(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.

(Table S1) Radiocarbon data of sediment core SO161/5 22SL

At the end of the Last Glacial Maximum (19,000 to 11,000 years ago), atmospheric carbon dioxide concentrations rose while the Delta14C of atmospheric carbon dioxide declined**1, 2. These changes have been attributed to an injection of carbon dioxide with low radiocarbon activity from an oceanic abyssal reservoir that was isolated from the atmosphere for several thousand years before deglaciation**3. The current understanding points to the Southern Ocean as the main area of exchange between these reservoirs4. Intermediate water formed in the Southern Ocean surrounding Antarctica would have then carried the old carbon dioxide signature to the lower-latitude oceans**5, 6. Here we reconstruct the Delta14C signature of Antarctic Intermediate Water off the coast of Chile for the past 20,000 years, using paired 14C ages of benthic and planktonic foraminifera. In contrast to the above scenario, we find that the delta14C signature of the Antarctic Intermediate Water closely matches the modelled surface ocean Delta14C, precluding the influence of an old carbon source. We suggest that if the abyssal ocean is indeed the source of the radiocarbon-depleted carbon dioxide, an alternative path for the mixing and propagation of its carbon dioxide may be required to explain the observed changes in atmospheric carbon dioxide concentration and radiocarbon activity.