Climatic Change

, Volume 149, Issue 2, pp 247–260 | Cite as

Towards Bayesian hierarchical inference of equilibrium climate sensitivity from a combination of CMIP5 climate models and observational data

  • Alexandra Jonko
  • Nathan M. Urban
  • Balu Nadiga


Despite decades of research, large multi-model uncertainty remains about the Earth’s equilibrium climate sensitivity to carbon dioxide forcing as inferred from state-of-the-art Earth system models (ESMs). Statistical treatments of multi-model uncertainties are often limited to simple ESM averaging approaches. Sometimes models are weighted by how well they reproduce historical climate observations. Here, we propose a novel approach to multi-model combination and uncertainty quantification. Rather than averaging a discrete set of models, our approach samples from a continuous distribution over a reduced space of simple model parameters. We fit the free parameters of a reduced-order climate model to the output of each member of the multi-model ensemble. The reduced-order parameter estimates are then combined using a hierarchical Bayesian statistical model. The result is a multi-model distribution of reduced-model parameters, including climate sensitivity. In effect, the multi-model uncertainty problem within an ensemble of ESMs is converted to a parametric uncertainty problem within a reduced model. The multi-model distribution can then be updated with observational data, combining two independent lines of evidence. We apply this approach to 24 model simulations of global surface temperature and net top-of-atmosphere radiation response to abrupt quadrupling of carbon dioxide, and four historical temperature data sets. Our reduced order model is a 2-layer energy balance model. We present probability distributions of climate sensitivity based on (1) the multi-model ensemble alone and (2) the multi-model ensemble and observations.



This research was supported by the U.S. Department of Energy (DOE) Office of Science (Biological and Environmental Research), Early Career Research program. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modeling, responsible for CMIP, and thank the climate modeling groups for producing and making available their model output. For CMIP, the DOE Program for Climate Model Diagnosis and Intercomparison (PCMDI) provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The data and code used in this analysis can be made available upon request. Please direct requests to the corresponding author.

Supplementary material

10584_2018_2232_MOESM1_ESM.docx (10.7 mb)
ESM 1 (DOCX 10983 kb)


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Earth and Environmental Sciences DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Computer, Computational and Statistical Sciences DivisionLos Alamos National LaboratoryLos AlamosUSA

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