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In the global monitoring of precipitation, extreme high values, even if relatively infrequent, are of particular interest to the research community, because of their strong hydrological and climatological impact and their impact on human activities. Moreover, the uncertainty regarding their evolution under a changing climate reinforces the necessity to have accurate measurements and records of precipitation extremes all around the globe. Global atmospheric models lack accuracy in reproducing precipitation extremes at scales relevant for decision making (sub-daily and sub-meso). The same applies to global observational precipitation products derived from gauges and/or satellite observations. Indeed, the information content of satellite-measured radiances and the limited spatio-temporal sampling allowed by the constellation of precipitation-relevant passive sensors does not always allow accurate deterministic mapping of extreme precipitation rates at resolution one degree and one day or finer. The global network of operational rain gauges also generally lacks the required density to produce accurate estimates of extreme precipitation amounts at these fine scales. Consequently, the many available global precipitation records are largely inconsistent with each other when it comes to precipitation extremes.

Moreover, the existing global precipitation estimates are generally designed to have minimal variance of their residual errors (minimum MSE estimates) or to produce the most likely estimate given the observations (maximum likelihood estimates). These types of estimators tend to produce smooth estimates and compress the dynamical range of the target variable, they don't preserve its statistical distribution and systematically underrepresent the occurrence of extremes. We discuss alternate techniques and optimization criteria for the statistical preservation of extremes in estimation products within a deep-learning framework. We also discuss the fact that the preservation of extremes must be assessed as a multiscale problem; indeed, preserving or correcting the statistical distribution of precipitation rates at the pixel level (i.e., at the native resolution of the estimate) does not guarantee that the distribution will be preserved at coarser aggregated scales. To preserve extremes across all scales one must consider the multiscale structure of precipitation fields and their spatial and temporal autocorrelation.

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