## 2 Materials and Methods
### Data Comparison Methodology
#### 2.4.4 Metrics for Accuracy Assessment  
Several widely used statistical indices (Table 2) were adopted to quantify the performance of the six GPPs against rain gauge observations: Coefficient of determination (R\({}^{2}\)), Slope of the linear regression (a), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).  
In addition, we also evaluated the capability of the GPPs in reproducing the distribution of observed precipitation intensities using the Probability Distribution Function (PDF) of daily rainfall intensities. For this purpose, we categorized precipitation into 12 different classes: 0-0.2 mm/day, 0.2-0.5 mm/day, 0.5-1 mm/day, 1-2 mm/day, 2-5 mm/day, 5-10 mm/day, 10-20 mm/day, 20-50 mm/day, 50-100 mm/day, 100-150 mm/day, 150-200 mm/day, and >200 mm/day.  
Finally, the probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) were calculated to evaluate the precipitation detection ability of the six  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name/Symbol** & **Formula** & **Optimal Value** \\ \hline Coefficient of determination/R\({}^{2}\) & R\({}^{2}=(\text{CC})^{2}=\left(\frac{\sum_{i=1}^{n}(\mathcal{O}i-\overline{ \mathcal{O}})^{2}\sum_{i=1}^{n}(P_{i}-\overline{\mathcal{P}})^{2}}{\sqrt{ \sum_{i=1}^{n}(\mathcal{O}i-\overline{\mathcal{O}})^{2}\sum_{i=1}^{n}(P_{i}- \overline{\mathcal{P}})^{2}}}\right)^{2}\) & 1 \\ Slope of linear regression/a & Y = aX + b & 1 \\ Root Mean Square Error/RMSE & RMSE = \(\sqrt{\frac{\sum_{i=1}^{n}(P_{i}-\mathcal{O})^{2}}{n}}\) & 0 \\ Mean Absolute Error/MAE & MAE = \(\frac{1}{n}*\sum\limits_{i=1}^{n}|\mathcal{O}i-P_{i}|\) & 0 \\ \multicolumn{3}{c}{**Categorical statistical metrics**} \\ Probability of Detection/POD & POD = \(\frac{Hits}{Hits+Mises}\) & 1 \\ False Alarm Ratio/FAR & FAR = \(\frac{FalseAlarm}{Hits+FalseAlarm}\) & 0 \\ Critical Success Index/CSI & CSI = \(\frac{Hits}{Hits+FalseAlarm+Mises}\) & 1 \\ \hline \hline P = Gridded Products value, O = Observed (rain gauge) value, \(\overline{\mathcal{P}}\) = average value of P, \(\overline{\mathcal{O}}\) = average value of O, \(n\) = number of samples, X is the explanatory variable (O), Y is the dependent variable (P). The coefficient of determination R\({}^{2}\) was computed using linear fit. _His_ denotes the number of observed precipitation occurrences correctly detected by the gridded products. _Misses_ represents the number of precipitation occurrences observed by the rain gauges but not detected by the gridded products. _False Alarm_ indicates the number of precipitation occurrences not observed by the rain gauges but detected by the gridded products. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical metrics used to quantify GPP performance.  
Figure 2: Data processing with two different approaches: (**a**) point-to-grid, (**b**) point-gridded.  
GPs (Table 2). These indices aim at evaluating whether the estimated daily precipitation coincides with the precipitation observed on the ground. Specifically, POD represents the fraction of observed precipitation occurrences correctly detected by a given GPP. FAR corresponds to the fraction of detected precipitation occurrences that are incorrectly detected by a given GPP, while CSI measures the overall fraction of (detected and observed) precipitation occurrences correctly detected by a given GPP. The POD, FAR, and CSI values all range between 0 and 1. POD and CSI have perfect scores of 1, while FAR has a perfect score of 0. These indices are calculated for the different daily rainfall classes defined above.