Restoration of temporal dependence in post-processed ensemble forecasts

An influential step in weather forecasting was the introduction of ensemble forecasts in operational use due 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 (EMOS) 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.

Our main objective is the comparison of different nonparametric multivariate approaches to modeling temporal dependence of ensemble weather forecasts with different forecast horizons. We investigate two-step methods, where after univariate post-processing, the EMOS predictive distributions corresponding to different forecast horizons are combined to a multivariate calibrated prediction using an (empirical) copula (Lerch et al, 2020). Based on global ensemble predictions 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 and Schaake Shuffle. In general, compared with the raw and independently calibrated forecasts, multivariate post-processing substantially improves the forecast skill; however, there is no unique winner, the best-performing approach strongly depends on the weather variable at hand. 

Reference

Lerch, S., Baran, S., Möller, A., Groß, J., Schefzik, R., Hemri, S., Graeter, M., Simulation-based comparison of multivariate ensemble post-processing methods. Nonlinear Process. Geophys. 27 (2020), 349-371.