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\begin{document}

\title{Combining Emergent Constraints for Climate Sensitivity}



\author[1]{Christopher Bretherton}%
\author[2]{Peter Caldwell}%
\affil[1]{University of Washington and Vulcan Inc.}%
\affil[2]{Lawrence Livermore National Laboratories}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
A method is proposed for combining information from several emergent
constraints into a probabilistic estimate for a climate sensitivity
proxy \$Y\$ such as equilibrium climate sensitivity (ECS) or the climate
feedback parameter \$\textbackslash{}lambda\$. The method is based on
fitting a multivariate Gaussian PDF for \$Y\$ and the emergent
constraints using an ensemble of global climate models (GCMs). For a
single perfectly-observed constraint \$X\$, it reduces to a linear
regression-based estimate of \$Y\$. The method accounts for
uncertainties in sampling this multidimensional PDF with a small number
of models, for observational uncertainties in the constraints, and for
overconfidence about the correlation of the constraints with the climate
sensitivity. Two methods are presented. Method C accounts for
correlations between emergent constraints but can fail if some
constraints are too strongly related. Method U assumes constraints are
uncorrelated except through their mutual relationship to the climate
proxy; it is robust to small GCM sample size and is appealingly
interpretable. These methods are applied to ECS and
\$\textbackslash{}lambda\$ using a previously-published set of 11
possible emergent constraints derived from climate models in the Coupled
Model Intercomparison Project (CMIP). This study corroborates and
quantifies past findings that most constraints predict higher climate
sensitivity than the CMIP mean. The
\$\textbackslash{}pm2\textbackslash{}sigma\$ posterior range of ECS for
Method C with no overconfidence adjustment is \$4.1 \textbackslash{}pm
0.8\$ K. For Method U with a large overconfidence adjustment, it is
\$4.0 \textbackslash{}pm 1.3\$ K.%
\end{abstract}%



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