Description: 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.

Description: The Last Interglacial period (LIG) is a period with increased summer insolation at high northern latitudes, which results in strong changes in the terrestrial and marine cryosphere. Understanding the mechanisms for this response via climate modelling and comparing the models' representation of climate reconstructions is one of the objectives set up by the Paleoclimate Modelling Intercomparison Project for its contribution to the sixth phase of the Coupled Model Intercomparison Project. Here we analyse the results from 16 climate models in terms of Arctic sea ice. The multi-model mean reduction in minimum sea ice area from the pre industrial period (PI) to the LIG reaches 50 % (multi-model mean LIG area is 3.20×106 km2, compared to 6.46×106 km2 for the PI). On the other hand, there is little change for the maximum sea ice area (which is 15–16×106 km2 for both the PI and the LIG. To evaluate the model results we synthesise LIG sea ice data from marine cores collected in the Arctic Ocean, Nordic Seas and northern North Atlantic. The reconstructions for the northern North Atlantic show year-round ice-free conditions, and most models yield results in agreement with these reconstructions. Model–data disagreement appear for the sites in the Nordic Seas close to Greenland and at the edge of the Arctic Ocean. The northernmost site with good chronology, for which a sea ice concentration larger than 75 % is reconstructed even in summer, discriminates those models which simulate too little sea ice. However, the remaining models appear to simulate too much sea ice over the two sites south of the northernmost one, for which the reconstructed sea ice cover is seasonal. Hence models either underestimate or overestimate sea ice cover for the LIG, and their bias does not appear to be related to their bias for the pre-industrial period. Drivers for the inter-model differences are different phasing of the up and down short-wave anomalies over the Arctic Ocean, which are associated with differences in model albedo; possible cloud property differences, in terms of optical depth; and LIG ocean circulation changes which occur for some, but not all, LIG simulations. Finally, we note that inter-comparisons between the LIG simulations and simulations for future climate with moderate (1 % yr−1) CO2 increase show a relationship between LIG sea ice and sea ice simulated under CO2 increase around the years of doubling CO2. The LIG may therefore yield insight into likely 21st century Arctic sea ice changes using these LIG simulations.

Description: In the Pliocene Model Intercomparison Project Phase 2 (PlioMIP2), coupled climate models have been used to simulate an interglacial climate during the mid-Piacenzian warm period (mPWP; 3.264 to 3.025 Ma). Here, we compare the Atlantic Meridional Overturning Circulation (AMOC), poleward ocean heat transport and sea surface warming in the Atlantic simulated with these models. In PlioMIP2, all models simulate an intensified mid-Pliocene AMOC. However, there is no consistent response in the simulated Atlantic ocean heat transport nor in the depth of the Atlantic overturning cell. The models show a large spread in the simulated AMOC maximum, the Atlantic ocean heat transport and the surface warming in the North Atlantic. Although a few models simulate a surface warming of ∼ 8–12 ∘C in the North Atlantic, similar to the reconstruction from Pliocene Research, Interpretation and Synoptic Mapping (PRISM) version 4, most models appear to underestimate this warming. The large model spread and model–data discrepancies in the PlioMIP2 ensemble do not support the hypothesis that an intensification of the AMOC, together with an increase in northward ocean heat transport, is the dominant mechanism for the mid-Pliocene warm climate over the North Atlantic.

Description: The Last Glacial Maximum (LGM, 21 000 years ago) is one of the suite of paleoclimate simulations included in the current phase of the Coupled Model Intercomparison Project (CMIP6). It is an interval when insolation was similar to the present, but global ice volume was at a maximum, eustatic sea level was at or close to a minimum, greenhouse gas concentrations were lower, atmospheric aerosol loadings were higher than today, and vegetation and land-surface characteristics were different from today. The LGM has been a focus for the Paleoclimate Modelling Intercomparison Project (PMIP) since its inception, and thus many of the problems that might be associated with simulating such a radically different climate are well documented. The LGM state provides an ideal case study for evaluating climate model performance because the changes in forcing and temperature between the LGM and pre-industrial are of the same order of magnitude as those projected for the end of the 21st century. Thus, the CMIP6 LGM experiment could provide additional information that can be used to constrain estimates of climate sensitivity. The design of the Tier 1 LGM experiment (lgm) includes an assessment of uncertainties in boundary conditions, in particular through the use of different reconstructions of the ice sheets and of the change in dust forcing. Additional (Tier 2) sensitivity experiments have been designed to quantify feedbacks associated with land-surface changes and aerosol loadings, and to isolate the role of individual forcings. Model analysis and evaluation will capitalize on the relative abundance of paleoenvironmental observations and quantitative climate reconstructions already available for the LGM.

Description: El Niño–Southern Oscillation (ENSO) is the strongest mode of interannual climate variability in the current climate, influencing ecosystems, agriculture, and weather systems across the globe, but future projections of ENSO frequency and amplitude remain highly uncertain. A comparison of changes in ENSO in a range of past and future climate simulations can provide insights into the sensitivity of ENSO to changes in the mean state, including changes in the seasonality of incoming solar radiation, global average temperatures, and spatial patterns of sea surface temperatures. As a comprehensive set of coupled model simulations is now available for both palaeoclimate time slices (the Last Glacial Maximum, mid-Holocene, and last interglacial) and idealised future warming scenarios (1 % per year CO2 increase, abrupt four-time CO2 increase), this allows a detailed evaluation of ENSO changes in this wide range of climates. Such a comparison can assist in constraining uncertainty in future projections, providing insights into model agreement and the sensitivity of ENSO to a range of factors. The majority of models simulate a consistent weakening of ENSO activity in the last interglacial and mid-Holocene experiments, and there is an ensemble mean reduction of variability in the western equatorial Pacific in the Last Glacial Maximum experiments. Changes in global temperature produce a weaker precipitation response to ENSO in the cold Last Glacial Maximum experiments and an enhanced precipitation response to ENSO in the warm increased CO2 experiments. No consistent relationship between changes in ENSO amplitude and annual cycle was identified across experiments.

Description: The mid-Holocene (6000 years ago) is a standard time period for the evaluation of the simulated response of global climate models using palaeoclimate reconstructions. The latest mid-Holocene simulations are a palaeoclimate entry card for the Palaeoclimate Model Intercomparison Project (PMIP4) component of the current phase of the Coupled Model Intercomparison Project (CMIP6) – hereafter referred to as PMIP4-CMIP6. Here we provide an initial analysis and evaluation of the results of the experiment for the mid-Holocene. We show that state-of-the-art models produce climate changes that are broadly consistent with theory and observations, including increased summer warming of the Northern Hemisphere and associated shifts in tropical rainfall. Many features of the PMIP4-CMIP6 simulations were present in the previous generation (PMIP3-CMIP5) of simulations. The PMIP4-CMIP6 ensemble for the mid-Holocene has a global mean temperature change of −0.3 K, which is −0.2 K cooler than the PMIP3-CMIP5 simulations predominantly as a result of the prescription of realistic greenhouse gas concentrations in PMIP4-CMIP6. Biases in the magnitude and the sign of regional responses identified in PMIP3-CMIP5, such as the amplification of the northern African monsoon, precipitation changes over Europe, and simulated aridity in mid-Eurasia, are still present in the PMIP4-CMIP6 simulations. Despite these issues, PMIP4-CMIP6 and the mid-Holocene provide an opportunity both for quantitative evaluation and derivation of emergent constraints on the hydrological cycle, feedback strength, and potentially climate sensitivity.

Description: The pre-industrial millennium is among the periods selected by the Paleoclimate Model Intercomparison Project (PMIP) for experiments contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6) and the fourth phase of the PMIP (PMIP4). The past1000 transient simulations serve to investigate the response to (mainly) natural forcing under background conditions not too different from today, and to discriminate between forced and internally generated variability on interannual to centennial timescales. This paper describes the motivation and the experimental set-ups for the PMIP4-CMIP6 past1000 simulations, and discusses the forcing agents orbital, solar, volcanic, and land use/land cover changes, and variations in greenhouse gas concentrations. The past1000 simulations covering the pre-industrial millennium from 850 Common Era (CE) to 1849 CE have to be complemented by historical simulations (1850 to 2014 CE) following the CMIP6 protocol. The external forcings for the past1000 experiments have been adapted to provide a seamless transition across these time periods. Protocols for the past1000 simulations have been divided into three tiers. A default forcing data set has been defined for the Tier 1 (the CMIP6 past1000) experiment. However, the PMIP community has maintained the flexibility to conduct coordinated sensitivity experiments to explore uncertainty in forcing reconstructions as well as parameter uncertainty in dedicated Tier 2 simulations. Additional experiments (Tier 3) are defined to foster collaborative model experiments focusing on the early instrumental period and to extend the temporal range and the scope of the simulations. This paper outlines current and future research foci and common analyses for collaborative work between the PMIP and the observational communities (reconstructions, instrumental data).

Description: Two interglacial epochs are included in the suite of Paleoclimate Modeling Intercomparison Project (PMIP4) simulations in the Coupled Model Intercomparison Project (CMIP6). The experimental protocols for simulations of the mid-Holocene (midHolocene, 6000 years before present) and the Last Interglacial (lig127k, 127 000 years before present) are described here. These equilibrium simulations are designed to examine the impact of changes in orbital forcing at times when atmospheric greenhouse gas levels were similar to those of the preindustrial period and the continental configurations were almost identical to modern ones. These simulations test our understanding of the interplay between radiative forcing and atmospheric circulation, and the connections among large-scale and regional climate changes giving rise to phenomena such as land–sea contrast and high-latitude amplification in temperature changes, and responses of the monsoons, as compared to today. They also provide an opportunity, through carefully designed additional sensitivity experiments, to quantify the strength of atmosphere, ocean, cryosphere, and land-surface feedbacks. Sensitivity experiments are proposed to investigate the role of freshwater forcing in triggering abrupt climate changes within interglacial epochs. These feedback experiments naturally lead to a focus on climate evolution during interglacial periods, which will be examined through transient experiments. Analyses of the sensitivity simulations will also focus on interactions between extratropical and tropical circulation, and the relationship between changes in mean climate state and climate variability on annual to multi-decadal timescales. The comparative abundance of paleoenvironmental data and of quantitative climate reconstructions for the Holocene and Last Interglacial make these two epochs ideal candidates for systematic evaluation of model performance, and such comparisons will shed new light on the importance of external feedbacks (e.g., vegetation, dust) and the ability of state-of-the-art models to simulate climate changes realistically.

Description: The Last Glacial Maximum (LGM, 21 000 years ago) is one of the suite of paleoclimate simulations included in the current phase of the Coupled Model Intercomparison Project (CMIP6). It is an interval when insolation was similar to the present, but global ice volume was at a maximum, eustatic sea level was at or close to a minimum, greenhouse gas concentrations were lower, atmospheric aerosol loadings were higher than today, and vegetation and land-surface characteristics were different from today. The LGM has been a focus for the Paleoclimate Modelling Intercomparison Project (PMIP) since its inception, and thus many of the problems that might be associated with simulating such a radically different climate are well documented. The LGM state provides an ideal case study for evaluating climate model performance because the changes in forcing and temperature between the LGM and pre-industrial are of the same order of magnitude as those projected for the end of the 21st century. Thus, the CMIP6 LGM experiment could provide additional information that can be used to constrain estimates of climate sensitivity. The design of the Tier 1 LGM experiment (lgm) includes an assessment of uncertainties in boundary conditions, in particular through the use of different reconstructions of the ice sheets and of the change in dust forcing. Additional (Tier 2) sensitivity experiments have been designed to quantify feedbacks associated with land-surface changes and aerosol loadings, and to isolate the role of individual forcings. Model analysis and evaluation will capitalize on the relative abundance of paleoenvironmental observations and quantitative climate reconstructions already available for the LGM.

Description: 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.