## 2 Materials and Methods
### Statistical Analysis  
The performance of the IMERG precipitation estimates was evaluated using five statistical indices, namely: bias (BIAS), root mean squared error (RMSE), Pearson's correlation coefficient (r), probability of detection (POD) and false alarm ratio (FAR). BIAS represents the systematic errors in satellite precipitation estimates based on observations from rain gauges, and is calculated by Equation (1). RMSE measures the average absolute error of the satellite's precipitation estimates, Equation (2). The lower the RMSE, the better the estimates of IMERG product to represent rain gauges dataset. The value of r quantifies the relationship between the precipitation values estimated by the satellite and observed by the rain gauges, Equation (3):  
\[\text{BIAS}=\frac{\sum_{\text{i}=1}^{\text{n}}X_{\text{i}}-Y_{\text{i}}}{n} \tag{1}\]  
\[\text{RMSE}=\sqrt{\frac{\sum_{\text{i}=1}^{\text{n}}(X_{\text{i}}-Y_{\text{i} })^{2}}{n}} \tag{2}\]  
\[\text{r}=\frac{\sum_{\text{i}=1}^{\text{n}}\big{(}X_{\text{i}}-\ \overline{X}\big{)}\big{(}Y_{\text{i}}-\ \overline{Y}\big{)}}{\sqrt{\sum_{\text{i}=1}^{\text{n}}\big{(}Y_{\text{i}}- \ \overline{Y}\big{)}^{2}}} \tag{3}\]  
where \(X_{\text{i}}\) represents the satellite precipitation estimate on day/month i; \(Y_{\text{i}}\) denotes the precipitation value observed by the rain gauge on day/month i; n is the number of days/months analyzed in the study; and \(\ \overline{X}\ \text{ and}\ \ \overline{Y}\ \text{ represent the mean values of}\ X_{\text{i}}\) and \(Y_{\text{i}}\), respectively. For the categorical analysis of precipitation estimated by the IMERG, the variables POD and FAR from Equations (4) and (5) were used. POD measures the fraction of the total precipitation events correctly detected by the satellite, while FAR measures the total fraction of precipitation events incorrectly detected by the satellite:  
\[\text{POD}=\frac{N_{\text{a}}}{N_{\text{a}}+N_{\text{c}}} \tag{4}\] \begin{table}
\begin{tabular}{l r r r r} \hline \hline \multicolumn{1}{c}{**Municipalities**} & \multicolumn{1}{c}{**Latitude**} & \multicolumn{1}{c}{**Longitude**} & \multicolumn{1}{c}{**Elevation (m)**} & \multicolumn{1}{c}{**Missing Data (\%)**} \\ \hline Agua Branca & \(-9.26\) & \(-37.94\) & \(603.42\) & \(8.48\) \\ Barra & \(-11.08\) & \(-43.14\) & \(407.50\) & \(2.86\) \\ Barreiras & \(-12.16\) & \(-45.01\) & \(447.51\) & \(4.72\) \\ Belo Horizonte & \(-19.93\) & \(-43.95\) & \(915.47\) & \(0.01\) \\ Bom Jesus da Lapa & \(-13.25\) & \(-43.41\) & \(447.75\) & \(0.19\) \\ Cabrobo & \(-8.50\) & \(-39.32\) & \(342.78\) & \(6.99\) \\ Carinhanha & \(-14.3\) & \(-43.77\) & \(455.25\) & \(4.42\) \\ Curvelo & \(-18.75\) & \(-44.45\) & \(668.26\) & \(0.78\) \\ Formosa & \(-15.55\) & \(-47.34\) & \(938.68\) & \(0.01\) \\ Ibipetuba & \(-11.00\) & \(-44.52\) & \(450.01\) & \(1.47\) \\ Januaria & \(-15.45\) & \(-44.37\) & \(480.00\) & \(0.82\) \\ Montes Claros & \(-16.69\) & \(-43.84\) & \(645.87\) & \(1.85\) \\ Pao de aúccar & \(-9.75\) & \(-37.43\) & \(20.86\) & \(9.75\) \\ Paracatu & \(-17.24\) & \(-46.88\) & \(711.41\) & \(0.34\) \\ Petrolina & \(-9.39\) & \(-40.52\) & \(372.54\) & \(0.10\) \\ Pirapora & \(-17.35\) & \(-44.92\) & \(509.52\) & \(7.85\) \\ Propriá & \(-10.21\) & \(-36.84\) & \(18.46\) & \(0.06\) \\ Remanso & \(-9.63\) & \(-42.08\) & \(397.39\) & \(0.51\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information about the surface gauge.