertheless, the inconsistent responses across different basins to the changing climate highlight the complex geographic conditions of these basins (Tables A1-A6).Looking at the overall percentage of area showing significant trend (Figure 3b), slightly above 60% of the total area of the 176 study basins exhibits increasing trend for number of warm nights (TN90), maximum six-hourly temperature (TX6h), and annual mean minimum temperature (TNM).There is roughly 60% of the total area showing decreasing trend in the number of cold nights (TN10).About half of the area observes increasing minimum six-hourly temperature (TN6h), while the basins showing a smaller daily diurnal temperature ranges also accounts for about half of the total area.For the remaining indices, the area with either increasing or decreasing trend accounts for less than one third of the total area.On the regional scale (Figure 4), all six regions exhibit significant increasing trend in the annual mean minimum temperature (TNM).All regions except for the Upper Sacramento region (UPS) show significant decreasing trend (with changing rate ranging from −0.44 to −0.31 day/year) in the number of cold nights (TN10) and increasing trend (with trend slope varying from 0.26 to 0.56 day/year) number of warm nights (TN90).Those five regions also observe decreasing (with rate varying from −0.31 to −0.13 • C/decade) diurnal temperature range (DTR).Five out of six regions (except for North San Joaquin) also show increasing tendency in maximum six-hourly temperature (TX6h).Across all regions, Tulare (TUL) is the only one exhibiting significant trends in all nine temperature indices, highlighting its sensitivity to temperature change.Except for Tulare region, the other five regions show no significant changes in the number of cold days (TX10), warm days (TX90), and annual mean maximum temperature (TXM).
Hydrology 2018, 5, 1 9 of 25 On the regional scale (Figure 4), all six regions exhibit significant increasing trend in the annual mean minimum temperature (TNM).All regions except for the Upper Sacramento region (UPS) show significant decreasing trend (with changing rate ranging from −0.44 to −0.31 day/year) in the number of cold nights (TN10) and increasing trend (with trend slope varying from 0.26 to 0.56 day/year) number of warm nights (TN90).Those five regions also observe decreasing (with rate varying from −0.31 to −0.13 °C/decade) diurnal temperature range (DTR).Five out of six regions (except for North San Joaquin) also show increasing tendency in maximum six-hourly temperature (TX6h).Across all regions, Tulare (TUL) is the only one exhibiting significant trends in all nine temperature indices, highlighting its sensitivity to temperature change.Except for Tulare region, the other five regions show no significant changes in the number of cold days (TX10), warm days (TX90), and annual mean maximum temperature (TXM).Different basins show significantly different distribution patterns in the first half and second half (hereinafter referred to as "two sub-periods") of the study period across different temperature indices (Figure 5).More than half of the study area shows different distributions for four indices including number of cold nights (TN10) and warm nights (TN90), minimum six-hourly temperature (TN6h), and the annual mean of minimum temperature (TNM).Specifically, 77% of the study area has different TNM distributions in two sub-periods of the entire study period (Figure 5i).For these four indices, their corresponding study areas exhibiting significant trend are also high (around 60%, Figure 3b).The index with the smallest amount of area (9%) showing different distributions in two sub-periods is the number of warm days (TX90; Figure 5b).This confirms the observation in Figure 3 that changes in this index are the least consistent among all indices.Particularly, for the basins with significant trend in this index, about half of them have increasing trend and the other half show negative trends (Figure 3b).For the remaining four indices, the area showing different distributions in two sub-periods accounts for about 23% (number of cold nights, TX10) to 38% (annual mean maximum temperature, TXM).
Looking at differences in distribution patterns in the two sub-periods at the regional scale, annual mean minimum temperature (TNM) is the only index showing significant differences across all six study regions (Figure 6), with the p-value ranging from near zero (TUL) up to 0.01 (UPS).It is also the only index exhibiting significant trends for all regions (Figure 4).In contrast, the number of warm days (TX90) tends to preserve the same distribution in two sub-periods for all regions.For the number of cold nights (TN10) and minimum six-hourly temperature (TN6h), five out of six regions have significant differences in distribution patterns in two sub-periods.Across all study regions,  Different basins show significantly different distribution patterns in the first half and second half (hereinafter referred to as "two sub-periods") of the study period across different temperature indices (Figure 5).More than half of the study area shows different distributions for four indices including number of cold nights (TN10) and warm nights (TN90), minimum six-hourly temperature (TN6h), and the annual mean of minimum temperature (TNM).Specifically, 77% of the study area has different TNM distributions in two sub-periods of the entire study period (Figure 5i).For these four indices, their corresponding study areas exhibiting significant trend are also high (around 60%, Figure 3b).The index with the smallest amount of area (9%) showing different distributions in two sub-periods is the number of warm days (TX90; Figure 5b).This confirms the observation in Figure 3 that changes in this index are the least consistent among all indices.Particularly, for the basins with significant trend in this index, about half of them have increasing trend and the other half show negative trends (Figure 3b).For the remaining four indices, the area showing different distributions in two sub-periods accounts for about 23% (number of cold nights, TX10) to 38% (annual mean maximum temperature, TXM).
Looking at differences in distribution patterns in the two sub-periods at the regional scale, annual mean minimum temperature (TNM) is the only index showing significant differences across all six study regions (Figure 6), with the p-value ranging from near zero (TUL) up to 0.01 (UPS).It is also the only index exhibiting significant trends for all regions (Figure 4).In contrast, the number of warm days (TX90) tends to preserve the same distribution in two sub-periods for all regions.For the number of cold nights (TN10) and minimum six-hourly temperature (TN6h), five out of six regions have significant differences in distribution patterns in two sub-periods.Across all study regions, Tulare region (TUL) again shows most significant changes with eight out of nine indices having significantly different distribution patterns in two sub-periods.The probability distributions of those indices in two sub-periods are further explored for the Tulare region (TUL) (Figure 7).It is evident that, except for TX90 index (number of warm days; Figure 7b), other indices have remarkable shifts in the distributions in two sub-periods.This is consistent with the observation in Figure 6 that TX90 is the only index with a p-value (0.12) greater than 0.05.Among other indices, minimum six-hourly temperature (TN6h) has the highest p-value (0.03).Compared to the first sub-period , the second sub-period (1980-2010) observes less number of cold days (TX10; Figure 7a) and cold nights (TN10; Figure 7c) on average, while it has higher number of warm nights (TN90; Figure 7d).Meanwhile, the second sub-period generally has higher maximum (TX6h; Figure 7e) and minimum (TN6h; Figure 7f) six-hourly temperature as well as higher annual mean maximum (TXN; Figure 7g) and minimum (TNM; Figure 7h) temperature.Those observations collectively indicate a transition to more warming conditions in the recent decades .The second sub-period also has a smaller diurnal temperature range (DTR; Figure 7i) compared to the first sub-period, implying that the daily minimum temperature is increasing at a faster rate than the daily maximum temperature.The probability distributions of those indices in two sub-periods are further explored for the Tulare region (TUL) (Figure 7).It is evident that, except for TX90 index (number of warm days; Figure 7b), other indices have remarkable shifts in the distributions in two sub-periods.This is consistent with the observation in Figure 6 that TX90 is the only index with a p-value (0.12) greater than 0.05.Among other indices, minimum six-hourly temperature (TN6h) has the highest p-value (0.03).Compared to the first sub-period , the second sub-period (1980-2010) observes less number of cold days (TX10; Figure 7a) and cold nights (TN10; Figure 7c) on average, while it has higher number of warm nights (TN90; Figure 7d).Meanwhile, the second sub-period generally has higher maximum (TX6h; Figure 7e) and minimum (TN6h; Figure 7f) six-hourly temperature as well as higher annual mean maximum (TXN; Figure 7g) and minimum (TNM; Figure 7h) temperature.Those observations collectively indicate a transition to more warming conditions in the recent decades .The second sub-period also has a smaller diurnal temperature range (DTR; Figure 7i) compared to the first sub-period, implying that the daily minimum temperature is increasing at a faster rate than the daily maximum temperature.

Precipitaiton Indices
For precipitation, only four out of nine investigated indices show significant trend in a certain number of basins (Figure 8).Specifically, only four basins that account for 1.6% of the total study area exhibit decreasing trend in maximum six-hour precipitation (R6h; Figure 8a).The decreasing rate is generally small, ranging from −0.15 mm/year to −0.10 mm/year.There are 11 basins (7.5% of the entire study area) showing decreasing trend in maximum daily precipitation (R1D), with trend slope ranging from −0.47 mm/year to −0.24 mm/year (Figure 8b).There is only one basin (1% of the study area) showing significant declining tendency in 99th percentile precipitation (R99).As for the simple daily intensity index (SDII), 23 basins (9.3% of the study area) exhibit decreasing tendency (Figure 8d).However, the decreasing rate is not remarkable in terms of magnitude.The correlation coefficient between the slope value of R1D (SDII) and basin median elevation is −0.62 with p = 0.04

Precipitaiton Indices
For precipitation, only four out of nine investigated indices show significant trend in a certain number of basins (Figure 8).Specifically, only four basins that account for 1.6% of the total study area exhibit decreasing trend in maximum six-hour precipitation (R6h; Figure 8a).The decreasing rate is generally small, ranging from −0.15 mm/year to −0.10 mm/year.There are 11 basins (7.5% of the entire study area) showing decreasing trend in maximum daily precipitation (R1D), with trend slope ranging from −0.47 mm/year to −0.24 mm/year (Figure 8b).There is only one basin (1% of the study area) showing significant declining tendency in 99th percentile precipitation (R99).As for the simple daily intensity index (SDII), 23 basins (9.3% of the study area) exhibit decreasing tendency (Figure 8d).However, the decreasing rate is not remarkable in terms of magnitude.The correlation coefficient between the slope value of R1D (SDII) and basin median elevation is −0.62 with p = 0.04 (−0.64 with p = 0.001), indicative of a milder decreasing rate for high elevations for those basins exhibiting significant trends.Looking at the regional scale, generally all regions show a declining tendency in maximum sixhourly (T6h), daily (R1D), three-day (R3D), and 99th percentile precipitation (R99) as well as the simply daily intensity index (SDII) (Table 4).However, only the trends in R6h and SDII for American region (AME) are significant (α = 0.05).In both cases, the decreasing rates are generally small (−0.11 mm/year and −0.05mm/year, respectively).Table 4. Trend slope of precipitation indices at the regional scale 1 .Looking at the regional scale, generally all regions show a declining tendency in maximum six-hourly (T6h), daily (R1D), three-day (R3D), and 99th percentile precipitation (R99) as well as the simply daily intensity index (SDII) (Table 4).However, only the trends in R6h and SDII for American region (AME) are significant (α = 0.05).In both cases, the decreasing rates are generally small (−0.11 mm/year and −0.05 mm/year, respectively).The distribution patterns in two sub-periods for those precipitation indices are also investigated.Unlike their temperature counterparts, those indices show no significant shifts in distributions for any basin or any region (p-value consistently above 0.05).All in all, the changes in precipitation extremes are generally insignificant in terms of change rate and spatially incoherent.

Runoff Indices
In addition to precipitation and temperature indices, this study further investigates the changes in runoff indices since runoff, as opposed to precipitation and temperature, is often the variable directly used to inform decision making in most water resources planning and management practices.Surprisingly, none of the 12 locations exhibit any statistically significant (at 0.05 significance level) in peak volume indices (including maximum daily, three-day, and five-day runoff and snowmelt) and the timing indices (QP, QC, and SP).Only Lake Isabella (ISAC1) shows significant decreasing trend in peak snowmelt timing (occurs earlier at a rate about 0.23 day/year)) when the significant level is slightly increased (using 0.06 instead of 0.05 as the significance level).With an even higher significance level (0.10), one additional location (Folsom Lake, FOLC1) shows significant trend in peak runoff timing (occurs later at a rate of 1 day/year).This is likely due to the decreasing tendency observed in most precipitation extremes (Table 4) in the American region (AME) which drains into Folsom Lake.For other indices and other locations, no significant trends are detected at this significant level (0.10).
Looking at index PDFs in two sub-periods of the record period, it is largely unlikely to favor the hypothesis that the index in two sub-periods comes from two different distributions only with one exception (peak snowmelt timing for Lake Isabella; Table 5).This is likely due to the fact that its drainage basins are the most southern ones (drier conditions are typically expected moving south).Snowmelt makes up a large contribution to runoff at this location (April-July runoff accounts for 63% of the annual runoff; Table 2).While snowmelt is very sensitive to warming, no significant changes in precipitation extremes are observed (Figure 8).In brief, changes in runoff extremes are even less significant and consistent (spatially) compared to changes in precipitation indices.

Temperature Indices
The results show significant decreasing trend in the number of cold nights (TN10) along with increasing trends in the number warm nights (TN90), maximum six-hourly temperature (TX6h), and annual mean minimum temperature (TNM) for about 60% of the entire study area.At the regional scale, changes in these indices are also evident.Specifically, all six study regions show increasing trends in annual mean minimum temperature (TNM) and five regions exhibit significant trend in cold nights (TN10; decreasing trend), warm nights (TN90; increasing trend), and maximum six-hourly temperature (TX6h; increasing trend).This transition toward more warm extremes has also been noticed in previous studies in other regions around the world [17,[32][33][34]51].The current study further identifies decreasing trends in diurnal temperature range (DTR) at both basin (statistically significant at about half of the entire study area) and regional (significant over five out of six regions) scales.This finding was also reported in previous studies [10,16,33,35].This decreasing trend is likely due to the fact that increasing trend observed in annual mean maximum temperature (TXM) is not as significant (in terms of change rate) and consistent (in terms of area exhibiting trends) as that of the annual mean minimum temperature (TNM).The correlation between the changing rate and the elevation of the corresponding basin (exhibiting changes) is generally not strong.There are remarkable shifts in the empirical probability distribution functions (PDFs) in the first half  of the study period and second half (1980-2010) of the study period over half of the entire study area for the number of cold nights (TN10), warm nights (TN90), minimum six-hourly temperature (TN6h), and annual mean minimum temperature (TNM), indicating more warming conditions in the second half of the study period.Comparing different regions, Tulare region (TUL) preserves the most consistent changes measured by both trend (all nine indices show significant warming tendency) and PDFs pattern change (eight out of nine indices with PDFs shifts toward warming conditions in the second half of the study period).This is not surprising given its elevation (highest and thus coolest region) and geographic location (most southern and thus driest region) which make it the region most sensitive to any changes in temperature extremes.

Precipitation Indices
In contrast to temperature indices, precipitation indices show much less significant and coherent changes.Five indices including annual count of heavy precipitation days (R10) and very heavy precipitation days (R20), maximum three-day (R3D) and five-day precipitation (R5D), along with annual count of precipitation above 95th percentile (R95) show no significant increasing or decreasing trends at any of the 176 study basins.Only four basins (1.6% of the entire study area) show statistically significant decreasing trend in maximum six-hourly precipitation (R6h) and only one basin (1% of the study area) has decreasing trend in the 99th percentile precipitation (R99).A slightly larger number of basins (11; 7.5% of the study area) exhibits decreasing tendency in maximum daily precipitation (R1D).However, the decreasing rates are generally small.Decreasing trends are also observed in the simple daily precipitation intensity index (SDII) for 23 basins (9.3% of the study area).At the regional scale, most regions show weak and insignificant trends for most indices.Only one region (American) observes statistically significant decreasing trend in two indices.When comparing the PDFs of these indices in two halves of the study periods, no basins or regions show remarkable shifts in the distribution pattern.Lack of strong (in terms of changing rate) and consistent (spatially) changes in precipitation has also been reported in previous work [11,33,52,53].In general, this observation implies that natural variability in precipitation may still dominate the influence of climate change, which is most likely the case in the current study given the fact that California has the largest year-to-year natural variability in precipitation across the United States [19].

Runoff Indices
In another finding, this study identifies that there are generally no significant changes in peak volume and timing of runoff and snowmelt draining into 12 major water supply reservoirs in the Central Valley, with the sole exception being the peak snowmelt timing for Lake Isabella.This is somewhat contradictory to previous studies on changes in runoff in the Western United States [37,38,[54][55][56][57] that noted increasing fractions of annual runoff occurring earlier than usual in the water year and earlier occurrence of snowmelt peak.This discrepancy likely stems from the fact that the study methods, study locations, study data, and record period of the current work are not necessarily included in those previous studies.Additionally, the pre-whitening procedure [43] applied in this study may mask potential trend in the raw data.To test this assumption, the Mann-Kendall test (MKT) approach without pre-whitening is applied to those runoff indices.Moreover, to illustrate how differently the MKT method performs from the traditional method, the linear regression method is also utilized in identifying the significance of the linear slope identified for those indices.The resulting z-value from the MKT and the p-value from the linear regression are tabulated in Tables 6 and 7, respectively.Additionally, to assess the potential influence of the length of study period on the results, both the MKT and traditional linear regression methods are applied in every single 30-year sub-period within the record period of the study indices.A 30-year window is applied to allow enough sample size (30) for trend analysis.The number of 30-year windows showing statistically significant changes at a significance level of 0.05 are counted and tabulated in Table 8.
All in all, no wide spread significant changes in inflows to the 12 study Reservoirs are identified in this study.Similar findings have also been reported in the literature.For instance, Tamaddun et al. [60] investigated changes in unimpaired streamflow measured at 600 USGS stations (including 40 in California) across the Continental United States at the annual and seasonal scales.They identified no significant trends in annual and spring streamflow volumes at any of those 40 California stations via the MKT method either with or without the pre-whitening procedure incorporated.They used at a significance level at 0.10 rather than 0.05.In the current study, the lack of significant trend in runoff extremes may attribute to the lack of widespread changes in precipitation extremes (Table 4 and Figure 8).It is also worth noting that the unimpaired runoff is calculated based on streamflow observations as well as the forecasters' best knowledge on upstream regulations.Evaporation from reservoirs is typically neglected from the calculation.Fine-tuning the equations determining unimpaired reservoir inflow is an on-going effort of the forecasters.A follow-up study will be conducted and reported when the updated dataset is available.

Implications of This Study
The study is unique in that it uses the operational dataset exclusively.These data are quality controlled by the forecasters based on their knowledge of the natural characteristics of the study areas as well as diversions and regulations in those areas.Real-time decisions on water management planning and management operations in the Central Valley are directly based on these data.The findings of this study have both scientific and practical significance.
From a scientific perspective, increasing warm extremes observed in certain areas in the Central Valley can guide the enhancement of the current forecasting model specifically for those areas.For instance, the current snow forecasting model SNOW-17 [61] uses a parameter to represent the maximum possible snow melt rate.The parameter is typically determined from historical temperature data.In light of the increasing warm extremes, the actual snow melt rate is most likely to increase accordingly.As such, this parameter needs to be refined to better reflect the new reality and thus provide more skillful forecasting.Another area for enhancement is developing new snow accumulation and ablation processes and incorporating them to the operational forecasting model.The current model is built on snow measurements available about four decades ago [61] when anthropogenic change of climate was not as substantial and the stationarity assumption may still have been sound.In the past several decades, significant changes in snowpack volume have been recorded in the Sierra Nevada Mountains [62][63][64] and are projected to continue to change in the future [65].Snow monitoring techniques have also evolved and advanced significantly, providing more comprehensive data sources which likely revolutionize the snow sciences [66][67][68][69].How to capitalize on these advancements to modernize our forecasting tools remains to be a challenging task for (particularly the next generation) forecasters.
From a practical perspective, these findings have significant implications for adaptive water resources planning and management practices.For example, the current reservoir operation rule curves in the Central Valley are mostly built on historical record of runoff, precipitation, and temperature with the assumption being no changes in those variables, while this study shows increasing warm extremes in a range of areas across the Central Valley.The warming trend is projected to continue [70][71][72], mostly likely leading to increased flooding risks [73,74] and more precipitation falling as rainfall instead of snowfall [75,76].The traditional operation rules need to be updated accordingly to better manage water resources to satisfy increasing and often competing demands in California.Potential changes to the current rule curves may include reserving a larger flood pool and adjusting the top of conservation pool downward throughout the winter.Additionally, identifying the vulnerability of the current water system (including both natural watersheds and man-made water transfer and storage systems including the SWP and CVP) to a changing climate is the foremost step in developing and implementing any adaptation strategies [77].This study shows that Tulare region observes the most significant warming among all six study regions in the Central Valley, suggesting that it is highly vulnerable to climate change and requires timely adaptation and mitigation responses.

Conclusions
This study presents a comprehensive trend analysis of temperature, precipitation, and runoff extremes in the Central Valley of California using available long-term operational datasets.Overall, this study highlights that Central Valley's precipitation, temperature, and runoff extremes are not immune from a globally changing climate.Specifically, about 60% of the study area shows increasing warm extremes and decreasing cold extremes.In comparison, changes in precipitation extremes are not as widespread.Only four out of nine precipitation indices show significant trends in a limited number (ranging from 4-22 out of 176) of basins.As for runoff, only one study location (out of 12) shows significant earlier snowmelt peak timing.Additional analysis on runoff indices using different trend analysis methods and different analysis periods also indicates limited changes in these runoff indices.These findings are meaningful in term of guiding water resources planning and management operations (e.g., prioritizing investment towards the most vulnerable region) and enhancing our forecasting tools for improved hydrologic forecasts.

Figure 1 .
Figure 1.Location map showing study regions, basins, and reservoirs in the Central Valley of California.Figure 1. Location map showing study regions, basins, and reservoirs in the Central Valley of California.

Figure 1 .
Figure 1.Location map showing study regions, basins, and reservoirs in the Central Valley of California.Figure 1. Location map showing study regions, basins, and reservoirs in the Central Valley of California.

Figure 3 .Figure 3 .
Figure 3. (a) Slope of significant trend of temperature indices at basin-scale in the study period 1949-2010.The unit of the slope for the first four indices (TX10, TX90, TN10 and TN90) is days/year; for other indices, the unit is °C/decade.The numbers in parentheses represent the correlation values between the slope and basin elevation; the numbers above these correlation values designate the sample size (i.e., number of basins showing significant trends).(b) Aggregated area of basins showing negative or positive trends over the total area of all 176 study basins.

Figure 4 .
Figure 4. Slope of significant trend of temperature indices at regional (forecasting group) scale in the study period 1949-2010.Slope unit is day/year for TX10, TX90, TN10 and TN90; for other indices, the unit is °C/decade.White color indicates that there is no significant trend.Slope values of significant decreasing trends are provided.

Figure 4 .
Figure 4. Slope of significant trend of temperature indices at regional (forecasting group) scale in the study period 1949-2010.Slope unit is day/year for TX10, TX90, TN10 and TN90; for other indices, the unit is • C/decade.White color indicates that there is no significant trend.Slope values of significant decreasing trends are provided.

Figure 5 .
Figure 5. Study basins (highlighted in blue) with significantly (at a significance level of 0.05) different probability distributions in two different sub-periods of the study period for temperature indices (a) TX10, (b) TX90, (c) TN10, (d) TN90, (e) TX6h, (f) TN6h, (g) TXM, (h) TNM, and (i) DTR.Percentage numbers show how much the aggregated area of those basins accounts for the entire study area.

Figure 5 .
Figure 5. Study basins (highlighted in blue) with significantly (at a significance level of 0.05) different probability distributions in two different sub-periods of the study period for temperature indices (a) TX10, (b) TX90, (c) TN10, (d) TN90, (e) TX6h, (f) TN6h, (g) TXM, (h) TNM, and (i) DTR.Percentage numbers show how much the aggregated area of those basins accounts for the entire study area.

Figure 6 .Figure 6 .
Figure 6.p-Values of the Kolmogorov-Smirnov test for nine temperature indices in the study period from water year 1949-2010.White color indicates that the null hypothesis (index in two sub-periods comes from the same distribution) is favored (p-value > 0.05).
64 with p = 0.001), indicative of a milder decreasing rate for high elevations for those basins exhibiting significant trends.

Figure 8 .
Figure 8. Study basins with significant (at a significance level of 0.05) trend in precipitation indices (a) R6h, (b) R1D, (c) R99, and (d) SDII.Other precipitation indices show no significant trend in any study basins.Different colors indicate different trend slopes (in mm/year).Percentages show how much the aggregated area of those basins (with significant trend) accounts for the entire study area.

Figure 8 .
Figure 8. Study basins with significant (at a significance level of 0.05) trend in precipitation indices (a) R6h, (b) R1D, (c) R99, and (d) SDII.Other precipitation indices show no significant trend in any study basins.Different colors indicate different trend slopes (in mm/year).Percentages show how much the aggregated area of those basins (with significant trend) accounts for the entire study area.

Figure A1 .
Figure A1.Study basins of (a) Upper Sacramento Group; (b) Feather Yuba Group; (c) American Group; (d) North San Joaquin Group; (e) San Joaquin Group and (f) Tulare Group.

Table 1 .
General information of six forecasting groups.

Table 1 .
General information of six forecasting groups.

Table 2 .
General information of study reservoirs.

Table 2 .
General information of study reservoirs.

Table 4 .
Trend slope of precipitation indices at the regional scale 1 .

Table 5 .
p-Value of the KS test on runoff indices 1 .

Table 6 .
z-Value of the MKT on runoff indices 1 .

Table 8 .
Number of 30-year periods showing significant trends via the MKT and linear regression methods 1 .

Table A1 .
Study basins in the Upper Sacramento Group.
Figure A1.Study basins of (a) Upper Sacramento Group; (b) Feather Yuba Group; (c) American Group; (d) North San Joaquin Group; (e) San Joaquin Group and (f) Tulare Group.

Table A1 .
Study basins in the Upper Sacramento Group.

Table A2 .
Study basins in the Feather Yuba Group.

Table A3 .
Study basins in the American Group.

Table A4 .
Study basins in the North San Joaquin Group.

Table A5 .
Study basins in the San Joaquin Group.

Table A6 .
Study basins in the Tulare Group.