2.1. Overview of the study area

Xinjiang is surrounded by high mountains that prevent the arrival of moist air currents, resulting in a temperate continental climate. The land area is 1.66 million km², accounting for 1/6 of China’s land area (^{Fan et al. 2018}). The average temperature in Xinjiang is 8.1 ºC and the annual precipitation is about 150mm. However, the spatial distribution of precipitation is very uneven, with large evaporation and potential evapotranspiration (PET) of about 3000mm (^{Zhang et al. 2019}). Xinjiang has diverse landforms, including the Altai Mountains in the north, the Kunlun Mountains and A-erh-chin Mountains in the south, and the Tianshan 3 Mountains across the central part of Xinjiang. The three major mountain ranges surround the Junggar Basin and the Tarim Basin (Fig. 1).

Fig. 1 Distribution of meteorological stations in Xinjiang. 

2.2. Data sources

The monthly mean temperature and precipitation data of 55 representative stations in Xinjiang from 1961 to 2015, as well as the geographic information data such as longitude, latitude, and altitude of each station, were analyzed. Their location is also shown in Figure 1. These data are provided by the Xinjiang Meteorological Information Center, and after strict data quality control, they can be used in climate change analyses. The SPEI index in each station was estimated for the past 55 years, to study the characteristics of dryness and wetness changes.

3.1. Calculation method of SPEI index

The standardized precipitation evapotranspiration index SPEI takes monthly average temperature and monthly precipitation as input data, calculates the difference between monthly precipitation and potential evapotranspiration and fits the corresponding probability distribution function, and finally obtains it through normal standardization (^{Zhang et al. 2018}). There are three methods for calculating potential evapotranspiration: Thornthwaite, Hargreavea, and Penman-Monteith. The Thornthwaite method was relatively simple and only needs temperature data to obtain potential evapotranspiration, while the Penman-Monteith method requires more meteorological parameters resulting in a more accurate estimate. ^{Mavromatis (2007)} show that similar results are found using simple or complex methods to calculate the potential evapotranspiration in drought indicators. ^{Vicente-Serrano et al. (2010)} also show that the choice of potential evapotranspiration method has little influence on the calculation results of SPEI. Since an appropriate calculation method can be chosen according to the availability of meteorological data (^{Xuan et al. 2016}), the Thornthwaite method is used here to calculate the monthly potential evapotranspiration of meteorological stations in Xinjiang over the recent 55 years. The calculation process is detailed in Zhang et al. (2018) and then the SPEI index at each station is calculated. The SPEI index’s dryness and wetness rating criteria (Table I) is used to determine the extent to which a site experienced a change in drought conditions in each month.

3.2. Empirical orthogonal function analysis method

Empirical orthogonal functions (EOF) are a common method used in climatology to analyze the spatiotemporal variation characteristics of research areas (^{Guo et al. 2018}). The basic principle is to transform the meteorological data matrix formed by n observations in m space points by principal component analysis, decompose it into a linear combination of space eigenvector matrix and corresponding time coefficient matrix, and estimate and interpret the original field by using the value of space vector eigenmatrix and corresponding time coefficient function. The n observations in the SPEI series for the m space points are used here as input for the EOF analysis. The EOF decomposition method can accurately express the temporal variation and spatial mode of drought and is an important means to decompose the drought characteristics. Therefore, the drought analyzed by this method has strong regularity and consistency (^{Wang et al. 2016}).

3.3. Cross Wavelet Transform

Cross wavelet is a signal analysis method which combines wavelet transformation and cross-spectrum analysis. This method provides the energy resonance and covariance distribution of two time series in the time-frequency space. It is used to study the relationship between two time series in the time-frequency domain from multiple time scales (^{Ge et al. 2020}). The annual average values of SPEI and AMO, ENSO, NAO and PDO, are used here as input to the cross wavelet transform. This method can reveal the correlation and consistency of the two sequences at different time scales and reproduce the phase relationship in time-frequency space. The cross wavelet transform can reveal the high energy region and phase relationship of the two series, but when there is a strong peak in the energy spectrum, the Cross Wavelet may produce misleading results. Therefore, it is necessary to standardize the wavelet energy in the cross wavelet transform to obtain the wavelet coherence spectrum, which can measure the correlation between the two variables (^{Wang et al. 2019}; ^{Qi et al. 2018}).

4.1. Changes in precipitation and temperature in Xinjiang

Figure 2 shows that precipitation in Xinjiang has an obvious increasing trend in the recent 55 years, with a change rate of 8.90 mm per decade (P<0.01). Note the variability over the period 1961-1985 and the sudden change in precipitation that occurred in 1986, significant at the 95 % reliability test. From 1986 to 2015, the precipitation increased by 3.35 mm per decade (which failed the significance test) and the average precipitation increased by 31.07 mm. Overall, the average annual temperature in Xinjiang showed a first a decreasing trend and then increased significantly, with a change rate of 0.39 ºC per decade (P<0.01). An obvious abrupt change in temperature occurred in 1994, which passed the 95 % reliability test, over the period 1961-2015. The temperature increased by 0.68 ºC per decade (P<0.05) from 1994 to 2015, and the average temperature increased by 1.21 ºC.

Fig. 2 Mann-Kendall tests for mean annual precipitation and mean annual temperature in Xinjiang. 

4.2. Characteristics of climate change in Xinjiang

Figure 3 shows annual averaged of SPEI-3 and SPEI-6 at 55 meteorological stations in Xinjiang from 1961 to 2015; note that changes in trends are similar for annual averages of SPEI-3 and SPEI-6. The rate of change of SPEI-3 and SPEI-6 was 0.005 and 0.007 per decade, respectively. From 1961 to 1987, the SPEI index was alternately positive and negative, while from 1987 to 1996, the SPEI index was mainly positive, and Xinjiang was in a period of drought relief. After 1997, the SPEI index alternated between positive and negative, but from 2005 to 2015, the negative value of SPEI increased. The SPEI values of SPEI-3 in April 1997, October 2006, and July 2008 were relatively small, being -1.99, -1.69, and -1.79 respectively; SPEI-6 was SPEI in January 2007 and June 2008 the values are relatively small, respectively -1.70 and -1.69, indicating that severe drought in those years.

Fig. 3 The annual average SPEI-3 and SPEI-6 time series of 55 stations in Xinjiang from 1961 to 2015. 

4.3. Dryness and wetness distribution characteristics of different climate grades in Xinjiang

The SPEI-3 and SPEI-6 values at each station in Xinjiang from 1961 to 2015 were divided into degrees of dryness and wetness. The number of stations with different levels of dryness and wetness observed each year was counted, to indicate the inter-annual variability of the different levels. Figure 4 shows that the overall variation pattern of SPEI-3 and SPEI-6 was similar. SPEI-6 has more wet years than SPEI-3, and SPEI-3 has more normal wet years than SPEI-6. The wettest years were 1987 and 1988, 1992, and 1993. Particularly in 1993 SPEI-6, the number of moderately humid stations reached 63.64 % of all stations; in 1987 SPEI-3, the number of moderately humid meteorological stations reached 36.36 % of all stations. The number of stations experiencing drought was relatively large in 1997 and 2008. In 1997, the number of meteorological stations with moderate drought and extreme drought reached 45.45 % of all stations, while in 2008 the number of moderate and extreme drought stations reaching 60.00 % of all stations in SPEI-3.

Fig. 4 Number of sites with different levels of wet and dry events in Xinjiang SPEI-3 and SPEI-6 from 1961 to 2015. 

4.4. Temporal and spatial patterns of dry and wet changes in Xinjiang

In order to further study the spatial and temporal distribution climate characteristics in Xinjiang, empirical orthogonal function analysis was carried out on SPEI values of three-month time scale (EOF_3) and six-month scale (EOF_6). Table II shows that the cumulative contribution to the variance of the first three eigenvectors reaches 66.04 % and 60.77 % in three-month time scale and six-month time scale, respectively, which relate to the main spatial-temporal distribution of dryness and wetness changes in Xinjiang.

Figure 5 shows that the contribution to the variance of the first eigenvectors of EOF_3 and EOF_6 were 37.32 % and 34.59 %, respectively. The eigenvector values of the first mode were all positive, indicating that the distribution of climate changes in Xinjiang were consistent throughout the region, e.g. the whole region was either wetter or drier. The high-value centers of the first modes of EOF_3 and EOF_6 are located in Turpan, Hami Basin, and the southwestern part of the Jungar Basin. The range of the first mode of EOF_6 is larger than that of the first mode of EOF_3. In the first mode, the low value of the range EOF_3 is greater than in EOF_6. The time coefficient of the first mode corresponds to the time-varying trend. From 1961 to 1986, the time coefficient showed an upward trend, which indicated that Xinjiang had experience increasing humidity. From 1987 to 1996, it fluctuated with positive values, indicating that Xinjiang was in a relatively humid period, reaching peak values in 1987 and 1993. However, there was an obvious downward trend after 1996, indicating that the consistency of changes in dryness and wetness in Xinjiang was weakening, and there was an obvious drying trend. In terms of spatial distribution, the change characteristics in northern Xinjiang were more obvious than in southern Xinjiang.

Fig. 5 Spatial distribution of the first mode of the (a) three-month time scale and (b) the six-month time scale in Xinjiang. 

The contribution to the variance of the second eigenvectors of EOF_3 and EOF_6 were 18.59 % and 16.75 %, respectively. The spatial distribution of the second mode was obviously different from the first mode (Fig. 6). Considering the Tianshan Mountains as the boundary, it shows a North-South opposite pattern of Xinjiang, with a wet northern part and a dry southern part. The spatial distribution of the second mode from SPEI-3 and SPEI-6 was similar but with differences in the local range, the lowest value range was -0.18, and the highest difference was 0.23. The time coefficient of the second mode, indicates that from 1961 to 1997, Xinjiang experienced a relatively humid period. Considering 1997 as the turning point, the regional drying trend becomes more obvious, especially in northern Xinjiang, with drought years in 2007, 2009, and 2011. The linear trend indicates that the aridity in northern Xinjiang was intensified, while it weakened in southern Xinjiang.

Fig. 6 Spatial distribution of the second mode of the (a) three-month time scale and (b) the six-month time scale in Xinjiang. 

Figure 7 shows that the contribution to the variance of the third eigenvectors of EOF_3 and EOF_6 were 10.13 % and 9.43 % respectively, showing the opposite pattern in eastern and western Xinjiang, but with a complex distribution. Moist centers were mainly located in the western part of southern Xinjiang, the Yili River Valley, and the Middle Tianshan region, while eastern Tianshan experienced a drying trend. In the wettest year of the western region, the eastern region was relatively dry. The time coefficient corresponding to the third mode indicates that 2012 is a typical wet year in the west and dry in the east; in contrast, 1970, 1973, and 1979 were dry years in the west and wet years in the east. The growth rate of the linear change indicates that the dry-wet spatial distribution of this mode increased, with moisture increasing in the western part of southern Xinjiang, also confirmed for example, by stable or expanding glaciers in the Karakorum mountain area in the recent ten years (^{Asad et al. 2017}).

Fig. 7 Spatial distribution of the third mode of the (a) three-month time scale and (b) the six-month time scale in Xinjiang. 

4.5. Relationships between SPEI and atmospheric circulation indexes

Wavelet coherence transform (WTC) and Cross Wavelet Transform (XWT) were used to analyze the multi-time scale correlation between annual SPEI and AMO, ENSO, NAO, and PDO. Coherent wavelet transforms mainly reveal the relationship between annual SPEI value and low energy of climatic factors in the time-frequency domain, while the cross wavelet transform highlights the relationship between the change in SPEI and the high energy region of atmospheric circulation index in the time-frequency domain.

Figure 8 shows that in the power spectrum of wavelet coherence transform and cross wavelet transform, the range surrounded by thick black line has passed the test of a standard spectrum of red noise at the significance level of α = 0.05; power spectrum outside the thin black line was not considered due to the influence of boundary effects. The arrow indicates the relative phase difference: arrow from left to right indicates change in the same phase, from right to left indicates the reverse phase change; arrow upward indicates that the change phase of SPEI was 90º earlier than that of AMO, ENSO, NAO, and PDO; arrow downward indicates that the change phase of SPEI was 90º behind that of AMO, ENSO, NAO, and PDO. The cross wavelet transform (XWT) indicates there was a resonance period of 0-3 years between SPEI and AMO and coherent wavelet power spectrum from 1994 to 1999. Moreover, the two directions were downward, which indicates that the phase lag between the two was 90º. There are regions of high-energy of SPEI and ENSO in the coherent wavelet power spectrum in 1963-1965, 1971-1975 and 1983-1992 for period of 1-2 years, 3-4 years, and 4-6 years, respectively. There were 1-3 years resonance period between SPEI and high-energy region of NAO in the coherent wavelet power spectrum from 1963 to 1968, and their direction was upward, which indicates that the change phase between the two was ahead 90º. In 1975-1976, 1989-1992 and 1996-2003, the high energy region of the wavelet power spectrum of SPEI and PDO coherence had resonance periods of 3-4 years, 5-6 years, 1-2 years, and 9-10 years, respectively.

Fig. 8 Coherent wavelet power spectrum (WTC, right column) and cross wavelet power spectrum (XWT, left column) of SPEI and AMO, ENSO, NAO, and PDO in Xinjiang. 

From the perspective of wavelet coherence transform (WTC), there were resonance periods of 0-3 years, 2-4 years, and 7-8 years respectively between SPEI and AMO coherent wavelet power spectrum from 1992 to 2011, and downward in the direction of 2-4 years, indicating that the change phase of SPEI and ENSO coherent wavelet power spectrum was backward by 90º. The low-energy region of SPEI and ENSO coherent wavelet power spectrum has a resonance period of 2-4 years and 4-6 years in 1987-2000. From 1964 to 1968 and 1978 to 1990, there were resonance periods of 0-2 years and 6-7 years between SPEI and NAO in the low-energy region of the coherent wavelet power spectrum, and their direction was upward, with a 90º change phase. SPEI and PDO coherent wavelet power spectrum low-energy region in 1964-1966, 1985-1991, and 1994-2011 have resonance periods of 0-2 years, 6-7 years, and 10-11 years, respectively.