## 3 Results and Discussion
### Daily Estimates
With respect to previous research related to the filling of daily missing data by means of statistical methods (e.g., [46; 47; 48; 49; 50]), our results have indicated slightly larger values of RMSE and MAE, but moderately lower values for CC, particularly for the MLR approach;of course, the distinct climate conditions, which drive the alternation between wet and dry states, as well as the occurrence of large rainfall amounts, may render this direct comparison unfair across different geographic regions. On the other hand, one should note that, in most studies, the filling procedures are applied to relatively shorter periods (i.e., less than a full water year), or in more densely gauged areas, in which a better description of the rainfall fields is possible. To some extent, these facts may justify the poorer performance of the statistical models in our case study. For further analyses, we have also plotted the observed and the estimated time series, as derived from each method for filling missing values, for the testing sites (Figures 4-9). One may notice from Figures 4-9 that, overall, the \"dry state\" conditions are poorly represented by the MLR models (remember that the estimates are bounded from below by the equations' intercepts). In fact, the rainfall amounts estimated with the referred method are, very frequently, much larger than the correspondent intercepts; only the lengthy dry spells, towards the beginning and the end of the water year, were properly captured, as no rainfall was recorded at the \"donor\" sites. This fact illustrates how the use of fixed \"donor\" stations may impact the filling of missing values: the complex distribution of storm patterns may induce the frequent imputation of rainfall amounts significantly larger than the lower bounds even when only localized (yet not too small) events are recorded in the vicinities of the target site by one of the \"donor\" stations. The outlined problem is largely attenuated when the SLR models and the IMERG-GPM retrievals are used, although the latter, to a much lesser extent, still fails in capturing dry spells during some periods of the year. In this case, however, the area-averaged imputed values are closer to zero and the mismatching is probably related to the false alarms from the satellite. Figure 4: Direct comparisons between daily precipitation estimates and observed data for the period from 1 September 2016 to 31 August 2016 at the Cachoeira de Goias station. OBS, observed data; MLR, multiple linear regression method; SLR, simple linear regression; GPM, Global Precipitation Measurement method. Another aspect worth noting in Figures 4-9 is that both MLR and SLR models are unable to reproduce the actual patterns of rainfall variability in the target sites. In fact, for most cases, the rainfall amounts appear to be bounded from above at approximately 20 mm and 30 mm for these methods, respectively. As a result, the largest rainfall events are not reproduced by the statistical models, which may justify the larger values of RMSE in most testing stations when such approaches are used for filling missing values. On the other hand, the IMERG-GPM product was able to describe larger rainfall amounts, albeit, due to the spatial averaging across the correspondent pixel; the most extreme events were consistently underestimated by satellite retrievals after downscaling [51]. This condition is more noticeable for the largest events recorded by the gauges, such as those in the Campo Alegre gauging station that exceeded about 70 mm. Finally, it is clear from Figures 4-9 that the temporal dynamics of the largest observed events were best represented by the satellite retrievals and MLR models, whereas, for the SLR counterparts, some lag between observed and estimated rainfall amounts was verified for most cases. Obviously, this may be ascribed to the simplified rationale of SLR models - the timings of the best \"donor\" station may be different from that of the target site due to storms' transit along the two gauges.