## 3 Results and Discussion
### Monthly Estimates
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & & \multicolumn{2}{c}{**CC**} & \multicolumn{2}{c}{**MAE (mm)**} & \multicolumn{2}{c}{**RMSE (mm)**} & \multicolumn{2}{c}{**PBias (\%)**} \\ \cline{2-11}  & **MLR** & **SLR** & **GPM** & **MLR** & **SLR** & **GPM** & **MLR** & **SLR** & **GPM** & **MLR** & **SLR** & **GPM** \\ \hline Cachoeira de Goias & **0.83** & 0.72 & 0.70 & **41.24** & 49.05 & 54.45 & **65.16** & 67.61 & 79.34 & \(-30.90\) & \(\mathbf{-3.20}\) & 27.80 \\ Campo Alegre & 0.84 & 0.84 & 0.94 & 55.48 & 59.38 & 35.71 & 71.89 & 80.22 & 47.48 & \(-8.60\) & \(-23.3\) & \(-12.00\) \\ Corrego do Ouro & 0.89 & **0.95** & 0.93 & 46.17 & 42.11 & **33.47** & 61.98 & 61.42 & **47.36** & \(-10.10\) & \(-26.70\) & \(\mathbf{2.10}\) \\ Crominia & 0.98 & 0.91 & 0.98 & 21.61 & 32.20 & 19.36 & 27.78 & 48.16 & 24.79 & \(-8.40\) & 2.00 & \(-6.00\) \\ Montividiu & **0.93** & 0.78 & 0.87 & **19.51** & 32.36 & 33.07 & **29.31** & 57.47 & 49.28 & 13.00 & \(\mathbf{5.40}\) & 18.60 \\ Quirinópolis & 0.88 & 0.77 & **0.97** & 41.28 & 56.90 & **31.25** & 62.76 & 85.23 & **40.84** & \(\mathbf{-2.12}\) & \(-13.80\) & \(-6.80\) \\ \hline \end{tabular} Note: Best methods for filling missing values are indicated in bold. CC, Correlation coefficient; MAE, mean absolute error; RMSE, root mean square error; MLR, multiple linear regression method; SLR, simple linear regression; GPM, Global Precipitation Measurement method.  
\end{table} 
Table 3: Performance indexes of the three methods for filling monthly missing data at the target sites. As for the IMERG-GPM product, a tendency of overestimation was observed for most target sites, which is in agreement with the results of [34] for the study region. The seasonal patterns of the observed rainfall were, to some extent, captured in the Corrego do Ouro, the Quirinopolis, and the Montividiu gauging stations, but were grossly misrepresented in the Cachoeira de Goias (such lack of fit was also observed for the daily time scale). Overall, none of the methods proved able to properly describe the time evolution of monthly rainfall during the water year of 2016-2017. Nonetheless, the goodness of fit assessment in Table 3 and the better agreement with the seasonal features of rainfall, mainly in terms month-to-month variability, as well as the principle of parsimony, seem to suggest that the direct imputation of satellite retrievals is also a more effective alternative for filling missing values in the monthly time scale in our study region. As compared to previous research efforts at the monthly time scale (e.g., [37; 52; 53], and references therein), no marked distinctions were found in the performances of the regression-based models, particularly in terms of RMSE and CC, despite the differences in long-term climate conditions in the study regions. Of course, this may be ascribed to the smoother variations of the rainfall fields for the aggregated process, as well as to the smaller degrees of fluctuation around the correspondent mean values at a given site for large time scales [11]. We note, however, the reproduction of seasonal precipitation patterns, which is paramount for drought assessment, is not fully addressed by these studies, which may limit a broader comparison with respect to the overall performance of the regression models. On the other hand, as opposed to the daily time scale, the filling of monthly rainfall with remote-sensing data, after bias correction through a linear model, has been discussed in [36]. Similarly to our results, the referred study concluded that seasonal rainfall patterns are reasonably captured by the satellite retrievals. However, as the satellite estimates are corrected prior to imputation, lower values of RMSE and higher levels of linear correlation were obtained by [36], which again suggests that a bias correction procedure might improve rainfall estimation.