Abstract
<p>In this study we introduce a Bayesian framework, which is flexible and explicit about the prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on Ordinary Least Squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (1.1 - 4.8, 5 - 95 percentiles) using the PMIP2, PMIP3 and PMIP4 data sets for the LGM, and 2.4 K (0.4 - 5.0) with the PlioMIP1 and PlioMIP2 data sets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (1.1 - 4.3) using the LGM and  2.4 K (0.4 - 5.1) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a slightly tighter constraint of 2.6 K (1.1 - 3.9). We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95% probability of climate sensitivity mostly below 5 and never exceeding 6 K. The approach is compared with other approaches based on OLS, a Kalman filter method and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, suggesting a higher bound by construction in case of weaker correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation of their potential use in future probabilistic estimation of climate sensitivity.</p>
Highlights
Researchers have identified a number of relationships between observational properties and a future climate change, which was not immediately obvious a priori but which exists across the ensemble of global climate models (GCMs) (Allen and Ingram, 2002; Hall and Qu, 2006; Boé et al, 2009; Cox et al, 2018) participating in the Climate Model Intercomparison Project (CMIP)
We focus on the relationship between equilibrium climate sensitivity, defined here as S, and the temperature change in the tropics which is observed at the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period, defined as Ttropical
To compare with our previous analysis, we investigate the effect of the model inadequacy using the dataset of PMIP2 and PMIP3 combined for the case of the LGM and the dataset of PlioMIP1 for the case of the mid-Pliocene Warm Period (mPWP)
Summary
Researchers have identified a number of relationships between observational properties and a future climate change, which was not immediately obvious a priori but which exists across the ensemble of global climate models (GCMs) (Allen and Ingram, 2002; Hall and Qu, 2006; Boé et al, 2009; Cox et al, 2018) participating in the Climate Model Intercomparison Project (CMIP) These relationships are generally referred to as “emergent constraints” as they emerge from the ensemble behaviour as a whole rather than from explicit physical analysis. We present an alternative Bayesian linear regression approach in which the regression relationship is used as a likelihood model for the problem This allows the prior over the predictand to be defined separately from and entirely independently of the model ensemble and emergent constraint analysis.
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