On combining climate models into weighted ensembles

Abstract. Several methods have been proposed and used to refine estimates of future climate change based on combined output from comprehensive climate models. While previously the so-called model democracy approach was used to combine model predictions, where every model is given equal weight, it is now widely accepted that using model weights that account for model performance and model independence is necessary to obtain more reliable results. However, most existing approaches rely, implicitly or explicitly, on a similar statistical basis, while describing things in different ways. Here we distinguish between approaches that are based on the performance of individual models (individual performance weighting) and approaches that are based on the performance of the weighted ensemble as a whole (ensemble performance weighting). At the same time, we formulate both in probabilistic Bayesian terms to make their application and comparison straightforward. Using simple constructed examples, we demonstrate that the ensemble performance weighting approach implicitly accounts for co-dependencies among models, which arguably makes the computation of independence weights for the purpose of model weighting obsolete. We also show that a set of weighted models within the ensemble weighting approach will naturally tend to artificially reduce uncertainty and that this is strongly influenced by the choice of the prior distribution over weight vectors. The distinction between individual and ensemble performance weighting is both methodological and conceptual. Formulating both approaches in general probabilistic Bayesian terms as done here, can serve as a common basis for future developments with regard to ensemble model weighting in Earth system science.