Description: Some studies suggest that specific equilibrium climate sensitivity S might be state-dependent. Reanalyzing existing paleodata of global mean surface temperature ∆Tg and radiative forcing ∆R of CO2 and land ice albedo for the last 800,000 years we show that this state-dependency of S is only found if ∆Tg is based on reconstructions, and not when ∆Tg is based on model simulations. Furthermore, during times of decreasing obliquity (periods of land-ice sheet growth and sea level fall) the multi-millennial component of reconstructed ∆Tg is diverging from atmospheric CO2, while in simulations both variables vary more synchronously. For a reconstruction-based extrapolation of S to the future we eliminate these periods due to an expected sea level rise. Consequently, S determined from proxy-based reconstructions without these data with strong ∆Tg-CO2 divergence is less state-dependent or even constant (state-independent), and yields into an equilibrium warming for 2 × CO2 of 1.9–3.8 K.

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: We reanalyze existing paleodata of global mean surface temperature ΔTg and radiative forcing ΔR of CO2 and land ice albedo for the last 800,000 years to show that a state‐dependency in paleoclimate sensitivity S, as previously suggested, is only found if ΔTg is based on reconstructions, and not when ΔTg is based on model simulations. Furthermore, during times of decreasing obliquity (periods of land ice sheet growth and sea level fall) the multimillennial component of reconstructed ΔTg diverges from CO2, while in simulations both variables vary more synchronously, suggesting that the differences during these times are due to relatively low rates of simulated land ice growth and associated cooling. To produce a reconstruction‐based extrapolation of S for the future, we exclude intervals with strong ΔTg‐CO2 divergence and find that S is less state‐dependent, or even constant state‐independent), yielding a mean equilibrium warming of 2–4 K for a doubling of CO2.

Description: Since the inception of the Antarctic ice sheet at the Eocene–Oligocene transition (∼ 34 Myr ago), land ice has played a crucial role in Earth's climate. Through feedbacks in the climate system, land ice variability modifies atmospheric temperature changes induced by orbital, topographical, and greenhouse gas variations. Quantification of these feedbacks on long timescales has hitherto scarcely been undertaken. In this study, we use a zonally averaged energy balance climate model bidirectionally coupled to a one-dimensional ice sheet model, capturing the ice–albedo and surface–height–temperature feedbacks. Potentially important transient changes in topographic boundary conditions by tectonics and erosion are not taken into account but are briefly discussed. The relative simplicity of the coupled model allows us to perform integrations over the past 38 Myr in a fully transient fashion using a benthic oxygen isotope record as forcing to inversely simulate CO2. Firstly, we find that the results of the simulations over the past 5 Myr are dependent on whether the model run is started at 5 or 38 Myr ago. This is because the relation between CO2 and temperature is subject to hysteresis. When the climate cools from very high CO2 levels, as in the longer transient 38 Myr run, temperatures in the lower CO2 range of the past 5 Myr are higher than when the climate is initialised at low temperatures. Consequently, the modelled CO2 concentrations depend on the initial state. Taking the realistic warm initialisation into account, we come to a best estimate of CO2, temperature, ice-volume-equivalent sea level, and benthic δ18O over the past 38 Myr. Secondly, we study the influence of ice sheets on the evolution of global temperature and polar amplification by comparing runs with ice sheet–climate interaction switched on and off. By passing only albedo or surface height changes to the climate model, we can distinguish the separate effects of the ice–albedo and surface–height–temperature feedbacks. We find that ice volume variability has a strong enhancing effect on atmospheric temperature changes, particularly in the regions where the ice sheets are located. As a result, polar amplification in the Northern Hemisphere decreases towards warmer climates as there is little land ice left to melt. Conversely, decay of the Antarctic ice sheet increases polar amplification in the Southern Hemisphere in the high-CO2 regime. Our results also show that in cooler climates than the pre-industrial, the ice–albedo feedback predominates the surface–height–temperature feedback, while in warmer climates they are more equal in strength.

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.