## 3 Results
### Correlation Analysis
#### 3.4.2 Correlations between Meteorological Factors and Extreme Climatic Indices  
The Pearson correlation coefficients of PWV with extreme temperature indices are provided in Figure 10a. A strong correlation of above 0.78 was found between PWV and extreme temperature indices, such as TMAXmean, TMINmean, TNn, TXx, TNx, and TXn. The Pearson correlation coefficients of the extreme temperature indices showed a decreasing trend from southwest to northeast, which is possibly associated with the PWV distribution. [PERSON] et al. [25] found that a high temperature corresponds to high atmospheric moisture content. Figure 11 shows the correlation coefficient distribution statistics of extreme temperature index, extreme rainfall index and PWV in the Loess Plateau; five different colors in the figure represent different statistical intervals of correlation coefficient. It can be found that the coefficients of the correlations of PWV with TMAXmean, TMINmean, TXx, TNx, TXn, and TNn were higher than 0.4. Weak correlations existed between PWV and other extreme temperature indices, such as FD0, SU25, WSDI, CSDI, and GSL, accounting for 55.07%, 45.65%, 58.70%, 44.20%, and 63.77% of Loess Plateau, respectively. The increase in extreme cold indices could accelerate the transformation of atmospheric water vapor into the rain, further causing a decrease in atmospheric PWV. Therefore, the extreme cold indices FD0 and CSDI showed negative relationships with PWV, accounting for 42% and 59.4% of Loess Plateau, respectively.  
Figure 9: Correlations of NDVI with (**a**) PWV, (**b**) RHU, and (**c**) SSD.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **mean** & **Max-Year** & **Max** & **Min-Year** & **Min** & **Rate (/10a)** & **Jump Year** \\ \hline RX1 day & 48.09 & 2016 & 62.71 & 2015 & 38.74 & 1.2 & — \\ RX5 day & 75.71 & 2013 & 90.48 & 1986 & 58.08 & 1.3 & — \\ R95p & 112.3 & 2003 & 147.43 & 2015 & 66.59 & 2.1 & — \\ R99p & 35.81 & 2016 & 70.47 & 2015 & 15.55 & 2.7 & — \\ R10 & 74.36 & 1999 & 126.27 & 1980 & 50.20 & \(-\)0.98 & — \\ R20 & 4.75 & 1985 & 6.22 & 2012 & 3.75 & \(-\)0.32 & — \\ R25 & 13.65 & 2003 & 18.46 & 1986 & 9.64 & 0.89 & — \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._The statistical results of the Pearson correlation coefficients of extreme climate indices with RHU and SSD are also presented in Figures 12 and 13, respectively. Figure 12 shows that the Pearson correlation coefficients of the relationships of RHU with TMAXmean, TMINmean, TXx, TNx, TXn, and TNn are higher than 0.2, accounting for 67.39%, 80.43%, 60.15%, 68.37%, 72.74%, and 82.6% of Loess Plateau, respectively. Extreme temperature cold indices did not show evident correlations with RHU, whereas negative correlations existed between RHU and extreme temperature warm indices (SU25, WSDI, and GSL). Some extreme precipitation indices, such as RX1 day and RX5 day, showed good correlations with RHU (0.2-1), accounting for 88.40% and 92.75% of Loess Plateau, respectively. Extreme temperature indices, such as TMAXmean, TMINmean, TXx, TNx, TXn, and TNn, also showed positive relationships with SSD with Pearson correlation coefficients ranging from 0.2-1, accounting for 88.5%, 84.05%, 88.41%, 84.05%, 87.68%, and 84.78% of Loess Plateau, respectively.  
Figure 11: Statistical results of the Pearson correlation coefficients of PWV with extreme temperature indices, where TMAXm and TMINm represent TMAXmean and TMINmean, respectively.  
Figure 10: Pearson correlation coefficients of PWV with extreme climatic indices in the Loess Plateau region, the extreme climatic indices are (**a**) TMAXmean, (**b**) TMINmean, (**C**) TNn, (**d**) TXx. (**e**)TNx, (**f**) TXn. (**g**)FD0, (**h**) SU25. (**i**)WSDI, (**j**) CSDI and (**k**) GSL.