A Bayesian approach to climate model evaluation and multi‐model averaging with an application to global mean surface temperatures from IPCC AR4 coupled climate models

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Abstract
A Bayesian approach is introduced to model evaluation and multi‐model averaging with a systematic consideration of model uncertainty, and its application to global mean surface air temperature (SAT) changes is shown from multi‐AOGCM ensembles of IPCC AR4 simulations. The Bayes factor or likelihood ratio of each model to the reference model (where mean is identical to the observation) provides a skill ranging from 0 to 1. Four categories of model skill are derived on the basis of the previous studies. Legendre series expansions are used to get a temporally refined model evaluation, which allow efficient analyses of time mean (scale) and linear trend. Application results show that all AOGCMs with natural plus anthropogenic forcing can simulate well the scale and trend of observed global mean SAT changes over the 20th century and its first and second halves. However, more than 50% of the models with anthropogenic‐only forcing cannot reproduce the observed warming reasonably. This indicates the important role of natural forcing although other factors like different climate sensitivity, forcing uncertainty, and a climate drift might be responsible for the discrepancy in anthropogenic‐only models. Besides, Bayesian and conventional skill comparisons demonstrate that a skill‐weighted average with the Bayes factors (Bayesian model averaging, BMA) overwhelms the arithmetic ensemble mean and three other weighted averages based on conventional statistics, illuminating future applicability of BMA to climate predictions.