# Temporal-Spatial Characteristics and Future Changes of Temperature Extremes in Longtan Watershed Based on Multiple Indices

Authors: Chongxun Mo; Shiting Long; Yuli Ruan; Yanping Xie; Xingbi Lei; Shufeng Lai; Guikai Sun; Zhenxiang Xing
Journal: Advances in Meteorology
 (2022)

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## Abstract

Global warming and the intensification of extreme temperature events have been major issues around the world in recent decades. Understanding changes in temperature extremes is critical to assessing and responding to the risks associated with regional temperature change. This paper takes the Longtan watershed as the research object, and 11 extreme temperature indices were calculated based on the meteorological observation data from 1959 to 2017. The Mann-Kendall trend mutation test, Empirical Orthogonal Function, and other methods were used to explore the spatial and temporal distribution characteristics of temperature extremes. Meanwhile, the simulation effects of temperature were analyzed based on 11 CMIP5 climate models, and the extreme temperature change in 2021–2050 under the high emission scenario RCP8.5 and low emission scenario RCP4.5 was estimated. The main results are as follows: both the warm-related indices and the extreme minimum temperature show an increasing trend. The cold-related frequency indices all show a decreasing trend. The spatial distribution of most temperature extremes increases or decreases from southwest to northeast, and the fluctuation is obvious with the alternation of positive and negative positions of the time. In the next 30 years, compared with the reference period 1961–1990, under the RCP4.5, the multiyear average of the ExtremeTmax and the multiyear average of the Extreme Tmin increase by 2.1°C and 0.4°C, respectively, and by 2.0°C and 0.3°C under the RCP8.5. Overall, the frequency of extreme cold events decreases, and the frequency of extreme warm events increases. There is a warming trend in temperature extremes.


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## Body

## 1. Introduction

Since the 20th century, as the global climate continues to warm, the frequency of extreme temperature events has increased significantly, and a series of problems caused by climate change have aroused wide public concern. For example, the summer heat wave that occurred in Japan in 2007 reached a maximum temperature of 40.9°C [1]. An extreme cold surge event caused record-breaking low temperatures in East Asia during 20–25 January 2016 [2]. From the 1960s to the 2010s, the Diurnal temperature range (DTR) decreased significantly in China, the warm extremes increase significantly, and the hot extremes continue the significant warming trend nationally and in climate regions of East China, Southwest China, and the Tibetan Plateau [3–5]. Regarding Iturbide et al. [6] bias adjustment for predicted changes in extreme heat, the results unveil a stronger and more rapid increase of the frequency of heat extremes in the future than that one may expect using the raw model outputs alone. Long-term changes to Earth’s energy balance are increasing the frequency and intensity of many extreme events and the likelihood of compound events, with trends being projected to accelerate under certain greenhouse gas emissions scenarios [7]. The intensification of extreme temperature events has caused serious damage to ecological and socioeconomic environments. According to the Fifth Assessment Report of the International Intergovernmental Panel on Climate Change (IPCC), the global average temperature increased by 0.65–1.06°C from 1880 to 2012. As global warming increases, extreme temperature events will occur frequently in the future [8]. Therefore, it is important to analyze the historical spatial and temporal variability of temperature extremes and their future trends. Differences between climate models tend to make the results of climate predictions uncertain, and it is necessary to evaluate the simulation effects of different models [9]. Therefore, a suitable climate model for the study basin needs to be selected to provide the basis for future urban strategy development. The increase in extreme temperature events can have significant negative impacts on society, which include changes in ecosystems, disruption in food production and water supply, destruction of infrastructure and residential areas, and increased morbidity and mortality [10, 11]. Analysis of temperature extremes is important in terms of helping to carry out meteorological disaster prediction and early warning studies and reducing the negative impacts of extreme temperature events on local production and life.In recent years, extreme temperature events have been extensively studied by many scholars from different perspectives. On a global scale, the cold days (TX10p) and cold nights (TN10p) had decreased, and the warm days (TX90p) and warm nights (TN90p) had increased across Indonesia over the past 30 years, showing a clear warming trend [12]. New Zealand [13], Nepal [14], Barbados, and Caribbean [15] all showed trends of increasing extreme high temperature events and decreasing extreme low temperature events. For China, the trends of extreme temperatures were consistent with global trends. Some scholars [16] have studied extreme temperatures in northwest China from 1960 to 2004 and concluded that the spatial distribution of extreme high and extreme low temperature events could be divided into five subregions, namely, northern Qinghai and western Gansu, northern Xinjiang, southern Xinjiang, eastern northwest China, and southern Qinghai; all of these five regions showed a significant increasing trend of extreme high temperature events. Extreme temperatures have regional and seasonal characteristics, with increasing trends in both autumn and winter, and decreasing trends in both spring and summer. The extreme low temperature events have a significant increasing trend in the northern basin of China, while the extreme high temperature events have an insignificant or even decreasing trend in the southern region of China [17]. Zhan et al. [18] analyzed the extreme temperature characteristics of global land regions based on coupled 37 climate model simulations of CMIP5, and the results showed that the probability of both dry/wet and hot/cold events will increase under both RCP4.5 and RCP8.5 emission scenarios.Although many scholars have used different methods to study the characteristics of the spatial and temporal distribution of temperature extremes and future trends, there are still some urgent problems that need to be solved: (1) Most studies have used a single or inadequate index to analyze the spatial and temporal characteristics of temperature extremes, but comprehensive analysis of extreme temperatures is still relatively rare; (2) no single climate model has been accepted as a global standard, and how to select the best climate models still requires further study; and (3) there is still lack of long-tern temperature extremes trend analysis in Longtan watershed. Therefore, this study aims to comprehensively examine temporal-spatial characteristics and future trends of temperature extremes in the watershed. It can contribute to the response to climate change, and reduce the negative impacts of extreme temperature events on the ecological environment and people’s production and life. The research framework mainly includes the following: (1) analyzing the spatial and temporal characteristics of extreme temperature changes; (2) selecting the climate models; (3) predicting the extreme temperature changes in the watershed from 2021 to 2050.


## 2. Study Area and Data

Longtan watershed is distributed at the junction of Yunnan, Guizhou, and Guangxi provinces with a geographical location of 102°14′E∼107°32′E, 23°11′N∼27°01′N. The watershed covers an area of 98500 km2. The topography of the watershed gradually decreases from northwest to southeast. It is located in the southeast of the Yunnan-Guizhou Plateau and the area south of the Guizhou Plateau. The terrain is rugged and complex with plateaus, mountains, hills, and basins intermixed. The limestone is widely distributed, the landform is mainly an erosion landform, and karst development is extensive. The basin belongs to the subtropical climate zone, with high temperatures and rain in summer, and dry winters with little rain. The average annual temperature is 20.1°C, the extreme maximum temperature is 38.9°C, and the extreme minimum temperature is −2.9°C. The Longtan Water Control Project was prepared for construction in 1990s in the basin, with an installed capacity of 6.3 million kw and an annual power generation capacity of 18.7 billion kw·h. It is a landmark project of “west-east power transmission” and a key project of China’s Western Development Policy.In this study, historical observations of daily maximum and daily minimum temperatures from 15 meteorological stations within and adjacent to the Longtan watershed were obtained from the China Meteorological Data Center (https://data.cma.cn/wa). The daily missing data of meteorological stations for some years were interpolated by using the correlation of adjacent stations. The distribution of stations is shown in Figure 1. The temporal and spatial characteristics of extreme temperature were analyzed based on the 27 extreme climate indices proposed by the ETCCDI expert group [19]. Longtan watershed belongs to the subtropical climate zone, and some indices show a little temporal trend, and some indices are continuously zero, such as the number of frost days, which is extremely rare in the watershed. According to the situation of the study area, 11 extreme temperature indices including both cold and warm extreme temperature were selected from a total of 27 extreme climate indices, which are shown in Table 1, including 3 intensity indices, 6 frequency indices, and 2 duration indices. All extreme temperature indices in this study were annualized using 1961–1990 as the base period. Model selection and analysis of future changes in extreme temperatures referring to the results of Chen et al. [20] and Xiao et al. [21] assessment of the simulation capability of CMIP5 climate models in the Chinese region, 11 CMIP5 climate models with a daily scale were selected, and the data under the high emission (RCP8.5) and low emission (RCP4.5) scenarios from 2021 to 2050 were applied to study in the Longtan Basin. The climate models are shown in Table 2, and the data of the climate models are obtained from the CMIP5 official website (https://esgf-node.llnl.gov/search/cmip5/). To compare those with the station data, downscaling methods are often used to process the model output data. Due to the limited information available, the inverse distance weighted (IDW) method [22] was adopted to downscale the grid data of the model information to the sites; that is, the four grid points of the grid were interpolated to the stations.Figure 1
Distribution of main river systems and stations.Table 1
Definition of extreme temperature index.
IndexNameDefinitionUnitIntensity index1TXxExtremeTmaxThe maximum value of dailyTmax in a year°C2TNnExtremeTminThe minimum value of dailyTmin in a year°C3DTRDiurnal temperature rangeAverage difference between annual dailyTmax and Tmin°CFrequency index4SU25Summer daysTotal number of days with dailyTmax >25°Cd5FDFrost daysTotal number of days with dailyTmin <0°Cd6TX90pWarm daysAnnual count of dailyTmax >90% percentile valued7TN90pWarm nightsAnnual count of dailyTmin >90% percentile valued8TX10pCold daysAnnual count of dailyTmax <10% percentile valued9TN10pCold nightsAnnual count of dailyTmin <10% percentile valuedDuration index10WSDIWarm spell duration indicatorAnnual count of at least six consecutive days ofTmax >90% percentile valued11CSDICold spell duration indicatorAnnual count of at least six consecutive days ofTmin <10% percentile valuedTable 2
CMIP5 climate model information.
Abbreviation of GCMModel nameInstitution/CountriesResolution (Lon × Lat)1BC1BCC-CSM1.1BCC/China128 × 642BNUBNU-ESMGCESS/China128 × 643CaECanESM2CCCMA/Canada128 × 644CCSCCSM4NCAR/USA288 × 1925GF3GFDL-ESM2GNOAA GFDL/USA144 × 906GF4GFDL-ESM2MNOAA GFDL/USA144 × 907IP2IPSL-CM5A-MRIPSL/France144 × 1438MI3MIROC-ESMMIROC/Japan128 × 649MI4MIROC-ESM-CHEMMIROC/Japan128 × 6410MP1MPI-ESM-LRMPI-M/Germany192 × 9611NE1NorESM1-MNCC/Norway144 × 96


## 3. Methodology

The main research methods applied in this study can be divided into four parts. (1) The Kendall rank correlation method [23], Spearman rank correlation method [24], and linear trend regression method [25] were used for significance testing, and the trends of each extreme temperature index were analyzed by combining the three methods. The M-K trend mutation test was adopted to further analyze the variation characteristics of extreme temperature in different years, combined with the sliding t-test to analyze the mutation trend [26]. (2) The Empirical Orthogonal Function (EOF) method was applied to analyze the spatial characteristics of extreme temperature. The significance of the decomposed modes was tested using the North criterion. Then, the significant modes and their corresponding time coefficients were analyzed. The mode that passes the significance test maximally characterized the distribution structure of the variability of extreme temperature in the Longtan watershed. (3) The simulation effects of 11 climate models were evaluated by composite rating metrics to select a suitable climate model for the Longtan watershed. (4) Based on the selected climate model, the future extreme temperature changes in the basin under different emission scenarios were analyzed.


### 3.1. M-K Trend Mutation Test

Mann-Kendall trend mutation test is a widely used trend analysis method in the field of meteorology. The test series does not need to follow a certain distribution. The method is not disturbed by outliers and is easy to calculate [27–29]. For a sequence x1, x2,…,xn of n sample sizes, construct the statistical variables:(1)Sk=∑i=1krik=2,3,…,n,ri=1,xj>xi,0,xj≤xi,j=1,2,…,i,where Sk denotes the total number of ith sample xi>xj1≤i≤j. Assuming that the Sk are randomly independent, their means and variances are calculated as follows:(2)ESk=kk−14,VarSk=kk−12k+572,k=1,2,…,n.The standardized statistics for the one-tailed test are formulated as(3)UFk=Sk−ESkVarSk,where UF1 = 0. When UFk > 0, the sequence shows an upward trend; otherwise, it shows a downward trend. At the 5% significance level, the hypothesis of no trend is rejected if |UFk| > 1.96. The sequence x1,x2,....,xn is arranged in reverse order, and the above calculation procedure is repeated to obtain the statistic UBk sequence. When the intersection of two curves (UBk and UFk) lies between the significance levels, the intersection is the mutation point.


### 3.2. Empirical Orthogonal Function (EOF) Method

Empirical Orthogonal Function (EOF) can separate the spatial distribution structure and time-series variation of meteorological element variable fields [30]. The calculation is as follows:(1)
Perform distance leveling on the data and output the data matrixXm × n, where m denotes the number of stations, and n denotes the number of years.(2)
Calculate the cross product ofX and XT to obtain the covariance matrix Cm × m.(3)
Compute the characteristic root (λ1,λ2,...,λn) and the eigenvector Vm × m of Cm × m, satisfying(4)Cm×m×Vm×m=Vm×m×Em×m,E=λ10⋯00λ2⋯0⋯⋯⋯⋯00⋯λm.Each characteristic root corresponds to a column of eigenvector values, which is the EOF mode, andλ1≥λ1≥⋯≥λm≥0.(4)
Project the EOF onto the original matrix and calculate the time coefficients PC corresponding to the spatial eigenvectors.(5)
Calculate the variance contribution of the eigenvectors.(5)Rk=λk∑i=1mλi×100%.The cumulative variance contribution of the firstp vectors is(6)G=∑i=1pλi∑i=1mλi.(6)
Significance tests were using the North criterion. At the 95% confidence level, the error rate of the eigenvalues is(7)ej=λj2n.Ifλ satisfies, Δ=λj−λj+1−ej≥0, it means that the modes correspond to two eigenvalues that are independent of each other and they are valuable. The characteristic roots are checked in turn, and the error range is calculated. If the error ranges of two adjacent characteristic roots have overlapping parts, the significance of the two characteristic roots does not differ significantly.


### 3.3. Climate Model Simulation Evaluation Indicators

To better reflect the degree of fit between the simulated and measured values, the following statistics were chosen for this study:(1)
Root mean square error:(8)RMSE=1n∑i=1nXoi−Xmi2.(2)
Correlation coefficient:(9)r=∑i=1nXmi−Xm¯Xoi−Xo¯∑i=1nXoi−Xo¯2∑i=1nXmi−Xm¯2.(3)
Mean absolute error:(10)MAE=1n∑i=1nXmi−Xoi.(4)
Nash efficiency coefficient:(11)NSE=1−∑i=1nXoi−Xmi2∑i=1nXoi−Xo¯2.(5)
Trend errorThere is an error between the linear trend of the simulated series and the measured series:whereXmi is the simulated value, Xoi is the measured value, and n is the total number of time series.


### 3.4. Composite Rating Metrics

Composite Rating Metrics (MR) is a method to judge the consistency and get a composite ranking based on the ranking of each rating index [31]. In this study, multiple statistical indicators of annual and monthly scale simulated and measured series are calculated separately, and then each model is ranked according to the merit of the fit, and the best climate model is selected by judging the comprehensive simulation ability of each model.(12)MR=1−1nm∑i=1nri,where m is the number of models involved in the evaluation, n is the number of indexes used for the evaluation, and ri is the overall ranking of each model (i = 1,2,...,11), and the model with the best simulation ability has a ri value of 1. The closer the MR is to 1, t the better the model simulation is.


## 3.1. M-K Trend Mutation Test

Mann-Kendall trend mutation test is a widely used trend analysis method in the field of meteorology. The test series does not need to follow a certain distribution. The method is not disturbed by outliers and is easy to calculate [27–29]. For a sequence x1, x2,…,xn of n sample sizes, construct the statistical variables:(1)Sk=∑i=1krik=2,3,…,n,ri=1,xj>xi,0,xj≤xi,j=1,2,…,i,where Sk denotes the total number of ith sample xi>xj1≤i≤j. Assuming that the Sk are randomly independent, their means and variances are calculated as follows:(2)ESk=kk−14,VarSk=kk−12k+572,k=1,2,…,n.The standardized statistics for the one-tailed test are formulated as(3)UFk=Sk−ESkVarSk,where UF1 = 0. When UFk > 0, the sequence shows an upward trend; otherwise, it shows a downward trend. At the 5% significance level, the hypothesis of no trend is rejected if |UFk| > 1.96. The sequence x1,x2,....,xn is arranged in reverse order, and the above calculation procedure is repeated to obtain the statistic UBk sequence. When the intersection of two curves (UBk and UFk) lies between the significance levels, the intersection is the mutation point.


## 3.2. Empirical Orthogonal Function (EOF) Method

Empirical Orthogonal Function (EOF) can separate the spatial distribution structure and time-series variation of meteorological element variable fields [30]. The calculation is as follows:(1)
Perform distance leveling on the data and output the data matrixXm × n, where m denotes the number of stations, and n denotes the number of years.(2)
Calculate the cross product ofX and XT to obtain the covariance matrix Cm × m.(3)
Compute the characteristic root (λ1,λ2,...,λn) and the eigenvector Vm × m of Cm × m, satisfying(4)Cm×m×Vm×m=Vm×m×Em×m,E=λ10⋯00λ2⋯0⋯⋯⋯⋯00⋯λm.Each characteristic root corresponds to a column of eigenvector values, which is the EOF mode, andλ1≥λ1≥⋯≥λm≥0.(4)
Project the EOF onto the original matrix and calculate the time coefficients PC corresponding to the spatial eigenvectors.(5)
Calculate the variance contribution of the eigenvectors.(5)Rk=λk∑i=1mλi×100%.The cumulative variance contribution of the firstp vectors is(6)G=∑i=1pλi∑i=1mλi.(6)
Significance tests were using the North criterion. At the 95% confidence level, the error rate of the eigenvalues is(7)ej=λj2n.Ifλ satisfies, Δ=λj−λj+1−ej≥0, it means that the modes correspond to two eigenvalues that are independent of each other and they are valuable. The characteristic roots are checked in turn, and the error range is calculated. If the error ranges of two adjacent characteristic roots have overlapping parts, the significance of the two characteristic roots does not differ significantly.


## 3.3. Climate Model Simulation Evaluation Indicators

To better reflect the degree of fit between the simulated and measured values, the following statistics were chosen for this study:(1)
Root mean square error:(8)RMSE=1n∑i=1nXoi−Xmi2.(2)
Correlation coefficient:(9)r=∑i=1nXmi−Xm¯Xoi−Xo¯∑i=1nXoi−Xo¯2∑i=1nXmi−Xm¯2.(3)
Mean absolute error:(10)MAE=1n∑i=1nXmi−Xoi.(4)
Nash efficiency coefficient:(11)NSE=1−∑i=1nXoi−Xmi2∑i=1nXoi−Xo¯2.(5)
Trend errorThere is an error between the linear trend of the simulated series and the measured series:whereXmi is the simulated value, Xoi is the measured value, and n is the total number of time series.


## 3.4. Composite Rating Metrics

Composite Rating Metrics (MR) is a method to judge the consistency and get a composite ranking based on the ranking of each rating index [31]. In this study, multiple statistical indicators of annual and monthly scale simulated and measured series are calculated separately, and then each model is ranked according to the merit of the fit, and the best climate model is selected by judging the comprehensive simulation ability of each model.(12)MR=1−1nm∑i=1nri,where m is the number of models involved in the evaluation, n is the number of indexes used for the evaluation, and ri is the overall ranking of each model (i = 1,2,...,11), and the model with the best simulation ability has a ri value of 1. The closer the MR is to 1, t the better the model simulation is.


## 4. Results

### 4.1. Temporal Variation Characteristic

#### 4.1.1. Variation Tendency

The trend test results of the change of the mean extreme temperature indices in the basin for the past 59 years are shown in Table3. The significance level was selected as 0.05, and the trend was obtained by combining the three methods of testing. The results of the three methods are consistent. Therefore, they have certain reliability. All indices passed the significance trend test at the 0.05 confidence level except for the cold days (TX10p) and the cold spell duration indicator (CSDI). Overall, the warm-related indices all showed an increasing trend.Table 3
Results of the extreme temperature trend test.
IndexKendall’s rank correlation methodSpearman rank correlation methodLinear trend regressionSignificance testTrendInterannual variability °C·(10a)−1TXx2.9932.81SignificantIncrease0.14TNn4.394.984.66SignificantIncrease0.37DTR4.585.295.97SignificantDecrease−0.12SU253.423.613.56SignificantIncrease2.4FD4.34.764.6SignificantDecrease−1.7TX90p4.34.664.88SignificantIncrease1.1TN90p6.379.059.41SignificantIncrease2.3TX10p1.141.171.19NonsignificantDecrease−0.2TN10p5.296.256.52SignificantDecrease−1.0WSDI4.274.614.49SignificantIncrease1.9CSDI0.860.520.08NonsignificantDecrease−0.2To further analyze the trend changes of the extreme temperature indices in different years, the M-K trend test was adopted in this study and used to calculate the UF, thus analyzing the changes of each index in different years. The results of the analysis are shown in Figure2. Most indices tend to change significantly in trend after 2000, with large fluctuations in the 1980s and 1990s. TXx, TNn, TX90p, and TN90p all showed an increasing trend around 1990, while DTR, FD, and TN10p all showed a decreasing trend and fluctuated greatly in the 1960s. SU25 and WSDI showed a decreasing trend at first and then an increasing trend.Figure 2
M-K mutation trend test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


#### 4.1.2. Mutation Test

The results of the extreme temperature mutation trend test are shown in Figure2, when there were multiple intersections in the M-K mutation test, the mutation points were determined by combining the results of the sliding t-test. The intersection of UF and UB curves of TXx at the confidence interval is 2002, indicating that TXx mutated around 2002. TNn mutated around 1986, DTR mutated around 1981, SU25 may have mutated around 2002, and FD mutated around 1990. The mutation time of TX90p, TN90p, and TX10p was 2001, 1997, and 2012, respectively. TN10p was mutated around 1994, and WSDI was mutated in 2002. The trend of CSDI is not significant, and UF and UB curves have multiple intersection points within the confidence interval. Combined with the sliding t-test results, the mean value has no significant jump, and there is no mutation point. Overall, TNn and DTR had a mutation in the 1980s. FD, TN90p, and TN10p had mutations in the 1990s. TXx, SU25, and TX90p had mutations around 2000.


### 4.2. Spatial Variation characteristics

The variance contribution rate, cumulative variance contribution rate, and North test results of the EOF for the first four modes decomposed from the extreme temperature are shown in Table4. The first three modes of TX90p and the first two modes of TN90p and WSDI passed the test, and the first four modes of the remaining indices passed the test. Combining the extreme temperature characteristic roots and 95% confidence error (Figure 3), the first two more significant modes and their time coefficients were selected for analysis in terms of the intensity index (TXx, TNn, and DTR), frequency index (SU25, FD, TX90p, TN90p, TX10p, and TN10p), and duration index (WSDI, CSDI) of the extreme temperature.Table 4
Variance contribution rate and North significance test results of the first four modes of extreme temperature index.
TXxTNnEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)4215129541685G (%)4257697854707884∆400013210DTRSU25EOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)541895541486G (%)5471808554687581∆1000988112034FDTX90pV1V2V3V4V1V2V3V4R (%)631775661165G (%)6380879166778389∆1876283828818025−1141417214−26TN90pTX10pEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)711363521995G (%)7183899252717985∆3513513531921TN10pWSDIEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)571276591286G (%)5769768359717884∆735−1257129718CSDIEOF1EOF2EOF3EOF4R (%)33201310G (%)33526676∆3615318Figure 3
Characteristic root of extreme temperature and 95% confidence error.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


#### 4.2.1. Intensity Indices

As shown in Figure4, the first eigenvectors of the extreme temperature intensity indices are all positive, indicating that the trend of extreme temperature intensity change in the basin is basically the same, but the high-value centers are different. The high-value center of TXx (V1) is distributed in the mid-basin region and decreases in all directions, and the high-value center of TNn (V1) is in the upper reaches of the watershed. It can be found that the temporal coefficients of TXx(PC1) and TNn(PC1) increase significantly from 1959 to 2017, so both extreme maximum and extreme minimum temperatures show increasing trends in the past 59 years. The areas of high values of DTR (V1) are distributed in the lower part of the basin, and the amount of change in the areas of high values is greater than the change in other areas. Combined with the temporal coefficients, the temporal coefficients from 1969 to 2017 show a significant decreasing trend. Therefore, the diurnal temperature range (DTR) is significantly lower. The second eigenvectors are all positive and negatively distributed, and the negative areas are distributed in the southwest of the watershed. The negative areas of TXx (V2) and DTR (V2) are larger, and the high-value center of TXx (V2) is in the northeast region, decreasing along the southwest. The high-value center of TNn (V2) is in the northern region, decreasing along the south. The high-value center of DTR (V2) is negative and located in the southwest region, decreasing along the east. The positive and negative distribution indicated that the TXx (V2), TNn (V2), and DTR (V2) represent two types of distribution, that is, the positive regions with opposite trends of negative regions.Figure 4
The first and second eigenvectors and their time coefficients of extreme temperature intensity index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)


#### 4.2.2. Frequency Indices

As shown in Figure5, the first eigenvectors of FD (V1), TX10p (V1), and TN10p (V1) are all positive, indicating that the spatial variation trends of FD, TX10p, and TN10p are basically the same. The other eigenvectors are positive and negative, but most regions are positive, with small differences in trends. The component values of FD (V1) are distributed along the south-north, with the center of high values located in the north of the basin and decreasing to the south. The center of high values of TX10p (V1) is located in the middle part of the watershed, with the component values decreasing along the surrounding area. The values of the other eigenvectors all change along the southwest or northeast direction, but the locations of the high-value centers are different. The component values of the second eigenvector were increasing or decreasing along the southwest-northeast direction, and all of them were positively and negatively distributed. For example, the component value of SU25 (V2) tends to decrease along the southwest to northeast direction, while that of TX10p (V2) tends to increase. The indices with more negative areas of component values were SU25 (V2), TX90p (V2), and TN90p (V2). The positive high-value center of TN90p (V2) is located in the southwest, and the negative high-value center is located in the southeast part, with an inverse distribution pattern; that is, southwest increased, and northeast decreased, or southwest decreased and northeast increased distribution pattern.Figure 5
The first and second eigenvectors and their time coefficients of extreme temperature frequency index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)(q)(r)(s)(t)(u)(v)(w)(x)As can be seen from the time coefficients, SU25 (PC1) and SU25 (PC2) have relatively smooth trend changes, and both show an increasing trend after 2007. FD (PC1) has an overall decreasing trend with four significant fluctuations, showing an upward and then a downward trend, while FD (PC2) has relatively stable changes from 1964 to 1996 and a significant upward trend from 1997 to 2012. TX90p (PC1) has a decreasing and then increasing trend with the alternation point near 1984. TX90p (PC2) has a significant fluctuation between 1986 and 1998, while it has an increasing trend before 1986 and was relatively stable after 1998. TN90p (PC1) changed smoothly until 1986, showed a clear upward trend after 1986, and gradually stabilized after 2002. TN90p (PC2) showed an upward trend after 1990 and a downward trend after 2003. TX10p (PC1) showed a fluctuating change, with an upward trend from 1964 to 1971. TX10p (PC2) showed a relatively stable change until 2004 and an increasing trend after 2004. TN10p (PC1) showed a decreasing trend, TN10p (PC2) showed two significant fluctuations in 1965–1977 and 2000–2015, and it was relatively stable in 1978–1999.


#### 4.2.3. Duration Indices

As shown in Figure6, the trends of WSDI and CSDI reflected by the first eigenvector are basically the same in space. The center of high value of WSDI (V1) is in the southwest of the watershed, decreasing along the northeast, while the center of high value of CSDI (V1) is in the northeast part, decreasing along the west. The time coefficients show that WSDI (PC1) changed smoothly until 1992 and then showed a clear upward trend, and WSDI (PC2) started to rise around 1992 and decreased after 2000. The second eigenvector WSDI (V2) has a positive and negative type of distribution, with positive values in the southwest and negative values in the northeast representing two types of distribution; that is, there is a distribution pattern of WSDI in the watershed increased in the southwest and decreased in the northeast or decreased in the southwest and increased in the northeast in different years. While CSDI (V2) is all positive, it showed spatial consistency overall. WSDI (V2) and CSDI (V2) correspond to time coefficients WSDI (PC2) and CSDI (PC2) with different change characteristics. WSDI (PC2) changed smoothly before 1990 and showed a trend of rising and then fell from 1991 to 2010. CSDI (V2) changed relatively smoothly, with one fluctuation in 1971–1977, and the eigenvector distribution type was significant in 1972.Figure 6
The first and second eigenvectors and their time coefficients of extreme temperature duration index.
(a)(b)(c)(d)(e)(f)(g)(h)


### 4.3. Model Selection

As stated in the study area section, there is a Longtan Control Project built in the basin, and preparatory construction work such as resettlement was carried out in the 1990s, and the environment of the watershed has changed significantly due to human activities. The study of the temporal variation characteristics of the extreme temperature indices revealed that, in the Longtan watershed, most of the extreme indices changed abruptly in the 1990s and 2000s, and the 30-year time series was sufficient for the simulated evaluation of climate models [32–35]. Therefore, the period from 1961 to 1990 with relatively little climate change was used as the simulation period for model evaluation in this study. Based on the temperature observation data of the Longtan watershed from 1961 to 1990, the root mean square error (RMSE), correlation coefficient (R), mean absolute error (MAE), Nash efficiency coefficient (NSE), and trend error (TE) of the simulated maximum and minimum temperatures of each climate model at monthly and annual scales were used as evaluation indicators, and the simulation effects of 11 climate models were evaluated by comprehensive rating metrics. According to the analysis of the spatial and temporal characteristics of extreme temperatures in the previous sections, most of the indices show a distribution of more in the southwest and less in the northeast or more in the southwest and less in the northeast. Therefore, the Luxi station in the southwest and Xingren station in the northeast are chosen as the representative station for showing the simulations of 11 climate models. The evaluation statistics by each climate model simulated at Luxi and Xingren stations are shown in Table 5 and Table 6, respectively. The composite rating results of each model are shown in Table 7.Table 5
The evaluation statistics by each climate model simulated at Luxi Station.
BC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Annual scaleTmaxRMSE1.621.701.571.431.431.651.431.521.531.601.68R0.18−0.040.030.290.23−0.100.100.070.42−0.17−0.02MAE1.341.501.181.031.071.271.101.221.231.341.43NSE−0.84−1.03−0.73−0.45−0.44−0.91−0.44−0.63−0.65−0.79−0.99TE0.120.180.080.360.280.000.180.410.280.030.03TminRMSE2.852.742.923.032.732.882.892.842.723.013.06R0.210.180.24−0.180.010.280.320.19−0.150.100.17MAE2.192.072.132.442.132.232.162.232.122.442.35NSE−0.34−0.23−0.40−0.50−0.22−0.36−0.37−0.32−0.22−0.49−0.54TE0.080.060.060.410.160.180.340.600.500.470.40Monthly scaleTmaxRMSE2.772.762.732.762.732.752.712.772.812.772.77R0.800.790.800.800.800.790.790.780.840.780.80MAE2.342.302.282.292.282.302.242.322.372.322.31NSE0.400.400.420.090.420.410.430.400.380.400.40TE0.000.010.000.400.010.000.010.010.030.000.00TminRMSE2.552.512.392.502.452.502.552.492.522.412.46R0.920.920.930.920.930.920.920.920.920.930.92MAE1.961.951.821.921.931.961.961.961.951.921.92NSE0.840.850.860.850.850.850.840.850.850.860.85TE0.020.010.020.030.020.020.010.020.000.030.01Table 6
The evaluation statistics by each climate model simulated at Xingren Station.
BC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Annual scaleTmaxRMSE1.631.431.511.521.571.461.411.621.551.421.60R0.100.160.110.07−0.090.19−0.05−0.310.260.02−0.10MAE1.321.131.271.281.251.221.141.261.221.121.30NSE−1.87−1.21−1.46−1.48−1.64−1.31−1.16−1.84−1.59−1.17−1.78TE0.090.060.160.160.200.060.140.120.030.080.12TminRMSE1.961.811.961.651.762.131.982.032.061.971.76R−0.060.100.030.300.10−0.25−0.01−0.34−0.11−0.060.09MAE1.651.391.521.411.421.661.491.591.531.691.32NSE−0.84−0.56−0.83−0.30−0.48−1.16−0.87−0.96−1.02−0.85−0.48TE0.510.440.350.730.490.930.811.220.860.600.84Monthly scaleTmaxRMSE2.772.762.732.762.732.752.712.772.812.772.77R0.800.790.800.800.800.790.790.780.840.780.80MAE2.342.302.282.292.282.302.242.322.372.322.31NSE0.400.400.420.090.420.410.430.400.380.400.40TE0.000.010.000.400.010.000.010.010.030.000.00TminRMSE2.552.512.392.502.452.502.552.492.522.412.46R0.920.920.930.920.930.920.920.920.920.930.92MAE1.961.951.821.921.931.961.961.961.951.921.92NSE0.840.850.860.850.850.850.840.850.850.860.85TE0.020.010.020.030.020.020.010.020.000.030.01Table 7
Results of the composite rating metrics of each climate model.
StationBC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Luxi0.350.400.630.470.640.470.500.370.430.380.38Xingren0.330.520.510.540.590.310.330.260.470.520.62At Luxi station, except for CCS, MP1, and NE1, most climate models simulate annual-scale maximum and minimum temperatures within a root mean square error of 3. The mean absolute error is within 2.5°C, and the MI3 model had the largest temperature trend error. At the monthly scale, the root mean square error of the simulations of each climate model is between 2.39 and 2.81, and the mean absolute error is within 2.5°C. The variation temperature trend of the simulated minimum temperature of CCS is opposite to the measured trend, and the trend error is large compared with other models. In a comprehensive evaluation, the GF3 model scored higher than other climate models at Luxi station. At the Xingren station, the root mean square error of each model at the annual scale ranged from 1.41 to 2.13, and the mean absolute error was less than 2°C. On the monthly scale, the simulation results of NE1 are mostly better than other models. The comprehensive evaluation results show that the NE1 climate model simulated the temperature of the Xingren station best. In summary, the evaluation results are as follows: the GF3 model performs best at Luxi station, and NE1 simulates best at Xingren station. Therefore, the GF3 model is selected at the Luxi station, and the NE1 model is selected at the Xingren station to evaluate the future temperature change.


### 4.4. Future Trends

Figures7 and 8 show the spatial distribution of interdecadal changes in each extreme temperature index predicted by the selected models for 2021–2050 under the RCP4.5 and RCP8.5, respectively. Under the RCP4.5 scenario, the multiyear average of TXx will increase by 2.1°C, and the multiyear average of TNn will increase by 0.4°C relative to the reference period 1961–1990. In the basin, the TXx showed a decreasing trend in a small part of the southwest, but with little interannual variation, and an increasing trend in the middle and lower reaches of the basin with relatively large interannual variation and an interannual tendency rate of 0.19–1.10°C·(10a)−1. The TNn showed a decreasing trend in the basin, and from the interannual variation, the interannual variation of the TNn is lower than that of the TXx, and the interannual variation in the middle and lower reaches is greater than that in the upper reaches. FD changes in an opposite trend in the upstream and downstream, and CSDI does not change significantly. The other warm-related indices (SU25, TX90p, TN90p, and WSDI) showed an increasing trend in most areas of the basin, and the cold-related indices (TX10p, TN10p) all showed a decreasing trend. Under the RCP8.5 scenario, the TXx will increase by 2.0°C, and the TNn will increase by 0.3°C relative to the base period 1961–1990. In the basin, the TXx showed an increasing trend, and the interannual variation is greater in the downstream area than in the upstream area. The TNn showed an increasing trend except for some areas in the northeast, which showed a decreasing trend. CSDI does not change significantly. All other warm-related indices showed increasing trends, and all cold-related indices showed decreasing trends. The comparison of the two scenarios revealed that the TXx showed an increasing trend in most regions, but there were differences in the spatial distribution of interannual variation, and the interannual variation of the TXx was larger in most regions under the RCP4.5 scenario than under the RCP8.5 scenario. The TNn showed a decreasing trend under the RCP4.5 scenario and an increasing trend in most regions under the RCP8.5 scenario, and there is a large interannual variation under the RCP8.5 scenario. In summary, the extreme temperature in the watershed may show a warming trend in 2021–2050.Figure 7
Spatial distribution of interdecadal variability of temperature extremes for 2021–2050 under the RCP4.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figure 8
Spatial distribution of interdecadal variability of temperature extremes for 2021–2050 under the RCP8.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figures9 and 10 show the spatial distribution of the multiyear averages of each extreme temperature index in the watershed predicted by the selected models for 2021–2050 under the RCP4.5 and RCP8.5, respectively. Under the RCP4.5 scenario, TXx, SU25, TN90p, TX10p, and CSDI showed a spatial characteristic of high northeast and low southwest, while the other indices showed a distribution of low northeast and high southwest. The spatial distributions of TXx and TNn indices under the two scenarios are slightly different. The region of TXx greater than 33.7°C is larger in RCP8.5 than in RCP4.5, and the TXx reaches 34.4°C under RCP8.5, while the maximum value of TXx is 33.9°C under RCP4.5. Most areas of TNn under RCP4.5 are above −3.6°C. And the spatial distribution of TNn under the RCP8.5 scenario did not differ significantly, all above −3.6°C. The prediction results reveal that there is a warming trend of the extreme temperature in the next 30 years, and the risk of extreme high temperature may exist in the downstream areas of the basin in the future. Under the RCP4.5 scenario, the TXx index increases interannually in the downstream region, increasing the risk of extreme high temperature. The interannual variation of the extreme low temperature in the northeastern part of the watershed weakens, and the risk of extreme low temperatures may decrease. Under the RCP8.5 scenario, the interannual variability of TXx increases in the northeastern region, and the extreme high-temperature risk likewise increases.Figure 9
Spatial distribution of temperature extremes for 2021–2050 under RCP4.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figure 10
Spatial distribution of temperature extremes for 2021–2050 under RCP8.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


## 4.1. Temporal Variation Characteristic

### 4.1.1. Variation Tendency

The trend test results of the change of the mean extreme temperature indices in the basin for the past 59 years are shown in Table3. The significance level was selected as 0.05, and the trend was obtained by combining the three methods of testing. The results of the three methods are consistent. Therefore, they have certain reliability. All indices passed the significance trend test at the 0.05 confidence level except for the cold days (TX10p) and the cold spell duration indicator (CSDI). Overall, the warm-related indices all showed an increasing trend.Table 3
Results of the extreme temperature trend test.
IndexKendall’s rank correlation methodSpearman rank correlation methodLinear trend regressionSignificance testTrendInterannual variability °C·(10a)−1TXx2.9932.81SignificantIncrease0.14TNn4.394.984.66SignificantIncrease0.37DTR4.585.295.97SignificantDecrease−0.12SU253.423.613.56SignificantIncrease2.4FD4.34.764.6SignificantDecrease−1.7TX90p4.34.664.88SignificantIncrease1.1TN90p6.379.059.41SignificantIncrease2.3TX10p1.141.171.19NonsignificantDecrease−0.2TN10p5.296.256.52SignificantDecrease−1.0WSDI4.274.614.49SignificantIncrease1.9CSDI0.860.520.08NonsignificantDecrease−0.2To further analyze the trend changes of the extreme temperature indices in different years, the M-K trend test was adopted in this study and used to calculate the UF, thus analyzing the changes of each index in different years. The results of the analysis are shown in Figure2. Most indices tend to change significantly in trend after 2000, with large fluctuations in the 1980s and 1990s. TXx, TNn, TX90p, and TN90p all showed an increasing trend around 1990, while DTR, FD, and TN10p all showed a decreasing trend and fluctuated greatly in the 1960s. SU25 and WSDI showed a decreasing trend at first and then an increasing trend.Figure 2
M-K mutation trend test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


### 4.1.2. Mutation Test

The results of the extreme temperature mutation trend test are shown in Figure2, when there were multiple intersections in the M-K mutation test, the mutation points were determined by combining the results of the sliding t-test. The intersection of UF and UB curves of TXx at the confidence interval is 2002, indicating that TXx mutated around 2002. TNn mutated around 1986, DTR mutated around 1981, SU25 may have mutated around 2002, and FD mutated around 1990. The mutation time of TX90p, TN90p, and TX10p was 2001, 1997, and 2012, respectively. TN10p was mutated around 1994, and WSDI was mutated in 2002. The trend of CSDI is not significant, and UF and UB curves have multiple intersection points within the confidence interval. Combined with the sliding t-test results, the mean value has no significant jump, and there is no mutation point. Overall, TNn and DTR had a mutation in the 1980s. FD, TN90p, and TN10p had mutations in the 1990s. TXx, SU25, and TX90p had mutations around 2000.


## 4.1.1. Variation Tendency

The trend test results of the change of the mean extreme temperature indices in the basin for the past 59 years are shown in Table3. The significance level was selected as 0.05, and the trend was obtained by combining the three methods of testing. The results of the three methods are consistent. Therefore, they have certain reliability. All indices passed the significance trend test at the 0.05 confidence level except for the cold days (TX10p) and the cold spell duration indicator (CSDI). Overall, the warm-related indices all showed an increasing trend.Table 3
Results of the extreme temperature trend test.
IndexKendall’s rank correlation methodSpearman rank correlation methodLinear trend regressionSignificance testTrendInterannual variability °C·(10a)−1TXx2.9932.81SignificantIncrease0.14TNn4.394.984.66SignificantIncrease0.37DTR4.585.295.97SignificantDecrease−0.12SU253.423.613.56SignificantIncrease2.4FD4.34.764.6SignificantDecrease−1.7TX90p4.34.664.88SignificantIncrease1.1TN90p6.379.059.41SignificantIncrease2.3TX10p1.141.171.19NonsignificantDecrease−0.2TN10p5.296.256.52SignificantDecrease−1.0WSDI4.274.614.49SignificantIncrease1.9CSDI0.860.520.08NonsignificantDecrease−0.2To further analyze the trend changes of the extreme temperature indices in different years, the M-K trend test was adopted in this study and used to calculate the UF, thus analyzing the changes of each index in different years. The results of the analysis are shown in Figure2. Most indices tend to change significantly in trend after 2000, with large fluctuations in the 1980s and 1990s. TXx, TNn, TX90p, and TN90p all showed an increasing trend around 1990, while DTR, FD, and TN10p all showed a decreasing trend and fluctuated greatly in the 1960s. SU25 and WSDI showed a decreasing trend at first and then an increasing trend.Figure 2
M-K mutation trend test results.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


## 4.1.2. Mutation Test

The results of the extreme temperature mutation trend test are shown in Figure2, when there were multiple intersections in the M-K mutation test, the mutation points were determined by combining the results of the sliding t-test. The intersection of UF and UB curves of TXx at the confidence interval is 2002, indicating that TXx mutated around 2002. TNn mutated around 1986, DTR mutated around 1981, SU25 may have mutated around 2002, and FD mutated around 1990. The mutation time of TX90p, TN90p, and TX10p was 2001, 1997, and 2012, respectively. TN10p was mutated around 1994, and WSDI was mutated in 2002. The trend of CSDI is not significant, and UF and UB curves have multiple intersection points within the confidence interval. Combined with the sliding t-test results, the mean value has no significant jump, and there is no mutation point. Overall, TNn and DTR had a mutation in the 1980s. FD, TN90p, and TN10p had mutations in the 1990s. TXx, SU25, and TX90p had mutations around 2000.


## 4.2. Spatial Variation characteristics

The variance contribution rate, cumulative variance contribution rate, and North test results of the EOF for the first four modes decomposed from the extreme temperature are shown in Table4. The first three modes of TX90p and the first two modes of TN90p and WSDI passed the test, and the first four modes of the remaining indices passed the test. Combining the extreme temperature characteristic roots and 95% confidence error (Figure 3), the first two more significant modes and their time coefficients were selected for analysis in terms of the intensity index (TXx, TNn, and DTR), frequency index (SU25, FD, TX90p, TN90p, TX10p, and TN10p), and duration index (WSDI, CSDI) of the extreme temperature.Table 4
Variance contribution rate and North significance test results of the first four modes of extreme temperature index.
TXxTNnEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)4215129541685G (%)4257697854707884∆400013210DTRSU25EOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)541895541486G (%)5471808554687581∆1000988112034FDTX90pV1V2V3V4V1V2V3V4R (%)631775661165G (%)6380879166778389∆1876283828818025−1141417214−26TN90pTX10pEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)711363521995G (%)7183899252717985∆3513513531921TN10pWSDIEOF1EOF2EOF3EOF4EOF1EOF2EOF3EOF4R (%)571276591286G (%)5769768359717884∆735−1257129718CSDIEOF1EOF2EOF3EOF4R (%)33201310G (%)33526676∆3615318Figure 3
Characteristic root of extreme temperature and 95% confidence error.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


### 4.2.1. Intensity Indices

As shown in Figure4, the first eigenvectors of the extreme temperature intensity indices are all positive, indicating that the trend of extreme temperature intensity change in the basin is basically the same, but the high-value centers are different. The high-value center of TXx (V1) is distributed in the mid-basin region and decreases in all directions, and the high-value center of TNn (V1) is in the upper reaches of the watershed. It can be found that the temporal coefficients of TXx(PC1) and TNn(PC1) increase significantly from 1959 to 2017, so both extreme maximum and extreme minimum temperatures show increasing trends in the past 59 years. The areas of high values of DTR (V1) are distributed in the lower part of the basin, and the amount of change in the areas of high values is greater than the change in other areas. Combined with the temporal coefficients, the temporal coefficients from 1969 to 2017 show a significant decreasing trend. Therefore, the diurnal temperature range (DTR) is significantly lower. The second eigenvectors are all positive and negatively distributed, and the negative areas are distributed in the southwest of the watershed. The negative areas of TXx (V2) and DTR (V2) are larger, and the high-value center of TXx (V2) is in the northeast region, decreasing along the southwest. The high-value center of TNn (V2) is in the northern region, decreasing along the south. The high-value center of DTR (V2) is negative and located in the southwest region, decreasing along the east. The positive and negative distribution indicated that the TXx (V2), TNn (V2), and DTR (V2) represent two types of distribution, that is, the positive regions with opposite trends of negative regions.Figure 4
The first and second eigenvectors and their time coefficients of extreme temperature intensity index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)


### 4.2.2. Frequency Indices

As shown in Figure5, the first eigenvectors of FD (V1), TX10p (V1), and TN10p (V1) are all positive, indicating that the spatial variation trends of FD, TX10p, and TN10p are basically the same. The other eigenvectors are positive and negative, but most regions are positive, with small differences in trends. The component values of FD (V1) are distributed along the south-north, with the center of high values located in the north of the basin and decreasing to the south. The center of high values of TX10p (V1) is located in the middle part of the watershed, with the component values decreasing along the surrounding area. The values of the other eigenvectors all change along the southwest or northeast direction, but the locations of the high-value centers are different. The component values of the second eigenvector were increasing or decreasing along the southwest-northeast direction, and all of them were positively and negatively distributed. For example, the component value of SU25 (V2) tends to decrease along the southwest to northeast direction, while that of TX10p (V2) tends to increase. The indices with more negative areas of component values were SU25 (V2), TX90p (V2), and TN90p (V2). The positive high-value center of TN90p (V2) is located in the southwest, and the negative high-value center is located in the southeast part, with an inverse distribution pattern; that is, southwest increased, and northeast decreased, or southwest decreased and northeast increased distribution pattern.Figure 5
The first and second eigenvectors and their time coefficients of extreme temperature frequency index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)(q)(r)(s)(t)(u)(v)(w)(x)As can be seen from the time coefficients, SU25 (PC1) and SU25 (PC2) have relatively smooth trend changes, and both show an increasing trend after 2007. FD (PC1) has an overall decreasing trend with four significant fluctuations, showing an upward and then a downward trend, while FD (PC2) has relatively stable changes from 1964 to 1996 and a significant upward trend from 1997 to 2012. TX90p (PC1) has a decreasing and then increasing trend with the alternation point near 1984. TX90p (PC2) has a significant fluctuation between 1986 and 1998, while it has an increasing trend before 1986 and was relatively stable after 1998. TN90p (PC1) changed smoothly until 1986, showed a clear upward trend after 1986, and gradually stabilized after 2002. TN90p (PC2) showed an upward trend after 1990 and a downward trend after 2003. TX10p (PC1) showed a fluctuating change, with an upward trend from 1964 to 1971. TX10p (PC2) showed a relatively stable change until 2004 and an increasing trend after 2004. TN10p (PC1) showed a decreasing trend, TN10p (PC2) showed two significant fluctuations in 1965–1977 and 2000–2015, and it was relatively stable in 1978–1999.


### 4.2.3. Duration Indices

As shown in Figure6, the trends of WSDI and CSDI reflected by the first eigenvector are basically the same in space. The center of high value of WSDI (V1) is in the southwest of the watershed, decreasing along the northeast, while the center of high value of CSDI (V1) is in the northeast part, decreasing along the west. The time coefficients show that WSDI (PC1) changed smoothly until 1992 and then showed a clear upward trend, and WSDI (PC2) started to rise around 1992 and decreased after 2000. The second eigenvector WSDI (V2) has a positive and negative type of distribution, with positive values in the southwest and negative values in the northeast representing two types of distribution; that is, there is a distribution pattern of WSDI in the watershed increased in the southwest and decreased in the northeast or decreased in the southwest and increased in the northeast in different years. While CSDI (V2) is all positive, it showed spatial consistency overall. WSDI (V2) and CSDI (V2) correspond to time coefficients WSDI (PC2) and CSDI (PC2) with different change characteristics. WSDI (PC2) changed smoothly before 1990 and showed a trend of rising and then fell from 1991 to 2010. CSDI (V2) changed relatively smoothly, with one fluctuation in 1971–1977, and the eigenvector distribution type was significant in 1972.Figure 6
The first and second eigenvectors and their time coefficients of extreme temperature duration index.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.2.1. Intensity Indices

As shown in Figure4, the first eigenvectors of the extreme temperature intensity indices are all positive, indicating that the trend of extreme temperature intensity change in the basin is basically the same, but the high-value centers are different. The high-value center of TXx (V1) is distributed in the mid-basin region and decreases in all directions, and the high-value center of TNn (V1) is in the upper reaches of the watershed. It can be found that the temporal coefficients of TXx(PC1) and TNn(PC1) increase significantly from 1959 to 2017, so both extreme maximum and extreme minimum temperatures show increasing trends in the past 59 years. The areas of high values of DTR (V1) are distributed in the lower part of the basin, and the amount of change in the areas of high values is greater than the change in other areas. Combined with the temporal coefficients, the temporal coefficients from 1969 to 2017 show a significant decreasing trend. Therefore, the diurnal temperature range (DTR) is significantly lower. The second eigenvectors are all positive and negatively distributed, and the negative areas are distributed in the southwest of the watershed. The negative areas of TXx (V2) and DTR (V2) are larger, and the high-value center of TXx (V2) is in the northeast region, decreasing along the southwest. The high-value center of TNn (V2) is in the northern region, decreasing along the south. The high-value center of DTR (V2) is negative and located in the southwest region, decreasing along the east. The positive and negative distribution indicated that the TXx (V2), TNn (V2), and DTR (V2) represent two types of distribution, that is, the positive regions with opposite trends of negative regions.Figure 4
The first and second eigenvectors and their time coefficients of extreme temperature intensity index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)


## 4.2.2. Frequency Indices

As shown in Figure5, the first eigenvectors of FD (V1), TX10p (V1), and TN10p (V1) are all positive, indicating that the spatial variation trends of FD, TX10p, and TN10p are basically the same. The other eigenvectors are positive and negative, but most regions are positive, with small differences in trends. The component values of FD (V1) are distributed along the south-north, with the center of high values located in the north of the basin and decreasing to the south. The center of high values of TX10p (V1) is located in the middle part of the watershed, with the component values decreasing along the surrounding area. The values of the other eigenvectors all change along the southwest or northeast direction, but the locations of the high-value centers are different. The component values of the second eigenvector were increasing or decreasing along the southwest-northeast direction, and all of them were positively and negatively distributed. For example, the component value of SU25 (V2) tends to decrease along the southwest to northeast direction, while that of TX10p (V2) tends to increase. The indices with more negative areas of component values were SU25 (V2), TX90p (V2), and TN90p (V2). The positive high-value center of TN90p (V2) is located in the southwest, and the negative high-value center is located in the southeast part, with an inverse distribution pattern; that is, southwest increased, and northeast decreased, or southwest decreased and northeast increased distribution pattern.Figure 5
The first and second eigenvectors and their time coefficients of extreme temperature frequency index.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)(q)(r)(s)(t)(u)(v)(w)(x)As can be seen from the time coefficients, SU25 (PC1) and SU25 (PC2) have relatively smooth trend changes, and both show an increasing trend after 2007. FD (PC1) has an overall decreasing trend with four significant fluctuations, showing an upward and then a downward trend, while FD (PC2) has relatively stable changes from 1964 to 1996 and a significant upward trend from 1997 to 2012. TX90p (PC1) has a decreasing and then increasing trend with the alternation point near 1984. TX90p (PC2) has a significant fluctuation between 1986 and 1998, while it has an increasing trend before 1986 and was relatively stable after 1998. TN90p (PC1) changed smoothly until 1986, showed a clear upward trend after 1986, and gradually stabilized after 2002. TN90p (PC2) showed an upward trend after 1990 and a downward trend after 2003. TX10p (PC1) showed a fluctuating change, with an upward trend from 1964 to 1971. TX10p (PC2) showed a relatively stable change until 2004 and an increasing trend after 2004. TN10p (PC1) showed a decreasing trend, TN10p (PC2) showed two significant fluctuations in 1965–1977 and 2000–2015, and it was relatively stable in 1978–1999.


## 4.2.3. Duration Indices

As shown in Figure6, the trends of WSDI and CSDI reflected by the first eigenvector are basically the same in space. The center of high value of WSDI (V1) is in the southwest of the watershed, decreasing along the northeast, while the center of high value of CSDI (V1) is in the northeast part, decreasing along the west. The time coefficients show that WSDI (PC1) changed smoothly until 1992 and then showed a clear upward trend, and WSDI (PC2) started to rise around 1992 and decreased after 2000. The second eigenvector WSDI (V2) has a positive and negative type of distribution, with positive values in the southwest and negative values in the northeast representing two types of distribution; that is, there is a distribution pattern of WSDI in the watershed increased in the southwest and decreased in the northeast or decreased in the southwest and increased in the northeast in different years. While CSDI (V2) is all positive, it showed spatial consistency overall. WSDI (V2) and CSDI (V2) correspond to time coefficients WSDI (PC2) and CSDI (PC2) with different change characteristics. WSDI (PC2) changed smoothly before 1990 and showed a trend of rising and then fell from 1991 to 2010. CSDI (V2) changed relatively smoothly, with one fluctuation in 1971–1977, and the eigenvector distribution type was significant in 1972.Figure 6
The first and second eigenvectors and their time coefficients of extreme temperature duration index.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.3. Model Selection

As stated in the study area section, there is a Longtan Control Project built in the basin, and preparatory construction work such as resettlement was carried out in the 1990s, and the environment of the watershed has changed significantly due to human activities. The study of the temporal variation characteristics of the extreme temperature indices revealed that, in the Longtan watershed, most of the extreme indices changed abruptly in the 1990s and 2000s, and the 30-year time series was sufficient for the simulated evaluation of climate models [32–35]. Therefore, the period from 1961 to 1990 with relatively little climate change was used as the simulation period for model evaluation in this study. Based on the temperature observation data of the Longtan watershed from 1961 to 1990, the root mean square error (RMSE), correlation coefficient (R), mean absolute error (MAE), Nash efficiency coefficient (NSE), and trend error (TE) of the simulated maximum and minimum temperatures of each climate model at monthly and annual scales were used as evaluation indicators, and the simulation effects of 11 climate models were evaluated by comprehensive rating metrics. According to the analysis of the spatial and temporal characteristics of extreme temperatures in the previous sections, most of the indices show a distribution of more in the southwest and less in the northeast or more in the southwest and less in the northeast. Therefore, the Luxi station in the southwest and Xingren station in the northeast are chosen as the representative station for showing the simulations of 11 climate models. The evaluation statistics by each climate model simulated at Luxi and Xingren stations are shown in Table 5 and Table 6, respectively. The composite rating results of each model are shown in Table 7.Table 5
The evaluation statistics by each climate model simulated at Luxi Station.
BC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Annual scaleTmaxRMSE1.621.701.571.431.431.651.431.521.531.601.68R0.18−0.040.030.290.23−0.100.100.070.42−0.17−0.02MAE1.341.501.181.031.071.271.101.221.231.341.43NSE−0.84−1.03−0.73−0.45−0.44−0.91−0.44−0.63−0.65−0.79−0.99TE0.120.180.080.360.280.000.180.410.280.030.03TminRMSE2.852.742.923.032.732.882.892.842.723.013.06R0.210.180.24−0.180.010.280.320.19−0.150.100.17MAE2.192.072.132.442.132.232.162.232.122.442.35NSE−0.34−0.23−0.40−0.50−0.22−0.36−0.37−0.32−0.22−0.49−0.54TE0.080.060.060.410.160.180.340.600.500.470.40Monthly scaleTmaxRMSE2.772.762.732.762.732.752.712.772.812.772.77R0.800.790.800.800.800.790.790.780.840.780.80MAE2.342.302.282.292.282.302.242.322.372.322.31NSE0.400.400.420.090.420.410.430.400.380.400.40TE0.000.010.000.400.010.000.010.010.030.000.00TminRMSE2.552.512.392.502.452.502.552.492.522.412.46R0.920.920.930.920.930.920.920.920.920.930.92MAE1.961.951.821.921.931.961.961.961.951.921.92NSE0.840.850.860.850.850.850.840.850.850.860.85TE0.020.010.020.030.020.020.010.020.000.030.01Table 6
The evaluation statistics by each climate model simulated at Xingren Station.
BC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Annual scaleTmaxRMSE1.631.431.511.521.571.461.411.621.551.421.60R0.100.160.110.07−0.090.19−0.05−0.310.260.02−0.10MAE1.321.131.271.281.251.221.141.261.221.121.30NSE−1.87−1.21−1.46−1.48−1.64−1.31−1.16−1.84−1.59−1.17−1.78TE0.090.060.160.160.200.060.140.120.030.080.12TminRMSE1.961.811.961.651.762.131.982.032.061.971.76R−0.060.100.030.300.10−0.25−0.01−0.34−0.11−0.060.09MAE1.651.391.521.411.421.661.491.591.531.691.32NSE−0.84−0.56−0.83−0.30−0.48−1.16−0.87−0.96−1.02−0.85−0.48TE0.510.440.350.730.490.930.811.220.860.600.84Monthly scaleTmaxRMSE2.772.762.732.762.732.752.712.772.812.772.77R0.800.790.800.800.800.790.790.780.840.780.80MAE2.342.302.282.292.282.302.242.322.372.322.31NSE0.400.400.420.090.420.410.430.400.380.400.40TE0.000.010.000.400.010.000.010.010.030.000.00TminRMSE2.552.512.392.502.452.502.552.492.522.412.46R0.920.920.930.920.930.920.920.920.920.930.92MAE1.961.951.821.921.931.961.961.961.951.921.92NSE0.840.850.860.850.850.850.840.850.850.860.85TE0.020.010.020.030.020.020.010.020.000.030.01Table 7
Results of the composite rating metrics of each climate model.
StationBC1BNUCaECCSGF3GF4IP2MI3MI4MP1NE1Luxi0.350.400.630.470.640.470.500.370.430.380.38Xingren0.330.520.510.540.590.310.330.260.470.520.62At Luxi station, except for CCS, MP1, and NE1, most climate models simulate annual-scale maximum and minimum temperatures within a root mean square error of 3. The mean absolute error is within 2.5°C, and the MI3 model had the largest temperature trend error. At the monthly scale, the root mean square error of the simulations of each climate model is between 2.39 and 2.81, and the mean absolute error is within 2.5°C. The variation temperature trend of the simulated minimum temperature of CCS is opposite to the measured trend, and the trend error is large compared with other models. In a comprehensive evaluation, the GF3 model scored higher than other climate models at Luxi station. At the Xingren station, the root mean square error of each model at the annual scale ranged from 1.41 to 2.13, and the mean absolute error was less than 2°C. On the monthly scale, the simulation results of NE1 are mostly better than other models. The comprehensive evaluation results show that the NE1 climate model simulated the temperature of the Xingren station best. In summary, the evaluation results are as follows: the GF3 model performs best at Luxi station, and NE1 simulates best at Xingren station. Therefore, the GF3 model is selected at the Luxi station, and the NE1 model is selected at the Xingren station to evaluate the future temperature change.


## 4.4. Future Trends

Figures7 and 8 show the spatial distribution of interdecadal changes in each extreme temperature index predicted by the selected models for 2021–2050 under the RCP4.5 and RCP8.5, respectively. Under the RCP4.5 scenario, the multiyear average of TXx will increase by 2.1°C, and the multiyear average of TNn will increase by 0.4°C relative to the reference period 1961–1990. In the basin, the TXx showed a decreasing trend in a small part of the southwest, but with little interannual variation, and an increasing trend in the middle and lower reaches of the basin with relatively large interannual variation and an interannual tendency rate of 0.19–1.10°C·(10a)−1. The TNn showed a decreasing trend in the basin, and from the interannual variation, the interannual variation of the TNn is lower than that of the TXx, and the interannual variation in the middle and lower reaches is greater than that in the upper reaches. FD changes in an opposite trend in the upstream and downstream, and CSDI does not change significantly. The other warm-related indices (SU25, TX90p, TN90p, and WSDI) showed an increasing trend in most areas of the basin, and the cold-related indices (TX10p, TN10p) all showed a decreasing trend. Under the RCP8.5 scenario, the TXx will increase by 2.0°C, and the TNn will increase by 0.3°C relative to the base period 1961–1990. In the basin, the TXx showed an increasing trend, and the interannual variation is greater in the downstream area than in the upstream area. The TNn showed an increasing trend except for some areas in the northeast, which showed a decreasing trend. CSDI does not change significantly. All other warm-related indices showed increasing trends, and all cold-related indices showed decreasing trends. The comparison of the two scenarios revealed that the TXx showed an increasing trend in most regions, but there were differences in the spatial distribution of interannual variation, and the interannual variation of the TXx was larger in most regions under the RCP4.5 scenario than under the RCP8.5 scenario. The TNn showed a decreasing trend under the RCP4.5 scenario and an increasing trend in most regions under the RCP8.5 scenario, and there is a large interannual variation under the RCP8.5 scenario. In summary, the extreme temperature in the watershed may show a warming trend in 2021–2050.Figure 7
Spatial distribution of interdecadal variability of temperature extremes for 2021–2050 under the RCP4.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figure 8
Spatial distribution of interdecadal variability of temperature extremes for 2021–2050 under the RCP8.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figures9 and 10 show the spatial distribution of the multiyear averages of each extreme temperature index in the watershed predicted by the selected models for 2021–2050 under the RCP4.5 and RCP8.5, respectively. Under the RCP4.5 scenario, TXx, SU25, TN90p, TX10p, and CSDI showed a spatial characteristic of high northeast and low southwest, while the other indices showed a distribution of low northeast and high southwest. The spatial distributions of TXx and TNn indices under the two scenarios are slightly different. The region of TXx greater than 33.7°C is larger in RCP8.5 than in RCP4.5, and the TXx reaches 34.4°C under RCP8.5, while the maximum value of TXx is 33.9°C under RCP4.5. Most areas of TNn under RCP4.5 are above −3.6°C. And the spatial distribution of TNn under the RCP8.5 scenario did not differ significantly, all above −3.6°C. The prediction results reveal that there is a warming trend of the extreme temperature in the next 30 years, and the risk of extreme high temperature may exist in the downstream areas of the basin in the future. Under the RCP4.5 scenario, the TXx index increases interannually in the downstream region, increasing the risk of extreme high temperature. The interannual variation of the extreme low temperature in the northeastern part of the watershed weakens, and the risk of extreme low temperatures may decrease. Under the RCP8.5 scenario, the interannual variability of TXx increases in the northeastern region, and the extreme high-temperature risk likewise increases.Figure 9
Spatial distribution of temperature extremes for 2021–2050 under RCP4.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)Figure 10
Spatial distribution of temperature extremes for 2021–2050 under RCP8.5.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)


## 5. Discussion

In this study, the trends of extreme temperature in the Longtan watershed from 1959 to 2017 were comprehensively analyzed by using several extreme temperature indices, and the results of the study showed that the extreme temperature changes showed a warming trend, which is generally consistent with similar studies in other regions. For example, the results of Supari et al. [12] showed that the cold days (TX10p) and cold nights (TN10p) both showed decreasing trends in Indonesia, the warm days (TX90p) and warm nights (TN90p) both showed increasing trends, and all other extreme temperature indices showed warming trends. In Malaysia, most of the extreme warm indices increased significantly, and the warm night (TN90p) increased significantly at more than 75% of the stations [36]. Similar studies have been learned in Korea [37], New Zealand [13], and globally [38], where extreme temperature indices indicate a warming trend in extreme temperature changes. However, the extreme temperature indices change at different rates in different regions. Shen et al. [4] found that the annual Tmax increased by 0.28°C·(10a)−1 in North Central China, while this study found that the TXx increased by 0.14°C·(10a)−1 in the Longtan watershed, which increased slowly compared with North Central China. Therefore, it is necessary to study the temperature extremes in different regions. In addition, the extreme temperature indices with significant trends all changed abruptly and mainly occurred in the 1980s, 1990s, and after the 2000s, which was generally consistent with the findings of Wang et al. [39]. Empirical orthogonal function (EOF) analysis is a common spatiotemporal analysis method in atmospheric science. Jia [40] used this method to study the characteristics of spatiotemporal distribution of high and low-temperature climate variables in Liaoning Province, and the results showed that the first mode reflected a good spatial consistency of extreme temperature variation patterns in Liaoning Province. In Chongqing, Guo et al. [41] found from the EOF decomposition results that the first mode was the main type of spatial variation of extreme maximum temperature in Chongqing in summer, and the spatial distribution of extreme maximum temperature had a good consistency. These results are all similar to the conclusion that the first eigenvectors of all indices in this study reflect the general consistency of the trends in the spatial variation of each index, indicating a good spatial consistency of the extreme temperature variation across locations. In summary, the trend of extreme temperature in the Longtan watershed is consistent with the trend of extreme temperature in other regions, and the spatial distributions all have good spatial consistency.The results of the climate model evaluation found that the climate models selected by the comprehensive rating metrics for the simulation effect were different at different stations in the basin, which may be due to the different geographical characteristics among the different stations, GF3 fitted the temperature at Luxi station best and NE1 simulation at Xingren station the best. Under the RCP4.5 and RCP8.5 emission scenarios, an increasing trend of the extreme warm index and a decreasing trend of the extreme cold index are predicted for Shanghai from 2021 to 2030 [42]. This result is generally consistent with the predicted warming trend of extreme temperatures in the Longtan watershed for the next 30 years in this study. However, due to the different geographical characteristics of the region, the rate of change of extreme temperature indices and their trends may differ in different areas, and the results show that there may be a risk of extreme high temperature in the downstream area. Xiao et al. [43] found that the TXn index increases most significantly in the eastern part of the Han River basin in the next 40 years under the RCP4.5 emission scenario. Therefore, further attention to the influence of regional characteristics on future temperature extremes is needed.There is evidence that extreme temperature events may hurt human life. For example, extreme heat and cold temperatures are positively associated with respiratory mortality in China [44]. Global warming and extreme temperature events may also have adverse ecological impacts; for example, increased temperature extremes may cause the uneven distribution of water resources spatially and seasonally [42]. In addition, Haile et al. [45] found that temperature extremes may hurt the production of crops such as rice and corn. The contribution of urbanization to temperature warming trends cannot be ignored, there was a significant urbanization impact on the occurrences of extremely warm and cold nights, and the effect of urbanization contributed about 12.7% to the increasing trend of warm nights and 29% to the decreasing trend of cold nights in Beijing [46]. Nowadays, China’s urbanization process is accelerating, and related departments should pay attention to the impact of urbanization on temperature extremes in the process of urbanization, so that the extreme temperatures will not cause harm to people’s production and life. It also recommended that policymakers and managers in the watershed fully consider the negative impacts of extreme temperature increases in future urban construction, increase urban greenery coverage, and establish safe public drinking water areas to reduce the hazards associated with the occurrence of extreme heat events.The innovation of this study is to use more extreme temperature indices and more mathematical methods to study the extreme temperature variation characteristics of the Longtan basin, so that the research results are clearer and can reflect the extreme temperature variation characteristics of the Longtan watershed more comprehensively. One of the advantages of the proposed framework is that this study does not only study the spatial and temporal distribution characteristics of regional extreme temperatures, but also combine the historical spatial and temporal characteristics of extreme temperatures and use representative stations to further study the future extreme temperature changes, which can better provide data support for the prevention of various extreme temperature disasters in the future.However, there are still some shortcomings to be addressed. Due to the differences in the results obtained by different mutation testing methods, the M-K mutation test in this study was only used to preliminarily obtain the year of possible mutation, and a more systematic mutation analysis needs further study. In addition, there are differences between seasonal and monthly temperature extremes, and the selection of indices can be further improved. This study failed to make a quantitative assessment and analysis of the disaster risk results of each extreme temperature index. In the future, based on the analysis of the spatial and temporal characteristics of extreme temperature and the results of future change prediction, combined with social, economic, and environmental indicators of the basin, a comprehensive risk evaluation of meteorological disasters should be studied.


## 6. Conclusion

To explore the simulation and early warning assessment of extreme temperatures, quantitatively evaluate and describe extreme events, and reduce the adverse effects of frequent extreme events on the ecological environment, social economy, and human production, the temporal-spatial characteristics and future change trends of extreme temperature were studied in the Longtan watershed. It is expected to provide a reference for the establishment of extreme climate event early warning systems, the formulation of disaster prevention and mitigation plans, and the operation and management of water conservancy projects. It was found that (1) from 1959 to 2017, the extreme temperature in the Longtan watershed changed significantly and showed a warming trend. The extreme temperature indices with significant trends all showed abrupt changes, mainly occurring in the 1980s, 1990s, and after 2000. (2) The spatial distribution of extreme temperature indices is generally increasing or decreasing from southwest to northeast, with alternating positive and negative phases over time and obvious fluctuations. Most of the indices have the following spatial variation characteristics: ① spatial variation consistency; ② southwest more northeast less or southwest less northeast more distribution. (3) The analysis of the future trend of extreme temperature indices from 2021 to 2050 using the GF3 model at Luxi station and NE1 model at Xingren station found that the high-temperature area above 33.7°C increased with the increase of emission concentration. The temperature in the basin shows a warming trend, and the risk of extreme high temperatures may exist in the downstream area in the future. In response to the warming trend of extreme temperature, it is recommended that the management in the watershed should pay more attention to extreme temperature events and take measures such as establishing safe public drinking water areas to reduce the hazards of extreme heat events. In addition, this study failed to quantitatively analyze the disaster risk results of each extreme temperature index, and future studies should be based on this study to combine various socioeconomic indicators to conduct a comprehensive risk evaluation of extreme temperature disasters.



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*Source: 1611015-2022-05-03.xml*