Thomas Laloë

Highly resolved and accurate daily precipitation data are required for impact models to perform adequately and correctly measure the impacts of high-risk events. In order to produce such data, bias correction is often needed. Most of those statistical methods correct the probability distributions of daily precipitation by modeling them with either empirical or parametric distributions. A recent semi-parametric model based on a penalized Berk–Jones (BJ) statistical test, which allows for automatic and personalized splicing of parametric and non-parametric distributions, has been developed. This method, called the Stitch-BJ model, was found to be able to model daily precipitation correctly and showed interesting potential in a bias correction setting. In the present study, we will consolidate these results by taking into account the seasonal properties of daily precipitation in an out-of-sample context and by considering dry days probabilities in our methodology. We evaluate the performance of the Stitch-BJ method in this seasonal bias correction setting against more classical models such as the Gamma, Exponentiated Weibull (ExpW), Extended Generalized Pareto (EGP) or empirical distributions. Results show that a seasonal separation of data is necessary in order to account for intra-annual non-stationarity. Moreover, the Stitch-BJ distribution was able to consistently perform as well as or better than all the other considered models over the validation set, including the empirical distribution, which is often used due to its robustness. Finally, while methods for correcting dry day probabilities can be easily applied, their relevance can be discussed as temporal and spatial correlations are often neglected.

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.

This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+ 2. A plug-in approach is followed. That is, given a consistent estimator F n of F, we estimate L(c) by L n (c) = {F n (x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In particular we propose a new bivariate version of the conditional tail expectation by conditioning the two-dimensional random vector to be in the level set L(c). We also present simulated and real examples which illustrate our theoretical results.