## 2 Data and Method
### Sources of Uncertainty and Datasets
#### 2.2.3 Uncertainties Obtained by Comparisons with Rain-Gauge Network  
Beyond the intrinsic error sources identified above, the uncertainty of the accumulated daily integrated precipitation estimation is often assessed, in bulk, by conducting a comparison of rain-gauges networks. It is useful to estimate if the satellite product is characterized by a bias with respect to the in-situ measurements. To illustrate the simple modelling of this source of uncertainty, we used the JAXA's Global Satellite Mapping of Precipitation (GSMaP, [37]) near-real-time version 6 (NRT V6) product. The hourly 0.1\({}^{\circ}\) original data were averaged over 1\({}^{\circ}\times 1^{\circ}\) grid cells and accumulated over one day, from 12Z to 12Z to match the rain-gauge network reporting convention. In this section, the analyses were carried out considering, as ground reference, the in-situ data from several daily accumulated precipitation observations (12Z-12Z) distributed over Brazil. After applying multiple and sequential quality control checks, also performed by the Centre for Weather Forecasting and Climatic Studies of Brazil (CPTEC/INPE) and the HYdrro-geochemistry of the AMazonian Basin (HYBAM), daily accumulated gridded precipitation fields were created by computing the arithmetic average of all available stations within a pre-defined grid cell of 1\({}^{\circ}\times 1^{\circ}\) of spatial resolution. The approach considers the number of available gauges inside each grid cell (i.e., at least 5 rain gauges) as well as the standard error, in order to reduce the impact of the ground truth uncertainties [15]. Although these Brazilian gauge observations have long-term availability, the analyses here  
Figure 2: The uncertainty distribution due to sampling (\(y\)-axis, in %) as a function of the daily precipitation (\(x\)-axis, in mm day\({}^{-1}\)) for June-July-August of 2014, between 30\({}^{\circ}\)N/S and over oceanic surfaces from TAPEER product. Panel shows the density scatterplot (colored scale) superimposed by the log-binned IQR distributions (in black) of the relative error vs. the daily accumulated precipitation (log-scale distributed). Outliers are represented by blue dots. focused on the period from December to March across 3 years (2014, 2015 and 2016)--which represents the rainy season in much of Brazil [38]. Figure 3 depicts the RE distribution of the GSMaP NRT satellite-based precipitation product as a function of the daily precipitation intensity. A large amount of low-to-moderate daily precipitation accumulations were observed, especially due to the substantial contribution of the RE overestimations that reached, for instance, up to +500% at 1 mm day\({}^{-1}\). This dispersion tends to decrease considerably as the precipitation intensity increases. However, the RE density peaks were often located in the underestimation portion throughout the precipitation intensity range. From 1 to 10 mm day\({}^{-1}\), the RE density peaks were mostly observed at about \(-\)90%, whereas for precipitation accumulations greater than 10 mm day\({}^{-1}\) the RE density peaks were located around \(-\)50%. This pattern was also followed by the negatively biased IQR distributions, in which Q\({}_{3}\) and Q\({}_{2}\) presented a constant decrease from +50% to \(-\)10% and from \(-\)10% to \(-\)55%, respectively. No significant changes were observed for the Q\({}_{1}\) component (values were constant at \(-\)75%, varying between \(\pm\)5%). Yet, it is noteworthy that the RE density distribution changed from a non-normal distribution (highly positive skewed) at low-to-moderate precipitation intensities, to normal distributions at high precipitation intensities, both of which were negatively biased. This overall uncertainty distribution scenario, for satellite-based daily accumulated precipitation products, can be explained by the impact and influence of different uncertainty sources [39]. According to [PERSON] et al.