A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

Abstract

Abstract. In this paper we introduce a Bayesian framework, which is explicit about 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 (0.6–5.2, 5th–95th percentiles) using the PMIP2, PMIP3, and PMIP4 datasets for the LGM and 2.3 K (0.5–4.4) with the PlioMIP1 and PlioMIP2 datasets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (0.7–5.2) using the LGM and 2.3 K (0.4–4.5) 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 tighter constraint of 2.5 K (0.8–4.0) using the restricted ensemble. 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 K and only exceeding 6 K in a single and most uncertain case assuming a large structural uncertainty. 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, an artefact due to a flatter regression line in the case of lack of correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation for their potential use in future probabilistic estimations of climate sensitivity.

PMIP4 experiments using MIROC-ES2L Earth system model

“…The temperature anomaly of LGM relative to PI over the tropics is negative and there is general quantitative agreement between the anomaly derived from the model and that from proxy data (Bartlein et al, 2011;MARGO project members et al, 2009). This could be useful in constraining future projections, given that Annan and Hargreaves (2006) and Renoult et al (2020) revealed the correlation between tropical cooling at LGM and ECS. It has been pointed out in Stocker et al (2013) Fifth Assessment Report that the cooling over Greenland during the LGM relative to PI is underestimated in the models.…”

“…As LGM cooling relative to the pre-industrial (PI) experiment over the tropics is at a comparable level to equilibrium climate sensitivity (ECS), LGM modeling can provide useful information to constrain climate sensitivity for projections of future climate (Annan and Hargreaves, 2006;Renoult et al, 2020). Intercomparison studies of proxy-based reconstructions of climate variables and model output continue to be conducted (Braconnot et al, 2007;Bartlein et al, 2011;Kageyama et al, 2020).…”

“…The interglacial periods of 6000 and 127 000 years before present were characterized by differences in solar radiation at the top of the atmosphere caused by orbital states that were different from those of the present day (Brierley et al, 2020;Otto-Bliesner et al, 2021), resulting in seasonalities that were different from the PI period (1850 CE). As it was in the recent past and because various paleo-proxy records are available (Ritchie et al, 1985;Drake et al, 2011;Hely et al, 2014;Tierney et al, 2013Tierney et al, , 2017, the interglacial period of 6000 years before present was the only interglacial included in earlier phases of PMIP (Braconnot et al, 2007;Abe-Ouchi, 2007, 2009;Ohgaito et al, 2013). Following efforts to collect paleo-proxy data (Otto-Bliesner and Brady, 2001;Lunt et al, 2013;Capron et al, 2014Capron et al, , 2017, it is now also possible to conduct the same experiment for 127 000 years before present; experiments on this interglacial period have the advantage of strong seasonality in the Northern Hemisphere (NH).…”

Emergent constraints on equilibrium climate sensitivity in CMIP5: do they hold for CMIP6?

“…For all emergent constraints, we use the historical simulations of CMIP5 and CMIP6 in order to ensure maximum agreement with the observational data. If necessary, the historical simulation of CMIP5 is extended after its final year 2005 with data from the RCP8.5 scenario (Riahi et al, 2011). Note that we only use data through 2014, during which time all RCP scenarios behave similarly and the choice of the scenario is not expected to affect results considerably.…”

“…Similar to many other emergent constraint studies, we use an ordinary least-squares linear regression model for each emergent constraint. However, in some cases this might not be appropriate, e.g., when we expect nonlinear behavior or when physical constraints can be used to derive further constraints for the regression model like a zero intercept (Annan et al, 2020; Jimenez-de-la-Cuesta and Renoult et al, 2020).…”