## 3 Methodology
### SWAT Model  
In the 1990s, the soil and water assessment tool (SWAT) model was proposed by the Agricultural Research Service (ARS) of the United States Department of Agriculture (USDA) [36]. As a semidistributed hydrological model for medium-to-large watersheds and long time scales, the SWAT model is a widely utilized to model changes in hydrological processes, erosion, vegetation, and water resource management [33]. Compared with data-driven models and lumped hydrological models, distributed hydrological models can incorporate the physical characteristics of watersheds and the heterogeneous performance of precipitation in space and time, providing more accurate hydrological process predictions. The model is constructed based on hydrologic response units (HRUs). The watershed is split into multiple subwatersheds based on DEM data as well as the actual water network data, and these data are further subdivided into HRUs; subsequently, portions of a \begin{table}
\begin{tabular}{c c c} \hline
**Evaluation Indexes** & **Equation** & **Perfect Value** \\ \hline Correlation coefficient (CORR) & \(BIAS=\frac{\frac{\sum\limits_{i=1}^{n}(y_{i}-x_{i})}{\sum\limits_{i=1}^{n}x_{i}}}{ \sum\limits_{i=1}^{n}x_{i}}\) & 1 \\ \hline Relative bias (BIAS) & \(BIAS=\frac{\sum\limits_{i=1}^{n}(y_{i}-x_{i})}{\sum\limits_{i=1}^{n}x_{i}}\) & 0 \\ \hline Root-mean-square error (RMSE) & \(RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}\frac{(y_{i}-x_{i})^{2}}{n}}{n}}\) & 0 \\ \hline Probability of detection (POD) & \(POD=\frac{N_{11}}{N_{11}+N_{01}}\) & 1 \\ \hline False alarm rate (FAR) & \(FAR=\frac{N_{0}}{N_{11}+N_{10}}\) & 0 \\ \hline Heidke skill score (HSS) & \(HSS=\frac{2(N_{11}\cdot N_{01}-N_{01}\cdot N_{01})}{[(N_{11}+N_{01})(N_{01}+N_{ 0})+(N_{11}+N_{01})(N_{01}+N_{00})]}\) & 1 \\ \hline Nash-Sutcliffe efficiency (NSE) & \(NSE_{t}=1-\frac{\sum\limits_{i=1}^{n}(y_{i}-x_{i})^{2}}{\sum\limits_{i=1}^{n}(y _{i}-\overline{y})^{2}}\) & 1 \\ \hline \end{tabular} (Notation: \(n\) represents the number of variables; \(y_{i}\) represents the satellite-based precipitation data or simulated streamflow; \(x_{i}\) represents the rain gauge data or streamflow; \(y\) represents the mean value of satellite-based precipitation data or simulated streamflow; \(X\) represents the mean value of the rain gauge data or streamflow; \(N_{11}\) represents precipitation detected by both gauges and satellite-based products; \(N_{01}\) represents precipitation detected by gauges but not detected by the satellite-based precipitation product; and \(N_{10}\) is the opposite of \(N_{01}\)).  
\end{table} 
Table 1: List of statistical metrics used in the statistical and hydrologic evaluations. territory are characterized by unique land-use/management/soil attributes [37]. Finally, the hydrological cycle can be expressed by the following equation:  
\[SW_{t}=SW_{O}+\sum_{i=1}^{t}\Bigl{(}P_{day}-Q_{surf}-E_{a}-W_{scep}-Q_{gw}\Bigr{)} \tag{1}\]  
where \(SW_{t}\) denotes the final soil water content; \(t\) denotes time; \(SW_{O}\), \(P_{day}\), \(Q_{surf}\), and \(E_{a}\) represent the initial soil water content, precipitation, surface runoff, and evapotranspiration, respectively; \(W_{scep}\) stands for the amount of water entering the vadose zone from the soil profile on day \(i\) (mm); and \(Q_{gw}\) is the amount of return flow on day \(i\) (mm) [38]. In this paper, the runoff curve number method was chosen to estimate surface runoff, and the Penman-Monteith method was chosen to calculate evapotranspiration. The storage algorithm is used for the mid-soil flow evolution, and the Muskingen algorithm [39] is used for the mid-river flow evolution. The broad range of value parameters and their complex interaction complicate the model parameterization and calibration process. The autocalibration tool was used for the calibration of the SWAT model, via the standalone program SWAT-CUP using the Sequential Uncertainty Fitting version 2 (SUFI-2) algorithm [37]. It enables sensitivity analysis, calibration, validation, and uncertainty analysis of SWAT models.