## 4 Discussions and Conclusions  
A simple statistical model was introduced to characterize the distribution of uncertainty in gridded multi-platform satellite precipitation products. This Gaussian Mixture Model was shown to outperform a more simplistic single Gaussian model under a variety of ranges of daily accumulated precipitation. It also performed well across a variety of error sources, spanning the classic comparison to gauge networks, to the sampling uncertainty including more recently expressed, constellation configuration-based errors. Formulating such a simple model provides an additional understanding of using, for instance, a Look Up Table. Firstly, as exemplified in our companion paper on the changes of the constellation and the time-series, it is straightforward to formulate a stochastic perspective on the uncertainty. [PERSON] et al. [28] indeed used the Gaussian mixture and a bootstrap technique to estimate the uncertainty distribution over the last two decades and to highlight the relatively stronger impact of moderate-to-high rain accumulation of the evolution of the constellation configuration. Secondly, the suitability of the Gaussian mixture to characterize the uncertainty distribution may provide insights into the processes from which the uncertainty arises. Indeed, our results show that two additive processes can explain the full uncertainty distribution. To further illustrate this perspective, a comparison with the Brazil surface network (Section 3.2) was performed for the GIRAFE product using different detection thresholds in the process of retrieval (Figure 10). The mean of the first mode of the mixture did not reveal considerable sensitivity to this important algorithm assumption. Its variability across the accumulation amount range remained similar for each threshold, despite its slightly decreasing tendencies as a function of the detection threshold. On the other hand, the variance of the mode was strongly impacted by the selection of the threshold, particularly during low-to-moderate accumulation (<10 mm day\({}^{-1}\)). For M#2, the situation was similar with the impact being stronger in the range of low-to-moderate accumulation for both the mean and the variance. This suggests that for M#1 and #2, the impact of the detection step is to add random uncertainty and does not generate much bias at larger rain accumulation (>10 mm day\({}^{-1}\)). Such preliminary analysis emphasizes that improving the L2 precipitation detection will likely decrease the random uncertainty of the multi-platform product when compared to the rain gauge network. Further analysis should explore the sensitivity of the mixture parameters to other algorithms' intrinsic parameters, such as the propagation of the bias in the L2 estimate in the mixture parameters. The sampling uncertainty is likely to also benefit from the mixture analysis although more work is required to assess this. The current analysis was restricted to a given additive error model framework, but such a simple model could also be used to explore alternatives such as a multiplicative error framework or rainfall-runoff hydrological simulations [58]. **Author Contributions:** [PERSON] and [PERSON] designed the study and wrote the manuscript. [PERSON] conducted the analysis, software and the visualization. [PERSON] supported writing the original draft preparation and contributed to discussions and revisions. All authors have read and agreed to the published version of the manuscript. **Funding:** This study benefited from the IPSL mesocenter ESPRI facility, which is supported by CNRS, Sorbonne Universite, UVSQ, CNES, Ecole Polytechnique and national research infrastructures Climeri-France and DATA TERRA. This study was performed by the EUMETSAT Satellite Application Facility on Climate Monitoring, and we acknowledge the financial support from the EUMETSAT member states through CM SAF.