Description: It is still an open question how equilibrium warming in response to increasing radiative forcing – the specific equilibrium climate sensitivity S – depends on background climate. We here present palaeodata-based evidence on the state dependency of S, by using CO2 proxy data together with a 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo radiative forcing was a linear function of sea level change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and sea level. In our set-up, in which the radiative forcing of CO2 and of the land ice albedo (LI) is combined, we find a state dependence in the calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last 2.1 Myr). During Pleistocene intermediate glaciated climates and interglacial periods, S[CO2,LI] is on average ~ 45 % larger than during Pleistocene full glacial conditions. In the Pliocene part of our analysis (2.6–5 Myr BP) the CO2 data uncertainties prevent a well-supported calculation for S[CO2,LI], but our analysis suggests that during times without a large land ice area in the Northern Hemisphere (e.g. before 2.82 Myr BP), the specific equilibrium climate sensitivity, S[CO2,LI], was smaller than during interglacials of the Pleistocene. We thus find support for a previously proposed state change in the climate system with the widespread appearance of northern hemispheric ice sheets. This study points for the first time to a so far overlooked non-linearity in the land ice albedo radiative forcing, which is important for similar palaeodata-based approaches to calculate climate sensitivity. However, the implications of this study for a suggested warming under CO2 doubling are not yet entirely clear since the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet simulations and global temperature reconstructions are large.

Description: Past warm periods provide an opportunity to evaluate climate models under extreme forcing scenarios, in particular high ( 〉  800 ppmv) atmospheric CO2 concentrations. Although a post hoc intercomparison of Eocene ( ∼  50  Ma) climate model simulations and geological data has been carried out previously, models of past high-CO2 periods have never been evaluated in a consistent framework. Here, we present an experimental design for climate model simulations of three warm periods within the early Eocene and the latest Paleocene (the EECO, PETM, and pre-PETM). Together with the CMIP6 pre-industrial control and abrupt 4 ×  CO2 simulations, and additional sensitivity studies, these form the first phase of DeepMIP – the Deep-time Model Intercomparison Project, itself a group within the wider Paleoclimate Modelling Intercomparison Project (PMIP). The experimental design specifies and provides guidance on boundary conditions associated with palaeogeography, greenhouse gases, astronomical configuration, solar constant, land surface processes, and aerosols. Initial conditions, simulation length, and output variables are also specified. Finally, we explain how the geological data sets, which will be used to evaluate the simulations, will be developed.

Description: Over the last decade, our understanding of cli- mate sensitivity has improved considerably. The climate system shows variability on many timescales, is subject to non-stationary forcing and it is most likely out of equi- librium with the changes in the radiative forcing. Slow and fast feedbacks complicate the interpretation of geolog- ical records as feedback strengths vary over time. In the geological past, the forcing timescales were different than at present, suggesting that the response may have behaved differently. Do these insights constrain the climate sensitiv- ity relevant for the present day? In this paper, we review the progress made in theoretical understanding of climate sensitivity and on the estimation of climate sensitivity from proxy records. Particular focus lies on the background state dependence of feedback processes and on the impact of tipping points on the climate system. We suggest how to further use palaeo data to advance our understanding of the currently ongoing climate change.

Description: The evidence from both data and models indicates that specific equilibrium climate sensitivity S[X]—the global annual mean surface temperature change (ΔTg) as a response to a change in radiative forcing X (ΔR[X])—is state dependent. Such a state dependency implies that the best fit in the scatterplot of ΔTg versus ΔR[X] is not a linear regression but can be some nonlinear or even nonsmooth function. While for the conventional linear case the slope (gradient) of the regression is correctly interpreted as the specific equilibrium climate sensitivity S[X], the interpretation is not straightforward in the nonlinear case. We here explain how such a state-dependent scatterplot needs to be interpreted and provide a theoretical understanding—or generalization—how to quantify S[X] in the nonlinear case. Finally, from data covering the last 2.1 Myr we show that—due to state dependency—the specific equilibrium climate sensitivity which considers radiative forcing of CO2 and land ice sheet (LI) albedo, math formula, is larger during interglacial states than during glacial conditions by more than a factor 2.

Description: Climate sensitivity represents the global mean temperature change caused by changes in the radiative balance of climate; it is studied for both present/future (actuo) and past (paleo) climate variations, with the former based on instrumental records and/or various types of model simulations. Paleo-estimates are often considered informative for assessments of actuo-climate change caused by anthropogenic greenhouse forcing, but this utility remains debated because of concerns about the impacts of uncertainties, assumptions, and incomplete knowledge about controlling mechanisms in the dynamic climate system, with its multiple interacting feedbacks and their potential dependence on the climate background state. This is exacerbated by the need to assess actuo- and paleoclimate sensitivity over different timescales, with different drivers, and with different (data and/or model) limitations. Here, we visualize these impacts with idealized representations that graphically illustrate the nature of time-dependent actuo- and paleoclimate sensitivity estimates, evaluating the strengths, weaknesses, agreements, and differences of the two approaches. We also highlight priorities for future research to improve the use of paleo-estimates in evaluations of current climate change.

Description: It is still an open question how equilibrium warming in response to increasing radiative forcing – the specific equilibrium climate sensitivity S – depends on background climate. We here present palaeodata-based evidence on the state dependency of S, by using CO2 proxy data together with a 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. This nonlinearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo radiative forcing was a linear function of sea level change. The latitudinal dependency of icesheet area changes is important for the non-linearity between land ice albedo and sea level. In our set-up, in which the radiative forcing of CO2 and of the land ice albedo (LI) is combined, we find a state dependence in the calculated specific equilibrium climate sensitivity, STCO2,LIU, for most of the Pleistocene (last 2.1 Myr). During Pleistocene intermediate glaciated climates and interglacial periods, STCO2,LIU is on average � 45% larger than during Pleistocene full glacial conditions. In the Pliocene part of our analysis (2.6–5 MyrBP) the CO2 data uncertainties prevent a well-supported calculation for STCO2,LIU, but our analysis suggests that during times without a large land ice area in the Northern Hemisphere (e.g. before 2.82 MyrBP), the specific equilibrium climate sensitivity, STCO2,LIU, was smaller than during interglacials of the Pleistocene. We thus find support for a previously proposed state change in the climate system with the widespread appearance of northern hemispheric ice sheets. This study points for the first time to a so far overlooked non-linearity in the land ice albedo radiative forcing, which is important for similar palaeodata-based approaches to calculate climate sensitivity. However, the implications of this study for a suggested warming under CO2 doubling are not yet entirely clear since the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet simulations and global temperature reconstructions are large.