Comparison of multivariate post-processing methods using global ECMWF ensemble forecasts

An influential step in weather forecasting was the introduction of ensemble forecasts in operational use owing to their capability to account for the uncertainties in the future state of the atmosphere. However, ensemble weather forecasts are often underdispersive and might also contain bias, which calls for some form of post-processing. A popular approach to calibration is the ensemble model output statistics approach resulting in a full predictive distribution for a given weather variable. However, this form of univariate post-processing may ignore the prevailing spatial and/or temporal correlation structures among different dimensions. Since many applications call for spatially and/or temporally coherent forecasts, multivariate post-processing aims to capture these possibly lost dependencies. We compare the forecast skill of different non-parametric multivariate approaches to modeling temporal dependence of ensemble weather forecasts with different forecast horizons. The focus is on two-step methods, where, after univariate post-processing, the ensemble model output statistics predictive distributions corresponding to different forecast horizons are combined to a multivariate calibrated prediction using an empirical copula. Based on global ensemble predictions of temperature, wind speed, and precipitation accumulation of the European Centre for Medium-Range Weather Forecasts from January 2002 to March 2014, we investigate the forecast skill of different versions of ensemble copula coupling (ECC) and Schaake shuffle. In general, compared with the raw and independently calibrated forecasts, multivariate post-processing substantially improves the forecast skill. Although even the simplest ECC approach with low computational cost provides a powerful benchmark method, recently proposed advanced extensions of the ECC and the Schaake shuffle are found to not provide any significant improvements over their basic counterparts.