3.1 Trend of summer extreme precipitation
To analyze and compare the difference between summer total precipitation and extreme precipitation, the spatial distribution of averaged PRCPTOT during 1970–2021, PRCPTOT anomaly (difference of PRCPTOT between 2001–2021 and 1970–2020) and PRCPTOT trend are showed in Fig. 1. In the past 50 years, the averaged PRCPTOT of most stations in Xinjiang was more than 20 mm. In South Xinjiang (south of the red dotted line in Fig. 1a), the averaged PRCPTOT of most stations was between 20–50 mm, and some stations reached 60–70 mm. In North Xinjiang (north of the red dotted line in Fig. 1a), the PRCPTOT of most stations exceeded 50 mm, and some stations reached more than 90 mm. Compared with 1970–2000, the average PRCPTOT of most stations was increased from 2001 to 2021, while that of some stations in central Xinjiang was decreased. Among them, the PRCPTOT anomaly of most stations in western Xinjiang exceeded 15 mm, and some stations exceeded 25 mm (Fig. 1a). Meanwhile, it can be seen from Fig. 1 (c) 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 South Xinjiang showed a statistically significant increasing trend (significant at 0.05 level based on the MK test).
Over the past 50 years, the PRCPTOT of most stations in Xinjiang showed an increasing trend, and the precipitation in North Xinjiang was more than that in South Xinjiang. In order to further analyze the variation characteristics of summer extreme precipitation in Xinjiang during historical period, Fig. 2 shows the trend of RX1day, RX5day and CDD. It can be seen that the summer RX1day and RX5day of most stations in Xinjiang showed an increasing trend, while the summer RX1day and RX5day of some stations in central Xinjiang showed a decreasing trend. The stations with significant increases in summer RX1day and RX5day (significant at 0.1 level) are mainly located in the southern South Xinjiang, and the stations with significant increases in summer RX5day were more than the stations with significant increases in summer RX1day (Fig. 2a, b).
Meanwhile, the summer CDD of most stations in Xinjiang showed a decreasing trend, while that of some stations showed a decreasing trend, and the stations with a significant decrease in summer CDD (significant at 0.1 level) were mainly located in the southern South Xinjiang (Fig. 2c). Further, the stations with increasing trend of summer RX1day and RX5day and decreasing trend of summer CDD basically overlapped. Combined with the variation characteristics of PRCPTOT, RX1day, RX5day and CDD, it can be seen that the summer precipitation in the southern South Xinjiang increased from 1970 to 2021, while the continuous dry days decreased.
Further, Fig. 3 shows averaged summer extreme precipitation anomalies over North and South Xinjiang. As shown in Fig. 3, negative anomalies of the PRCPTOT, RX1day and RX5day in North Xinjiang were mainly occur during 1970s - mid 1990s, and positive anomalies were occur after mid 1990s. Meanwhile, positive anomalies of CDD was occur during 1970s - late 1980s, negative anomalies was occur after late-1980s. In South Xinjiang, the PRCPTOT, RX1day and RX5day showed negative anomalies during 1970s - mid 1990s and late 2000s - early 2010s, showed positive anomalies during mid 1990s - late 2000s and early 2010s − 2020s, and significantly increased after 2010s in South Xinjiang. The CDD showed positive anomalies during 1970s - late 1980s and showed negative anomalies late-1980s. It also can be seen from the Fig. 3 that compared with North Xinjiang, the increasing trend of the PRCPTOT, RX1day and RX5day are weaker while the decreasing trend of CDD is stronger.
3.2 Statistical modeling of extreme precipitation
In order to analyze the statistical characteristics of summer extreme precipitation indices in Xinjiang, the GEV distribution introduced in Section 2 was used to model the time series of summer RX1day, RX5day and CDD at each station. Table 3 shows the best statistical model and significance test results of summer extreme precipitation indices at X51482, X51827 and X51839 stations, and X51482 station is located in North Xinjiang, while X51827 and X51839 stations are located in South Xinjiang (black triangle in Fig. 2c). As can be seen from Table 3, the best statistical model of the summer extreme precipitation indices of X51482 and X51839 stations are stationary GEV model (significant at 0.05 level based on KS test). For the X51827 station, the best statistical model of summer RX1day and RX5day are non-stationary GEV model (significant at 0.1 level based on LRT test), while the best statistical model of summer CDD is 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 X51482 station are significantly larger than (smaller than) the other two example stations. Which means that the average intensity and variability of summer RX1day and RX5day (CDD) at X51482 station were greater than (less than) the other two stations. The shape parameters of summer RX1day and RX5day (CDD) of X51482 station are 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-value of KS test are shown, while the p-value of LRT are shown for the stations with non-stationary GEV models.

In order to further evaluate the fitting effect of GEV model on summer extreme precipitation indices of three example stations, Fig. 4 shows the probability and quantile plots of summer extreme precipitation. For the extreme precipitations with stationary (non-stationary) GEV models, the (residual) probability and quantile plots are given. As can be seen from Fig. 4 (a, c and e) that 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, GEV model can well describe the behavior of the RX1day, RX5day and CDD sequences example stations.
Figure 5 shows the variation curves of summer RX1day, RX5day and CDD return level with return periods at the three example stations. It can be seen that the observed values of the extreme precipitation index of example stations are basically within the confidence interval, that is, these extreme precipitation events conform to the GEV model. For extreme events with a return period of more than 20 years, the return level of summer RX1day and RX5day are more than 40 mm, and the return level of summer CDD is about 30 days at X51482 station (blue curves of Fig. 5a, d and g). However, when the return periods are more than 20 years, for X51827 and X51839 stations, the return level of summer RX1day and RX5day are 20–40 mm, and the return level of summer CDD are more than 60 days. At the same time, it can be seen that with the increase of 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.
In addition, rare extreme precipitation events occurred in some areas of South Xinjiang in the summer of 2021. Figure 5 also shows the return periods and return levels of extreme precipitation indexes in the summer of 2021 for three example stations (black square 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 a once-in-2.04 year event (i.e., the return level was 40 days). And the RX1day and RX5day of X51839 station were 1.33 years and 1.56 years (return level was 4.87 mm and 10.68 mm, respectively), and the CDD reached 74 days (17.67 years). Meanwhile, the RX1day, RX5day and the CDD of X51482 station were 1.83 years, 4.42 years and 55 years, respectively(return level are 25.45 mm, 45.34 mm and 34 days, respectively).
3.3 Probability distribution of extreme precipitation in summer
In order to further analyze the spatial characteristics of probability distribution of summer extreme precipitation indices, stationary and non-stationary GEV models are used to model time series of summer RX1day, RX5day and CDD of all stations. The non-stationary GEV model is used for stations with significant time trends (hollow stations in Fig. 2). The best statistical model of all stations are significant at 0.05 and 0.1 level based on K-S test (stationary model) and LRT (non-stationary model) respectively, indicating that the extreme value model can well simulate the characteristics of summer extreme precipitation in Xinjiang. Figure 6 shows the spatial distribution of average intensity (GEV model location parameters) and inter-annual variability (GEV model scale parameters) of the three extreme precipitation indices in Xinjiang during 1970–2021.
As can be seen from Fig. 6 (a), the spatial distribution of the average intensity of RX1day is basically consistent with the mean PRCPTOT (Fig. 1a). The average intensity of RX1day of most stations in North Xinjiang are more than 10 mm. Among them, some stations in the southern North Xinjiang reached 15 mm, and some stations are more than 25 mm. At most stations in South Xinjiang, the average intensity of RX1day are between 5 ~ 10 mm. Meanwhile, the interannual variability of RX1day at most stations in Xinjiang are between 4 ~ 8 mm, and only a few stations had a RX1day interannual variability of more than 8 mm (Fig. 6b). The average intensity of RX5day at most stations in North Xinjiang are between 10 ~ 20 mm, and some stations in southern North Xinjiang are between 30 ~ 40 mm. The average intensity of RX5day of most stations in South Xinjiang is less than 20 mm, and that of the southern stations is less than 10 mm. The interannual variability of RX5day of most stations in Xinjiang region is between 4 ~ 12 mm (Fig. 6c, d). In addition, the average intensity of CDD are 10 ~ 20 days at western stations, 20 ~ 30 days at central stations and eastern stations in North Xinjiang. The interannual variability of CDD at most stations in North Xinjiang are 4 ~ 8 days. The average intensity of CDD at the stations in South Xinjiang are more than 20 days, and the interannual variability are more than 8 days. The average intensity of CDD at the stations in South Xinjiang are 30 ~ 40 days (Fig. 6e, f).
As shown in Fig. 1 ~ 6, although the PRCPTOT, RX1day and RX5day showed an increasing trend in South Xinjiang, the mean intensity and interannual variability of summer RX1day and RX5day are weaker than those in North Xinjiang, and the mean intensity and interannual variability of summer CDD are stronger than those in North Xinjiang. Therefore, in order to further compare the differences of low-probability extreme precipitation events in North and South Xinjiang in historical periods, the spatial distribution of the 20-year return level (RL20) of summer RX1day, RX5day and CDD are presented in Fig. 7. It can be seen that the RL20 of RX1day and RX5day at stations in the central region of Xinjiang exceeded 40 mm and 60 mm, respectively, while the RL20 of RX1day and RX5day at other stations are 25 ~ 40 mm and 30 ~ 60 mm respectively. The RL20 of RX1day and RX5day at some stations are less than 30 mm (Fig. 7a, b). In addition, there are no significant spatial difference between RX1day and RX5day at stations in South Xinjiang and North Xinjiang stations. However, the RL20 of CDD at most stations in South Xinjiang exceeded 40 days, and the RL20 of CDD exceeded 60 days at most stations in southern South Xinjiang. However, the RL20 of CDD at most stations in North Xinjiang experienced 30 ~ 50 days, and some stations experienced more than (less than) 60 days (30 days).
According to the analysis in Fig. 7, there is no significant difference in the magnitude of extreme heavy precipitation events (except for stations in the central region) in North and South Xinjiang. However, record-breaking extreme precipitation events occurred at some stations in South Xinjiang in the summer 2021 (Fig. 5). In order to investigate the regional characteristics of this extreme precipitation event, Fig. 8 shows the spatial distribution of the return period of the extreme precipitation index in Xinjiang in summer 2021. For most stations, the return period of Rx1day, Rx5day and CDD in summer 2021 is less than 10 years. The return periods of Rx1day and Rx5day at stations in southern South Xinjiang exceeded 10 years, and the return periods of the two extreme precipitation indces at some stations exceeded 40 years. In addition, the return period of Rx5day at some stations in North Xinjiang was more than 10 years, and the return period of CDD at stations in eastern South Xinjiang was more than 30 years. Combined with Fig. 8 (a-c), it can be seen that the extreme precipitation events in 2021 are more precipitation in the southern South Xinjiang, and more drought in the eastern South Xinjiang. In other words, the southern South Xinjiang desert is wet, while the eastern South Xinjiang desert is dry.