The glacial–interglacial paradox: the relation between the global means of sea level and sea surface temperature

Sea level variability during the Quarternary is simulated using a stochastic climate model, and a sensitivity relation for the change in net oceanic evaporation due to a change in sea surface temperature. In the application of this relation, it is assumed that the greater part of the change in net oceanic evaporation causes changes in the land ice storage, rather than being directly returned to the ocean by rivers. The analysis suggests that the observed sea level changes can be interpreted as due to the transfer of heat to the deep ocean from the surface mixed layer, arising from random radiation perturbations of the same variance as would give rise to the interannual variability of the global temperature series. The paradox is that glacial conditions (increase in ice storage) are favoured by positive (temperate) sea surface temperature anomalies, and interglacial conditions (decrease in ice storage) by negative (temperate) sea surface temperature anomalies. The evolution of both these regimes, which are inherently unstable, appears to be controlled by the deep water formation process, while albedo feedback is of minor importance. Fluvial feedback, (in which as the ice storage increases the fluvial inflow decreases), however, is found to be an important process, and a small sensitivity of river inflow to storage is consistent with forcing by random variability or by astronomical forcing. A simple analytical model incorporating the key processes of oceanic evaporation and fluvial feedback is presented. The analysis points to the importance of an accurate river model for climate system modelling.