3.1. Spatiotemporal Changes in Temperature and Precipitation
The annual average temperature in the study area exhibits spatial heterogeneity (
Figure 2a). It decreases gradually from south to north and from the edges of the plateau to the interior. The spatial distribution of long-term (1970–2017) annual average temperature is shown in
Figure 2b. Most of the stations showed a significant upward trend, except for three, which showed a downward trend. Note that the increase was slower in warmer areas and more rapid in cooler areas. The spatial distribution of long-term (1970–2017) precipitation (PRCPTOT) is shown in
Figure 2c. Most of the stations showed significant increasing trends, although some stations in the southeast and on the edge of the plateau showed decreasing trends. The long-term precipitation exhibited spatial heterogeneity in the study area (
Figure 2d), with a gradual decrease from southeast to northwest.
Figure 3 shows the multi-time-scale variation in the annual average temperature and annual total precipitation. The average temperature exhibited fluctuations and increased linearly from 1970 to 2017 (
Figure 3a) at a rate of 0.33 °C/decade (slope: 0.033;
R: 0.77). The annual total precipitation also showed fluctuations, with an overall increase (RR ≥ 1 mm) at a rate of 6.7 mm/decade (slope: 0.67;
R: 0.3) (
Figure 3g). However, the EEMD analysis revealed that all of the IMF components showed multiple fluctuations and clearly oscillated on different time scales.
The amplitudes of the IMF1 components of both the temperature and the PRCPTOT in 1970–1985 were smaller than those in 1986–2017, with variation periods of about 3.3 and 2.8 years, respectively (
Figure 3b,h, respectively). The IMF2 component of the temperature had a significantly smaller amplitude in 1990–2010 than in the other periods, over a period of approximately 8.7 years (
Figure 3c), whereas the IMF2 component of the PRCPTOT had a significantly smaller amplitude in 1990–2010 than in the other periods, over a period of approximately 6.4 years (
Figure 3i). By contrast, the IMF3 component of temperature showed a significant increase in amplitude from the mid-to-late 1990s and then decreased in amplitude in the mid—to-late 2000s, over a period of approximately 13.7 years (
Figure 3d). The IMF3 component of the PRCPTOT exhibited greater fluctuation and stronger periodicity than the IMF3 component of temperature, with a significant increase in amplitude starting in the 1990s (
Figure 3j); the period was also 13.7 years. The IMF4 component of the temperature changed from the negative to the positive phase in 1994 and had an oscillation period of 48 years (
Figure 3e). That of the PRCPTOT was generally in the negative phase from 1983 onward and became significantly smaller in amplitude from the 1990s onward; the oscillation period was 19.2 years (
Figure 3k). The temperature and PRCPTOT trends may have reflected periodic oscillations on longer time scales, but they were not decomposed because of limitations in the length of the data. However, the temperature and PRCPTOT tended to increase with time (
Figure 3f,l).
To compare the IMF components of the temperature and PRCPTOT and to reveal the essential oscillations of the original series, the variance contributions of the IMF were calculated (
Table 2). The IMF1 component of the temperature accounted for 29.7% of the variance, which was the largest contribution, followed by the IMF2 (22.4%). That is, the interannual signal was the main component of the annual temperature variability in our study area. In addition, IMF3 and IMF4 showed periods of 13.7 and 48 years, respectively, on the interdecadal and multidecadal scales; together, they contribute 11.3% of the temperature variation. In addition, the overall trend accounted for 43.8% of the variation. The IMF1 component of the PRCPTOT accounted for 51.9% of the variance, followed by IMF4 (19.2%), IMF3 (15.8%), and IMF2 (9.6%). The interannual signal was also the main contributor to the PRCPTOT variability in our study area. By contrast, on the interdecadal and multidecadal scales, IMF3 and IMF4, with 13.7- and 19.2-year periods, respectively, contributed 19.1% of the PRCPTOT variability. However, the overall trend accounted for only 19.4% of the variance.
Figure 4 shows the oscillation period superimposed on the nonlinear variation. The temperature anomaly (
Figure 4a) entered the positive phase in the mid-1990s. For the oscillation period of 8.7 years, below-average temperatures were recorded in 1970–1995, with three cooler and two warmer periods, and above-average temperatures were recorded after 1996, with three warmer periods and two cooler periods. Compared with that of the 8.7-year period, the oscillation amplitude of the 13.7- and 48-year periods was small. In addition, the overall trend of the PRCPTOT changed from negative to positive in the mid-1980s (
Figure 4b). Over a period of 19.2 years, the PRCPTOT was below average from 1970 to 1997, and above average from 1998 onward; the oscillations were small in both cases. However, for the 13.7-year period, the PRCPTOT was also below average from 1970 to 1997, with two dry and wet periods. After 1998, the wet and dry periods clearly alternated, with a wet period from 1998 to 2004 and a dry period from 2005 to 2014. For the 6.4-year period, the PRCPTOT was below average overall from 1970 to 1997, but there were three wetter and three drier periods of variability. Thereafter, after a wet period in 1997–2004, there was a shift to a dry period in 2005–2012, with the PRCPTOT increasing again after 2012. In general, although both the temperature and precipitation showed an increasing trend, their oscillation periods differed significantly, indicating that the changes in temperature and precipitation were not completely synchronized.
The annual precipitation in our study area (PRCPTOT) was 505 mm. The average monthly precipitation as a percentage of the annual precipitation is shown in
Figure 5. It can be seen that the monthly precipitation was unevenly distributed throughout the year.
3.2. Variation in Precipitation Extremes
Figure 6 shows the annual precipitation extreme indices from 1970 to 2017. The numbers of consecutive dry days (CDD) and consecutive wet days (CWD) exhibited different trends from 1970 to 2017 (
Figure 6a,b, respectively). The maximum and minimum values of CDD were 144.4 and 74.3 days, respectively. The average CDD was 91.4 days, with a decreasing trend of −1.4 days/10a. The maximum and minimum values of the CWD were 8.1 and 6.7 days, respectively. The average CWD was 7.5 days, and no clear trend appeared; the rate of increase was only 0.0029 days/10a. The CDD and CWD trends showed decreasing drought intensity and wetter conditions in the study area. The R95P, SDII, R10, and Rx1-day all showed increasing trends, with fluctuation from 1970 to 2017 (
Figure 6c–f). The maximum and minimum R95p values were 134.7 and 74.2 mm, respectively. The average R95p was 105.7 days, with a rate of decrease of 4.34 mm/10a. The maximum and minimum SDII values were 7.0 and 5.9 mm/day, respectively. The average SDII was 6.5 days, with a rate of decrease of 0.08 mm/day/10a. The maximum and minimum Rx1-day values were 37.1 and 29.5 days, respectively. The average Rx1-day was 33.5 days, with a rate of decrease of 0.54 mm/10a. The maximum and minimum R10 values were 18.5 and 12.6 days, respectively. The average R10 was 15.0 days, with a rate of decrease of 0.24 day/10a.
To further analyze the nonlinear and periodic variation in the extreme-precipitation indices, an EEMD analysis was performed. The IMF components and oscillation periods of each index are shown in
Table 3. The variance contribution of each IMF component was calculated and is also presented in
Table 3. All the indices showed quasi-3-year and quasi-6-year interannual variability. The interannual variability was also a major component of each index (IMF1 and IMF2), accounting for 73.9% (CDD), 65.1% (CWD), 68.4% (R95p), 65% (SDII), 70.8% (R10), and 68.2% (Rx1day) of the variance. The quasi-3-year oscillation explains 40%–60% of the variance of each index. These results indicate that the extreme precipitation in the study area was dominated by interannual variability. On a multi-decade time scale, each index exhibited different characteristics. The CDD and R95p exhibited periodic oscillations of 13.7 and 24 years, and periodic oscillations of 13.7 and 19.2 years were found in the R10. The Rx1-day showed oscillations of 16 and 24 years on the interdecadal and multidecadal scales, respectively. The interdecadal periods of the CWD are 12 and 48 years, respectively, whereas the SDII exhibited interdecadal variations with periods of 19.2 and 48 years. Overall, the indices contributed 13.6% (CDD), 7% (CWD), 20.7% (R95p), 21.1% (SDII), 12.5% (R10), and 23% (Rx1-day) of the variance. Note that the 48-year period of the IMF4 components of the CWD and SDII may have been affected by the maximum length of the time series we used, as noted in the literature [
62,
63].
Figure 7 shows the oscillation period of each extreme-precipitation index superimposed on its nonlinear trend. The CDD anomaly (
Figure 7a) entered the negative phase in the mid-to-late 1980s. For the oscillation period of 13.7 years, above-average CDD occurred in 1970–1987, with a dryer period and a wetter period, and below-average CDD occurred after 1987, with two dryer periods and two wetter periods. On the 6-year scale, the oscillation cycle was more volatile, whereas on the 24-year scale, it did not change significantly. The overall decreasing trend indicates a gradual decrease in consecutive dry days. By contrast, the fluctuations on these three scales (
Figure 7b) show that the CWD was anomalously negative overall in the 1970s and anomalously positive from 1980 to the mid-1990s. It subsequently became negative and decreased gradually until the end of the 2000s, after which it showed a gradual upward trend. Overall, the trend was upward, indicating that the CWD increased. The changes in the CDD and CWD indicate that the climate in the study area is becoming wetter. The R95p and R10 showed very similar fluctuations on these three scales (
Figure 7c,e, respectively); they were anomalously negative overall from 1970 to the mid-1990s, after which they become positive. From 2000 to 2010, they decreased gradually and became negative, after which they showed an upward trend and become positive. Overall, they showed a gradual increase; that is, the amount of extreme precipitation and the number of extreme-precipitation days increased, and the precipitation extremes were greater in the study area. However, the SDII was anomalously negative on these three scales from 1970 to the mid-1990s (
Figure 7d), especially on the 7.4- and 19.2-year scales, with a dryer period (below zero) and a wetter period, and was anomalously positive overall thereafter. A dry period and wet period (above zero) occurred on the 19.2-year scale. Similarly, on these three scales, the Rx1-day was anomalously negative overall from 1970 to the late 1990s (
Figure 7f), with two partially dry and partially wet periods (below zero) on the same 16-year scale; it was anomalously positive overall thereafter. Overall, the SDII and Rx1-day exhibited an upward trend, indicating that the maximum monthly single-day precipitation and the intensity of the single-day precipitation both increased. Overall, the climate in the study area gradually became warmer and wetter from 1970 to 2000, and the climate fluctuations became more pronounced after 2000, with precipitation and extreme precipitation experiencing a slowing increase.
3.3. Spatial Distribution and Trends of Extreme Precipitation
Figure 8 shows the spatial distribution of the extreme precipitation indices in our study region. The spatial distribution of the CDD (
Figure 8a) indicates that the CDD was generally higher in the northern part of the plateau than in the southern part. The lowest CDD was found in the central plateau, and the highest CDD was near Qaidam Basin. The spatial pattern of the CWD showed the opposite distribution, as shown in
Figure 8b; the CWD was generally higher in the southern part of the plateau than in the northern part. The lowest CWD appeared near Qaidam Basin. The spatial distribution of the R95p (
Figure 8c) showed a gradual increase from north to south on the plateau. The lowest value appeared in the Qaidam Basin, and the highest value appeared on the Yunnan–Guizhou Plateau. The spatial distributions of SDII, R10, and Rx1-day (
Figure 8d–f, respectively) were similar to that of R95p. The highest value appeared on the Yunnan–Guizhou Plateau, and the lowest value appeared in the Qaidam Basin. Therefore,
Figure 8a–f suggests that precipitation is extremely low in the northern part of the plateau, whereas the southern part of the plateau, especially the Yunnan–Guizhou area, is relatively wet.
The spatial trend of each extreme precipitation index is shown in
Figure 9. The CDD exhibited clear spatial heterogeneity (
Figure 9a). Overall, most of the stations showed clear changes from 1970 to 2017. The trend was mainly downward on the Qinghai–TP and mainly upward on the Yunnan–Guizhou Plateau. By contrast, the CWD showed the opposite trend in spatial distribution (
Figure 9b): primarily upward and downward trends on the TP and Yunnan–Guizhou Plateau, respectively. The overall trend for the R95p (
Figure 9c) was upward, although some stations, mainly in the southeastern part of the plateau, showed decreases. Most of the stations showed increases in SDII; only 28 stations scattered across the TP showed overall decreases (
Figure 9d). The R10 decreased significantly on the Yunnan–Guizhou Plateau, and most of the stations on the TP showed significant increases (
Figure 9e). The Rx1-day increased significantly in much of the study area (
Figure 9f), although some of the stations across the study area showed decreases. Overall, most of the stations showed significant changes in the extreme-precipitation indices, with clear differences in spatial distribution. These results also indicate spatial heterogeneity and diversity in extreme precipitation in mountainous areas (plateaus).
3.4. Spatiotemporal Pattern of Extreme Precipitation
The empirical orthogonal function (EOF) was used to analyze the spatial and temporal patterns of extreme precipitation. North’s method [
64] was used to test the number of significant orthogonal functions.
Figure 10 shows the cumulative variance of the first five EOF eigenvectors of the extreme-precipitation indices. The first five EOFs account for 38.4–66.9% of the total variance. The variance of some of these indices does not make a large contribution to the total, indicating that the extreme-precipitation pattern in the study area is complex. The first two EOFs of each index were selected for analysis. These EOFs and their corresponding principal components therefore also reflect the spatial and temporal structure of the extreme precipitation to some degree.
The spatial patterns of modes 1 and 2 of the PRCPTOT accounted for 24.4% and 13.3% of the total variance, respectively; moreover, these two spatial modes passed the North test [
64] (
Figure 11). EOF mode 1 clearly showed an anti-phase distribution pattern, with higher PRCPTOT in the southern and northern parts of the plateau and lower PRCPTOT in the central part (
Figure 11a). The time coefficient of EOF mode 1 exhibited fluctuations characterized by interannual and intergenerational variation. In addition, it showed a weak upward trend before 2000 and a clear downward trend after 2000 (
Figure 11c). This result indicates that EOF mode 1 of the PRCPTOT decreased after 2000. However, EOF mode 2 clearly showed an anti-phase-distribution pattern, with higher and lower PRCPTOT east and west of longitude 100°E, respectively (
Figure 11b). The time coefficient of EOF mode 2 also showed interannual and intergenerational variation; it fluctuated before 2000, decreased from 2000 to 2010, and increased significantly after 2010 (
Figure 11d). These results indicates that EOF mode 2 of the PRCPTOT began to strengthen in 2000.
The spatial patterns of EOF modes 1 and 2 of the CDD accounted for 14.4% and 7.8% of the total variance, respectively, and passed the North test. They showed a consistent pattern, in which mode 1 exhibited the opposite behavior to mode 2, and they showed negative and positive values overall (
Figure 12a,b). The time coefficients of EOF modes 1 and 2 indicate that they were characterized by interannual and intergenerational variation (
Figure 13a,b). However, EOF modes 1 and 2 of the CWD accounted for 47.8% and 6.3% of the total spatial variance, respectively, and passed the North test. EOF mode 1 of CWD showed alternating positive and negative values, with no clear regional differences (
Figure 12c). The time coefficient of EOF mode 1 showed a clear downward trend after the mid-1990s (
Figure 13c). This result indicates that EOF mode 1 of the CWD decreased after the mid-1990s. However, EOF mode 2 showed an anti-phase distribution pattern; it was positive and negative north and south of approximately 32°N, respectively (
Figure 12d). The time coefficient of EOF mode 2 of the CWD increased significantly after 2000 (
Figure 13d), indicating that this mode began to strengthen in 2000.
The spatial patterns of EOF modes 1 and 2 of the R95p accounted for 11.6% and 8.6% of the total variance, respectively, and passed the North test. EOF mode 1 showed an anti-phase distribution pattern, where it was negative and positive in the southwestern and northeastern parts of the plateau, respectively (
Figure 12e). However, EOF mode 2 of the R95p showed alternating positive and negative values, with no clear regional differences (
Figure 12f). The time coefficients of modes 1 and 2 were characterized by interannual and intergenerational variation (
Figure 13e,f), indicating periodic changes.
The spatial patterns of modes 1 and 2 of SDII accounted for 18.1% and 9.5% of the total variance, respectively, and passed the North test. For mode 1, the negative values were mainly concentrated in the southern part of the TP, and positive values appeared in the central part (
Figure 12g). However, for mode 2, the negative values were mainly concentrated in the southeastern part of the study area (
Figure 12h). The time coefficient of EOF modes 1 and 2 fluctuated with an upward trend after 2000 (
Figure 13g,h), indicating that they began to strengthen after 2000.
The spatial patterns of EOF modes 1 and 2 of the R10 accounted for 17.4% and 10.2% of the total variance, respectively, and passed the North test. For mode 1, the negative and positive values were mainly concentrated south and north of approximately 32°N, respectively (
Figure 12i). However, for mode 2, the negative values were mainly concentrated in the southeastern and northeastern parts of the study area (
Figure 12j). The time coefficients of EOF modes 1 and 2 of the R10 are shown in
Figure 12i and
Figure 12j, respectively. That of mode 1 showed a clear downward trend from 1970 to 2000 and increased significantly after 2000 (
Figure 13i), indicating that this mode was weak from 1970 to 2000 and became stronger thereafter. However, the time coefficient of mode 2 showed fluctuations with an upward trend (
Figure 13j), indicating volatility with overall strengthening after the 1970s.
The spatial patterns of EOF modes 1 and 2 of the Rx1-day accounted for 9.6% and 8.3% of the total variance, respectively, and passed the North test. For EOF mode 1, the negative and positive values were mainly concentrated in the southeastern and northwestern parts of the plateau, respectively (
Figure 12k). By contrast, for mode 2, the negative values are concentrated mainly in the southwestern part of the study area, and the positive values are concentrated mainly in the northeastern and southwestern parts of the plateau (
Figure 12l). The time coefficient of EOF mode 1 of the Rx1-day showed fluctuations with an upward trend, indicating overall strengthening, and that of EOF mode 2 showed fluctuations with a downward trend, indicating overall weakening (
Figure 13k,l). Overall, the spatiotemporal patterns of EOF modes 1 and 2 of each extreme-precipitation index showed significant differences and were not uniform, suggesting that the extreme precipitation in the study area exhibited complex spatiotemporal patterns.
3.5. Correlation between Extreme Precipitation Indices and Their Association with Ocean-Oscillation Factors
Most precipitation indices are related to annual precipitation (PRCPTOT), which is strongly correlated with extreme precipitation [
65,
66]. To further analyze whether the extreme-precipitation indices selected in our study reflected the annual precipitation and to explore the correlation between the extreme-precipitation indices, the Spearman’s correlation coefficient was calculated.
Table 4 shows the correlations between the extreme-precipitation indices and the PRCPTOT. The Spearman correlation coefficients between the PRCPTOT and R10 exceeded 0.9, and those between the PRCPTOT and R95p, SDII, and Rx1-day exceeded 0.6 (
p < 0.01). However, although the PRCPTOT was positively correlated with CWD, with a correlation coefficient of 0.2, and negatively correlated with CDD, with a correlation coefficient of −0.2, neither result was statistically significant.
Therefore, the indices selected in our study (R95p, SDII, R10, and Rx1day) reflect the variation in annual precipitation. The Spearman correlation coefficients between the PRCPTOT (and other indicators), CDD, and CWD were not high. These results indicate that the factors affecting the CDD and CWD were complex in the highland and mountainous areas. In addition,
Table 4 shows that there was a statistically significant correlation between the precipitation indices. Overall, the timing of the extreme-precipitation events in the highlands was consistent, with increased total precipitation and increased frequency, intensity, and values of extreme precipitation; the PRCPTOT was most strongly correlated with the R10 and R95p.
To examine the relationship between the extreme-precipitation events and the SST indices, the correlation coefficients between the extreme precipitation in the study area and the various SST indices for the Pacific and Indian oceans during 1970–2017 were calculated, as shown in
Table 5. The TIOD was negatively correlated with the PRCPTOT, R95p, SDII, R10, and Rx1-day, but the correlation was significant (
p < 0.05) only for the PRCPTOT, with a correlation coefficient of −0.29. It was positively correlated with the CDD and CWD, but the correlations were not statistically significant. The IOBW and CDD were negatively correlated, with a correlation coefficient of −0.34 (
p < 0.05), but they were positively correlated with other extreme-precipitation indices; specifically, the relationships with the R95p, SDII, and Rx1day were statistically significant (
p < 0.01 or
p < 0.05), with correlation coefficients of 0.31, 0.42, and 0.29, respectively. In addition to the negative correlation between the IOWPS and CDD, the IOWPS was positively correlated with other extreme-precipitation indices; significant correlations were found with the CDD (correlation coefficient: −0.36), R95p (0.34), SDII (0.43), and Rx1day (0.32). The PDO and CDD were negatively correlated, with a correlation coefficient of 0.31 (
p < 0.05); they were positively correlated with other extreme-precipitation indices, but the correlations were not statistically significant. By contrast, strong positive correlations appeared between the WPWPS and PRCPTOT, R95p, SDII, R10, and Rx1day, with correlation coefficients of 0.40, 0.48, 0.57, 0.38, and 0.48, respectively; all of these correlations were statistically significant. However, the ENSOM was negatively correlated with all the precipitation indices, although the correlation was significant (
p < 0.01 or
p < 0.05) only for the R95p and Rx1day, with correlation coefficients of −0.29 and −0.4, respectively. By contrast, the SO was positively correlated with all the extreme-precipitation indices, but the correlation was significant only for the CDD and Rx1day (
p < 0.05), with correlation coefficients of 0.35 and 0.33, respectively. Note that the correlation coefficients between the SIOD and each extreme-precipitation index were small, and none were statistically significant. These findings suggest that the IOWPS and WPWPS were the most important SST indices affecting the study area. These results also show that the SST anomalies in the Pacific and Indian oceans affected the precipitation and extreme precipitation in the study area.
To further explore the relationship between the SST indices and the precipitation and extreme precipitation in the study area, an EEMD analysis was performed. The IMF components of the SST indices are presented in
Table 6. The IMF1 component for each SST index oscillated over a 3-year period; the IMF2 component showed periodic oscillation over a period of 6–10 years, and the IMF3 component shows periodic oscillation over a period of 13–19 years. On the basis of
Table 4 and
Table 5, we selected the extreme-precipitation index, R95p and the SST indices, IOWP and WPWPS, to further analyze the association between extreme precipitation and SST.
The relationship between the SST indices (IOWP and WPWPS) and extreme precipitation events (R95p) in terms of duration and frequency was determined using continuous wavelet transform (CWT), and the relationships of the IOWP and WPWPS with R95p were investigated using the XWT. Next, the wavelet-transform coherence (WTC) between the two CWTs was used to determine the statistical coherence and confidence in the noise control. The results are shown in
Figure 14. The XWT correlation between the IOWP and R95p revealed three significant power bands: a 3–4-year period from 1970 to 1980 (band (1)), a 6–7-year period from 1980 to 1990 (band (2)), and another from approximately 1990 to 2020 (band (3)) at low frequencies. The arrows indicating bands 1 and 2 are very similar and indicate that the two time series were in a positive phase, with a phase difference of 135°. However, the arrow for the third band indicates that the two time series were in a negative phase, with a phase difference of approximately 270° (
Figure 14a). The WTC between the IOWP and R95p showed a 2–3-year period around 1990–2000 (
Figure 14b), during which the two time series were in a positive phase, with a phase difference of approximately 90°.