## 3 Methodology
### Evaluation Statistics  
Several diagnostic indices were used to quantitatively evaluate the quality of eight SPPs versus ground precipitation observations and their feasibility in flood simulations. Pearson correlation coefficient (CC) measures the agreement between simulated and observed data (Equation (1)); in this study, \"simulated data\" refers to SPPs or simulated discharge, and \"observed data\" denotes ground  
Figure 3: Diagram of the assessment framework in this study.  
precipitation observations or measured discharge. Relative bias (BIAS) indicates the systematic bias of the simulated data (Equation (2)). Root mean square error (RMSE) represents the average absolute error magnitude between the simulated and observed data (Equation (3)). The probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) were selected to measure the contingency of satellite precipitation estimates. POD denotes the proportion of precipitation events that are correctly detected by satellites among all real precipitation events (Equation (4)). FAR describes the fraction of false events among all the rain events identified by the satellites (Equation (5)). CSI denotes the overall proportion of precipitation events that are correctly identified by the satellites (Equation (6)). Moreover, NSE was adopted to assess the performance of flood simulations (Equation (7)). These diagnostic indices are expressed as follows:  
\[CC=\frac{\sum_{i=1}^{n}\left(X_{i}^{o}-\overline{X}^{o}\right)\left(X_{i}^{s} -\overline{X}^{s}\right)}{\sqrt{\sum_{i=1}^{n}\left(X_{i}^{o}-\overline{X}^{o} \right)^{2}}\sqrt{\sum_{i=1}^{n}\left(X_{i}^{s}-\overline{X}^{s}\right)^{2}}} \tag{1}\]  
\[BIAS=\frac{\sum_{i=1}^{n}\left(X_{i}^{s}-X_{i}^{o}\right)}{\sum_{i=1}^{n}X_{i} ^{o}}\times 100\% \tag{2}\]  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(X_{i}^{s}-X_{i}^{o}\right)^{2}}{n}} \tag{3}\]  
\[POD=\frac{H}{H+M} \tag{4}\]  
\[FAR=\frac{F}{H+F} \tag{5}\]  
\[CSI=\frac{H}{H+M+F} \tag{6}\]  
\[NSE=1-\frac{\sum_{i=1}^{n}\left(X_{i}^{s}-X_{i}^{o}\right)^{2}}{\sum_{i=1}^{n} \left(X_{i}^{o}-\overline{X}^{o}\right)^{2}} \tag{7}\]  
where \(n\) is the sample size of the simulated and observed data pair; \(X_{i}^{s}\) and \(X_{i}^{o}\) denote the ith values of the simulated and observed data, respectively; \(\overline{X}^{s}\) and \(\overline{X}^{o}\) are the mean values of the simulated and observed data, respectively; H represents the number of real rain events correctly identified by the satellites; M denotes the number of real precipitation events that satellites failed to detect; and F is the number of precipitation events that satellites detected but did not actually occur. In addition, two diagnostic indices (BIAS\({}_{\text{P}}\) and PTE) were specifically adopted to measure the accuracy of the simulated flood peaks in major historical flood events. BIAS\({}_{\text{P}}\) represents the relative bias between the simulated and observed flood peak flows and is given by  
\[BIAS_{p}=\frac{Q_{p}^{s}-Q_{p}^{o}}{Q_{p}^{o}}\times 100\% \tag{8}\]  
where \(Q_{p}^{s}\) and \(Q_{p}^{o}\) are the simulated and measured flood peak flows, respectively. PTE indicates the flood peak time error and is expressed by  
\[PTE=T^{s}-T^{o} \tag{9}\]  
where \(T^{s}\) and \(T^{o}\) are the simulated and measured flood peak time, respectively. A negative PTE denotes that the simulated peak flow is ahead of the measured peak flow, and a positive value represents that the simulated peak flow appears behind the observed.