Marine ice sheets are grounded on land which was below sea level before it became depressed under the ice-sheet load. They are inherently unstable and, because of bedrock topography after depression, the collapse of a marine ice sheet may be very rapid. In this paper equations are derived that can be used to make a quantitative estimate of the maximum size of a marine ice sheet and of when and how rapidly retreat would take place under prescribed conditions. Ice-sheet growth is favored by falling sea level and uplift of the seabed. In most cases the buttressing effect of a partially grounded ice shelf is a prerequisite for maximum growth out to the edge of the continental shelf. Collapse is triggered most easily by eustatic rise in sea level, but it is possible that the ice sheet may self-destruct by depressing the edge of the continental shelf so that sea depth is increased at the equilibrium grounding line.Application of the equations to a hypothetical “Ross Ice Sheet” that 18,000 yr ago may have covered the present-day Ross Ice Shelf indicates that, if the ice sheet existed, it probably extended to a line of sills parallel to the edge of the Ross Sea continental shelf. By allowing world sea level to rise from its late-Wisconsin minimum it was possible to calculate retreat rates for individual ice streams that drained the “Ross Ice Sheet.” For all the models tested, retreat began soon after sea level began to rise (∼15,000 yr B.P.). The first 100 km of retreat took between 1500 and 2500 yr but then retreat rates rapidly accelerated to between 0.5 and 25 km yr−1, depending on whether an ice shelf was present or not, with corresponding ice velocities across the grounding line of 4 to 70 km yr−1. All models indicate that most of the present-day Ross Ice Shelf was free of grounded ice by about 7000 yr B.P. As the ice streams retreated floating ice shelves may have formed between promontories of slowly collapsing stagnant ice left behind by the rapidly retreating ice streams. If ice shelves did not form during retreat then the analysis indicates that most of the West Antarctic Ice Sheet would have collapsed by 9000 yr B.P. Thus, the present-day Ross Ice Shelf (and probably the Ronne Ice Shelf) serves to stabilize the West Antarctic Ice Sheet, which would collapse very rapidly if the ice shelves were removed. This provides support for the suggestion that the 6-m sea-level high during the Sangamon Interglacial was caused by collapse of the West Antarctic Ice Sheet after climatic warming had sufficiently weakened the ice shelves. Since the West Antarctic Ice Sheet still exists it seems likely that ice shelves did form during Holocene retreat. Their effect was to slow and, finally, to halt retreat. The models that best fit available data require a rather low shear stress between the ice shelf and its sides, and this implies that rapid shear in this region encouraged the formation of a band of ice with a preferred crystal fabric, as appears to be happening today in the floating portions of fast bounded glaciers.Rebound of the seabed after the ice sheet had retreated to an equilibrium position would allow the ice sheet to advance once more. This may be taking place today since analysis of data from the Ross Ice Shelf indicates that the southeast corner is probably growing thicker with time, and if this persists then large areas of ice shelf must become grounded. This would restrict drainage from West Antarctic ice streams which would tend to thicken and advance their grounding lines into the ice shelf.
Topographic control on the post-LGM grounding zone locations of the West Antarctic Ice Sheet in the Whales Deep Basin, Eastern Ross Sea