Philippe Ear

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.

Highly resoluted and accurate daily precipitation data are required for impact models to perform adequately and to correctly measure high-risk events' impact. 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 using either empirical or parametric distributions. A recent semi-parametric model based on a penalized Berk-Jones (BJ) statistical test which allows for an automatic and personalized splicing of parametric and nonparametric has been developed. This method, called 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. The Stitch-BJ distribution was able to consistently perform as well or better than all the other models over the validation set, including the empirical distribution, which is often used due to its robustness.

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.

Modeling the distribution of precipitation data is required in many applications regarding water resource management and planning, such as flood and drought events. A critical step in statistical modeling is to find probability distributions that correctly describe the occurrences and intensities of precipitation. The statistical modeling of daily precipitation via parametric distribution is often done using the Gamma, Pearson Type 3, and Weibull distributions. However, these statistical models used for precipitation have many drawbacks. As these models are either light or heavy-tailed, they are not suited for applications in large areas with varying tail characteristics. Over the last few years, multiple models of probability distributions of precipitation in compliance with extreme value theory on both ends of the spectrum have been developed, such as the Extended Generalized Pareto Distributions (EGPD). In particular, the EGPD family allows for an adaptable distribution that can model both low and extreme precipitations while dealing with the flexibility of modeling light and heavy tails. When it comes to testing the goodness-of-fit of parametric distributions, the Kolmogorov-Smirnov test is often referred to. However, this test fails to detect divergence in the tails of distributions, making it unfit for discriminating between distributions that must be well fitted to extreme precipitation events. A fast and efficient test called the exact Berk-Jones statistical test (also referred to as the Calibrated Kolmogorov-Smirnov test) is investigated. This test allows for theoretically better power for diverging extreme tails. In this study, the exact Berk-Jones statistical test is compared to the classical Kolmogorov-Smirnov test on multiple parametric distributions, including the EGPD, on a 38-year high-resolution grid dataset of daily precipitation over France.