Relationship between sea level and climate forcing by CO₂ on geological timescales

On 10³- to 10⁶-year timescales, global sea level is determined largely by the volume of ice stored on land, which in turn largely reflects the thermal state of the Earth system. Here we use observations from five well-studied time slices covering the last 40 My to identify a well-defined and clearly sigmoidal relationship between atmospheric CO₂ and sea level on geological (near-equilibrium) timescales. This strongly supports the dominant role of CO₂ in determining Earth's climate on these timescales and suggests that other variables that influence long-term global climate (e.g., topography, ocean circulation) play a secondary role. The relationship between CO₂ and sea level we describe portrays the 'likely' (68% probability) long-term sea-level response after Earth system adjustment over many centuries. Because it appears largely independent of other boundary condition changes, it also may provide useful long-range predictions of future sea level. For instance, with CO₂ stabilized at 400-450 ppm (as required for the frequently quoted 'acceptable warming' of 2 °C), or even at AD 2011 levels of 392 ppm, we infer a likely (68% confidence) long-term sea-level rise of more than 9 m above the present. Therefore, our results imply that to avoid significantly elevated sea level in the long term, atmospheric CO₂ should be reduced to levels similar to those of preindustrial times.