Climate Dynamics

, Volume 50, Issue 5–6, pp 2199–2216 | Cite as

Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

  • Nicholas LewisEmail author
  • Peter Grünwald


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 avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5–95% range for climate sensitivity of 1.1–4.05 K (median 1.87 K).


Climate sensitivity Combining evidence Objective Bayesian Profile likelihood Bayesian updating AR5 



We thank Marcel Crok and Tore Schweder for bringing us together; Paul Kirwan, Tore Schweder and an anonymous reviewer for helpful comments that improved the manuscript and Oliver Browne for supplying PDF data underlying AR5 Fig. 10.20b. Peter Grünwald was supported by an NWO VICI Grant. NWO is the Netherlands foundation for scientific research.

Supplementary material

382_2017_3744_MOESM1_ESM.pdf (364 kb)
Supplementary material 1 (PDF 363 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.BathUK
  2. 2.CWI Amsterdam and Leiden UniversityAmsterdamThe Netherlands

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