A barycenter-based approach for the multi-model combination of ensemble forecasts: an application to the sub-seasonal forecasts of 2m-temperature over Europe

Multi-model ensemble (MME) methods, i.e. combining ensemble forecasts produced by different models, have been shown to improve the skill of prediction at different scales. One important research question is how to best construct such multi-model ensemble. This is one of the challenges addressed by the subseasonal-to-seasonal (S2S) project for the subseasonal scale, and also the focus of this study. To answer this question, we compare two methods based on barycenters.

The main idea is to consider the ensemble forecasts as discrete probability distributions, and to use a barycentre to combine them. We compare two barycenters based on different distances, the L2 and the Wasserstein distance. Applying an L2-barycentre on ensemble forecasts is equivalent to concatenating their members, i.e. to the well-known MME method known as “pooling”. The Wasserstein distance corresponds to the cost of the optimal transport between two distributions and has interesting properties in the distribution space. The two methods potentially lead to very different multi-model ensembles. The barycenters also allow us to attribute weights to the models. These weights are learned from the data (using cross-validation on the forecasts) in order to optimize the skill of the barycenter-ensembles.

In order to investigate the benefits of these two multi-model ensemble methods, both methods are applied to the combination of two models from the S2S forecasts, namely the European Centre Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) models. The skill of the two barycenter-ensembles are evaluated for the prediction of weekly 2m-temperature over Europe for seven winters with respect to different metrics. Although the ECMWF model has an overall better performance than NCEP, the barycenter-ensembles are generally able to outperform both. However, the best ensemble depends on the chosen metric and on the location. Focusing on the combination of two models has allowed us to investigate the impact of the model’s weights on the performance of the barycenters. It also provides encouraging results for the next step, the combination of several models.