Bayesian deconstruction of climate sensitivity estimates using simple models: implicit priors and the confusion of the inverse

Abstract. Observational constraints on the equilibrium climate sensitivity have been generated in a variety of ways, but a number of results have been calculated which appear to be based on somewhat informal heuristics. In this paper we demonstrate that many of these estimates can be reinterpreted within the standard subjective Bayesian framework in which a prior over the uncertain parameters is updated through a likelihood arising from observational evidence. We consider cases drawn from paleoclimate research, analyses of the historical warming record, and feedback analysis based on the regression of annual radiation balance observations for temperature. In each of these cases, the prior which was (under this new interpretation) implicitly used exhibits some unconventional and possibly undesirable properties. We present alternative calculations which use the same observational information to update a range of explicitly presented priors. Our calculations suggest that heuristic methods often generate reasonable results in that they agree fairly well with the explicitly Bayesian approach using a reasonable prior. However, we also find some significant differences and argue that the explicitly Bayesian approach is preferred, as it both clarifies the role of the prior and allows researchers to transparently test the sensitivity of their results to it.