Multi-model Combination and Seamless Prediction

(Hydro-) Meteorological predictions are inherently uncertain. Forecasters are trying to estimate and to ultimately also reduce predictive uncertainty. Atmospheric ensemble prediction systems (EPS) provide forecast ensembles that give a first idea of forecast uncertainty. Combining EPS forecasts, issued by different weather services, to multi-model ensembles gives an even better understanding of forecast uncertainty. This article reviews state of the art statistical post-processing methods that allow for sound combinations of multi-model ensemble forecasts. The aim of statistical post-processing is to maximize the sharpness of the predictive distribution subject to calibration. This article focuses on the well-established parametric approaches: Bayesian model averaging (BMA) and ensemble model output statistics (EMOS). Both are readily available and can be used for straightforward implementation of methods for multi-model ensemble combination. Furthermore, methods to ensure seamless predictions in the context of statistical post-processing are summarized. These methods are mainly based on different types of copula approaches. Since skill of (statistically post-processed) ensemble forecasts is generally assessed using particular verification methods, an overview over such methods to verify probabilistic forecasts is provided as well.