1 Introduction

Climate extremes, such as heavy precipitation and droughts, are among the most influential natural disasters in the world, and extreme precipitation events have significantly increased under global warming (IPCC 2021). Since the late 1970s, extreme precipitation events have occurred frequently in China (Zhai et al. 2005). Xinjiang, located in northwestern China, has significantly less precipitation than eastern China due to factors such as uneven geographical distribution and complex climate systems (Yang et al. 2009, 2011). The precipitation in Xinjiang is mainly concentrated in summer, and the spatial distribution shows that the precipitation in northern Xinjiang is more than that in southern Xinjiang (Jiang et al. 2013; Xie et al. 2018; Hu et al. 2021).

It is notable that the global temperature continues to rise; precipitation and extreme precipitation events at the regional scale changed significantly (Ailiyaer et al. 2021). Since the 1960s, the intensity and frequency of extreme precipitation events such as rainstorms and floods have significantly increased while drought events decreased. There are spatial and temporal differences in the trend of extreme precipitation over Xinjiang (Zhang et al. 2019; Chen and Ma 2021). Jiang et al. (2013) and Wang et al. (2021) found that precipitation extremes and the annual precipitation of most stations in Xinjiang showed a significant increasing trend, but the increase of some stations was limited. Wang and Yang (2014) studied extreme precipitation in the surrounding area of the Taklimakan Desert. The results show that the consecutive dry day (CDD) index showed a decreasing trend from 1961 to 2009, while the number of days with daily precipitation less than 25% quantile showed an increasing trend. Guan et al. (2022) investigated the historical and future changes in extreme climate indices over Xinjiang based on climate models. They suggested that the consecutive wet days (CWDs) lengthened and CDDs shortened during the historical period. Besides, the impact of global warming on extreme climate indices was approximately linear.

In terms of the mechanism of extreme precipitation, Zhou et al. (2021b) analyzed the changes and circulation characteristics of extreme precipitation in northern Xinjiang based on summer precipitation and NCEP/NCAR reanalysis data during 1961–2017. The results show that the frequency of extreme precipitation of different grades increases in summer, and the abnormal water vapor transport in northern Xinjiang provides favorable conditions for the occurrence of extreme precipitation events. They also found that the mechanisms of summer extreme precipitation in Xinjiang are characterized by a zonal wave pattern with the deepening of the western Siberian trough, central Asian high, and Mongolian high. In addition, Yao et al. (2022) reviewed the changes and mechanisms of precipitation and extreme precipitation in Xinjiang in recent years. They pointed out that although it is traditionally believed that the water vapor transported from the Indian Ocean is difficult to reach inland Xinjiang due to the blocking effect of the Qinghai Tibet Plateau, some studies have found that the extreme precipitation in the Tarim Basin is closely related to the accelerated water vapor transport in the Indian Ocean and the Arabian Sea. Furtherly, summer extreme precipitation is linked to the SSTs from the Indian Ocean, the Kuroshio, the central-eastern Pacific, and part of the Atlantic Ocean (Wang and Yang 2017; Ning et al. 2021). Zhou et al. (2021a) also found that the summer extreme precipitation in North Xinjiang was positively correlated with the spring sea surface temperatures (SST) over the tropical Indian Ocean and the equatorial eastern Pacific, and when the SST showed a warm anomaly, the extreme precipitation in North Xinjiang was more.

In addition, extreme precipitation events have the characteristics of low frequency with large intensity, leading to serious social and economic losses. Extreme value theory can describe the distribution characteristics of extreme precipitation in summer, and it has been widely used in the research and analysis of extreme climate problems. For example, Li et al. (2005) used the generalized Pareto distribution (GPD) to establish a statistical model of extreme precipitation in Western Australia and tested the changes in annual and seasonal maximum daily precipitation. Villafuerte and Matsumoto (2015a) studied the response of global warming and ENSO to extreme precipitation in Southeast Asia by using a non-stationary generalized extreme value (GEV) model. Domestic scholars have also carried out a number of studies on regional extreme climate events in China using extremum theoretical models. Li et al. (2018) used a non-stationary GEV model to detect the impact of human activities on extreme precipitation at a regional scale in China. The study points out that the effects of human activities on precipitation extremes in historical periods are not detected by observations or simulations (not significant). Lu et al. (2019) used the non-stationary GEV model to study the influence of urbanization on annual maximum 1-day precipitation (RX1day) and annual maximum 5-day consecutive precipitation (RX5day). They found that the return levels of RX1day and RX5day were increased by 25.9% and 59.1% in highly urbanized stations, 34.2% and 36.9% in low urbanized stations, and 30.7% and 61.5% in rural stations, respectively.

There are many studies on the spatial–temporal variation characteristics of summer extreme precipitation in Xinjiang. However, the probability distribution characteristics of summer extreme precipitation indices and their differences in northern Xinjiang, southern Xinjiang, and eastern Xinjiang remain unclear. In this study, the stationary and non-stationary GEV distributions are used to investigate the probability characteristics of summer extreme precipitation indices in Xinjiang. Based on the best statistical models at observation stations, the climatology and variability of summer extreme precipitation indices are quantified, the intensity and frequency of summer extreme precipitation indices are explored, and the probability distribution characteristics of summer extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang are compared. Section 2 provides the data and the modeling process of the GEV model. Section 3 provides the observed changes in precipitation indices, the statistical modeling results, and probability distribution characteristics of extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. The discussion and conclusion are given in Section 4 and Section 5, respectively.

2 Data and method

2.1 Data

The daily precipitation data used in this study are from 105 national observation stations across Xinjiang during 1960–2021 and are provided by the National Meteorological Information Center, China Meteorological Administration (http://www.nmic.cn/). After eliminating the missing values and temporal inhomogeneity, 96 stations with relatively complete data from 1970 to 2021 are selected for subsequent analysis.

2.2 Definition of precipitation indices

Four precipitation indices of Climate Change Detection and Indices (ETCCDI) (i.e., PRCPTOT, RX1day, RX5day, and CDD) are calculated (http://etccdi.pacificclimate.org/list_27_indices.shtml). The definitions of the four precipitation indices are shown in Table 1.

Table 1 Definitions of the four precipitation indices used in the study
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2.3 Method

Suppose the summer daily precipitation series \({X}_{1}, {X}_{2}, \dots ,{X}_{n}\) is an independent and identically distributed sequence of random variables, and the n-year maximum \({Y}_{n}=max\{{X}_{1}, {X}_{2}, \dots ,{X}_{n}\}\) (i.e., time series of RX1day, RX5day, or CDD) from a distribution \(G\). It has been found that the GEV distribution can describe the characteristics of block maxima (i.e., \({Y}_{n}\)) (Coles 2001; Li et al. 2018; Kurniadi et al. 2021), the cumulative distribution function of the GEV model is given by:

$$G\left(X;\mu ,\sigma ,\xi \right)=\left\{\begin{array}{c}\mathrm{exp}\left\{-{\left(1+\xi \frac{x-\mu }{\sigma }\right)}^{-\frac{1}{\xi }}\right\},1+\frac{\xi (x-\mu )}{\sigma }>0,\xi \ne 0,\\ \mathrm{exp}\left[-\mathrm{exp}\left(-\frac{x-\mu }{\sigma }\right)\right], \xi =0.\end{array}\right.$$
(1)

where the \(\mu\),\(\sigma\), and \(\xi\) are location, scale, and shape parameters, respectively, and \(\mu\),\(\xi \in R\),\(\sigma\)>0.

There are many parameter estimation methods for an extreme model, but for a complex model, maximum likelihood estimation has better adaptability (Coles 2001). Then, the logarithmic likelihood function of GEV distribution is given by:

$$\mathcal{l}\left(\mu ,\sigma ,\xi \right)=\left\{\begin{array}{c}-nlog\sigma -\left(1+\frac{1}{\xi }\right)\sum\limits_{i=1}^{n}\mathrm{log}\left[1+\xi \left(\frac{{x}_{i}-\mu }{\sigma }\right)\right]-\sum\limits_{i=1}^{n}{\left[1+\xi \left(\frac{{x}_{i}-\mu }{\sigma }\right)\right]}^{-\frac{1}{\xi }},\\ 1+\xi \left(\frac{{x}_{i}-\mu }{\sigma }\right)>0, i=\mathrm{1,2},\dots ,n, \xi \ne 0\\ -nlog\sigma -\sum\limits_{i=1}^{n}\left(\frac{{x}_{i}-\mu }{\sigma }\right)-\sum\limits_{i=1}^{n}\mathrm{exp}\left[-\left(\frac{{x}_{i}-\mu }{\sigma }\right)\right], \xi =0.\end{array}\right.$$
(2)

Further, the index of time series (\(t\)= 1,…,52) is introduced as a covariate into the location parameter of the GEV model (i.e., \(G(X;\mu \left(t\right),\sigma ,\xi )\)) to explore the temporal trend of summer extreme precipitation in Xinjiang. For extreme precipitation indices of each station, two parameter assumptions are given in Table 2.

Table 2 Two parameter assumptions
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Then, Akaike’s information criteria (AIC) is used to select the best statistical model for each station, the model with the minimum AIC is selected as the best statistical model (Arpita et al., 2015). For the \({M}_{0}\) or \({M}_{Time}\), the statistical model of AIC is given by

$$AIC\left(p\right)=2nllh\left(p\right)+2p$$
(3)

where \(p\) is the number of parameters (\({p}_{0}=3\) and \({p}_{time}=4\)), and \(nllh\) is minimized negative log-likelihood of \({M}_{0}\) or \({M}_{Time}\).

At the same time, the likelihood ratio test (LRT) is used to test the significance of nonstationary models of summer extreme precipitation indices (Villafuerte et al., 2015b). The test statistics of LRT is given by the deviation function:

$$D=2({\mathcal{l}}_{Time}-{\mathcal{l}}_{0})$$
(4)

where \({\mathcal{l}}_{Time}\) and \({\mathcal{l}}_{0}\) are the maximum logarithmic likelihood estimators of non-stationary model \({M}_{Time}\) and stationary model \({M}_{0}\) respectively. In addition, the Kolmogorov–Smirnov (K-S) test is used to test the fitting effect of the stationary model \({M}_{0}\) on summer extreme precipitation, and Mann–Kendall (MK) test is used to test the trend of total summer precipitation during 1970–2021 (Libiseller and Grimvall 2002; Marco 2009). Based on the fitting results of the GEV model, the return period and return level (RL) of extreme precipitation indices can be calculated as follows:

$$RL\left(1-p\right)=\mu +\frac{\sigma }{\xi }\{{\left[-\mathrm{ln}\left(1-p\right)\right]}^{-\xi }-1\}$$
(5)

where the RL indicates that an extreme precipitation event of this magnitude occurred during the \(1/\mathrm{p}\)-year return period (i.e., extreme precipitation events are more likely to occur again in \(1/\mathrm{p}\)-year return period). In other words, the return period is the frequency of extreme precipitation for a given RL, and RL is the intensity of extreme precipitation for a given return period.

It is noted that, for the stations with the non-stationary model (i.e., the \({M}_{Time}\) is selected as the best statistical model), the return period and return level of extreme precipitation indices given in this study are multi-year averages.

3 Results

3.1 Observed changes in precipitation indices

Figure 1 shows the orographic of the study area and the location of 96 observation stations. As shown in Fig. 1, the terrain of the study area is complex and the distribution of observation stations is not uniform. Among them, the terrain of northern Xinjiang is mainly mountainous, and southern Xinjiang is mainly desert. In addition, southern Xinjiang is drought, with large diurnal temperature differences and complex climatic characteristics. And there were differences in precipitation (or extreme precipitation) and their water vapor sources between northern Xinjiang, southern Xinjiang, and eastern Xinjiang (Yao et al. 2022).

Fig. 1
figure 1

The orographic of study area and the location of 96 observation stations

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To understand the changes in summer total precipitation (PRCPTOT) and its regional characteristics over Xinjiang, the spatial distribution of mean PRCPTOT, the difference in PRCPTOT between 2001–2021 and 1970–2000, and the PRCPTOT trend during 1970–2021 are shown in Fig. 2. To compare the difference of precipitation (or extreme precipitation) in different regions, the Xinjiang region is divided into three sub-regions: northern Xinjiang, southern Xinjiang, and eastern Xinjiang. There are 45, 41, and 10 observation stations in the three sub-regions, respectively. In the past 50 years, the mean PRCPTOT of most stations in Xinjiang was more than 10 mm. In southern Xinjiang, the mean PRCPTOT of most stations was between 20 and 50 mm, and some stations reached 60–70 mm. In northern Xinjiang, the PRCPTOT of most stations exceeded 50 mm, and some stations reached more than 90 mm. In eastern Xinjiang, the mean PRCPTOT of most stations was between 0–40 mm. Compared with 1970–2000, the PRCPTOT of most stations increased from 2001 to 2021, while that of some stations decreased. Meanwhile, it can be seen from Fig. 2c that the PRCPTOT of most stations in Xinjiang showed an increasing trend, while some stations showed a decreasing trend. And the PRCPTOT at most stations in the west of southern Xinjiang showed a statistically significant increasing trend (significant at 0.05 level based on the MK test). Besides, the mean time series of summer PRCPTOT anomaly showed a statistically significant increasing trend during 1970–2021 (significant at 0.05 level based on the MK test), and negative and positive anomalies of the PRCPTOT mainly occurred during 1970s~mid-1990s and after the mid-1990s in Xinjiang, respectively (Fig. 2d).

Fig. 2
figure 2

The spatial distribution of a mean PRCPTOT (unit: mm) during 1970–2021, b PRCPTOT difference between 2001–2021 and 1970–2000 (unit: mm), c trend of PRCPTOT during 1970–2021 and d the mean time series of summer PRCPTOT anomaly (relative to the 1970–2021 mean, unit: mm) during 1970–2021 over Xinjiang. The gray line in figure (a–c) represents the dividing line between northern Xinjiang, southern Xinjiang, and eastern Xinjiang; the hollow circle in figure (c) represents the trend of PRCPTOT is significant at the 0.05 level based on the MK test. The bar diagram and the black solid line in figure (d) indicate the PRCPTOT anomaly and its 11-year running mean

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The spatial distribution of mean extreme precipitation indices and their trends during 1970–2021 are shown in Fig. 3. It can be seen that the mean summer maximum 1-day precipitation (RX1day) over most stations was 10–20 mm, except for the stations in the south of northern Xinjiang (Fig. 3a). The mean summer maximum 5-day precipitation (RX5day) was 0–20 mm at most stations in southern Xinjiang and eastern Xinjiang and more than 20 mm at most stations in northern Xinjiang (Fig. 3b). The mean summer consecutive dry days (CDD) also showed that more than 30 days at most stations in southern Xinjiang and eastern Xinjiang and below than 30 days at most stations in northern Xinjiang (Fig. 3c). And the summer RX1day and RX5day of most stations in Xinjiang showed an increasing trend, while some of the stations showed a decreasing trend. The stations with a significant increase in summer RX1day and RX5day (significant at 0.1 level) were mainly located in the west of southern Xinjiang (Fig. 3a, b).

Fig. 3
figure 3

The spatial distribution of mean a RX1day (unit: mm), b RX5day (unit: mm), c CDD (unit: days), and trend of summer d RX1day, e RX5day, and f CDD during 1970–2021. The hollow dots in (d–f) indicate that the extreme precipitation indices significant at 0.05 level based on the MK test. The black triangles represent the three example stations, respectively

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Meanwhile, the summer CDD of most stations in Xinjiang showed a decreasing trend, while that of some stations showed an increasing trend, and the stations with a significant decrease in summer CDD (significant at 0.1 level) were mainly located in the west of southern Xinjiang (Fig. 3c). The area with the increasing trend of summer RX1day (or RX5day) and decreasing trend of summer CDD basically overlapped. Combined with the variation characteristics of PRCPTOT, RX1day, RX5day, and CDD, in addition to the station in the east of southern Xinjiang, the summer precipitation events in most stations in Xinjiang increased from 1970 to 2021, while the drought events decreased.

3.2 Statistical modeling of extreme precipitation indices

3.2.1 Modeling of example stations

From the above analysis, except for the mean RX1day, there were differences in the mean of other three precipitation indices at stations in southern Xinjiang (and eastern Xinjiang) and northern Xinjiang over the past 50 years. The PRCPTOT, RX1day and RX5day at most stations in Xinjiang showed an increasing trend, the CDD at most stations showed a decreasing trend. Hence, the stationary (i.e., \({M}_{0}\)) and non-stationary (i.e., \({M}_{Time}\)) GEV models described in Sect. 2 were applied to model the probability distribution characteristics of the extreme precipitation indices at 96 observation stations from 1970 to 2021.

To simplify the presentation of the modeling process, Table 3 shows the model selection results from three example stations: X51482, X51827, and X51839 (the black triangles in Fig. 3f). For each extreme precipitation index at each station, only gives the best statistical model with the minimum AIC. X51482 station is located in northern Xinjiang, while X51827 and X51839 stations are located in southern Xinjiang (black triangle in Fig. 3f). Compared with the stations in northern Xinjiang, there were more stations that the extreme precipitation indices showed a significant increasing trend (Fig. 3). Therefore, two example stations are selected in southern Xinjiang. Among them, the RX1day and RX5day of the X51827 station showed a significant increasing trend, while the increasing trend of the extreme precipitation indices at the X51839 station was not significant. As can be seen from Table 3, the best statistical model of the summer extreme precipitation indices of X51482 and X51839 stations was the stationary GEV model (significant at 0.05 level based on the KS test). For the X51827 station, the best statistical model of summer RX1day and RX5day was the non-stationary GEV model (significant at 0.1 level based on LRT test), while the best statistical model of summer CDD was the stationary GEV model (significant at 0.05 level based on KS test). Further, the location parameter \(\mu\) and scale parameter \(\sigma\) of summer RX1day and RX5day (CDD) of the X51482 station were significantly larger than (smaller than) the other two example stations, which means that the climatology and variability of summer RX1day and RX5day (CDD) at the X51482 station were greater than (less than) the other two stations. The shape parameters of summer RX1day and RX5day (CDD) of the X51482 station were lower (higher) than those of X51827 and X51839.

Table 3 Parameter estimates of stationary and non-stationary GEV model of summer extreme precipitation indices at three example stations. For the stations with stationary GEV models, the p-values of the KS test are shown, while the p-values of LRT are shown for the stations with non-stationary GEV models
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Figure 4 shows the probability and quantile plots to evaluate the simulation effect of the GEV model on summer extreme precipitation indices of three example stations. For the extreme precipitations with stationary (non-stationary) GEV models, the (residual) probability and quantile plots are given. As can be seen from Fig. 4a, c, and e, the empirical and model-derived probabilities are basically on the diagonal. For quantile plots, except for a few unusually high values, model-derived and empirical quantiles are basically on the diagonal (the off-diagonal points in Figs. 4b, d, and f). In general, the GEV model can well describe the behavior of the RX1day, RX5day, and CDD series of example stations.

Fig. 4
figure 4

The (a, c, e) probability plot and the (b, d, f) quantile plot of the extreme precipitation indices at three example stations. The probability plot (Fig. a, c, e) shows the empirical and model-derived probabilities, the quantile graph (Fig. b, d, f) shows the model-derived and empirical quantiles, and the solid blue line represents the line 1–1

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3.2.2 Climatology and variability of extreme precipitation indices

The stationary and non-stationary GEV models are to model the time series of summer RX1day, RX5day, and CDD of all stations. Figure 5 shows the spatial distribution of the best statistical models for extreme precipitation indices. It can be seen that the stations with significant increasing/decreasing trends (Fig. 3 d–f) and the stations with nonstationary GEV models (Fig. 5) basically overlapped. And the best statistical model of all stations was significant at 0.05 and 0.1 significance levels based on the K-S test (stationary model) and LRT (non-stationary model), respectively, indicating that the GEV model can well simulate the characteristics of summer extreme precipitation indices in Xinjiang.

Fig. 5
figure 5

Map of 96 observation stations for which GEV models were fitted to the summer a RX1day, b RX5day, and c CDD from 1970 to 2021. Red and green dots represent stations where stationary and nonstationary GEV models were fitted, respectively

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The climatology and variability of extreme precipitation indices can be characterized by the parameters of the GEV model (Kurniadi et al. 2021). Based on the best statistical model of each station, Fig. 6 shows the spatial distribution of climatology (location parameter of GEV model, indicating mean intensity) and inter-annual variability (scale parameter of GEV model) of the three extreme precipitation indices in Xinjiang during 1970–2021. As can be seen from Fig. 6a, the spatial distribution of the climatology of RX1day was basically consistent with the mean PRCPTOT (Fig. 1a). The climatology of RX1day of most stations in northern Xinjiang was more than 10 mm. Among them, some stations in the south of northern Xinjiang reached 15 mm. At most stations in southern Xinjiang and eastern Xinjiang, the climatology of RX1day was 0–10 mm. Meanwhile, the inter-annual variability of RX1day at most stations in Xinjiang was 4–8 mm, and only a few stations were more than 8 mm (Fig. 6b).

Fig. 6
figure 6

(a, c, e) The climatology (location parameter of GEV model) and (b, d, f) inter-annual variability (scale parameter of GEV model) of summer RX1day, RX5day, and CDD

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The climatology of RX5day at most stations in northern Xinjiang were more than 15 mm, and some stations in the south of northern Xinjiang were more than 25 mm. The climatology of RX5day of most stations in southern Xinjiang and eastern Xinjiang were less than 15 mm. The inter-annual variability of RX5day of most stations in Xinjiang was 4–12 mm (Fig. 6c, d). In addition, the climatology of CDD was less than 25 days at most stations in northern Xinjiang and more than 25 days at stations in southern Xinjiang and eastern Xinjiang. The inter-annual variability of CDD was 4–8 days at most stations in northern Xinjiang. and more than 8 days at most stations in southern Xinjiang and eastern Xinjiang (Fig. 6e, f). It can be seen that there was no significant regional difference in the inter-annual variability of RX1day and RX5day, the differences in extreme precipitation indices between northern Xinjiang and southern (or eastern) Xinjiang were mainly reflected in climatology.

Table 4 shows the regional averaged climatology (i.e., mean intensity) and inter-annual variability of three extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. For RX1day and RX5day in southern Xinjiang and eastern Xinjiang, the regional averaged climatology and inter-annual variability were smaller than northern Xinjiang. For CDD, the regional averaged climatology and inter-annual variability over southern Xinjiang and eastern Xinjiang were larger than northern Xinjiang, and the differences of CDD over three sub-regions were opposite to that of RX1day (and RX5day).

Table 4 The regional averaged climatology and inter-annual variability of three extreme precipitation indices in northern Xinjiang, southern Xinjiang and eastern Xinjiang
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3.2.3 Probability distribution of summer extreme precipitation indices

Figure 7 shows the variation curves of the return level of summer RX1day, RX5day, and CDD with the return period at the three example stations. The observed extreme precipitation indices of example stations were within the confidence interval. For the extreme events with a return period of more than 20 years, the summer RX1day and RX5day at the X51482 station were above 40 mm, and the summer CDD was about 30 days (blue curves of Fig. 7a, d and g); and at the X51827 and X51839 stations, the return level of summer RX1day and RX5day was 20–40 mm, and the return level of summer CDD is more than 60 days. At the same time, with the increase in the return period, the confidence interval (uncertainty) of the return level of each extreme precipitation index increases. In other words, the extreme precipitation events corresponding to the longer return period have greater uncertainty.

Fig. 7
figure 7

Changes in the return level of extreme precipitation indices with the return period at three example stations. The solid black line and the dotted red line represent the GEV fitting curve and 95% confidence interval, respectively, while the blue origin and the green point represent historical observations and extreme events in 2021, respectively

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In addition, parts of southern Xinjiang experienced rare extreme precipitation events in the summer of 2021. Figure 7 also shows the return period and return levels of extreme precipitation indices at three example stations in the summer of 2021 (green dots). The summer RX1day and RX5day of X51827 station in 2021 reached 51.83 mm and 68.63 mm, respectively, a once-in-53-year event, while the summer CDD was 40 days (i.e., once-in-2.04-year event). And the summer RX1day and RX5day of the X51839 station were 4.87 mm and 10.68 mm (i.e., once-in-1.33-year and once-in-1.56-year events, respectively), and the CDD reached 74 days (i.e., once-in-17.67-year event). Meanwhile, the summer RX1day, RX5day, and the CDD of X51482 station were 25.45 mm, 45.34 mm, and 34 days, respectively (i.e., once-in-1.83-year, once-in-4.42-year, and once-in-55-year events, respectively).

As shown in Figs. 1-7, although the PRCPTOT, RX1day, and RX5day showed an increasing trend in southern Xinjiang and eastern Xinjiang, the climatology (mean intensity) and inter-annual variability of summer RX1day and RX5day were weaker than those in northern Xinjiang, and the summer CDD were stronger than those in northern Xinjiang. Figure 8 shows the regional averaged probability density curve of three extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. The climatology and inter-annual variability differences of extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang are more intuitively shown in Fig. 8 (i.e., higher and narrower probability density curve indicates smaller inter-annual variability, and the vertex of probability density curve closer to the vertical axis indicates smaller climatology). It also can be seen that for the given threshold (as an example), the occurrence probabilities of RX1day in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 0.125 (once-in-8.0-year), 0.077 (once-in-12.9-year), and 0.052 (once-in-19.1-year) respectively; the occurrence probabilities of RX5day were 0.304 (once-in-3.29-year), 0.171 (once-in-5.86-year), and 0.111 (once-in-9.0-year) respectively; the occurrence probabilities of CDD were 0.156 (once-in-6.43-year), 0.569 (once-in-1.76-year), and 0.630 (once-in-1.59-year) respectively (gray shaded area in Fig. 8). The occurrence probabilities of regional averaged RX1day and RX5day (CDD) in northern Xinjiang were larger (smaller) than that in southern Xinjiang and eastern Xinjiang for a given threshold.

Fig. 8
figure 8

The regional averaged probability density curve of a RX1day (unit: mm), b RX5day (unit: mm), and c CDD (unit: day) in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. Gray-shaded area indicates the probability of extreme precipitation indices occurring at a given threshold (the thresholds for RX1day, RX5day, and CDD are 20 mm, 30 mm, and 50 days, respectively)

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Figure 9 shows the boxplot of the 20-year return level (RL20) of extreme precipitation indices to explore the differences of low-probability extreme precipitation events in northern Xinjiang, southern Xinjiang and eastern Xinjiang. The RL20 of RX1day at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 19.38–56.57 mm, 21.31–46.07 mm, and 8.89–36.36 mm, respectively, while the median RL20 of RX5day were 32.51 mm, 33.27 mm, and 23.14 mm respectively. The RL20 of RX5day at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 28.05–70.91 mm, 23.99–72.89 mm, and 10.13–50.66 mm, respectively, while the median RL20 of RX5day were 46.65 mm, 43.64 mm, and 26.31 mm respectively. The RL20 of CDD at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 22.51–51.05 days, 14.94–89.80 days, and 26.75–92.00 days, respectively, while the median RL20 of CDD was 38.19 days, 64.52 days, and 66.39 days respectively.

Fig. 9
figure 9

The boxplot of the RL20 of summer a RX1day (unit: mm), b RX5day (unit: mm), and c CDD (unit: day) at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. The width of the boxplot indicates the number of stations

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It can be seen that the differences in RX1day/RX5day (CDD) between stations in southern Xinjiang and eastern Xinjiang were smaller (larger) than that in northern Xinjiang. The above analysis suggests that compared with northern Xinjiang, there were lesser RX1day and RX5day events, with weaker intensity and smaller variability in southern Xinjiang and eastern Xinjiang. And CDD events were opposite.

In summer 2021, some stations in southern Xinjiang experienced record-breaking extreme precipitation events (Fig. 7). Figure 10 shows the spatial distribution of the return period of the extreme precipitation indices in Xinjiang in summer 2021. For most stations, the return period of Rx1day, Rx5day, and CDD in summer 2021 was less than 10 years. The return period of Rx1day and Rx5day at some stations in the south of southern Xinjiang exceeded 40 years, and the return period of CDD at stations in the east of southern Xinjiang was more than 30 years. Combined with Fig. 10a–c, the extreme precipitation events in 2021 showed that there was more precipitation in the south of southern Xinjiang, and more drought in the east of southern Xinjiang. In other words, the south of the southern Xinjiang desert was wet, while the east of the southern Xinjiang desert was dry.

Fig. 10
figure 10

Spatial distribution of the return period of extreme precipitation indices in Xinjiang in 2021

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4 Discussion

This study investigated and analyzed the regional differences and probability distribution characteristics of summer extreme precipitation indices in southern and northern Xinjiang in the recent 50 years. In general, the extreme heavy precipitation at most stations in Xinjiang increased, while the drought events decreased. The extreme heavy precipitation events in southern Xinjiang and eastern Xinjiang were weaker than those in northern Xinjiang, while the drought events were stronger than those in northern Xinjiang. The stations with a statistically significant increasing trend of PRCPTOT and RX5day were more than RX1day. In addition, the summer extreme precipitation events in 2021 were obviously regional and local. The south of the southern Xinjiang desert was wet, while the east of the southern Xinjiang desert was dry.

Studies in recent years have shown that since the 1960s, the extreme precipitation increased at most stations in Xinjiang, and drought extremes decreased in Northwest China. (Zhang et al. 2015; Liu et al. 2019). Xiao et al. (2017) also pointed that Northwest China has become more humid and the precipitation intensity increased slightly. It is notable that our study analyzed the time trend and variability of extreme precipitation indices over Xinjiang based on extreme value theory, and our results are similar to the findings of these studies. Studies also indicated that the regional averaged summer extreme precipitation over Northwest China increased significantly, the annual extreme precipitation increased and annual CDD showed a decreasing trend at most areas of Xinjiang while the annual CDD showed an increasing trend northeast of Xinjiang (Long et al. 2016; Wang and Yang 2017). It should be pointed out that the findings of the CDD trend of this study are based on a seasonal scale.

Besides, the increase in regional precipitation and extreme precipitation events in Xinjiang is closely related to the impact of global warming on hydrological changes in Xinjiang, dynamic conditions, unstable conditions, and other factors (Yang et al. 2009, 2011). Possible mechanisms of extreme precipitation events in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were different. The water vapor in Xinjiang is mainly transported by the mid-latitude westerly belt from the western continent and the ocean (Guan et al. 2017; Yao et al. 2020a, 2022). The water vapor source area circulation anomalies are slightly different on the regional scale (Yang et al. 2011; Yang and Liu 2018). For instance, extreme precipitation in southern Xinjiang can be influenced by water vapor from the Arabian Sea and the Bay of Bengal (Yao et al. 2020b). The main water vapor sources of extreme precipitation in northern Xinjiang are the North Atlantic Ocean, the Arctic Ocean, the Indian Ocean, and the Eurasian continent (Yao et al. 2022).

5 Conclusion

The daily precipitation data in Xinjiang during 1970–2021 were used to analyze and compare the probability distribution characteristics of extreme precipitation indices in northern Xinjiang, southern Xinjiang, and eastern Xinjiang. Based on the extreme value theory, the probability distribution of extreme precipitation indices was modeled, the climatology and variability of extreme precipitation indices were quantified, and the intensity and frequency of extreme precipitation events were discussed.

In general, the mean PRCPTOT at most stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang exceeded 50 mm, 20–50 mm, and 0–40 mm in the past 50 years, respectively. The mean time series of the summer PRCPTOT anomaly showed a statistically significant increasing trend during 1970–2021 in Xinjiang. The summer RX1day and RX5day of most stations in Xinjiang showed an increasing trend, and the summer CDD at most stations in Xinjiang showed a decreasing trend. The summer precipitation events in most stations in Xinjiang increased from 1970 to 2021, while the drought events decreased.

The climatology (mean intensity) of RX1day at most stations in northern Xinjiang were more than 10 mm, while the climatology of RX1day at most stations in southern Xinjiang and eastern Xinjiang was 0–10 mm. The climatology of RX5day at most stations in northern Xinjiang was more than 15 mm, and less than 15 mm at most stations in southern Xinjiang and eastern Xinjiang. The climatology of CDD was less than 25 days at stations in northern Xinjiang, and more than 25 days at stations in southern Xinjiang and eastern Xinjiang. The inter-annual variability of RX1day, RX5day, and CDD at most stations in Xinjiang were 4–8 mm, 4–12 mm, and 4–16 days, respectively.

The occurrence probabilities of regional averaged RX1day and RX5day (CDD) in northern Xinjiang were larger (smaller) than that in southern Xinjiang and eastern Xinjiang for a given threshold. The RL20 of RX1day at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 19.38–56.57 mm, 21.31–46.07 mm, and 8.89–36.36 mm, respectively. The RL20 of RX5day at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 28.05–70.91 mm, 23.99–72.89 mm, and 10.13–50.66 mm, respectively. The RL20 of CDD at stations in northern Xinjiang, southern Xinjiang, and eastern Xinjiang were 22.51–51.05 days, 14.94–89.80 days, and 26.75–92.00 days, respectively. Compared with northern Xinjiang, there were lesser RX1day and RX5day events, with weaker intensity and smaller variability in southern Xinjiang and eastern Xinjiang. And the CDD events were opposite.

Extreme precipitation in Xinjiang had a significant relationship with North Atlantic Oscillation, Atlantic Multidecadal Oscillation, Multivariate ENSO Index, and Indian Ocean Dipole Index (Guo et al. 2014; Xiao et al. 2017; Xie et al. 2019; Hu et al. 2021). Further work will study and quantize the impact of different climate indices on extreme precipitation in Xinjiang and investigate the possible mechanism and the possible linkage between the mechanism of extreme precipitation and dust in southern Xinjiang.