Multivariate and spatial ensemble postprocessing methods

In the recent past the state of the art in meteorology has been to produce weather forecasts from ensemble prediction systems. Forecast ensembles are generated from multiple runs of dynamical numerical weather prediction models, each with different initial and boundary conditions or parameterizations of the model. However, ensemble forecasts are not able to catch the full uncertainty of numerical weather predictions and therefore often display biases and dispersion errors and thus are uncalibrated. To account for this problem, statistical postprocessing methods have been developed successfully. However, many state of the art methods are designed for a single weather quantity at a fixed location and for a fixed forecast horizon. This work introduces extensions of two established univariate postprocessing methods, Bayesian model averaging (BMA) and Ensemble model output statistics (EMOS) to recover inter-variable and spatial dependencies from the original ensemble forecasts. For this purpose, a multi-stage procedure is proposed that can be applied for modeling dependence structures between different weather quantities as well as modeling spatial or temporal dependencies. This multi-stage procedure combines the postprocessing of the margins by the application of a univariate method as BMA or EMOS with a multivariate dependence structure, for example via a correlation matrix or via the multivariate rank structure of the original ensemble. The multivariate postprocessing procedure that models inter-variable dependence employs the UWME 8-member forecast ensemble over the North West region of the US and the standard BMA method, resulting in predictive distributions with good multivariate calibration and sharpness. The spatial postprocessing procedure is applied to temperature forecasts of the ECMWF 50-member ensemble over Germany. The procedure employs a spatially adaptive extension of EMOS, utilizing recently proposed methods for fast and accurate Bayesian estimation in a spatial setting. It yields excellent spatial univariate and multivariate calibration and sharpness. Further the method is able to capture the spatial structure of observed weather fields. Both extensions improve calibration and sharpness in comparison to the raw ensemble and to the respective standard univariate postprocessing methods