Bayesian Modeling of Uncertainty in Ensembles of Climate Models

Projections of future climate change caused by increasing greenhouse gases depend critically on numerical climate models coupling the ocean and atmosphere (GCMs). However, different models differ substantially in their projections, which raises the question of how the different models can best be combined into a probability distribution of future climate change. For this analysis, we have collected both current and future projected mean temperatures produced by nine climate models for 22 regions of the earth. We also have estimates of current mean temperatures from actual observations, together with standard errors, that can be used to calibrate the climate models. We propose a Bayesian analysis that allows us to combine the different climate models into a posterior distribution of future temperature increase, for each of the 22 regions, while allowing for the different climate models to have different variances. Two versions of the analysis are proposed, a univariate analysis in which each region is analyzed separately, and a multivariate analysis in which the 22 regions are combined into an overall statistical model. A cross-validation approach is proposed to confirm the reasonableness of our Bayesian predictive distributions. The results of this analysis allow for a quantification of the uncertainty of climate model projections as a Bayesian posterior distribution, substantially extending previous approaches to uncertainty in climate models. ∗Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260 †National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307