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Since the inception of the Antarctic ice sheet at the\udEocene–Oligocene transition (∼ 34 Myr ago), land ice has\udplayed a crucial role in Earth's climate. Through feedbacks in the\udclimate system, land ice variability modifies atmospheric\udtemperature changes induced by orbital, topographical, and greenhouse\udgas variations. Quantification of these feedbacks on long timescales has hitherto scarcely been undertaken. In this study, we use\uda zonally averaged energy balance climate model bidirectionally\udcoupled to a one-dimensional ice sheet model, capturing the\udice–albedo and surface–height–temperature feedbacks. Potentially\udimportant transient changes in topographic boundary conditions by\udtectonics and erosion are not taken into account but are briefly\uddiscussed. The relative simplicity of the coupled model allows us\udto perform integrations over the past 38 Myr in a fully transient\udfashion using a benthic oxygen isotope record as forcing to\udinversely simulate CO2. Firstly, we find that the results\udof the simulations over the past 5 Myr are dependent on\udwhether the model run is started at 5 or 38 Myr ago. This\udis because the relation between CO2 and temperature is\udsubject to hysteresis. When the climate cools from very high\udCO2 levels, as in the longer transient 38 Myr run,\udtemperatures in the lower CO2 range of the past\ud5 Myr are higher than when the climate is initialised at low\udtemperatures. Consequently, the modelled CO2\udconcentrations depend on the initial state. Taking the realistic\udwarm initialisation into account, we come to a best estimate of\udCO2, temperature, ice-volume-equivalent sea level, and\udbenthic δ18O over the past 38 Myr. Secondly,\udwe study the influence of ice sheets on the evolution of global\udtemperature and polar amplification by comparing runs with ice\udsheet–climate interaction switched on and off. By passing only\udalbedo or surface height changes to the climate model, we can\uddistinguish the separate effects of the ice–albedo and\udsurface–height–temperature feedbacks. We find that ice volume\udvariability has a strong enhancing effect on atmospheric temperature\udchanges, particularly in the regions where the ice sheets are\udlocated. As a result, polar amplification in the Northern\udHemisphere decreases towards warmer climates as there is little land\udice left to melt. Conversely, decay of the Antarctic ice sheet\udincreases polar amplification in the Southern Hemisphere in the\udhigh-CO2 regime. Our results also show that in cooler\udclimates than the pre-industrial, the ice–albedo feedback\udpredominates the surface–height–temperature feedback, while in\udwarmer climates they are more equal in strength

The influence of ice sheets on temperature during the past 38 million years inferred from a one-dimensional ice sheet–climate model