## 2 Data and Method
### Sources of Uncertainty and Datasets
#### 2.2.2 Sampling Uncertainties  
The computation of daily 1\({}^{\circ}\times 1^{\circ}\) accumulation generates a simple uncertainty arising from the limited number of geostationary images used in the computation. In this context, geostationary images play a key role in the sampling uncertainty computation, for providing for instance the space and time rain/no-rain (detection) samples. The uncertainties due to sampling is akin to variance uncertainty of the mean and was developed under the Megha-Tropiques mission research efforts [36]. The associated error model \(S\), is described at length in [20] and reads as follows:  
\[S=\frac{\sigma}{\sqrt{\frac{A}{d^{2}}\frac{T}{\tau}}} \tag{2}\]  
where \(\sigma\) is the space/time indicator variance of the instantaneous geostationary pixels in a degree (surface \(A\)) during a day (duration \(T\)), multiplied by a conditional precipitation rain rate (see [20] for details). The \(d\) and \(\tau\) scales are autocorrelation scales, in space and time, respectively, obtained from the calculations of space and time variograms. These are required to estimate the number of independent samples for the estimation of the variance uncertainty of the mean. The daily precipitation accumulations and the associated sampling uncertainties, from the TAPEER product [19; 23], were considered. To assess this, we maintained a specific period of samples from the period June-July-August (JJA) of 2014 over the 30\({}^{\circ}\)S 30\({}^{\circ}\)N region, which is a product coverage zone (Tropics). Given that the uncertainty distributions did not differ considerably according to the surface type, as demonstrated by [PERSON] et al. [22], we chose to focus on the ocean surface, which provides a larger sample size (larger number of grids). Figure 2 shows the density scatterplot of the uncertainty distribution due to sampling, as a function of the daily precipitation intensity, for the JJA of 2014 over the tropics (30\({}^{\circ}\)N/S) over oceanic surfaces. In general, and as described by [PERSON] et al. [23], the relative sampling errors, which by definition are always positive, decrease as the rain accumulation intensity increases. In addition, the uncertainties have a large spread for lower precipitation amounts. The RE spread decreased markedly from 200% at 1 mm day\({}^{-1}\) to 80% at 10 mm day\({}^{-1}\), reaching about 40% at precipitation amounts of greater than 50 mm day\({}^{-1}\). Following that, the maximum RE density values were between 60% and 80% at lower precipitations (around mm day\({}^{-1}\)), decreasing to about 35% at 10 mm day\({}^{-1}\) and, subsequently, to 15% for large amounts (>80 mm day\({}^{-1}\)). Consequently, the same decreasing distribution, as a function of the precipitation, was also observed in the IQR, in which Q\({}_{1}\) (Q\({}_{3}\)) shifted downward from 65% (150%) to roughly 10% (20%) from low to large precipitation amounts, respectively. The IQR range diminished from 85% to approximately 10%. The median demonstrated a decreasing range of about 85% as precipitation intensity increased, varying from 100% (at 1 mm day\({}^{-1}\)) to roughly 15% (>80 mm day\({}^{-1}\)). Indeed, the overall error sampling distributions were preserved regardless of the surface type condition (land and ocean). The main surface type contrasts that can be accounted for are the larger RE spread at low-to-moderate (large) precipitation accumulations over ocean (land, not showed). The misrepresentation of the sampling errors, as a component of the error budget, can propagate to the final daily precipitation distributions [20]. This would impact both the detection and the quantification of a certain daily precipitation intensity category [23]. According to [PERSON] et al. [22], at intense precipitation accumulations the sampling relative uncertainty varies from 15% to 20%.