## 4 Results  
### Annual and Seasonal Assessments  
Figure 2 shows the total annual precipitation and total seasonal precipitation in different seasons based on the CGDPA, GPM and TRMM datasets in the TSM of China in 2014 accumulated from daily precipitation data. It can be seen from Figure 2 that there are obvious spatial differences of precipitation in different regions. The three groups of data have similar spatial patterns. According to the observations, the annual precipitation decreased from over 600 mm in the rainy northwest TSM area (TS1) to less than 100 mm in the east, especially in the vicinity of the Yili Valley. Although the Yili Valley is far from the ocean, its open westward (horn-shaped) topography is conducive to receiving humid water vapor from the Atlantic Ocean. Every year, westerly airflow enters the Yili Valley in spring, climbing from low to high. The airflow changes from warm to cold in the Piedmont zone, causing abundant precipitation. The spatial patterns of seasonal precipitation is higher in the northwest and lower in the east, and the precipitation is concentrated in summer. Overall, the annual precipitation in the TSM area shares certain common characteristics: precipitation is greater in the north than in the south and greater in the west than in the east. There is good agreement between the satellite precipitation estimates (GPM/TRMM) and the ground reference dataset (CGDPA) about annual precipitation. The spatial distribution of seasonal precipitation is similar to that of annual precipitation.  
The precipitation measured in the TRMM dataset is lower than the CGDPA measured in the ground, while the precipitation in the GPM dataset is significantly higher and closer to the true value. Notably, the spatial distribution of annual precipitation from GPM is subtler than that of TRMM. The geometry and distribution of the high precipitation areas over the northwestern part of the Tianshan Mountains is captured better in the GPM datasets than in the TRMM estimates.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Observed \(\geq\) 0.5 mm** & **Observed \textless{} 0.5 mm** \\ \hline Estimated \(\geq\) 0.5 mm & H & F \\ Estimated \(<\) 0.5 mm & M & Z \\ \hline \hline \end{tabular} Note: H is the observed precipitation detected correctly by the satellite, F is the observed precipitation detected incorrectly by the satellite, M is the observed precipitation missed by the satellite, and Z represents a correct estimate of no rain.  
\end{table}
Table 1: A 2 \(\times\) 2 contingency table for two types of precipitation estimation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name (Symbol)** & **Formula** & **Optimal Value** \\ \hline Correlation Coefficient (R) & \(R=\frac{\sum\limits_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{ \sum\limits_{i=1}^{n}(x_{i}-\overline{x})^{2}-\sum\limits_{i=1}^{n}(y_{i}- \overline{y})^{2}}}\) & 1 \\ Relative Bias (RB/\%) & \(RB=\frac{\sum\limits_{i=1}^{n}(x_{i}-y_{i})}{\sum\limits_{i=1}^{n}y_{i}}\times 100\%\) & 0 \\ Coefficient of Variation (CV/\%) & \(CV=\frac{\phi}{\mu}\times 100\%\) & \(\backslash\) \\ Root Mean Square Error (RMSE) & \(RMSE=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-x)^{2}}{n}}\) & 0 \\ Probability of Detection (POD) & \(POD=\frac{H}{H+M}\) & 1 \\ False Alarm Ratio (FAR) & \(FAR=\frac{F}{H+F}\) & 0 \\ Frequency Bias Index (FBI) & \(FBI=\frac{H+F}{H+M}\) & 1 \\ Critical Success Index (CSI) & \(CSI=\frac{H}{H+M+F}\) & 1 \\ \hline \hline \end{tabular} Note: \(n=\) number of samples, \(\sigma=\) standard deviation of the samples, \(\mu=\) the sample average, \(x_{i}=\) the estimated precipitation by satellites, \(y_{i}=\) the measured precipitation on the ground.  
\end{table}
Table 2: List of the statistical indicators.