# Analysis of Changes in Precipitation and Drought in Aksu River Basin, Northwest China

Authors: Yuhu Zhang; Wanyuan Cai; Qiuhua Chen; Yunjun Yao; Kaili Liu
Journal: Advances in Meteorology
 (2015)

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## Abstract

The analysis of the spatiotemporal trends of precipitation and drought is relevant for the future development and sustainable management of water resources in a given region. In this study, precipitation and Standardized Precipitation Index (SPI) trends were analyzed through applying linear regression, Mann–Kendall, and Spearman’s Rho tests at the 5% significance level. For this goal, meteorological data from 9 meteorological stations in and around Aksu Basin during the period 1960–2010 was used, and two main annual drought periods were detected (1978-1979 and 1983–1986), while the extremely dry years were recorded in 1975 and 1985 at almost all of the stations. The monthly analysis of precipitation series indicates that all stations had increasing trend in July, October, and December, while both increasing and decreasing trends were found in other months. For the seasonal scale, precipitation series had increasing trends in summer and winter. 33% of the stations had the decreasing trend on precipitation in the spring series, and it was 11% in the autumn. At the same time, the SPI-12 values of all stations had the increasing trend. The significant trends were detected at Aheqi, Baicheng, Keping, and Kuche stations.


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## Body

## 1. Introduction

Drought is the result of insufficient or lack of rainfall for an extended period, which causes a substantial hydrological (water) imbalance. Numerous indices have been applied to determine different drought characteristics depending on the study purpose. Precipitation-based drought indices with prearranged thresholds are valid since the main reason of drought is rainfall deficit [1, 2].In the past decade, many scientists have analyzed the spatial variability of drought using drought indices and precipitation characteristics [2–8]. There were a lot of studies on drought [8–13] and various indices have been applied to measure different drought characteristics depending on research goals. The study related to precipitation is a prerequisite for other research studies. Analysis of precipitation data outputs helpful conclusion, which will be applied to plan and manage water resources system. For arid and semiarid regions, precipitation is a particularly important factor for water resources planning and drought risk management. Moreover, arid areas propose a challenge due to large contradistinction between dry and wet conditions within a temporal cycle.The arid region of northwest China is one of the most sensitive areas in the world in terms of responding to global climate change [14, 15]. The Aksu River Basin is located in the western part of the middle southern slope of the Tianshan Mountains and at the northwestern edge of the Tarim Basin in Xinjiang Uygur Autonomous Region of northwestern China. Research on drought for this area can contribute to early warning and water resource plan. Therefore, it is important to research the spatiotemporal trend of precipitation and drought in the past several decades in the Aksu River Basin.Many scholars have studied the characteristics of precipitation changes in different regions in China over the past 50 years [16–20]. The major results indicated that precipitation in summer in eastern China shifted southward in the late 1970s [21, 22], national average precipitation increased with the increasing precipitation in spring but slightly decreasing in autumn in the last decades [23] and the frequency of heavy precipitation events increased in China [24]. Mechanisms have also been proposed to explain precipitation changes [25–27]. Affected by decadal changes of the global climate system, precipitation in China is characterized with significant decadal changes, especially since the 1990s, and the increased global warming plus the reenhanced East Asian monsoon are bound to influence the regional precipitation distribution and its changing trend. Precipitation changes might greatly affect regional climate stability, hydrological processes, and water availability.Furthermore, there have been a number of drought and precipitation studies for different periods in Aksu River Basin. Related studies [28–35] have indicated that there is a change about precipitation and drought indices. For example, Chen et al. [36] summarized that the streamflow from the headwaters of the Tarim River shows significant increase and is sensitive to precipitation, but the streamflow along the mainstream of the river has decreased. Chen et al. [37, 38] analyzed the fifty-year climate change and its effect on annual runoff at Aksu River Basin. The streamflow showed a significant increasing monotonic trend. The annual runoff in the Aksu River had increased by 10.9% since 1990. They also detected the long-term trends of the hydrological time series using both parametric and nonparametric techniques based on temperature and precipitation data from the past 50 years. The temperature, the precipitation, and the streamflow from the headwater of the Tarim River exhibited a significant increase during the last 20 years. Lee and Zhang [39] further developed the relationship between NAO and drought disasters in northwestern China. Statistical results show that NAO and drought disaster were negatively correlated, as positive modes of NAO caused northward-displaced, stronger-than-average midlatitude Westerlies with an enhanced latitudinal water vapor gradient into the central Asian drylands, resulting in reduced drought frequency and intensity in northwestern China. Ling et al. [40] investigated intra-annual runoff trends and periods in the headstream areas of the Tarim River Basin by nonparametric tests and wavelet analysis. The results showed that the runoff, air temperature, and precipitation of the headstreams increased remarkably during both high-flow and low-flow periods.However, most of the previous work on a comprehensive analysis of trends and variability using statistical test and drought indices in precipitation series over Aksu River Basin is still lacking. Thus, it is necessary to analyze the trend of precipitation and characteristics of drought to explore the causes and the formation mechanism of Aksu River Basin drought, which is vital for drought forecast, defense, and mitigation. The analysis of drought variability can improve water resources management in the area.The main goals of the study were to study variability of precipitation on monthly, seasonal, and annual time scale through applying the linear regression, Mann–Kendall, and Spearman’s Rho methods to assess precipitation prediction for the Aksu River Basin in China and to analyze the impact of serial correlation in detecting trends and to investigate the drought in study area from 1960 to 2010.


## 2. Materials and Methods

### 2.1. Study Area and Database

The Aksu River Basin (75°35–82°00′E; 40°17–42°27′N) is located in the western part of the middle southern slope of the Tianshan Mountains and at the northwestern edge of the Tarim Basin. The total area is 5.14 × 104 km2, of which the area of the region in China is 3.1 × 104 km2. The basin is in the interior of the Eurasian continent. Vast territory, diverse topography, complex terrain, and typical regional climate variations made up the characteristics of the northwest mountain climate. It has lower temperatures, plentiful precipitation, and aged snow in the high mountain zone, while the middle mountain zone brings about changes in temperature clearly and is the largest precipitation distribution area. The low mountain zone suffers from drought, large temperature changes, and is fairly well in heat conditions. Due to the Taklimakan Desert in the south and the Tianshan Mountains in the north, the cool air and vapor derived from Central Asia, Siberia, and Arctic Ocean do not straightly enter into the southeastern plain region, which causes typical temperate continental dry climate regional characteristics such as minimal precipitation, intense evaporation, adequate sunshine, and extreme heat [41].Daily precipitation, saturation vapor pressure, net radiation, soil heat flux density, temperature, average 24 h wind speed at 2 m height, and vapor pressure data were collected from 9 meteorological stations distributed in study area (shown in Figure1) for the period 1961–2010 and were obtained from meteorological data shared in service system of China (http://data.cma.gov.cn/). Seasons were defined as follows: winter = December, January, and February; spring = March, April, and May; summer = June, July, and August, and autumn = September, October, and November. The geographical location of the selected meteorological stations is presented in Table 1.Table 1
Location of the stations.
Site name
Code
Lat. (N)
Long (E)
Elev. (m)
Aksu
51628
41. 10
80. 14
1105
Aheqi
51711
40. 93
78. 45
1986
Alar
51730
40.55
81.27
1012
Baichen
51633
41.79
81.9
1229
Keping
51720
40.5
79.05
1162
Kuche
51644
41.72
82.97
1082
Turgat
51701
40. 31
75. 24
3507
Wuqia
51705
39.72
75.25
2176
Kashi
51709
39. 28
75. 59
1291Figure 1
Location map of the 9 synoptic stations in Aksu River Basin of China.The precipitation datasets were investigated for homogeneity and absence of trends. The autocorrelation analysis was applied to the monthly precipitation time series of each station. The precipitation data were quality controlled (QC) from [42].


### 2.2. Rainfall Variability Index (RVI)

RVI (δ) is calculated as follows:(1)δi=(Pi-μ)σ,where δi = Rainfall Variability Index for year i, Pi = annual rainfall for year i, and μ and σ are the mean annual rainfall and standard deviation for the period of the year 1961–2010. A drought year occurs if the δ is negative.According to WMO [43], rainfall time series can be classified into different climatic regimes:(2)extreme dry:P<μ-2·σ,dry:μ-2·σ<P<μ-σ,normal:μ-σ<P<μ+σ,wet:P>μ+σ.


### 2.3. Aridity Index (AI)

In this study, we employed Aridity Index [44] to quantify the drought occurrence as a numerical indicator of the degree of dryness of the climate at each study location. According to the ratio of precipitation (P) to potential evapotranspiration (PET), regions were classified from extremely arid to humid. PET was calculated using the FAO Penman-Monteith method widely [45]. It can be calculated as [46](3)PET=0.408·Δ·Rn-G+γ·(900/(T+273))U2·VPDΔ+γ·1+0.34·U2,where PET = potential evapotranspiration (mm day−1); Δ = slope of the saturation vapor pressure function (kPa°C−1); Rn = net radiation (MJ m−2 day−1); G = soil heat flux density (MJ m−2 day−1); γ = psychometric constant (kPa°C−1); T = mean air temperature (°C); U2 = average 24-h wind speed at 2 m height (ms−1); and VPD = vapor pressure deficit (kPa).The locations were then classified as extremely arid (P/PET≤0.05), arid (0.05<P/PET≤0.2), semiarid (0.2<P/PET≤0.5), subhumid (0.5<P/PET≤0.65), or humid (P/PET>0.65) [2, 47].


### 2.4. Drought Indices

Drought indices are the most indispensable elements for drought analysis and monitoring since they enable identification and quantification of droughts. There have been numerous drought indices such as Standardized Precipitation Index (SPI), the Palmer Hydrological Drought Index (PHDI), Standardized Precipitation Evapotranspiration Index (SPEI), the Surface Water Supply Index (SWSI), Palmer Drought Severity Index (PDSI), and the Standardized Anomaly Index (SAI). The establishment of unique and universally accepted drought indices does not exist, although a number of drought indices have been proposed [13, 48, 49].In this study, the SPI was applied, because of its good characteristics in drought identification and prediction of drought class transitions [8–10]. During the first decade of the 21st century, the Standardized Precipitation Index (SPI) was widely used. And it is simple and considers only precipitation data, which can be found nearly everywhere.


#### 2.4.1. Standardized Precipitation Index

The Standardized Precipitation Index (SPI) was proposed by McKee et al. [50, 51] to indicate the precipitation deficit at different time scales (i.e., accumulated over given time spans). The SPI is a probability index that involves only precipitation. The probabilities are standardized so that an index of zero indicates the mean precipitation amount. The relative simplicity of the SPI is one solid advantage of the index [52]. The main criticism to the SPI is that its calculation is based solely on precipitation data, not considering other variables that determine drought conditions such as temperature, evapotranspiration, wind speed, or the soil water holding capacity.Calculating the SPI for a certain time period at any places requires completed monthly data for the quantity of precipitation, at least 30-annual sequence [53, 54].SPI is mathematically based on the cumulative probability of some precipitation recorded at the observation post. Research has shown that precipitation is subject to the law of gamma distribution [55–57]. One whole period of observation at one meteorological station is used to determine the parameters of scaling and the forms of precipitation probability density function:(4)g(x)=1βα·Γαxα-1·e-x/β,x>0,where α = form parameter; β = scale parameter; x = precipitation quantity; Γ(α) = gamma function defined by the following statement:(5)Γα=∫0∞yα-1e-ydy.Parameters α and β are determined by the method of maximum probability for a multiyear data sequence; that is,(6)αpro=14A1+1+4A3,A=ln⁡xsr⁡-∑i=1nln⁡xin,βpro=xsr⁡αpro,where xsr⁡ is the mean value of precipitation quantity; n is the precipitation measurement number; xi is the quantity of precipitation in a sequence of data.The acquired parameters are further applied to the determination of a cumulative probability of certain precipitation for a specific time period in a time scale of all the recorded precipitation. The cumulative probability can be presented as(7)Gx=∫0xgxdx=1βproxproΓαpro∫0xxαpro-1e-x/βprodx.Because the gamma function has not been defined forx = 0 and the precipitation may be up to zero, the cumulative probability becomes(8)Hx=q+1-qGx,where q is the probability that the quantity of precipitation equals zero, which is calculated using the following equation:(9)q=mn,where m is the number which represented how many times the precipitation was zero in a temporal sequence of data and n is the precipitation observation number in a sequence of data.The calculation of the SPI is presented on the basis of the following equation [58–60]:(10)SPI=-t-c0+c1t+c2t21+d1t+d2t2+d3t3,0<H(x)≤0.5,+t-c0+c1t+c2t21+d1t+d2t2+d3t3,0.5<H(x)≤1.0,where t is determined as(11)t=ln⁡1Hx2,0<Hx≤0.5,ln⁡11-Hx2,0.5<Hx≤1.0.Andc0, c1, c2, d1, d2, and d3 are coefficients whose values are [58–60](12)c0=2.515517,c1=0.802853,c2=0.010328,d1=1.432788,d2=0.189269,d3=0.001308.The drought classification of SPI is presented in Table2 that grouped the severe and extremely severe drought classes for modeling aims since transitions referring to the extremely severe droughts are much less frequent than those for other classes [9]. The SPI on shorter time scales (e.g., 3 and 6 months) describes drought events affecting agricultural practices. In this study, the SPI at 12-month time scale was selected and analyzed because it is more suitable for water resources management purposes in a certain region and more appropriate for identifying the persistence of dry periods [8, 10, 13, 61, 62].Table 2
Drought classification of SPI.
Drought class
SPI value
Nondrought
SPI ≥ 0
Near normal
−1 < SPI < 0
Moderate
−1.5 < SPI ≤ −1
Severe/extreme
SPI ≤ −1.5According to the criteria of McKee et al. [50, 51], severe and extreme droughts corresponding to the categories, respectively, are as shown in Table 2.


### 2.5. Statistical Methods

Many statistical techniques (parametric or nonparametric) have been developed to detect trends within time series such as linear regression, Spearman’s Rho test, Mann–Kendall test, Sen’s slope estimator, and Bayesian procedure [63–68]. In this study, the Mann–Kendall and Spearman’s Rho tests were used to analyze the precipitation trends, while the linear regression was used to calculate magnitude of trends.


#### 2.5.1. Mann–Kendall Trend Test

The Mann–Kendall test statisticS [69, 70] is calculated as(13)S=∑i=1n-1∑j=i+1nsgn(xj-xi),where n is the number of data points, xi and xj are the data values in time series i and j (j>i), respectively, and sgn(xj-xi) is the sign function determined as(14)sgn(xj-xi)=+1,ifxj-xi>0,0,ifxj-xi=0,-1,ifxj-xi<0.In cases where the sample sizen>10, the mean and variance are given by(15)μ(S)=0,σ2S=nn-12n+5-∑i=1mtiti-12ti+518,where m is the number of tied groups and ti denotes the number of ties of extent i. A tied group is a set of sample data having the same value.In the absence of ties between the observations, the variance is computed as(16)σ2S=nn-12n+518.The standard normal test statisticZS is computed as(17)ZS=S-1σ2S,ifS>0,0,ifS=0,S+1σ2S,ifS<0.Positive values ofZS indicate increasing trends while the negative ZS shows decreasing trends.Testing of trends is done at a specificα significance level. In this study, the significance level of α = 0.05 was used. At the 5% significance level, the null hypothesis of no trend is rejected if ZS>1.96.


#### 2.5.2. Spearman’s Rho Test

Spearman’s Rho test is nonparametric method commonly used to verify the absence of trends. Its statisticD and the standardized test statistic ZD are expressed as follows [71, 72]:(18)D=1-6∑i=1nRXi-i2nn2-1,ZD=Dn-21-D2,where R(Xi) is the rank of ith observation Xj in the time series and n is the length of the time series.Positive values ofZD indicate increasing trends while negative ZD show decreasing trends. At the 5% significance level, the null hypothesis of no trend is rejected if ZD>2.08.


#### 2.5.3. Serial Autocorrelation Test

To remove serial correlation from the series, von Storch and Navarra [73] suggested to prewhiten the series before applying the Mann–Kendall and Spearman’s Rho tests. The lag-1 serial correlation coefficient of sample data xi (designated by r1) is computed as [74, 75](19)r1=(1/n-1)∑i=1n-1(xi-μ(xi))·(xi+1-μ(xi))(1/n)∑i=1nxi-μxi2,μxi=1n∑i=1nxi,where μxi is the mean of sample data and n is the sample size.For the two-sided test, Unkašević and Tošić [68] recommended that the 0.05 significance level for r1 can be computed by(20)r10.05=-1±1.96n-2n-1,where n is the sample size.


## 2.1. Study Area and Database

The Aksu River Basin (75°35–82°00′E; 40°17–42°27′N) is located in the western part of the middle southern slope of the Tianshan Mountains and at the northwestern edge of the Tarim Basin. The total area is 5.14 × 104 km2, of which the area of the region in China is 3.1 × 104 km2. The basin is in the interior of the Eurasian continent. Vast territory, diverse topography, complex terrain, and typical regional climate variations made up the characteristics of the northwest mountain climate. It has lower temperatures, plentiful precipitation, and aged snow in the high mountain zone, while the middle mountain zone brings about changes in temperature clearly and is the largest precipitation distribution area. The low mountain zone suffers from drought, large temperature changes, and is fairly well in heat conditions. Due to the Taklimakan Desert in the south and the Tianshan Mountains in the north, the cool air and vapor derived from Central Asia, Siberia, and Arctic Ocean do not straightly enter into the southeastern plain region, which causes typical temperate continental dry climate regional characteristics such as minimal precipitation, intense evaporation, adequate sunshine, and extreme heat [41].Daily precipitation, saturation vapor pressure, net radiation, soil heat flux density, temperature, average 24 h wind speed at 2 m height, and vapor pressure data were collected from 9 meteorological stations distributed in study area (shown in Figure1) for the period 1961–2010 and were obtained from meteorological data shared in service system of China (http://data.cma.gov.cn/). Seasons were defined as follows: winter = December, January, and February; spring = March, April, and May; summer = June, July, and August, and autumn = September, October, and November. The geographical location of the selected meteorological stations is presented in Table 1.Table 1
Location of the stations.
Site name
Code
Lat. (N)
Long (E)
Elev. (m)
Aksu
51628
41. 10
80. 14
1105
Aheqi
51711
40. 93
78. 45
1986
Alar
51730
40.55
81.27
1012
Baichen
51633
41.79
81.9
1229
Keping
51720
40.5
79.05
1162
Kuche
51644
41.72
82.97
1082
Turgat
51701
40. 31
75. 24
3507
Wuqia
51705
39.72
75.25
2176
Kashi
51709
39. 28
75. 59
1291Figure 1
Location map of the 9 synoptic stations in Aksu River Basin of China.The precipitation datasets were investigated for homogeneity and absence of trends. The autocorrelation analysis was applied to the monthly precipitation time series of each station. The precipitation data were quality controlled (QC) from [42].


## 2.2. Rainfall Variability Index (RVI)

RVI (δ) is calculated as follows:(1)δi=(Pi-μ)σ,where δi = Rainfall Variability Index for year i, Pi = annual rainfall for year i, and μ and σ are the mean annual rainfall and standard deviation for the period of the year 1961–2010. A drought year occurs if the δ is negative.According to WMO [43], rainfall time series can be classified into different climatic regimes:(2)extreme dry:P<μ-2·σ,dry:μ-2·σ<P<μ-σ,normal:μ-σ<P<μ+σ,wet:P>μ+σ.


## 2.3. Aridity Index (AI)

In this study, we employed Aridity Index [44] to quantify the drought occurrence as a numerical indicator of the degree of dryness of the climate at each study location. According to the ratio of precipitation (P) to potential evapotranspiration (PET), regions were classified from extremely arid to humid. PET was calculated using the FAO Penman-Monteith method widely [45]. It can be calculated as [46](3)PET=0.408·Δ·Rn-G+γ·(900/(T+273))U2·VPDΔ+γ·1+0.34·U2,where PET = potential evapotranspiration (mm day−1); Δ = slope of the saturation vapor pressure function (kPa°C−1); Rn = net radiation (MJ m−2 day−1); G = soil heat flux density (MJ m−2 day−1); γ = psychometric constant (kPa°C−1); T = mean air temperature (°C); U2 = average 24-h wind speed at 2 m height (ms−1); and VPD = vapor pressure deficit (kPa).The locations were then classified as extremely arid (P/PET≤0.05), arid (0.05<P/PET≤0.2), semiarid (0.2<P/PET≤0.5), subhumid (0.5<P/PET≤0.65), or humid (P/PET>0.65) [2, 47].


## 2.4. Drought Indices

Drought indices are the most indispensable elements for drought analysis and monitoring since they enable identification and quantification of droughts. There have been numerous drought indices such as Standardized Precipitation Index (SPI), the Palmer Hydrological Drought Index (PHDI), Standardized Precipitation Evapotranspiration Index (SPEI), the Surface Water Supply Index (SWSI), Palmer Drought Severity Index (PDSI), and the Standardized Anomaly Index (SAI). The establishment of unique and universally accepted drought indices does not exist, although a number of drought indices have been proposed [13, 48, 49].In this study, the SPI was applied, because of its good characteristics in drought identification and prediction of drought class transitions [8–10]. During the first decade of the 21st century, the Standardized Precipitation Index (SPI) was widely used. And it is simple and considers only precipitation data, which can be found nearly everywhere.


### 2.4.1. Standardized Precipitation Index

The Standardized Precipitation Index (SPI) was proposed by McKee et al. [50, 51] to indicate the precipitation deficit at different time scales (i.e., accumulated over given time spans). The SPI is a probability index that involves only precipitation. The probabilities are standardized so that an index of zero indicates the mean precipitation amount. The relative simplicity of the SPI is one solid advantage of the index [52]. The main criticism to the SPI is that its calculation is based solely on precipitation data, not considering other variables that determine drought conditions such as temperature, evapotranspiration, wind speed, or the soil water holding capacity.Calculating the SPI for a certain time period at any places requires completed monthly data for the quantity of precipitation, at least 30-annual sequence [53, 54].SPI is mathematically based on the cumulative probability of some precipitation recorded at the observation post. Research has shown that precipitation is subject to the law of gamma distribution [55–57]. One whole period of observation at one meteorological station is used to determine the parameters of scaling and the forms of precipitation probability density function:(4)g(x)=1βα·Γαxα-1·e-x/β,x>0,where α = form parameter; β = scale parameter; x = precipitation quantity; Γ(α) = gamma function defined by the following statement:(5)Γα=∫0∞yα-1e-ydy.Parameters α and β are determined by the method of maximum probability for a multiyear data sequence; that is,(6)αpro=14A1+1+4A3,A=ln⁡xsr⁡-∑i=1nln⁡xin,βpro=xsr⁡αpro,where xsr⁡ is the mean value of precipitation quantity; n is the precipitation measurement number; xi is the quantity of precipitation in a sequence of data.The acquired parameters are further applied to the determination of a cumulative probability of certain precipitation for a specific time period in a time scale of all the recorded precipitation. The cumulative probability can be presented as(7)Gx=∫0xgxdx=1βproxproΓαpro∫0xxαpro-1e-x/βprodx.Because the gamma function has not been defined forx = 0 and the precipitation may be up to zero, the cumulative probability becomes(8)Hx=q+1-qGx,where q is the probability that the quantity of precipitation equals zero, which is calculated using the following equation:(9)q=mn,where m is the number which represented how many times the precipitation was zero in a temporal sequence of data and n is the precipitation observation number in a sequence of data.The calculation of the SPI is presented on the basis of the following equation [58–60]:(10)SPI=-t-c0+c1t+c2t21+d1t+d2t2+d3t3,0<H(x)≤0.5,+t-c0+c1t+c2t21+d1t+d2t2+d3t3,0.5<H(x)≤1.0,where t is determined as(11)t=ln⁡1Hx2,0<Hx≤0.5,ln⁡11-Hx2,0.5<Hx≤1.0.Andc0, c1, c2, d1, d2, and d3 are coefficients whose values are [58–60](12)c0=2.515517,c1=0.802853,c2=0.010328,d1=1.432788,d2=0.189269,d3=0.001308.The drought classification of SPI is presented in Table2 that grouped the severe and extremely severe drought classes for modeling aims since transitions referring to the extremely severe droughts are much less frequent than those for other classes [9]. The SPI on shorter time scales (e.g., 3 and 6 months) describes drought events affecting agricultural practices. In this study, the SPI at 12-month time scale was selected and analyzed because it is more suitable for water resources management purposes in a certain region and more appropriate for identifying the persistence of dry periods [8, 10, 13, 61, 62].Table 2
Drought classification of SPI.
Drought class
SPI value
Nondrought
SPI ≥ 0
Near normal
−1 < SPI < 0
Moderate
−1.5 < SPI ≤ −1
Severe/extreme
SPI ≤ −1.5According to the criteria of McKee et al. [50, 51], severe and extreme droughts corresponding to the categories, respectively, are as shown in Table 2.


## 2.4.1. Standardized Precipitation Index

The Standardized Precipitation Index (SPI) was proposed by McKee et al. [50, 51] to indicate the precipitation deficit at different time scales (i.e., accumulated over given time spans). The SPI is a probability index that involves only precipitation. The probabilities are standardized so that an index of zero indicates the mean precipitation amount. The relative simplicity of the SPI is one solid advantage of the index [52]. The main criticism to the SPI is that its calculation is based solely on precipitation data, not considering other variables that determine drought conditions such as temperature, evapotranspiration, wind speed, or the soil water holding capacity.Calculating the SPI for a certain time period at any places requires completed monthly data for the quantity of precipitation, at least 30-annual sequence [53, 54].SPI is mathematically based on the cumulative probability of some precipitation recorded at the observation post. Research has shown that precipitation is subject to the law of gamma distribution [55–57]. One whole period of observation at one meteorological station is used to determine the parameters of scaling and the forms of precipitation probability density function:(4)g(x)=1βα·Γαxα-1·e-x/β,x>0,where α = form parameter; β = scale parameter; x = precipitation quantity; Γ(α) = gamma function defined by the following statement:(5)Γα=∫0∞yα-1e-ydy.Parameters α and β are determined by the method of maximum probability for a multiyear data sequence; that is,(6)αpro=14A1+1+4A3,A=ln⁡xsr⁡-∑i=1nln⁡xin,βpro=xsr⁡αpro,where xsr⁡ is the mean value of precipitation quantity; n is the precipitation measurement number; xi is the quantity of precipitation in a sequence of data.The acquired parameters are further applied to the determination of a cumulative probability of certain precipitation for a specific time period in a time scale of all the recorded precipitation. The cumulative probability can be presented as(7)Gx=∫0xgxdx=1βproxproΓαpro∫0xxαpro-1e-x/βprodx.Because the gamma function has not been defined forx = 0 and the precipitation may be up to zero, the cumulative probability becomes(8)Hx=q+1-qGx,where q is the probability that the quantity of precipitation equals zero, which is calculated using the following equation:(9)q=mn,where m is the number which represented how many times the precipitation was zero in a temporal sequence of data and n is the precipitation observation number in a sequence of data.The calculation of the SPI is presented on the basis of the following equation [58–60]:(10)SPI=-t-c0+c1t+c2t21+d1t+d2t2+d3t3,0<H(x)≤0.5,+t-c0+c1t+c2t21+d1t+d2t2+d3t3,0.5<H(x)≤1.0,where t is determined as(11)t=ln⁡1Hx2,0<Hx≤0.5,ln⁡11-Hx2,0.5<Hx≤1.0.Andc0, c1, c2, d1, d2, and d3 are coefficients whose values are [58–60](12)c0=2.515517,c1=0.802853,c2=0.010328,d1=1.432788,d2=0.189269,d3=0.001308.The drought classification of SPI is presented in Table2 that grouped the severe and extremely severe drought classes for modeling aims since transitions referring to the extremely severe droughts are much less frequent than those for other classes [9]. The SPI on shorter time scales (e.g., 3 and 6 months) describes drought events affecting agricultural practices. In this study, the SPI at 12-month time scale was selected and analyzed because it is more suitable for water resources management purposes in a certain region and more appropriate for identifying the persistence of dry periods [8, 10, 13, 61, 62].Table 2
Drought classification of SPI.
Drought class
SPI value
Nondrought
SPI ≥ 0
Near normal
−1 < SPI < 0
Moderate
−1.5 < SPI ≤ −1
Severe/extreme
SPI ≤ −1.5According to the criteria of McKee et al. [50, 51], severe and extreme droughts corresponding to the categories, respectively, are as shown in Table 2.


## 2.5. Statistical Methods

Many statistical techniques (parametric or nonparametric) have been developed to detect trends within time series such as linear regression, Spearman’s Rho test, Mann–Kendall test, Sen’s slope estimator, and Bayesian procedure [63–68]. In this study, the Mann–Kendall and Spearman’s Rho tests were used to analyze the precipitation trends, while the linear regression was used to calculate magnitude of trends.


### 2.5.1. Mann–Kendall Trend Test

The Mann–Kendall test statisticS [69, 70] is calculated as(13)S=∑i=1n-1∑j=i+1nsgn(xj-xi),where n is the number of data points, xi and xj are the data values in time series i and j (j>i), respectively, and sgn(xj-xi) is the sign function determined as(14)sgn(xj-xi)=+1,ifxj-xi>0,0,ifxj-xi=0,-1,ifxj-xi<0.In cases where the sample sizen>10, the mean and variance are given by(15)μ(S)=0,σ2S=nn-12n+5-∑i=1mtiti-12ti+518,where m is the number of tied groups and ti denotes the number of ties of extent i. A tied group is a set of sample data having the same value.In the absence of ties between the observations, the variance is computed as(16)σ2S=nn-12n+518.The standard normal test statisticZS is computed as(17)ZS=S-1σ2S,ifS>0,0,ifS=0,S+1σ2S,ifS<0.Positive values ofZS indicate increasing trends while the negative ZS shows decreasing trends.Testing of trends is done at a specificα significance level. In this study, the significance level of α = 0.05 was used. At the 5% significance level, the null hypothesis of no trend is rejected if ZS>1.96.


### 2.5.2. Spearman’s Rho Test

Spearman’s Rho test is nonparametric method commonly used to verify the absence of trends. Its statisticD and the standardized test statistic ZD are expressed as follows [71, 72]:(18)D=1-6∑i=1nRXi-i2nn2-1,ZD=Dn-21-D2,where R(Xi) is the rank of ith observation Xj in the time series and n is the length of the time series.Positive values ofZD indicate increasing trends while negative ZD show decreasing trends. At the 5% significance level, the null hypothesis of no trend is rejected if ZD>2.08.


### 2.5.3. Serial Autocorrelation Test

To remove serial correlation from the series, von Storch and Navarra [73] suggested to prewhiten the series before applying the Mann–Kendall and Spearman’s Rho tests. The lag-1 serial correlation coefficient of sample data xi (designated by r1) is computed as [74, 75](19)r1=(1/n-1)∑i=1n-1(xi-μ(xi))·(xi+1-μ(xi))(1/n)∑i=1nxi-μxi2,μxi=1n∑i=1nxi,where μxi is the mean of sample data and n is the sample size.For the two-sided test, Unkašević and Tošić [68] recommended that the 0.05 significance level for r1 can be computed by(20)r10.05=-1±1.96n-2n-1,where n is the sample size.


## 2.5.1. Mann–Kendall Trend Test

The Mann–Kendall test statisticS [69, 70] is calculated as(13)S=∑i=1n-1∑j=i+1nsgn(xj-xi),where n is the number of data points, xi and xj are the data values in time series i and j (j>i), respectively, and sgn(xj-xi) is the sign function determined as(14)sgn(xj-xi)=+1,ifxj-xi>0,0,ifxj-xi=0,-1,ifxj-xi<0.In cases where the sample sizen>10, the mean and variance are given by(15)μ(S)=0,σ2S=nn-12n+5-∑i=1mtiti-12ti+518,where m is the number of tied groups and ti denotes the number of ties of extent i. A tied group is a set of sample data having the same value.In the absence of ties between the observations, the variance is computed as(16)σ2S=nn-12n+518.The standard normal test statisticZS is computed as(17)ZS=S-1σ2S,ifS>0,0,ifS=0,S+1σ2S,ifS<0.Positive values ofZS indicate increasing trends while the negative ZS shows decreasing trends.Testing of trends is done at a specificα significance level. In this study, the significance level of α = 0.05 was used. At the 5% significance level, the null hypothesis of no trend is rejected if ZS>1.96.


## 2.5.2. Spearman’s Rho Test

Spearman’s Rho test is nonparametric method commonly used to verify the absence of trends. Its statisticD and the standardized test statistic ZD are expressed as follows [71, 72]:(18)D=1-6∑i=1nRXi-i2nn2-1,ZD=Dn-21-D2,where R(Xi) is the rank of ith observation Xj in the time series and n is the length of the time series.Positive values ofZD indicate increasing trends while negative ZD show decreasing trends. At the 5% significance level, the null hypothesis of no trend is rejected if ZD>2.08.


## 2.5.3. Serial Autocorrelation Test

To remove serial correlation from the series, von Storch and Navarra [73] suggested to prewhiten the series before applying the Mann–Kendall and Spearman’s Rho tests. The lag-1 serial correlation coefficient of sample data xi (designated by r1) is computed as [74, 75](19)r1=(1/n-1)∑i=1n-1(xi-μ(xi))·(xi+1-μ(xi))(1/n)∑i=1nxi-μxi2,μxi=1n∑i=1nxi,where μxi is the mean of sample data and n is the sample size.For the two-sided test, Unkašević and Tošić [68] recommended that the 0.05 significance level for r1 can be computed by(20)r10.05=-1±1.96n-2n-1,where n is the sample size.


## 3. Results and Discussion

### 3.1. Summary of Statistical Parameters

Statistical parameters of monthly precipitation time series at 9 synoptic stations during the period 1960–2010 are summarized in Table3. The minimal monthly precipitation is 0 mm for all stations. The mean monthly precipitation is ranged from 4.076 mm to 20.554 mm. Moreover, it is obvious that 3 mountainous synoptic stations in the northwest (Aheqi, Turgat, and Wuqia) had the highest mean monthly precipitation.Table 3
Statistical parameters of monthly precipitation time series at 9 synoptic stations during the period 1960–2010.
Station name
Min (mm)
Max (mm)
Mean (mm)
Standard deviation (mm)
CV (%)
Skewness
Kurtosis
Aksu
0
92.2
6.162
10.148
164.672
3.343
16.699
Aheqi
0
145.2
17.920
23.597
131.676
1.983
4.520
Alar
0
50.9
4.076
7.546
185.139
2.737
8.473
Baicheng
0
76.8
9.920
12.367
124.664
2.115
5.874
Keping
0
81.2
8.029
13.348
166.253
2.553
7.537
Kuche
0
65.3
5.818
8.832
151.812
2.499
7.620
Turgat
0
122.1
20.554
21.380
104.015
1.615
2.682
Wuqia
0
121.6
15.009
18.471
123.071
1.878
4.080
Kashi
0
78.5
5.615
9.561
170.283
3.099
12.861
Note: cv-coefficient of variation.The highest kurtosis of the precipitation values was observed at Aksu station with 16.699, while the lowest kurtosis of 2.682 was found at Turgat. This phenomenon indicated that the monthly precipitation in Turgat is relatively homogeneous. But it is converse in Aksu.Time series of annual precipitation at the 9 synoptic stations are shown in Figure2. The results indicated that the annual precipitation had a certain degree of variance during the observed period. In Aksu, Alar, Kuche, and Kashi, the annual precipitation is relatively low and basic by about 50 mm. However, the annual precipitation in Aheqi, Wuqia, and Turgat, is above 200 mm. In addition, the annual precipitation in Baicheng, Kuche, and Keping has obvious upward trend during the observed period. These results show that the precipitation in upstream of Aksu basin is larger than that in downstream.Figure 2
Annual precipitation time series at the 9 synoptic stations.


### 3.2. Aridity Index

The estimated UNEP Aridity Index for the 9 synoptic stations is given in Table4. The FAO-56 Penman–Monteith equation as a part of the model based on service-oriented paradigm [76, 77] is used for estimating PET. The results indicated that the Aridity Index ranged from 0.048 at the Alar station to 0.397 at the Turgat station. The Alar station is extremely arid and the Aheqi station and the Turgat station are semiarid, while all other stations are arid. The upper limit for extremely arid climate is 0.05, but Alar had a slightly lower value. The Alar station is extremely arid because of the highest PET, minimum of the annual precipitation, and the highest value of the temperature difference.Table 4
Aridity Index, annual precipitation, and reference evapotranspiration estimated using FAO-56 Penman–Monteith equation.
Station name
Precipitation (mm/year)
PET (mm/year)
Aridity index
Climate
Aksu
73.947
972.22
0.076
Arid
Aheqi
215.045
985.51
0.218
Semiarid
Alar
48.910
1023.91
0.048
Extreme arid
Baicheng
119.041
832.52
0.143
Arid
Keping
96.343
1102.73
0.087
Arid
Kuche
69.812
1164.73
0.060
Arid
Turgat
246.653
621.34
0.397
Semiarid
Wuqia
180.106
1082.91
0.166
Arid
Kashi
67.380
1125.91
0.060
Arid


### 3.3. Rainfall Variability

Annual rainfall variability indices for the observed synoptic stations are shown in Figure3, while the percentage distribution of dry, normal, and wet years during the period 1960–2010 is given in Figure 4. It is obvious that there was no extremely dry year for all stations. Although, considering both time series of precipitation and annual rainfall variability indices for the 9 synoptic stations, there were two main periods which were characterized by long and severe droughts, namely, 1978-1979 and 1983–1986.Figure 3
Annual rainfall variability indices for the 9 synoptic stations.Figure 4
Distribution in percentage of dry, normal, and wet years for the 9 synoptic stations during the period 1960–2010.During the first period, the drought years were approximately 55% of the total years. The second period is characterized by approximately 47% of the drought years. In addition, it should be noticed that there were 4 dry years, 1961, 1975, 1985, and 2007. These four years were characterized by approximately 89% negative values of the annual rainfall variability index.


### 3.4. Analysis of Precipitation

The serial correlation coefficient can improve the verification of the independence of precipitation time series. If the time series are completely random, the autocorrelation function will be zero for all lags other than zero. In this study, to accept the hypothesisH0: r1=0 (that there is no correlation between two consecutive observations and there is no persistence in the time series), the value of r1 should fall between −0.2544 and 0.2544.Autocorrelation plot for the annual precipitation at the 9 synoptic stations is presented in Figure5. As shown, the precipitation had both positive and negative serial correlations. The highest and at the same time the significant serial correlation of 0.260 was obtained at the Baicheng station, while the lowest serial correlation of −0.104 was detected at the Wuqia station.Figure 5
Lag-1 serial correlation coefficient for the precipitation at the synoptic stations.Lag-1 serial correlation coefficients for seasonal precipitation data at the observed stations during the period 1960–2010 are presented in Table5. As shown, a positive serial correlation was found in the spring, summer, autumn, and winter series at 77.8%, 88.9%, 66.7%, and 77.8% of the stations, respectively. The significant serial correlation was detected in the autumn at Aheqi station. Trends of precipitation are considered statistically at the 5% significance level using the Mann–Kendall test and the Spearman’s Rho test. When a significant trend is identified by two statistical methods, the trend is presented in bold character in Table 6.Table 5
Lag-1 serial correlation coefficients for seasonal precipitation data.
Station name
Spring
Summer
Autumn
Winter
Aksu
0.102
0.105
−0.042
0.181
Aheqi
0.199
0.009
0.395
0.102
Alar
−0.006
0.147
−0.108
−0.078
Baicheng
0.192
0.160
0.140
0.187
Keping
0.059
0.167
0.014
0.113
Kuche
0.106
0.035
−0.077
0.077
Turgat
0.028
0.019
0.090
0.163
Wuqia
−0.020
0.100
0.131
−0.068
Kashi
0.054
−0.050
0.090
0.019Table 6
Results of the statistical tests for the monthly precipitation during the period 1960–2010.
Station
Test
Month
January
February
March
April
May
June
July
August
September
October
November
December
Aksu
Z
S
0.233
0.760
0.411
−0.579
0.276
1.755
0.796
−0.926
1.365
0.976
0.000
1.588
Z
D
0.410
0.884
0.586
−0.279
0.232
2.014
0.793
−0.890
1.318
1.203
0.789
2.060
b
0.023
0.060
0.058
0.016
0.011
0.184
0.036
−0.075
0.138
0.122
−0.008
0.038
Aheqi
Z
S
0.139
0.383
0.789
0.545
0.016
−0.244
1.576
0.390
1.673
2.795
*
0.798
1.088
Z
D
0.159
0.319
0.816
0.615
0.026
−0.146
1.766
0.524
1.729
3.249
*
1.020
1.250
b
0.014
0.019
0.129
0.019
0.058
−0.054
0.513
0.236
0.877
0.227
−0.001
0.024
Alar
Z
S
1.454
1.175
−0.102
−0.171
0.073
1.276
1.186
−0.016
−0.552
0.026
0.603
1.523
Z
D
1.964
2.166
*
0.658
0.494
−0.025
1.439
1.309
0.021
−0.399
0.521
2.088
*
2.747
*
b
0.025
0.028
0.023
−0.014
−0.050
0.078
0.106
0.069
−0.067
0.013
−0.003
0.027
Baicheng
Z
S
1.206
1.007
0.253
0.262
1.089
2.193
*
1.901
1.324
2.161
*
1.322
0.886
1.605
Z
D
1.394
0.786
0.247
0.339
1.155
2.477
*
1.926
1.175
2.207
*
1.339
1.313
1.783
b
0.042
0.083
0.037
−0.025
0.077
0.268
0.234
0.122
0.228
0.231
0.089
0.042
Keping
Z
S
0.311
1.171
1.308
−0.198
−0.073
0.918
1.706
1.405
2.278
*
1.363
−0.249
0.937
Z
D
0.525
1.064
1.665
−0.185
−0.026
0.999
1.849
1.485
2.447
*
1.726
1.112
1.482
b
0.045
0.037
0.102
0.009
−0.014
0.112
0.273
0.367
0.284
0.079
−0.012
0.031
Kuche
Z
S
2.633
*
0.919
−0.694
0.679
0.699
2.437
*
0.999
1.357
0.553
0.513
1.896
2.533
*
Z
D
2.893
*
1.024
−0.541
0.773
0.808
2.747
*
1.057
1.279
0.476
0.651
2.626
*
3.113
*
b
0.048
0.052
−0.036
0.023
0.106
0.207
0.061
0.063
0.019
0.013
−0.010
0.039
Turgat
Z
S
0.033
−0.455
0.723
0.227
−0.382
1.527
0.796
0.398
−0.106
2.713
*
0.122
2.211
*
Z
D
−0.046
−0.428
0.619
0.254
−0.387
1.498
0.794
0.392
−0.066
2.810
*
0.190
2.307
*
b
−0.003
−0.018
0.019
0.091
−0.058
0.285
0.164
0.130
0.023
0.253
−0.006
0.093
Wuqia
Z
S
0.708
−1.122
−0.228
−0.041
0.195
1.600
1.787
−0.024
0.699
2.847
*
−0.016
1.027
Z
D
0.699
−1.394
−0.375
−0.097
0.007
1.822
2.194
*
−0.008
0.677
2.983
*
−0.151
1.176
b
0.032
−0.039
−0.048
0.011
−0.092
0.465
0.407
−0.076
0.141
0.239
−0.015
0.029
Kashi
Z
S
0.507
−0.638
1.455
−0.156
0.602
0.999
1.406
0.268
1.223
3.249
*
0.365
1.035
Z
D
0.685
−0.387
1.758
−0.164
0.401
1.146
1.327
0.199
1.294
3.908
*
1.071
1.430
b
0.048
−0.015
0.106
−0.058
−0.115
0.096
0.111
−0.025
0.104
0.170
0.024
0.020
Z
S
: Mann–Kendall test, ZD: Spearman’s Rho test, and b: slope of linear regression.
Bold characters represent trends identified by 2 statistical methods together.
*Statistically significant trends at the 5% significance level.The results of the statistical tests for the monthly precipitation series during the period 1960–2010 are summarized in Table6. As shown, the precipitation in Baicheng station had the significant increasing trend in June and September. The significant increasing trend was also detected at the Kuche station in January, June, and December. There was no decreasing trend. Besides, A statistically significant trend ZS = 2.380 was detected in September at the Aheqi station before eliminating the effect of serial correlation. After removing lag-1 serial correlation effect, an insignificant trend of ZS = 1.673 was obtained. Furthermore, an insignificant trend ZD = 1.633 was detected in January at the Kuche station before eliminating the effect of serial correlation. After removing lag-1 serial correlation effect a significant trend of ZS = 2.893 was obtained.Seasonal and annual trends of precipitation obtained by statistical methods are given in Table7. According to these results, the increasing trends in annual precipitation series were detected at Aheqi, Baicheng, Keping, and Kuche, while there is no significant trend for other stations which is consistent with our analysis in Section 3.1. On annual level, precipitation quantities are increasing, with the highest increase in winter.Table 7
Results of the statistical tests for seasonal and annual precipitation during the period 1960–2010.
Station
Test
Season
Spring
Summer
Autumn
Winter
Annual
Aksu
Z
S
0.341
0.780
1.673
1.154
1.495
Z
D
0.295
0.952
1.696
1.264
1.690
b
0.084
0.145
0.253
0.125
0.603
Aheqi
Z
S
0.309
1.056
2.209
*
0.739
2.819
*
Z
D
0.434
1.106
2.338
*
0.529
3.026
*
b
0.206
0.695
1.103
0.055
2.062
Alar
Z
S
−0.520
1.592
−0.390
1.947
1.129
Z
D
−0.567
1.793
−0.325
2.152*
1.159
b
−0.041
0.253
−0.057
0.083
0.235
Baicheng
Z
S
0.390
2.713
*
2.266
*
2.112
*
2.193
*
Z
D
0.392
3.029
*
2.444
*
2.214
*
2.620
*
b
0.089
0.624
0.548
0.166
1.427
Keping
Z
S
0.244
2.372
*
2.429
*
1.357
2.875
*
Z
D
0.404
2.567
*
2.552
*
1.483
3.300
*
b
0.097
0.752
0.351
0.113
1.313
Kuche
Z
S
0.430
1.852
0.423
2.145
*
2.494
*
Z
D
0.416
2.050*
0.263
2.274
*
2.743
*
b
0.093
0.331
0.023
0.141
0.585
Turgat
Z
S
0.195
1.503
1.194
1.803
1.527
Z
D
0.283
1.379
1.225
1.874
1.667
b
0.052
0.579
0.270
0.099
0.973
Wuqia
Z
S
−0.260
1.462
1.698
0.065
1.251
Z
D
−0.342
1.599
1.579
0.062
1.281
b
−0.129
0.796
0.365
0.014
1.054
Kashi
Z
S
−0.195
1.121
2.527
*
0.390
1.129
Z
D
−0.223
1.150
2.547
*
0.499
1.055
b
−0.067
0.182
0.297
0.041
0.466
Z
S: Mann–Kendall test, ZD: Spearman’s Rho test, and b: slope of linear regression.
Bold characters represent trends identified by 2 statistical methods together.
*Statistically significant trends at the 5% significance level.For the seasonal scale, there were increasing trends in summer and winter precipitation series. The decreasing precipitation trend was found in the spring and autumn series at 33% and 11% of the stations, respectively. Besides, the significant increasing trends were found at Aheqi and Kashi in autumn and at Alar and Kuche in winter. Furthermore, the significant increasing trends were detected at Baicheng in summer, autumn, and winter. The precipitation of Keping also had increasing trends in summer and autumn.


### 3.5. Analysis of SPI-12

Time series of SPI-12 at the 9 synoptic stations during the period 1960–2010 are shown in Figure7. Characteristics of drought at 12-month time scale are shown in Table 8. It should be observed that the most severe drought of Aheqi and Alar was 1975, while that of Keping and Wuqia occurred in 1985. Besides, the most severe drought year was 1976 at Bacheng station and 1986 at Aksu station. The Wuqia station had the lowest SPI-12 with −2.5986 in 1985. The number of drought years during the observed period at the stations is presented in Table 8. According to the results, the total drought years ranged between 14 (at Wuqia and Kashi station) and 19 (at Alar station). Almost 32.2% of the observed years were drought years at all the 9 stations.Table 8
Characteristics of droughts at 12-month time scale.
Station
The most severe drought
Number of drought years during the observed period
SPI
Year
Near normal
Moderate
Severe/extreme
Total
Aksu
−2.2748
1986
7
7
3
17
Aheqi
−2.1138
1975
10
6
2
18
Alar
−2.2262
1975
11
6
2
19
Keping
−2.5112
1985
8
5
3
16
Baicheng
−1.9470
1961
5
6
4
15
Kuche
−1.8056
1965
8
6
4
18
Turgat
−2.1432
1976
7
5
5
17
Wuqia
−2.5986
1985
3
8
3
14
Kashi
−1.9757
1994
6
3
5
14Lag-1 serial correlation coefficient for the SPI-12 at the observed synoptic stations is illustrated in Figure8. The highest and at the same time the significant positive serial correlation coefficient of 0.2676 was detected at the Aksu station. On the other hand, negative values were observed at the Turgat, Wuqia, and Kashi stations.The results of the Mann–Kendall and Spearman’s Rho tests for the SPI-12 series are presented in Figure9. It can be noted that all stations have the increasing trend. The significant trends were detected at Aheqi, Baicheng, Keping, and Kuche stations.Although a significantly increasing trend was detected in the SPI-12 series of all the observed stations, it can be determined that the western regions of Aksu River Basin have become much drier than the other parts during the period 1960–2010. This had significant impact on agriculture and water supply.


## 3.1. Summary of Statistical Parameters

Statistical parameters of monthly precipitation time series at 9 synoptic stations during the period 1960–2010 are summarized in Table3. The minimal monthly precipitation is 0 mm for all stations. The mean monthly precipitation is ranged from 4.076 mm to 20.554 mm. Moreover, it is obvious that 3 mountainous synoptic stations in the northwest (Aheqi, Turgat, and Wuqia) had the highest mean monthly precipitation.Table 3
Statistical parameters of monthly precipitation time series at 9 synoptic stations during the period 1960–2010.
Station name
Min (mm)
Max (mm)
Mean (mm)
Standard deviation (mm)
CV (%)
Skewness
Kurtosis
Aksu
0
92.2
6.162
10.148
164.672
3.343
16.699
Aheqi
0
145.2
17.920
23.597
131.676
1.983
4.520
Alar
0
50.9
4.076
7.546
185.139
2.737
8.473
Baicheng
0
76.8
9.920
12.367
124.664
2.115
5.874
Keping
0
81.2
8.029
13.348
166.253
2.553
7.537
Kuche
0
65.3
5.818
8.832
151.812
2.499
7.620
Turgat
0
122.1
20.554
21.380
104.015
1.615
2.682
Wuqia
0
121.6
15.009
18.471
123.071
1.878
4.080
Kashi
0
78.5
5.615
9.561
170.283
3.099
12.861
Note: cv-coefficient of variation.The highest kurtosis of the precipitation values was observed at Aksu station with 16.699, while the lowest kurtosis of 2.682 was found at Turgat. This phenomenon indicated that the monthly precipitation in Turgat is relatively homogeneous. But it is converse in Aksu.Time series of annual precipitation at the 9 synoptic stations are shown in Figure2. The results indicated that the annual precipitation had a certain degree of variance during the observed period. In Aksu, Alar, Kuche, and Kashi, the annual precipitation is relatively low and basic by about 50 mm. However, the annual precipitation in Aheqi, Wuqia, and Turgat, is above 200 mm. In addition, the annual precipitation in Baicheng, Kuche, and Keping has obvious upward trend during the observed period. These results show that the precipitation in upstream of Aksu basin is larger than that in downstream.Figure 2
Annual precipitation time series at the 9 synoptic stations.


## 3.2. Aridity Index

The estimated UNEP Aridity Index for the 9 synoptic stations is given in Table4. The FAO-56 Penman–Monteith equation as a part of the model based on service-oriented paradigm [76, 77] is used for estimating PET. The results indicated that the Aridity Index ranged from 0.048 at the Alar station to 0.397 at the Turgat station. The Alar station is extremely arid and the Aheqi station and the Turgat station are semiarid, while all other stations are arid. The upper limit for extremely arid climate is 0.05, but Alar had a slightly lower value. The Alar station is extremely arid because of the highest PET, minimum of the annual precipitation, and the highest value of the temperature difference.Table 4
Aridity Index, annual precipitation, and reference evapotranspiration estimated using FAO-56 Penman–Monteith equation.
Station name
Precipitation (mm/year)
PET (mm/year)
Aridity index
Climate
Aksu
73.947
972.22
0.076
Arid
Aheqi
215.045
985.51
0.218
Semiarid
Alar
48.910
1023.91
0.048
Extreme arid
Baicheng
119.041
832.52
0.143
Arid
Keping
96.343
1102.73
0.087
Arid
Kuche
69.812
1164.73
0.060
Arid
Turgat
246.653
621.34
0.397
Semiarid
Wuqia
180.106
1082.91
0.166
Arid
Kashi
67.380
1125.91
0.060
Arid


## 3.3. Rainfall Variability

Annual rainfall variability indices for the observed synoptic stations are shown in Figure3, while the percentage distribution of dry, normal, and wet years during the period 1960–2010 is given in Figure 4. It is obvious that there was no extremely dry year for all stations. Although, considering both time series of precipitation and annual rainfall variability indices for the 9 synoptic stations, there were two main periods which were characterized by long and severe droughts, namely, 1978-1979 and 1983–1986.Figure 3
Annual rainfall variability indices for the 9 synoptic stations.Figure 4
Distribution in percentage of dry, normal, and wet years for the 9 synoptic stations during the period 1960–2010.During the first period, the drought years were approximately 55% of the total years. The second period is characterized by approximately 47% of the drought years. In addition, it should be noticed that there were 4 dry years, 1961, 1975, 1985, and 2007. These four years were characterized by approximately 89% negative values of the annual rainfall variability index.


## 3.4. Analysis of Precipitation

The serial correlation coefficient can improve the verification of the independence of precipitation time series. If the time series are completely random, the autocorrelation function will be zero for all lags other than zero. In this study, to accept the hypothesisH0: r1=0 (that there is no correlation between two consecutive observations and there is no persistence in the time series), the value of r1 should fall between −0.2544 and 0.2544.Autocorrelation plot for the annual precipitation at the 9 synoptic stations is presented in Figure5. As shown, the precipitation had both positive and negative serial correlations. The highest and at the same time the significant serial correlation of 0.260 was obtained at the Baicheng station, while the lowest serial correlation of −0.104 was detected at the Wuqia station.Figure 5
Lag-1 serial correlation coefficient for the precipitation at the synoptic stations.Lag-1 serial correlation coefficients for seasonal precipitation data at the observed stations during the period 1960–2010 are presented in Table5. As shown, a positive serial correlation was found in the spring, summer, autumn, and winter series at 77.8%, 88.9%, 66.7%, and 77.8% of the stations, respectively. The significant serial correlation was detected in the autumn at Aheqi station. Trends of precipitation are considered statistically at the 5% significance level using the Mann–Kendall test and the Spearman’s Rho test. When a significant trend is identified by two statistical methods, the trend is presented in bold character in Table 6.Table 5
Lag-1 serial correlation coefficients for seasonal precipitation data.
Station name
Spring
Summer
Autumn
Winter
Aksu
0.102
0.105
−0.042
0.181
Aheqi
0.199
0.009
0.395
0.102
Alar
−0.006
0.147
−0.108
−0.078
Baicheng
0.192
0.160
0.140
0.187
Keping
0.059
0.167
0.014
0.113
Kuche
0.106
0.035
−0.077
0.077
Turgat
0.028
0.019
0.090
0.163
Wuqia
−0.020
0.100
0.131
−0.068
Kashi
0.054
−0.050
0.090
0.019Table 6
Results of the statistical tests for the monthly precipitation during the period 1960–2010.
Station
Test
Month
January
February
March
April
May
June
July
August
September
October
November
December
Aksu
Z
S
0.233
0.760
0.411
−0.579
0.276
1.755
0.796
−0.926
1.365
0.976
0.000
1.588
Z
D
0.410
0.884
0.586
−0.279
0.232
2.014
0.793
−0.890
1.318
1.203
0.789
2.060
b
0.023
0.060
0.058
0.016
0.011
0.184
0.036
−0.075
0.138
0.122
−0.008
0.038
Aheqi
Z
S
0.139
0.383
0.789
0.545
0.016
−0.244
1.576
0.390
1.673
2.795
*
0.798
1.088
Z
D
0.159
0.319
0.816
0.615
0.026
−0.146
1.766
0.524
1.729
3.249
*
1.020
1.250
b
0.014
0.019
0.129
0.019
0.058
−0.054
0.513
0.236
0.877
0.227
−0.001
0.024
Alar
Z
S
1.454
1.175
−0.102
−0.171
0.073
1.276
1.186
−0.016
−0.552
0.026
0.603
1.523
Z
D
1.964
2.166
*
0.658
0.494
−0.025
1.439
1.309
0.021
−0.399
0.521
2.088
*
2.747
*
b
0.025
0.028
0.023
−0.014
−0.050
0.078
0.106
0.069
−0.067
0.013
−0.003
0.027
Baicheng
Z
S
1.206
1.007
0.253
0.262
1.089
2.193
*
1.901
1.324
2.161
*
1.322
0.886
1.605
Z
D
1.394
0.786
0.247
0.339
1.155
2.477
*
1.926
1.175
2.207
*
1.339
1.313
1.783
b
0.042
0.083
0.037
−0.025
0.077
0.268
0.234
0.122
0.228
0.231
0.089
0.042
Keping
Z
S
0.311
1.171
1.308
−0.198
−0.073
0.918
1.706
1.405
2.278
*
1.363
−0.249
0.937
Z
D
0.525
1.064
1.665
−0.185
−0.026
0.999
1.849
1.485
2.447
*
1.726
1.112
1.482
b
0.045
0.037
0.102
0.009
−0.014
0.112
0.273
0.367
0.284
0.079
−0.012
0.031
Kuche
Z
S
2.633
*
0.919
−0.694
0.679
0.699
2.437
*
0.999
1.357
0.553
0.513
1.896
2.533
*
Z
D
2.893
*
1.024
−0.541
0.773
0.808
2.747
*
1.057
1.279
0.476
0.651
2.626
*
3.113
*
b
0.048
0.052
−0.036
0.023
0.106
0.207
0.061
0.063
0.019
0.013
−0.010
0.039
Turgat
Z
S
0.033
−0.455
0.723
0.227
−0.382
1.527
0.796
0.398
−0.106
2.713
*
0.122
2.211
*
Z
D
−0.046
−0.428
0.619
0.254
−0.387
1.498
0.794
0.392
−0.066
2.810
*
0.190
2.307
*
b
−0.003
−0.018
0.019
0.091
−0.058
0.285
0.164
0.130
0.023
0.253
−0.006
0.093
Wuqia
Z
S
0.708
−1.122
−0.228
−0.041
0.195
1.600
1.787
−0.024
0.699
2.847
*
−0.016
1.027
Z
D
0.699
−1.394
−0.375
−0.097
0.007
1.822
2.194
*
−0.008
0.677
2.983
*
−0.151
1.176
b
0.032
−0.039
−0.048
0.011
−0.092
0.465
0.407
−0.076
0.141
0.239
−0.015
0.029
Kashi
Z
S
0.507
−0.638
1.455
−0.156
0.602
0.999
1.406
0.268
1.223
3.249
*
0.365
1.035
Z
D
0.685
−0.387
1.758
−0.164
0.401
1.146
1.327
0.199
1.294
3.908
*
1.071
1.430
b
0.048
−0.015
0.106
−0.058
−0.115
0.096
0.111
−0.025
0.104
0.170
0.024
0.020
Z
S
: Mann–Kendall test, ZD: Spearman’s Rho test, and b: slope of linear regression.
Bold characters represent trends identified by 2 statistical methods together.
*Statistically significant trends at the 5% significance level.The results of the statistical tests for the monthly precipitation series during the period 1960–2010 are summarized in Table6. As shown, the precipitation in Baicheng station had the significant increasing trend in June and September. The significant increasing trend was also detected at the Kuche station in January, June, and December. There was no decreasing trend. Besides, A statistically significant trend ZS = 2.380 was detected in September at the Aheqi station before eliminating the effect of serial correlation. After removing lag-1 serial correlation effect, an insignificant trend of ZS = 1.673 was obtained. Furthermore, an insignificant trend ZD = 1.633 was detected in January at the Kuche station before eliminating the effect of serial correlation. After removing lag-1 serial correlation effect a significant trend of ZS = 2.893 was obtained.Seasonal and annual trends of precipitation obtained by statistical methods are given in Table7. According to these results, the increasing trends in annual precipitation series were detected at Aheqi, Baicheng, Keping, and Kuche, while there is no significant trend for other stations which is consistent with our analysis in Section 3.1. On annual level, precipitation quantities are increasing, with the highest increase in winter.Table 7
Results of the statistical tests for seasonal and annual precipitation during the period 1960–2010.
Station
Test
Season
Spring
Summer
Autumn
Winter
Annual
Aksu
Z
S
0.341
0.780
1.673
1.154
1.495
Z
D
0.295
0.952
1.696
1.264
1.690
b
0.084
0.145
0.253
0.125
0.603
Aheqi
Z
S
0.309
1.056
2.209
*
0.739
2.819
*
Z
D
0.434
1.106
2.338
*
0.529
3.026
*
b
0.206
0.695
1.103
0.055
2.062
Alar
Z
S
−0.520
1.592
−0.390
1.947
1.129
Z
D
−0.567
1.793
−0.325
2.152*
1.159
b
−0.041
0.253
−0.057
0.083
0.235
Baicheng
Z
S
0.390
2.713
*
2.266
*
2.112
*
2.193
*
Z
D
0.392
3.029
*
2.444
*
2.214
*
2.620
*
b
0.089
0.624
0.548
0.166
1.427
Keping
Z
S
0.244
2.372
*
2.429
*
1.357
2.875
*
Z
D
0.404
2.567
*
2.552
*
1.483
3.300
*
b
0.097
0.752
0.351
0.113
1.313
Kuche
Z
S
0.430
1.852
0.423
2.145
*
2.494
*
Z
D
0.416
2.050*
0.263
2.274
*
2.743
*
b
0.093
0.331
0.023
0.141
0.585
Turgat
Z
S
0.195
1.503
1.194
1.803
1.527
Z
D
0.283
1.379
1.225
1.874
1.667
b
0.052
0.579
0.270
0.099
0.973
Wuqia
Z
S
−0.260
1.462
1.698
0.065
1.251
Z
D
−0.342
1.599
1.579
0.062
1.281
b
−0.129
0.796
0.365
0.014
1.054
Kashi
Z
S
−0.195
1.121
2.527
*
0.390
1.129
Z
D
−0.223
1.150
2.547
*
0.499
1.055
b
−0.067
0.182
0.297
0.041
0.466
Z
S: Mann–Kendall test, ZD: Spearman’s Rho test, and b: slope of linear regression.
Bold characters represent trends identified by 2 statistical methods together.
*Statistically significant trends at the 5% significance level.For the seasonal scale, there were increasing trends in summer and winter precipitation series. The decreasing precipitation trend was found in the spring and autumn series at 33% and 11% of the stations, respectively. Besides, the significant increasing trends were found at Aheqi and Kashi in autumn and at Alar and Kuche in winter. Furthermore, the significant increasing trends were detected at Baicheng in summer, autumn, and winter. The precipitation of Keping also had increasing trends in summer and autumn.


## 3.5. Analysis of SPI-12

Time series of SPI-12 at the 9 synoptic stations during the period 1960–2010 are shown in Figure7. Characteristics of drought at 12-month time scale are shown in Table 8. It should be observed that the most severe drought of Aheqi and Alar was 1975, while that of Keping and Wuqia occurred in 1985. Besides, the most severe drought year was 1976 at Bacheng station and 1986 at Aksu station. The Wuqia station had the lowest SPI-12 with −2.5986 in 1985. The number of drought years during the observed period at the stations is presented in Table 8. According to the results, the total drought years ranged between 14 (at Wuqia and Kashi station) and 19 (at Alar station). Almost 32.2% of the observed years were drought years at all the 9 stations.Table 8
Characteristics of droughts at 12-month time scale.
Station
The most severe drought
Number of drought years during the observed period
SPI
Year
Near normal
Moderate
Severe/extreme
Total
Aksu
−2.2748
1986
7
7
3
17
Aheqi
−2.1138
1975
10
6
2
18
Alar
−2.2262
1975
11
6
2
19
Keping
−2.5112
1985
8
5
3
16
Baicheng
−1.9470
1961
5
6
4
15
Kuche
−1.8056
1965
8
6
4
18
Turgat
−2.1432
1976
7
5
5
17
Wuqia
−2.5986
1985
3
8
3
14
Kashi
−1.9757
1994
6
3
5
14Lag-1 serial correlation coefficient for the SPI-12 at the observed synoptic stations is illustrated in Figure8. The highest and at the same time the significant positive serial correlation coefficient of 0.2676 was detected at the Aksu station. On the other hand, negative values were observed at the Turgat, Wuqia, and Kashi stations.The results of the Mann–Kendall and Spearman’s Rho tests for the SPI-12 series are presented in Figure9. It can be noted that all stations have the increasing trend. The significant trends were detected at Aheqi, Baicheng, Keping, and Kuche stations.Although a significantly increasing trend was detected in the SPI-12 series of all the observed stations, it can be determined that the western regions of Aksu River Basin have become much drier than the other parts during the period 1960–2010. This had significant impact on agriculture and water supply.


## 4. Conclusions

Based on the analysis of the variation of precipitation and drought indices and correlation in the multisites in this study area during 1960–2010, the following conclusions can be drawn from this study.Precipitation trends and drought behavior at monthly, seasonal, and annual time scale in Aksu River Basin between 1960 and 2010 were investigated, respectively. In order to achieve this, monthly, seasonal, and annual precipitation data from 9 Serbian synoptic stations were analyzed using the Mann–Kendall test and the Spearman’s Rho test after eliminating the effect of significant lag-1 serial correlation from the time series. Besides, aridity and annual rainfall variability indices were estimated.According to these results, two main annual drought periods were detected (1978-1979 and 1983–1986), while the dry year was 1975 and 1985 at almost all of the stations. The monthly analysis of precipitation series suggests that all stations had increasing trend in July, October, and December, while both increasing and decreasing trends were found in other months. At the seasonal scale, there were increasing trends in summer and winter precipitation series. The decreasing precipitation trend was found in the spring and autumn series at 33% and 11% of the stations, respectively.For the SPI-12, all stations have the increasing trend. The significant trends were detected at Aheqi, Baicheng, Keping, and Kuche stations (As shown in Figure6). Based on the analysis of trends of precipitation and drought behavior, precipitation in Aksu River Basin had an increasing trend. And drought condition, including drought severity and drought duration, became better. The analyzed results of precipitation and SPI-12 series can be helpful for basin-scale water resources management, agricultural production. Further research in analyzing the spatial variation of precipitation trends and the relationship with the climate change projection is recommended. Moreover, the future work will be oriented into developing an information system for monitoring and early drought warning.Figure 6
Variations of monthly precipitation in stations with the significant trends during the study period.Figure 7
Time series of SPI-12 at the 9 synoptic stations.Figure 8
Lag-1 serial correlation coefficient for the SPI-12 at the 9 synoptic stations.Figure 9
Mann–Kendall test (ZS) and Spearman’s Rho test (ZD) for the SPI-12 series.



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*Source: 215840-2015-09-20.xml*