The sea level to temperature relationships in this review are based on long-term changes (>1 Ma), which, given that the response time of the ice sheets is <1 Ma [ Miller et al
Nonlinear functions, in both one-step and two-step forms, are a more plausible fit to the DST and Southern Hemisphere high-latitude data against sea level plots. It is difficult to determine whether the single-step or two-step function is the most appropriate function given the wide errors in the currently available data. The two-step hypothesis originates from GCM and ice sheet modeling studies where ice build up on Antarctica occurs nonlinearly in a series of steps in response to declining atmospheric CO2 and temperature [ Pollard and ]. The first step occurs with the formation of isolated ice caps in the mountain regions of Antarctica before the formation of a continent sized ice sheet in the second step. We underline an important caveat of using the NJ sea level record: the long-term sea level change contains thermosteric and ocean basin volume components and potentially regional tectonic effects. The two-step hypothesis is a glacioeustatic concept, yet when it is applied to the DST and sea level data in this review it shows a greater sea level range (?75 m in the two steps, 100 m in total) than can be explained solely by the formation of the modern ice sheets (?43–54 m as seen from the NJ margin). Additionally, the first step occurs at ?42–44 Ma, implying that large, permanent Antarctic ice caps formed in the Eocene, for which there is at present limited supporting evidence. The second step at the EOT in the DST against sea level plot is, at least in part, an artifact of the lack of cooling in Lear et al.’s Mg/Ca DST data set across the EOT. A steep step is not apparent for the SST against sea level plots for the EOT.
e., cooler than present) [ Rohling et al., 2009 ; Siddall et al., 2010b ] or pre-Pleistocene temperatures (i.e., warmer than present, this review) suggests that the present interglacial state is relatively stable compared to the overall sea level change observed for the past 50 Ma. However, the implied nonlinear relationship in the DST and high-latitude Southern Hemisphere SST data suggests there are large sea level thresholds for temperatures warmer and colder than present. These are caused by the different glacial thresholds for Northern Hemisphere and Southern Hemisphere glaciation and the size of the Antarctic continent restricting further growth of the East Antarctic Ice Sheet. Given the significant limitations of the currently available DST data, due in part to uncertainties in the past seawater Mg/Ca concentration, it is difficult to determine precisely the temperatures of these thresholds. Unfortunately, the uncertainties within the sea level and temperature proxy data used here are currently too large to resolve potential thresholds associated with smaller-scale glaciation (e.g., <10 m, which could, for example, include the Greenland Ice Sheet and West Antarctic Ice Sheet).
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