Generative machine learning methods for multivariate ensemble post-processing

Statistical post-processing of ensemble forecasts has become a common practice in research to correct biases and errors in calibration. While many of the developments have been focused on univariate methods that calibrate the marginal distributions, practical applications often require accurate modeling of spatial, temporal, and inter-variable dependencies. Copula-based multivariate post-processing methods, such as ensemble copula coupling, have been proposed to address this issue and proceed by reordering univariately post-processed ensembles with copula functions to retain the dependence structure. We propose a novel multivariate post-processing method based on generative machine learning where post-processed multivariate ensemble forecasts are generated from random noise, conditional on the inputs of raw ensemble forecasts. Moving beyond the two-step strategy of separately modeling marginal distributions and multivariate dependence structure, the generative modelling approach allows for directly obtaining multivariate probabilistic forecasts as output. The flexibility of the generative model also enables us to incorporate additional predictors straightforwardly and to generate an arbitrary number of post-processed ensemble members. In a case study on the surface temperature and wind speed forecasts from the European Centre of Medium-Range Weather Forecasts at weather stations in Germany, our generative model that incorporates additional weather predictors substantially improves upon the multivariate spatial forecasts from copula-based approaches. And the model shows competitive performance even with state-of-the-art neural network-based post-processing models applied for the marginal distributions.