  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) 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 nonparametric 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 EMOS
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 (SSh).
In general, compared with the raw and independently calibrated forecasts,
multivariate post-processing substantially improves the forecast skill. While
even the simplest ECC approach with low computational cost provides a powerful
benchmark method, recently proposed advanced extensions of the ECC and the SSh
are found to not provide any significant improvements over their basic
counterparts.
