## 2 Materials and Methods
### Performance Indicators  
The daily, monthly, and annual precipitation estimates as provided by these different products were analyzed only when there were no data gaps in the corresponding observations from conventional weather stations. The geographic location of each weather stations was matched with a corresponding pixel (closest to the center of a pixel) of the gridded products (i.e., from remote sensing and reanalysis) (Figure 2). Direct comparison of point to pixel values allowed to preserve the integrity of the gridded precipitation estimates (without altering their values). Thus, no resampling or aggregation of the gridded data in terms of the spatial resolution was conducted since this also requires running all precipitation algorithms used to develop these products--which is beyond the scope of this analysis. Thus, the comparison of the gridded data with station data was conducted using their native spatial resolution. Figure 2: Spatial representation of the weather stations locations and the grid resolution (as shown in Table 2) of the precipitation products. The daily, monthly, and annual averages of precipitation values (both estimates and measurements) along with their respective confidence intervals (\(\pm\)95%) were calculated using a bootstrapping resampling technique with 1000 interactions. The bootstrap allows to estimate randomly repeated samples for a dataset of the same size as the original sample. The confidence interval indicates the reliability of an estimate. Based on this method, the obtained averages particularly of those of the measurements from nearby stations (i.e., CBA and PRR) are significantly different. The correlation between measured and estimated precipitation values was evaluated using the Pearson correlation index--, which indicates the degree of the agreement between two data sets (Equation (1)):  
\[r=\frac{\sum(P_{i}-P)(O_{i}-O)}{\sqrt{\sum(P_{i}-P)^{2}\sum(O_{i}-O)^{2}}}, \tag{1}\]  
where \(P_{i}\) is the estimated precipitation value (on daily, monthly, or annual time scale), i represents a numerator for the number of observations from 1 to n with n the total number (days, month, years). \(P\) is the average of the estimated precipitation value, \(O_{i}\) is the measured precipitation value, and \(O\) is the average of the measured precipitation. The agreement between observed and estimated precipitation was also assessed using the index of agreement--d (Equation (2)) as proposed by [26]. This index ranges from zero to one, representing non-agreement and perfect agreement, respectively [11]:  
\[d=1-\left[\frac{\sum(P_{i}-O_{i})^{2}}{\sum(|P_{i}-O|+|O_{i}-O|)^{2}}\right]. \tag{2}\]  
The analysis of the average error in precipitation estimates was assessed using the root mean square error (RMSE) (Equation (3)), where \(n\) is the number of observations. RMSE values close to zero is expected for reduced error and increased accuracy [11]:  
\[RMSE=\sqrt{\frac{\sum(P_{i}-O_{i})^{2}}{n}}. \tag{3}\]  
The performance of the products in detecting daily precipitation events was evaluated using the Wilks method proposed by [27], which utilizes categorical indices (Equations (4)-(7)) that are based on the correctness or error criteria of the estimates relative to the measured values (Table 3). The contingency table suggested that if a product indicated that there was (or was not) precipitation during a particular day, so as the measurements from a weather station, then this day can be accounted in category \(a\) (or \(d\)). Thus, the total number of days that were correctly assigned precipitation values (regardless of their accuracy) can be calculated. On the other hand, if a product indicated that there was (or was not) precipitation during a particular day but actually there was not (or was), based on measurements, then this day can be accounted in category \(b\) (or \(c\)).