## 2 Data and Method
### Sources of Uncertainty and Datasets
#### 2.2.1 Constellation Changes-Induced Uncertainties
The relative error distribution shows strong variability depending firstly on the constellation configuration (Figure 1). As anticipated, the experiment closest to the reference configuration exhibited few relative differences and the distribution was narrow across the considered range of daily accumulation. For C\({}_{04}\), as an intermediate case, the distribution reached up to 50% uncertainty at maximum (i.e., IQR range rule). On the other hand, for the idealized one single SSMI/S configuration case (C\({}_{99}\)), the distribution was characterized by large errors (up to 200%) and a large spread, even at intense daily precip \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Available Period** & **Plat. N\({}^{\circ}\)** & **Platforms** \\ \hline \(C_{REF}\) & 4 March 2014–8 April 2015 & 12 & SSMI/S(3), GCOMM1, TMI, GMI, SAPHIR \({}^{*}\), MHS(4), ATMS \\ \(C_{gg}\) & 1 January 1988–31 December 1990 & 1 & SSMI/S(1) \\ \(C_{04}\) & 1 December 2006–29 February 2008 & 10 & SSMI/S(3), GCOMM1, TMI, MHS(4), ATMS \\ \hline \hline \end{tabular} \(C\) = Constellation configuration experiments. \(REF\) = Reference. \({}^{*}\) Through PRPS2019 algorithm.  
\end{table} 
Table 1: The adopted data denial experiments and their respective constellation configurations, based on the number of platforms available for each corresponding period. itation accumulations. The secondary cause of variability was the surface type. Indeed, the spread over the ocean region was much larger than over land for each configuration (not showed). Finally, for all set-ups, the relative errors' range decreased as the daily precipitation accumulation increased. The relative error distribution due to the constellation configuration was further illustrated by focusing on the RE_C99 distributions that revealed the largest spread for small and a large daily accumulation cases (Figure 1a). The small accumulation distribution produced a truncated lower end and a large positive spread centered around a zero line. The IQR were negatively skewed and, despite the slightly positive tendency as precipitation increases, the higher densities were generally at about \(-15\%\) [\(\pm 5\)] of RE (systematic underestimation). The Q\({}_{1}\), Q\({}_{2}\) (median) and Q\({}_{3}\) ranged from [\(-50\%\), \(-20\%\), \(+40\%\)] to [\(-30\%\), \(-10\%\), \(+20\%\)] for low-to-moderate precipitation accumulations (0.5 to 10 mm day\({}^{-1}\)). In cases of larger precipitation amounts (e.g., \(>\)10 mm day\({}^{-1}\)), despite being negatively skewed, the distribution appeared more symmetrical and narrowed around the zeros. The overall RE distributions decreased, for instance, from approximately \(-80\%\) and \(+70\%\) for 10 mm day\({}^{-1}\) to \(-45\%\) and \(+50\%\) at 50 mm day\({}^{-1}\). However, for precipitation accumulations greater than 50 mm day\({}^{-1}\), a slight increase towards positive RE (overestimation) was observed. Q\({}_{3}\) increased by about 15%, from 50 to 100 mm day\({}^{-1}\). The uncertainty distribution at 100 mm day\({}^{-1}\) expressed a slightly right-skewed distribution with median and density peaks at about \(-12\%\). The closer the proximity in terms of constellation configuration (i.e., Figure 1b), the greater the chance that the uncertainty distribution acquires a unimodal and leptokurtic shape over the entire precipitation range. In summary, these overall observed RE distribution characteristics, due to the constellation configuration, are closely linked to the nature of the PMW rain rates as input data that were also propagated up to the daily precipitation accumulations [18; 20; 29]. In fact, the overall impact that can strongly biasing L3 estimates can be explained through the better representation of precipitating yields spatially and temporally, being accordingly sampled by the PMW radiometers that contributed to the final daily amounts [30; 31].