(Table S1) Boron isotope and trace element data and reconstructed carbonate system parameters, ODP Holes 122-761B and 154-926A

The middle Miocene Climatic Optimum (17-15 Ma; MCO) is a period of global warmth and relatively high CO2 and is thought to be associated with a significant retreat of the Antarctic Ice Sheet (AIS). We present here a new planktic foraminiferal d11B record from 16.6 to 11.8 Ma from two deep ocean sites currently in equilibrium with the atmosphere with respect to CO2. These new data demonstrate that the evolution of global climate during the middle Miocene (as reflected by changes in the cyrosphere) was well correlated to variations in the concentration of atmospheric CO2. What is more, within our sampling resolution (~1 sample per 300 kyr) there is no evidence of hysteresis in the response of ice volume to CO2 forcing during the middle Miocene, contrary to what is understood about the Antarctic Ice Sheet from ice sheet modelling studies. In agreement with previous data, we show that absolute levels of CO2 during the MCO were relatively modest (350-400 ppm) and levels either side of the MCO are similar or lower than the pre-industrial (200-260 ppm). These new data imply the presence of either a very dynamic AIS at relatively low CO2 during the middle Miocene or the advance and retreat of significant northern hemisphere ice. Recent drilling on the Antarctic margin and shore based studies indicate significant retreat and advance beyond the modern limits of the AIS did occur during the middle Miocene, but the complete loss of the AIS was unlikely. Consequently, it seems that ice volume and climate variations during the middle Miocene probably involved a more dynamic AIS than the modern but also some component of land-based ice in the northern hemisphere.

(Appendix 1) Coral analysis and isostatic rebound effects from different Holes of IODP Expedition 310

Past sea-level records provide invaluable information about the response of ice sheets to climate forcing. Some such records suggest that the last deglaciation was punctuated by a dramatic period of sea-level rise, of about 20 metres, in less than 500 years. Controversy about the amplitude and timing of this meltwater pulse (MWP-1A) has, however, led to uncertainty about the source of the melt water and its temporal and causal relationships with the abrupt climate changes of the deglaciation. Here we show that MWP-1A started no earlier than 14,650 years ago and ended before 14,310 years ago, making it coeval with the Bølling warming. Our results, based on corals drilled offshore from Tahiti during Integrated Ocean Drilling Project Expedition 310, reveal that the increase in sea level at Tahiti was between 12 and 22 metres, with a most probable value between 14 and 18 metres, establishing a significant meltwater contribution from the Southern Hemisphere. This implies that the rate of eustatic sea-level rise exceeded 40 millimetres per year during MWP-1A.