Exploring uncertainties in the relationship between temperature, ice volume, and sea level over the past 50 million years

Over the past decade, efforts to estimate temperature and sea level for the past 50 Ma have increased. In parallel, efforts to model ice sheet changes during this period have been ongoing. We review published paleodata and modeling work to provide insights into how sea level responds to changing temperature through changes in ice volume and thermal expansion. To date, the temperature to sea level relationship has been explored for the transition from glacial to interglacial states. Attempts to synthesize the temperature to sea level relationship in deeper time, when temperatures were significantly warmer than present, have been tentative. We first review the existing temperature and sea level data and model simulations, with a discussion of uncertainty in each of these approaches. We then synthesize the sea level and temperature data and modeling results we have reviewed to test plausible forms for the sea level versus temperature relationship. On this very long timescale there are no globally representative temperature proxies, and so we investigate this relationship using deep-sea temperature records and surface temperature records from high and low latitudes. It is difficult to distinguish between the different plausible forms of the temperature to sea level relationship given the wide errors associated with the proxy estimates. We argue that for surface high-latitude Southern Hemisphere temperature and deep-sea temperature, the rate of change of sea level to temperature has not remained constant, i.e., linear, over the past 50 Ma, although the relationship remains ambiguous for the available low-latitude surface temperature data. A nonlinear form between temperature and sea level is consistent with ice sheet modeling studies. This relationship can be attributed to (1) the different glacial thresholds for Southern Hemisphere glaciation compared to Northern Hemisphere glaciation and (2) the ice sheet carrying capacity of the Antarctic continent.