Statistical downscaling of extreme precipitation events using extreme value theory

Abstract

Present day weather forecast models usually cannot provide realistic descriptions of local and particularly extreme weather conditions. However, for lead times of about 0–5 days, they provide reliable forecasts of the atmospheric circulation that encompasses the sub-scale processes leading to extremes. Hence, forecasts of extreme events can only be achieved through a combination of dynamical and statistical analysis methods, where a stable and significant statistical model based on a-priori physical reasoning establishes a-posterior a statistical-dynamical model between the local extremes and the large scale circulation. Here we present the development and application of such a statistical model calibration on the basis of extreme value theory, in order to derive probabilistic forecasts for (extreme) local precipitation. Besides a semi-parametric approach (censored quantile regression, QR) to derive conditional quantile estimates, we use a Poisson point process representation (PP) with non-stationary parameters but a constant threshold, and a peak-over-threshold representation (POT) using the non-stationary generalized Pareto distribution and a variable threshold. The variable threshold is conditioned on the numerical model output and defined as the 0.95 conditional quantile. The performance of the different approaches is compared using the quantile verification score. The downscaling applies to ERA40 re-analysis, in order to derive estimates of the conditional quantiles of daily precipitation accumulations at German weather stations. In terms of the verification score, the differences between the downscaling approaches are marginal. However, the uncertainty of the quantile estimates is larger for the semi-parametric QR approach, particularly for the high quantiles. A constant shape parameter is to be preferred for a stable statistical downscaling model.