A Bayesian Assessment of Climate Change Using Multimodel Ensembles. Part I: Global Mean Surface Temperature

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Abstract
A Bayesian approach is applied to the observed global surface air temperature (SAT) changes using multimodel ensembles (MMEs) of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) simulations and single-model ensembles (SMEs) with the ECHO-G coupled climate model. A Bayesian decision method is used as a tool for classifying observations into given scenarios (or hypotheses). The prior probability of the scenarios, which represents a degree of subjective belief in the scenarios, is changed into the posterior probability through the likelihood where observations enter, and the posterior is used as a decision function. In the identical prior case the Bayes factor (or likelihood ratio) becomes a decision function and provides observational evidence for each scenario against a predefined reference scenario. Four scenarios are used to explain observed SAT changes: “CTL” (control or no change), “Nat” (natural forcing induced change), “GHG” (greenhouse gas–induced change), and “All” (natural plus anthropogenic forcing–induced change). Observed and simulated global mean SATs are decomposed into temporal components of overall mean, linear trend, and decadal variabilities through Legendre series expansions, coefficients of which are used as detection variables. Parameters (means and covariance matrices) needed to define the four scenarios are estimated from SMEs or MMEs. Taking the CTL scenario as reference one, application results for global mean SAT changes for the whole twentieth century (1900–99) show “decisive” evidence (logarithm of Bayes factor >5) for the All scenario only. While “strong” evidence (log of Bayes factor >2.5) for both the Nat and All scenarios are found in SAT changes for the first half (1900–49), there is decisive evidence for the All scenario for SAT changes in the second half (1950–99), supporting previous results. It is demonstrated that the Bayesian decision results for global mean SATs are largely insensitive to both intermodel uncertainties and prior probabilities.