Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

Equilibrium climate sensitivity (ECS)—the rise in global mean surface temperature (GMST) resulting from a doubling of atmospheric carbon dioxide (CO2) concentration, once the ocean has reached equilibrium—is a key climate system parameter. Effective radiative forcing (ERF) provides a metric, designed to be a good indicator of their impact on GMST, of the effects on the Earth’s radiative imbalance of changes in CO2, in other radiatively-active gases and in other drivers of climate change. For changes between equilibrium states, ECS may then be estimated as the ratio of the change in GMST (ΔT) to the change (ΔFn) in ERF normalised by division by the ERF from a doubling of CO2 concentration: ECS = ΔT∕ΔFn. It has proved difficult to narrow uncertainty about ECS, given observational data limitations and internal climate system variability. It may be possible better to constrain ECS by combining probabilistic evidence from different sources. Several authors have sought to do so (Hegerl et al. 2006; Annan and Hargreaves 2006; Aldrin et al. 2012; Stevens et al. 2016) using subjective Bayesian methods, however their results were significantly influenced by Abstract Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators’ beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods— objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which