Due to large uncertainties, predictions of high-impact weather on the atmospheric mesoscale are probabilistic in nature. Mesoscale weather ensemble prediction systems (EPS) are developed to obtain probabilistic guidance for high impact weather. An EPS not only issues a deterministic future state of the atmosphere but a sample of possible future states. Ensemble postprocessing then translates such a sample of forecasts into probabilistic measures.
We discuss Bayesian approaches for wind gust and quantitative precipitation forecasting. The Bayesian hierarchical model (BHM) for wind gusts uses extreme value theory, namely a generalized extreme value distribution (GEV), in the data level. A process level for the parameters is introduced which, on the one hand, models the spatial response surfaces of the GEV parameters as Gaussian random fields, and, on the other hand, incorporate the information of the COSMO-DE forecasts. The spatial BHM provides area wide forecasts of wind gusts in terms of a conditional GEV. It models the marginal distribution of the spatial gust process and provides not only forecasts of the conditional GEV at locations without observations, but also uncertainty information about the estimates. At this stage, the BHM ignores the conditional dependence between gusts at neighboring locations. However, an outline is given how this will be incorporated in a subsequent study using max-stable random fields.
For quantitative precipitation forecasting we use Bayesian quantile regression and its spatially adaptive extension together with a variable selection based on a Bayesian LASSO. All this is illustrated for the German-focused mesoscale weather prediction ensemble COSMO-DE-EPS, which runs operationally since December 2010 at the German Meteorological Service (DWD). We further discuss the issue of objective out-of-sample verification, where performance is measured using proper scoring rules and their decomposition.
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