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, which is crucial for predicting larger-scale events like total precipitation amount over areas such as river catchments that 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. This method works similarly to related approaches like the Schaake shuffle and ensemble copula coupling, i.e., by rearranging predictions at individual locations and reintroducing spatial correlation while maintaining the post-processed marginal distribution. Here, the copula measures how well an arrangement compares with the historical distribution of precipitation. No close relationship is needed between the post-processed marginal distributions and the spatial correlation source. This is an advantage compared to Schaake shuffle and ensemble copula coupling, which rely on a ranking with no ties at each considered location in their source for spatial correlations. However, weather variables such as the precipitation amount, whose distribution has an atom at zero, have rankings with ties. To evaluate the proposed method, it is applied to a precipitation forecast produced by a combination model with two input forecasts that deliver calibrated marginal distributions but without spatial correlations. The obtained results indicate that the calibration of the combination model carries over to the output of the proposed model, i.e., 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.