## 2 Materials and Methods
### Methodology
#### 2.2.5 Phase 5: Data Validation  
The performance of the extracted satellite data was validated by comparing it with the in situ ground observations (rain gauge) at the point-to-pixel scale. Five statistical measures, including the coefficient of correlation (\(CC\)), mean absolute error (\(MAE\)), percent bias (\(Pbias\)), root-mean-square error (\(RMSE\)), and the Kling-Gupta efficiency (\(KGE\)), were used in the validation. These metrics are commonly used in assessing the accuracy and reliability of rainfall estimation models [67; 68]. Equations (3)-(7) show the aforementioned statistical measures, where \(S\) and \(G\) represent satellite/gridded and gauge precipitation, respectively, and \(n\) is the total number of measurements, \(i\) is the index of data, \(S\) is the average value of \(S_{i}\), and \(G\) is the average value of \(G_{i}\). \(CC\) (also known as [PERSON]'s correlation coefficient) is a measure used to assess the strength of the association between two variables, indicating the degree of interconnect-edness between them [69]. It ranges between \(-1\) and \(1\), where \(-1\) represents a perfect negative correlation and \(1\) represents a perfect positive correlation. The sign of the \(CC\) indicates the direction of the trend, while the absolute value indicates the extent to which the relationship can be modeled linearly. A \(CC\) value of \(0\) implies no relationship between the variables. A \(CC\) value of \(1\) signifies a perfect positive relationship, suggesting that achange in one variable leads to a corresponding change in the other variable in the same direction and with the same magnitude. The \(P\)_Bias_ (also known as relative bias), is a statistical measure that quantifies the direction and magnitude of the bias in an estimator or a model. This measure has been applied in many data comparison studies [70; 71]. It is calculated by comparing the average difference between the estimated values and the true values to the true values themselves, expressed as a percentage. If \(P\)_Bias_ = 0, the estimator or model is unbiased and has no systematic deviation from the true values. A positive \(P\)_Bias_ indicates that the estimator or model tends to overestimate the true values, while a negative \(P\)_Bias_ indicates underestimation. _MAE_ represents the average absolute deviation of the predictions from the true value [72; 73]. Smaller \(MAE\) values indicate a better predictive performance, with zero representing a perfect prediction. On the other hand, \(RMSE\) is the standard deviation of the prediction errors [74]. The \(RMSE\) compares the difference between the estimated and observed values. The best approach computed the lowest value of the \(RMSE\). Both the \(MAE\) and \(RMSE\) can be used to diagnose the variation in the errors in a set of forecasts. Usually, the computed \(RMSE\) is larger or equal to the \(MAE\); the greater difference between them, the greater the variance in the individual errors in the sample. If the \(RMSE\) = \(MAE\), then all the errors are of the same magnitude. Kling-Gupta efficiency (\(KGE\)) is a multi-component performance metric. This goodness-of-fit measure was developed by [PERSON] et al. [75] to provide a diagnostically interesting decomposition of the Nash-Sutcliffe efficiency, which facilitates the analysis of the relative importance of its different components (correlation, bias, and variability) in the context of hydrological modeling. Later, [PERSON] et al. [76] proposed a revised version of this index, to ensure that the bias and variability ratios are not cross-correlated. Equation (7) shows the formula of \(KGE\), where \(r\) is the linear correlation coefficient, \(\alpha\) is a measure of relative variability in the estimated and observed rainfall values, and \(\beta\) is the ratio between the mean estimated and mean observed rainfalls.