A barycenter-based approach for the multi-model ensembling of subseasonal forecasts

Ensemble forecasts and their combination are examined from the perspective of probability spaces. By treating ensemble forecasts as discrete probability distributions, multi-model ensemble (MME) forecasts are reformulated as barycenters of these distributions. We consider two barycenters, each defined with respect to a different distance metric: the L 2 barycenter, which corresponds to the traditional pooling method, and the Wasserstein barycenter, which better preserves certain geometric properties of the input ensemble distributions. As a proof of concept, we apply the L 2 and Wasserstein barycenters to the combination of four models from the Subseasonal to Seasonal (S2S) prediction project database. Their performance is evaluated for the prediction of weekly 2 m temperature, 10 m wind speed, and 500 hPa geopotential height over European winters. By construction, both barycenter-based MMEs have the same ensemble mean but differ in their representation of forecast uncertainty. In particular, the L 2 barycenter has a larger ensemble spread, making it more prone to underconfidence. Although both methods perform similarly on average in terms of the Continuous Ranked Probability Score (CRPS), the Wasserstein barycenter performs better more frequently.