Area precipitation probabilities derived from point forecasts for operational weather and warning service applications

摘要

Probabilistic precipitation forecasts from numerical models are often calibrated using synoptic observations. The resulting probabilities of precipitation refer to the observation system and thus provide the likelihood that precipitation occurs exactly at the spot of the rain gauge. When probabilistic forecasts are required for larger areas, such as rural districts or catchment areas of rivers, it is not possible to interpolate the point probabilities. Instead area probabilities e.g. increase with the size of the area. In this paper we describe a general method to derive area probabilities from point forecasts based on models and methods of stochastic geometry. The method can be applied over arbitrary areas and can be used for operational applications, since it runs fully automatically without human interaction. The basic idea is to model precipitation patterns by circular precipitation cells using a germ-grain model driven by a spatial Poisson point process in a way that the point forecasts are fitted. Area probabilities can then be estimated statistically as relative frequencies based on repeated Monte Carlo simulations. As the area probabilities significantly depend on the sizes of the modelled precipitation cells, suitable cell radii are estimated based on the spatial correlation structure of given point probabilities. Verification with independent radar precipitation and comparison with area probabilities derived from the raw ensemble system COSMO-DE-EPS of DWD is provided and reveals essential advantages of the stochastic model in terms of bias and Brier skill score.