## 4 Evaluation Methods  
In situ observations from the synoptic stations were employed to validate and compare the performance of six GPPs (see Section 3.2). Hereafter, the precipitation values of GPPs and in situ observations are called target precipitation and reference precipitation, respectively. Two types of statistical metrics, including continuous and categorical metrics, were calculated to assess the performance of GPPs from two complementary perspectives. Continuous metrics are used to determine the accurateness (i.e., how close) of the target precipitation against the corresponding reference precipitation. In other words, continuous metrics are employed for precipitation intensity assessment. Pearson Correlation Coefficient (CC), Mean Bias Error (MBE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) are among the continuous metrics that were employed in this study. The CC (Equation (1)) is a unitless metric that describes how well the target precipitation corresponds to the reference precipitation. Its optimal value (i.e., 1) indicates the high representativeness of the target precipitation against the reference precipitation. The MBE (Equation (2)), with the same unit as the input data, measures the average bias between the target precipitation and reference precipitation, representing the systematic overestimation or underestimation of the target precipitation. The MBE is a signed metric with an optimal value of 0, meaning no bias between target and reference precipitation values. Accordingly, the positive and negative values of MBE represent overestimation and underestimation in the target precipitation when compared with the reference precipitation. Moreover, the MAE (Equation (3)) measures the average magnitude difference between the corresponding target and reference precipitation values without considering the direction and provides a quantitative value with the same scale as the input data. The RMSE (Equation (4)) is a standard scale-dependent metric representing the quadratic mean of error between target and reference precipitation values. High values of RMSE denote a higher dispersion degree, while theoretically, a zero RMSE indicates a perfect quantitative match. \[\text{CC}=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt {\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}\cdot\sqrt{\sum_{i=1}^{n}(y_{i}- \overline{y})^{2}}} \tag{1}\]  
\[\text{MBE}=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-x_{i}) \tag{2}\]  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-x_{i}\right| \tag{3}\]  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-x_{i})^{2}} \tag{4}\]  
In the above Equations, \(x_{i}\) is the reference precipitation (i.e., from synoptic stations), \(\overline{x}\) is the average value of reference precipitation, \(y_{i}\) is the target precipitation (i.e., from the GPPs), \(\overline{y}\) is the average value of target precipitation, and \(n\) is the number of corresponding reference and target precipitations. In addition to continuous metrics that measure the accurateness of GPPs, it is essential to investigate their capability of precipitation occurrence detection. Therefore, three categorical metrics, including the Probability of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI), with range values of 0 to 1 were calculated. The POD (Equation (5)) specifies the ability of GPPs to capture actual precipitation occurrence with an optimal value of 1. On the other hand, the FAR (Equation (6)) with an optimal value of 0 indicatesthe incorrect detection of actual precipitation occurrence (i.e., spurious events). Considering the one-sided investigations of POD and FAR, the CSI (Equation (7)) comprehensively illustrates the overall fraction of precipitation events correctly detected by GPPs [81]. Commonly, a fixed threshold value of 1 mm/day is adopted for precipitation/no-precipitation day identification due to high uncertainties for light precipitations [33,82]. However, a fixed threshold can either be small or large for humid and dry regions, respectively.