Description: Model output of the intermediate complexity climate model CLIMBER-2 over the past 5 million years. The simulations were forced with insolation data (O), insolation and land ice data (OI), insolation and carbon dioxide data (OC) and with insolation, land ice and carbon dioxide data (OIC). Sheet 1 contains the main results: northern hemispheric (30-90 deg N), southern hemispheric (30-90 deg S) and global temperatures. Sheet 2 contains the land ice and carbon dioxide forcing in terms of globally averaged radiative forcing. Details are given in the publication. More information or data can be obtained by contacting L.B. Stap (lennert.stap@awi.de).

Description: We present ice thickness and bedrock height from simulations of the Miocene Antarctic ice sheet (AIS), using the 3D thermodynamical Parallel Ice Sheet Model (PISM) version 0.7.3. The applied climate forcing consists of temperature and precipitation anomalies with respect to a preindustrial reference simulation, obtained from simulations using the atmosphere-ocean general circulation model COSMOS. These anomalies are added to an ERA-40/WOD-09 base climate. COSMOS was run using preindustrial settings, and Miocene settings with CO2 levels of 278 ppm (low), 450 ppm (medium), and 600 ppm (high). The steady state simulations using PISM are started with present-day bedrock conditions, with a present-day AIS (Bedmap2), and isostatically rebounded after removal of the ice. Additional simulations are started with the Wilson et al. (2012) late-Eocene bedrock topography reconstruction. The steady state simulations are conducted by applying the same climate forcing over 200 kyr. The transient simulations are performed by using an index method to interpolate between different forcing climate states. In these runs, the forcing climate state is gradually varied over quasi-orbital timescales of 400 kyr, 40 kyr, 1600 kyr, or 200 kyr. Details are given in the accompanying publication. For more information or data, please contact L.B. Stap mailto:lstap@awi.de. Dataset 2019_Stap_steadystate_startfrom_presentdayAIS.nc contains the data to plot Fig. 1. Dataset 2019_Stap_PISM_transient.xlsx contains the data to plot Fig. 2 and 3. Datasets 2019_Stap_steadystate_startfrom_noice.nc and 2019_Stap_steadystate_startfrom_Wilson_noice.nc contain additional data plotted in Fig. 2 and 3.

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: We present results from ice volume simulations, performed using a conceptual model of transient ice volume variability. This model is based on the notion that at any level of a control parameter (C), in our case a CO2-index, an ice sheet will grow or shrink towards an equilibrium state (Veq). Details are given in the accompanying publication. For more information or data, please contact the authors. Dataset 2020_Stap_data_pism.xlsx contains the results from the simulations using the input C-Veq relation, and growth and decay rates, which mimic Miocene Antarctic ice sheet results obtained using the 3D thermodynamical ice sheet model PISM. Dataset 2020_Stap_data_linear.xlsx contains the results from the simulations using the simple linear C-Veq relation and growth and decay rates specified per experiment. Dataset 2020_Stap_data_hysteresis.xlsx contains the results from the simulations using the piecewise linear C-Veq relation with hysteresis, and growth and decay rates specified per experiment, which are discussed in the Appendix of the accompanying publication.

Description: Model output of a coupled ice sheet-climate model, inversely forced by benthic d18O over the past 38 million years. Sheet 1 contains the main results from the reference simulation: benthic d18O, CO2, ice-volume-equivalent sea level and global temperature. Sheet 2 contains global, Northern Hemisphere (40-80 deg N), and Antarctic (60-90 deg S) temperatures, from the reference run and the run with ice uncoupled, only albedo coupled, and only surface height coupled. Sheet 3 contains global temperature, from the reference run, and the runs with fixed PD ice, fixed LGM ice, and no ice. Details are given in the publication. More information or data can be obtained by contacting L.B. Stap (lennert.stap@awi.de).

Description: During the past five million yrs, benthic d18O records indicate a large range of climates, from warmer than today during the Pliocene Warm Period to considerably colder during glacials. Antarctic ice cores have revealed Pleistocene glacial-interglacial CO2 variability of 60-100 ppm, while sea level fluctuations of typically 125 m are documented by proxy data. However, in the pre-ice core period, CO2 and sea level proxy data are scarce and there is disagreement between different proxies and different records of the same proxy. This hampers comprehensive understanding of the long-term relations between CO2, sea level and climate. Here, we drive a coupled climate-ice sheet model over the past five million years, inversely forced by a stacked benthic d18O record. We obtain continuous simulations of benthic d18O, sea level and CO2 that are mutually consistent. Our model shows CO2 concentrations of 300 to 470 ppm during the Early Pliocene. Furthermore, we simulate strong CO2 variability during the Pliocene and Early Pleistocene. These features are broadly supported by existing and new d11B-based proxy CO2 data, but less by alkenone-based records. The simulated concentrations and variations therein are larger than expected from global mean temperature changes. Our findings thus suggest a smaller Earth System Sensitivity than previously thought. This is explained by a more restricted role of land ice variability in the Pliocene. The largest uncertainty in our simulation arises from the mass balance formulation of East Antarctica, which governs the variability in sea level, but only modestly affects the modeled CO2 concentrations.

Description: We present results from simulations of the Miocene Antarctic ice sheet, that were performed using the 3D thermodynamical ice-sheet model IMAU-ICE (v1.1.1-MIO). Five steady-state present-day simulations were conducted for reference (PI_ref), and 12 experiments using Miocene settings. Each Miocene experiment comprises 11 steady-state and 4 transient simulations. In the README file, the experiments and simulations are listed. IMAU-ICE was run using a 40x40km grid covering the Antarctic continent. Initial conditions were obtained from reconstructions of the Antarctic bathymetry and bedrock topography pertaining to 23 to 24 million years (Myr) ago (dataset doi:10.1594/PANGAEA.923109). The simulations were forced by climate input data obtained from GENESIS simulations with varying CO2 levels (280 to 840 ppm) and Antarctic ice sheet cover (no ice to a large East-Antarctic ice sheet), and with present-day insolation. We utilized a matrix interpolation method to construct the time-varying climate forcing, based on the prescribed CO2 levels and ice cover simulated by IMAU-ICE. For each simulation, we provide the run script, 1D output variables including CO2 level and the sea level contribution of the Antarctic ice sheet, and 3D output variables including ice thickness, bedrock and surface height, surface mass balance, basal mass balance, ice velocities, and ice temperatures. For more information, please contact L.B. Stap at l.b.stap@uu.nl.

Description: We present basal melt rates for the ice shelves in equilibrium simulations of the Antarctic ice sheet (AIS), using the 3D thermodynamical Parallel Ice Sheet Model (PISM) version 1.1 with PICO as ocean component. The applied climate forcing consists of yearly mean present-day temperature and precipitation fields from RACMO2.3 (RACMO2 ANT27), and 400-800 m depth average ocean temperature and salinity, obtained from simulations using the atmosphere-ocean general circulation model COSMOS (ocean model MPIOM). COSMOS was run using pre-industrial settings (PID; 278 ppm CO2), settings from 40 kyr ago (40ka; 195 ppm CO2), and Last Glacial Maximum settings (LGM; 185 ppm CO2). All simulations are started with present-day bedrock conditions, and a present-day AIS size (Bedmap2). The steady state simulations are conducted by applying the same climate forcing over 200 kyr, after a thermodynamical spin-up (no mass changes) of 200,100 yr.