Vine Copula-Based Probabilistic Weather Forecasting: Review, Challenges, and Future Work

To quantify the uncertainty inherent in numerical weather prediction (NWP) models it is common practice to utilize so-called ensemble prediction systems (EPS). Various types of so-called postprocessing (PP) models have been developed over the last decades to improve NWP ensemble forecasts. In early times, PP was restricted to univariate methods, that is, the PP model was applied, e.g., to a single weather variable, for a single forecast horizon and a single station. More recent developments focus on multivariate PP incorporating different types of dependencies directly into the PP model or restoring this information from the raw ensemble after the PP step. Novel approaches that are able to deal with a large amount of spatial, temporal, or predictor information within a PP model are typically based on machine learning techniques. However, these methods are black box approaches, lack the possibility of model interpretation, and a mathematical understanding of the data generating process. In a joint research project with Claudia Czado several years ago, copulas and vine copulas were discovered to be a highly suitable toolbox for PP. Since then, different copula- and vine copula-based PP methods have been developed to tackle various challenges such as modeling dependencies between weather variables, ensemble members, station locations, or temporally varying dependence. This work gives an introduction to the probabilistic weather forecasting and PP application and provides an overview on the copula- and vine copula-based PP models developed so far.