Optimal transport for the multi-model combination of sub-seasonal ensemble forecasts

Combining ensemble forecasts from several models has been shown to improve the skill of S2S predictions. One of the most used method for such combination is the “pooled ensemble” method, i.e. the concatenation of the ensemble members from the different models. The members of the new multi-model ensemble can simply have the same weights or be given different weights based on the skills of the models. If one sees the ensemble forecasts as discrete probability distributions, then the “pooled ensemble” is their (weighted-)barycenter with respect to the L2 distance.
Here, we investigate whether a different metric when computing the barycenter may help improve the skill of S2S predictions. We consider in this work a second barycenter with respect to the Wasserstein distance. This distance is defined as the cost of the optimal transport between two distributions and has interesting properties in the distribution space, such as the possibility to preserve the temporal consistency of the ensemble members.
We compare the L2 and Wasserstein barycenters for the combination of two models from the S2S database, namely ECMWF and NCEP. Their performances are evaluated for the weekly 2m-temperature over seven winters in Europe (land) in terms of different scores. The weights of the models in the barycenters are estimated from the data using grid search with cross-validation. We show that the estimation of these weights is critical as it greatly impacts the score of the barycenters. Although the NCEP ensemble generally has poorer skills than the ECMWF one, the barycenter ensembles are able to improve on both single-model ensembles (although not for all scores). At the end, the best ensemble depends on the score and on the location. These results constitute a promising first step before implementing this methodology with more than two ensembles, and ensembles having less contrasting skills.