Generating synthetic rainfall fields by R‐vine copulas applied to seamless probabilistic predictions

Abstract

Many post‐processing methods improve forecasts at individual locations but remove their correlation structure. However, this information is essential for forecasting larger‐scale events, such as the total precipitation amount over areas like river catchments, which are relevant for weather warnings and flood predictions. We propose a method to reintroduce spatial correlation into a post‐processed forecast using an R‐vine copula fitted to historical observations. The method rearranges predictions at individual locations and ensures that they still exhibit the post‐processed marginal distributions. It works similarly to well‐known approaches, like the “Schaake shuffle” and “ensemble copula coupling.” However, compared to these methods, which rely on a ranking with no ties at each considered location in their source for spatial correlation, the copula serves as a measure of how well a given arrangement compares with the observed historical distribution. Therefore, no close relationship is required between the post‐processed marginal distributions and the spatial correlation source. This is advantageous for post‐processed seamless forecasts in two ways. First, meteorological parameters such as the precipitation amount, whose distribution has an atom at zero, have rankings with ties. Second, seamless forecasts represent an optimal combination of their input forecasts and may spatially shifted from them at scales larger than the areas considered herein, leading to non‐reasonable spatial correlation sources for the well‐known methods. Our results indicate that the calibration of the combination model carries over to the output of the proposed model, that is, the evaluation of area predictions shows a similar improvement in forecast quality as the predictions for individual locations. Additionally, the spatial correlation of the forecast is evaluated with the help of object‐based metrics, for which the proposed model also shows an improvement compared to both input forecasts.