DOI: 10.1594/pangaea.855449
title: Model-based changes in global annual mean surface temperature change (Delta T_g) and radiative forcing due to land ice albedo changes (Delta R_[LI]) over the last 5 Myr, supplementary material

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: With an inverse climate model setup, that include 3D-ice sheet models, the benthic d18O global stack LR04 of the last 5 Myr (Lisiecki and Raymo, 2005, doi:10.1029/2004PA001071) was in a previous study (de Boer et al., 2014, doi:10.1038/ncomms3999) deconvolved into a temperature component and a sea level (ice sheet) component. The calculated changes in land ice area (as function of time and latitude) combined with incoming solar radiation (Laskar et al., 2004, doi:10.1051/0004-6361:20041335) and a simplified energy balance scheme (Köhler et al., 2010, doi:10.1016/j.quascirev.2009.09.026) are used to calculate changes in radiative forcing due to land ice albedo changes (Delta R_[LI]) over the last 5 Myr (changes normalized to global changes in radiative forcing, units: W/m^2). Three different assumptions on polar amplification are then used to calculate out of the model-based changes in temperature over the northern hemispheric land ice sheets (related to deep ocean temperature and derived from the deconvolution of the LR04 d18O stack) three different estimates of changes in global annual mean surface temperature.
description: Supplement to: Köhler, Peter; de Boer, Bas; von der Heydt, Anna S; Stap, Lennert Bastiaan; van de Wal, Roderik S W (2015): On the state dependency of the equilibrium climate sensitivity during the last 5 million years. Climate of the Past, 11(12), 1801-1823