Abstract
Ensemble weather forecasting has been operational for two decades now. However, the related uncertainty analysis in terms of probabilistic postprocessing still focuses on single variables, grid points, or stations. Inevitable dependencies in space and time and between variables are often ignored. To address this problem, two probabilistic postprocessing methods are presented, which are multivariate versions of Gaussian fit and kernel dressing, respectively. The multivariate case requires the estimation of a full rank, invertible covariance matrix. For this purpose, a Graphical Least Absolute Shrinkage and Selection Operators (GLASSO) estimator has been employed that is based on sparse undirected graphical models regularized by an L1 penalty term in order to parameterize the full rank inverse covariance. In all cases, the result is a multidimensional probability density. The forecasts used to test the approach are station forecasts of 2-m temperature and surface pressure from four main global ensemble prediction systems (EPS) with medium-range weather forecasts: the NCEP Global Ensemble Forecast System (GEFS), the Met Office Global and Regional Ensemble Prediction System (MOGREPS), the Canadian Meteorological Centre (CMC) Global Ensemble Prediction System (GEPS), and the ECMWF EPS. To evaluate the multivariate probabilistic postprocessing, especially the uncertainty estimates, common verification methods such as the analysis rank histogram and the continuous ranked probability score (CRPS) are applied. Furthermore, a multivariate extension of the CRPS, the energy score, allows for the verification of a complete medium-range forecast as well as for determining its predictability. It is shown that the predictability is similar for all of the examined ensemble prediction systems, whereas the GLASSO proved to be a useful tool for calibrating the commonly observed underdispersion of ensemble forecasts during the first few lead days by using information from the full covariance matrix.
