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 2.7K (0.6-5.2, 5th-95th percentiles) using the PMIP2, PMIP3, and PMIP4 datasets for the LGM and 2.3K (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 2.7K (0.7-5.2) using the LGM and 2.3K (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 2.5K (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 5K and only exceeding 6K 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.

The use of paleoclimates to constrain the equilibrium climate sensitivity (ECS) has seen a growing interest. In particular, the Last Glacial Maximum (LGM) and the mid-Pliocene warm period have been used in emergent-constraint approaches using simulations from the Paleoclimate Modelling Intercomparison Project (PMIP). Despite lower uncertainties regarding geological proxy data for the LGM in comparison with the Pliocene, the robustness of the emergent constraint between LGM temperature and ECS is weaker at both global and regional scales. Here, we investigate the climate of the LGM in models through different PMIP generations and how various factors in the atmosphere, ocean, land surface and cryosphere contribute to the spread of the model ensemble. Certain factors have a large impact on an emergent constraint, such as state dependency in climate feedbacks or model dependency on ice sheet forcing. Other factors, such as models being out of energetic balance and sea surface temperature not responding below −1.8^∘C in polar regions, have a limited influence. We quantify some of the contributions and find that they mostly have extratropical origins. Contrary to what has previously been suggested, from a statistical point of view, the PMIP model generations do not differ substantially. Moreover, we show that the lack of high- or low-ECS models in the ensembles critically limits the strength and reliability of the emergent constraints. Single-model ensembles may be promising tools for the future of LGM emergent constraint, as they permit a large range of ECS and reduce the noise from inter-model structural issues. Finally, we provide recommendations for a paleo-based emergent constraint and notably which paleoclimate is ideal for such an approach.

Geological evidences of a snowball Earth state show persistent tropical sea ice cover during the Cryogenian (720 - 635 million years ago). Current theory is that a strengthening of the positive surface albedo feedback with cooling temperatures, eventually exceeding the sum of all other feedbacks, leads to a global climate instability. Here we show that clouds accelerate the transition to a snowball Earth state and lowers the barrier to trigger the climate instability. Positive cloud feedbacks over tropical oceans and ahead of the sea-ice edge act to cool down the oceans and promote sea ice formation. We find that snowball Earth transitions occur around -15°C below pre-industrial levels, or slightly below the freezing point temperature, simultaneously with the sea ice edge advancing into the sub-tropics thereby strengthening the feedback. Several recent high sensitivity climate models have not been able to stably simulate the relatively warmer Last Glacial Maximum state, suggestive that they cool too strongly in response to a modest decrease in atmospheric carbon dioxide levels and therefore enter the snowball instability.

The warm Pliocene epoch is used to estimate Earth's equilibrium climate sensitivity (ECS), which is the long-term temperature change after a sustained doubling of atmospheric CO₂ over pre-industrial levels.Using an emergent constraint on the relationship between mid-Pliocene Warm Period simulated temperatures and ECS, we estimate ECS to be 4.8 K, which is higher than previous studies on the Pliocene. This is partly due to using warmer SST reconstruction than before; a consequence of focusing modelling efforts on the mid-Pliocene warm period. Using the temperatures of a broader period within the Pliocene, we quantify ECS to be 3.1 K. Further uncertainties on proxy data and data-model disagreements are expected to affect ECS estimates. We find that CO₂ uncertainties are the main driver of variations in ECS estimates, followed by biases from seasonal temperatures. The bias from polar amplification is apparently small, but could be an overlooked source of error. We conclude that the Pliocene-based emergent constraint is nonetheless robust and is likely to improve further as geological reconstructions improve.