Generative machine learning methods for multivariate ensemble post-processing

Ensemble weather predictions typically show systematic errors that need to be corrected via post-processing. While much research interest has been focused on univariate approaches, many practical applications such as energy forecasting, hydrological applications and air traffic management require accurate modeling of spatial, temporal, and inter-variable dependencies. Over the past years, a variety of two-step approaches where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are restored via copula functions in a second step has been proposed to address this need [1]. However, these approaches share common limitations in that incorporating additional predictor variables beyond forecasts of the variable of interest is not possible in a straightforward manner in specifying the copula functions that govern the multivariate dependence structure, which makes it challenging to draw from substantial benefits that have recently been demonstrated in the context of univariate post-processing [2].

To address this challenge, we propose a novel data-driven one-step approach to multivariate ensemble post-processing based on conditional generative machine learning  which allows for obtaining multivariate probabilistic forecasts directly as output of a generative neural network while incorporating additional exogenous variables as predictors. In case studies on multivariate probabilistic forecasts of surface temperature and wind speed at observation stations in Germany, our conditional generative models show state-of-the-art forecast performance and advantages over benchmark approaches, for example by allowing for generating an arbitrary number of samples from the multivariate  forecast distributions. 

References
[1]  Lerch, S. et al. (2020) Simulation-based comparison of multivariate ensemble post-processing methods. Nonlinear Processes in Geophysics, 27: 349–371
[2] Rasp, S. and Lerch, S. (2018) Neural networks for post-processing ensemble weather forecasts. Monthly Weather Review, 146(11): 3885–3900