Towards rigorous mathematical approaches for forecast generation and uncertainty characterization using multi-model ensembles of climate

The Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) used multiple Atmosphere Ocean General Circulation Models (AOGCMs) for generating climate projections into the future. An underlying assumption driving the use of Multi-Model Ensembles (MMEs) is that AOGCMs have orthogonal skills. However, several AOGCMs share the same numerical schemes, parameters and even software components, therefore, correlated error patterns may be expected. Here we propose two novel MMEs-based approaches for forecast generation and uncertainty quantification. First, we propose a methodology based on the Proper Orthogonal Decomposition (POD). Second, we propose a predictive Bayesian mathematical framework for uncertainty quantification, which relies on a multitude of evidences, which in turn does not require prior knowledge of the uncertainty of each model within the MMEs. These two approaches are demonstrated using grid-based global mean temperature change projections from four AOGCM simulations and three Reanalysis datasets which are used as proxies for observations.