## 2 Materials and Methods
### Methodology  
The difference in spatial resolution of gauge-based (point) data and GPPs is a typical scale mismatch problem that needs to be addressed prudently. The primary cause of this issue is the difference in their source of spatial coverages. For instance, rain gauge stations provide point data, whereas GPPs exhibit the grid-scale precipitation measures (for example, 0.25\({}^{\circ}\) and 0.1\({}^{\circ}\) for the APHRO, CHIRPS, ERA5, PGMFD, and MSWEP datasets, respectively). For a fine comparison among GPPs, the datasets (i.e., MSWEP and CHIRPS 0.10\({}^{\circ}\), 0.05\({}^{\circ}\), respectively) were resampled to the standard grids (0.25) following [50]. However, serval methods are available for comparing GPPs data with gauging observations, case-in-point upscaling (US) [51], downscaling (DS) [52], and direct comparison (DC) [53] methods. In recent decades several interpolation methods have been applied for the upscaling point data, which include the Kriging Interpolation, Thiessen polygon, and the Inverse Distance Weighting (IDW) methods [9; 54; 55]. For the US method, many meteorological stations are required to create a high-resolution gridded dataset consisting of observations because coarser grids cannot resolve the processes at fine scales [56]. In contrast, the DS method can downscale the GPPs and compare them to the observed precipitation. However, the results from both US and DC have argued that these methods could contain significant errors and uncertainties [19; 57]. To overcome the uncertainties caused by US or DS, a third (DC) method is introduced [53]. In the DC method, the precipitation from a single station or the average of all stations within a grid cell is compared to the corresponding grid of the gridded dataset. DC method is regarded as the most appropriate method as it avoids the uncertainties caused by US or DS, particularly in the region where the distribution of gauging stations is heterogeneous. Considering the complexity of the basin (small number of gauging stations, topography, and influence of two different precipitation systems), the DC method suites the performance evaluation of GPPs against gauge-based observations. Hence, the performance of GPPs was assessed at different spatial (basin to basin) and temporal (daily, monthly, and annual) scales. For the credibility evaluation of the five GPPs against rain gauge data, various error evaluation metrics such as Correlation coefficient/CC, Root Mean square Error/RMSE, relative bias, and relative BIAS in percentage/rBIAS% were applied. The statistical metric CC was computed to appraise the degree of collinearity between reference rain gauge data and GPPs estimations. The RMSE was used to estimate the mean error magnitude (mm per unit) between reference data and GPPs; having smaller RMSE values of GPPs estimations indicates it is closer to the reference data. The BIAS (in millimeter) was applied to evaluate systematic bias in precipitation amounts procured by two data sources. Bias (in percent) was applied to quantify the differences between reference data and GPPs. These four continuous statistical metrics were conducted using the following equations:  
\[CC=\frac{\sum_{i=1}^{n}(O_{i}-\overline{O})\big{(}G_{i}-\overline{G}\big{)}}{ \sqrt{\sum_{i=1}^{n}\big{(}O_{i}-\overline{O}\big{)}^{2}}\sqrt{\sum_{i=1}^{n} \big{(}G_{i}-\overline{G}\big{)}^{2}}} \tag{1}\]  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\big{(}G_{i}-O_{i}\big{)}^{2}} \tag{2}\]  
\[Bias=\left[\frac{1}{n}\sum_{i=1}^{n}\big{(}G_{i}-O_{i}\big{)}\right] \tag{3}\]  
\[rBIAS=\left[\frac{\sum_{i=1}^{n}\big{(}G_{i}-O_{i}\big{)}}{\sum_{i=1}^{n}O_{i} }\times 100\right] \tag{4}\]  
where, \(n\) = number of samples, \(G_{i}\) = GPPs, \(O_{i}\) = gauge Observation data and \(\overline{G}\) and \(\overline{O}\) are the averages of GPPs and gauges Observation data, respectively. The GPPs are deemed perfect once the optimal values of CC, RMSE, Bias, and rBIAS are 1,0,0 and 0, respectively. Furthermore, some criteria for the performance acceptance of GPPs [58; 59].