A Bayesian approach to climate model evaluation and multi-model averaging

A Bayesian approach is introduced to model evaluation and multi-model averaging with a systematic consideration of model uncertainty and its application to multi-AOGCM ensembles of 20C3M simulations is shown using global mean surface air temperature (SAT) changes. The Bayes factor or likelihood ratio of each ensemble member to the perfect model (defined as the observation) provides a skill ranging from 0 to 1. Four categories based on the previous studies are derived. Legendre series expansions are used to get a temporally refined model evaluation, which allow analyses of overall warming (scale), linear trend, and decadal variations. Application results show that most models can simulate well the scale and trend of observed global mean SAT changes over the 20th century, but that about 20 % models cannot reproduce the observed early warming near 1940s. Skill comparisons of global mean SAT demonstrate that Bayesian model averaging (BMA), a skill-weighted average with the Bayes factors, always overwhelms the arithmetic ensemble mean and three weighted averages based on conventional statistics, illuminating its future applicability to climate predictions.