Multivariate postprocessing techniques for probabilistic hydrological forecasting

Hydrologic ensemble forecasts driven by atmospheric ensemble prediction systems need statistical postprocessing in order to account for systematic errors in terms of both location and spread. Runoff is an inherently multivariate process with typical events lasting from hours in case of floods to weeks or even months in case of droughts. This calls for multivariate postprocessing techniques that yield well-calibrated forecasts in univariate terms and ensure a realistic temporal dependence structure at the same time. To this end, the univariate ensemble model output statistics (EMOS) postprocessing method is combined with two different copula approaches that ensure multivariate calibration throughout the entire forecast horizon. The domain of this study covers three subcatchments of the river Rhine that represent different sizes and hydrological regimes: the Upper Rhine up to the gauge Maxau, the river Moselle up to the gauge Trier, and the river Lahn up to the gauge Kalkofen. In this study, the two approaches to model the temporal dependence structure are ensemble copula coupling (ECC), which preserves the dependence structure of the raw ensemble, and a Gaussian copula approach (GCA), which estimates the temporal correlations from training observations. The results indicate that both methods are suitable for modeling the temporal dependencies of probabilistic hydrologic forecasts.