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

Abstract. Ensemble forecasts and their combination are examined from the perspective of probability spaces. Manipulating 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 L₂ barycenter, which correspond 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 L₂ 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 the forecast uncertainty. Notably, the L₂ barycenter has a larger ensemble spread, making it more prone to under-confidence. While both methods perform similarly on average in terms of the Continuous Ranked Probability Score (CRPS), the Wasserstein barycenter performs better more frequently.