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.

Circum-Arctic glacial ice is melting in an unprecedented mode, and release of currently trapped geological methane may act as a positive feedback on ice-sheet retreat during global warming. Evidence for methane release during the penultimate (Eemian, ca. 125 ka) interglacial, a period with less glacial sea ice and higher temperatures than today, is currently absent. Here, we argue that based on foraminiferal isotope studies on drill holes from offshore Svalbard, Norway, methane leakage occurred upon the abrupt Eurasian ice-sheet wastage during terminations of the last (Weichselian) and penultimate (Saalian) glaciations. Progressive increase of methane emissions seems to be first recorded by depleted benthic foraminiferal δ13C. This is quickly followed by the precipitation of methane-derived authigenic carbonate as overgrowth inside and outside foraminiferal shells, characterized by heavy δ18O and depleted δ13C of both benthic and planktonic foraminifera. The similarities between the events observed over both terminations advocate for a common driver for the episodic release of geological methane stocks. Our favored model is recurrent leakage of shallow gas reservoirs below the gas hydrate stability zone along the margin of western Svalbard that can be reactivated upon initial instability of the grounded, marine-based ice sheets. Analogous to this model, with the current acceleration of the Greenland ice melt, instabilities of existing methane reservoirs below and nearby the ice sheet are likely.

Abstract. 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.

Abstract. In this paper 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>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>

<p>In recent years, simulations of the Paleoclimate Modelling Intercomparison Project (PMIP) of the cold Last Glacial Maximum (LGM) and the warm mid-Pliocene have been used to constrain the equilibrium climate sensitivity (ECS) in an emergent constraint framework. The constraint on ECS arising from Pliocene temperatures is surprisingly robust, as opposed to that based on LGM temperatures.<span class="Apple-converted-space"> </span>Nevertheless, observational uncertainties on proxy data from the Pliocene are large, in particular at high latitudes. We analyse the sensitivity of the Pliocene-based emergent constraint on ECS to different reconstructions as to verify if the well-constrained ECS is sensitive to the proxy data. We also investigate the boundary conditions of the Pliocene to identify key structural elements which may weaken the emergent constraint relationship. We show that the wider range of ECS in models simulating the Pliocene, as well as numerous sensitivity experiments, is a great advantage for the emergent constraint approach.</p>

<p>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 CO<sub>2</sub> 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 CO<sub>2</sub> 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.</p>

Abstract. 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 contribute to the spread of the model ensemble. Certain factors have 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. Finally, we show that the lack of high or low ECS models in the ensembles critically limits the strength and reliability of the emergent constraints.