A semi-parametric distribution stitch based on the Berk-Jones test for French daily precipitation bias correction

Modelling daily precipitation data in a large territory is a complex issue due to its asymmetric distribution with few and spatially sparse extremes. Most parametric distributions fail to model rainfall correctly over a large area, and many impact studies use the non-parametric empirical distribution instead of parametric ones, preferring the robustness of the model on the observed data to the extrapolation to unobserved extremes. In the present paper, we built a distributional semi-parametric model for the bias correction of the ERA5-Land reanalysis using the CERRA-Land reanalysis. The proposed inference procedure is constructed as follows.Firstly, we fit an Extended Generalized Pareto (EGP) distribution to the data. These EGP models give a Generalized Pareto distribution in the upper tail while allowing greater flexibility in the lower one. Secondly, for each location, using an adapted version of the Berk-Jones (BJ) statistical test, we propose to replace a portion of the EGP distribution with either the empirical distribution or an eventually lighter-tail parametric distribution such as the Exponentiated Weibull (ExpW) distribution. The final obtained model is a stitch between the EGP, ExpW and the empirical distributions. The proposed semi-parametric stitch model has been evaluated in a bias correction context against classical pure parametric quantile mapping based on Gamma, ExpWand EGP distributions. Comparisons to other classical models show a reduction of the mean absolute and extreme error metrics, especially by removing outliers.