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. Hourly precipitation over a region is often simultaneously simulated by numerical models and observed by multiple data sources. An accurate precipitation representation based on all available information is a valuable result for numerous applications and a critical aspect of climate monitoring. The inverse problem theory offers an ideal framework for the combination of observations with a numerical model background. In particular, we have considered a modified ensemble optimal interpolation scheme. The deviations between background and observations are used to adjust for deficiencies in the ensemble. A data transformation based on Gaussian anamorphosis has been used to optimally exploit the potential of the spatial analysis, given that precipitation is approximated with a gamma distribution and the spatial analysis requires normally distributed variables. For each point, the spatial analysis returns the shape and rate parameters of its gamma distribution. The ensemble-based statistical interpolation scheme with Gaussian anamorphosis for precipitation (EnSI-GAP) is implemented in a way that the covariance matrices are locally stationary, and the background error covariance matrix undergoes a localization process. Concepts and methods that are usually found in data assimilation are here applied to spatial analysis, where they have been adapted in an original way to represent precipitation at finer spatial scales than those resolved by the background, at least where the observational network is dense enough. The EnSI-GAP setup requires the specification of a restricted number of parameters, and specifically, the explicit values of the error variances are not needed, since they are inferred from the available data. The examples of applications presented over Norway provide a better understanding of EnSI-GAP. The data sources considered are those typically used at national meteorological services, such as local area models, weather radars, and in situ observations. For this last data source, measurements from both traditional and opportunistic sensors have been considered.

Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation