Criteria based on the glacial geology and topography were developed to assess which areas underneath ice sheets 18000 years ago were covered by freezing, frozen, melting, or melted beds, ice streams or lobes, and ice domes or saddles. Our ice sheets were then reconstructed using a finite-difference model that requires as input the ice thickness near the ice-sheet margin, the basal topography under ice-sheet surface flow lines, flow-line lengths, and basal shear-stress variations along flow lines. Initial ice thicknesses could be somewhat arbitrary because they only affected the flow-line surface profile close to the ice-sheet margin. Present bed topography was used for the areas covered by ice sheets 18000 years ago, this bed was then depressed isostatically by the reconstructed ice sheet, and a new ice sheet was reconstructed on the depressed bed.

Application of our model required snow accumulation-rates over the former ice sheets and evaluation of parameters in the standard flow and sliding laws of ice. All these were obtained from the present Greenland and Antarctic ice sheets. Snow accumulation-rates are not important variables in our ice-sheet reconstruction model. Flow- and sliding-law parameters were obtained by matching our reconstructed flow-line profiles with present Greenland and Antarctic profiles for regions where the basal topography is known and where our criteria for locating zones of frozen and melted beds agree with zones calculated from an Australian model which incorporates the equations of heat flow Reference Budd, Budd, Jenssen and Radok(Budd and others, 1970).

The last interglaciation peaked about 125000 years B.P. when mean global sea-level was about six meters higher than present and mean global temperature was apparently a few degrees warmer than present. Among ice sheets existing during the present interglaciation, the marine West Antarctic ice sheet is most likely to disintegrate as a result of small increases in sea-level and air temperature. The 125000 B.P. increase in sea-level is nearly identical to the increase expected from collapse of the present West Antarctic ice sheet, and the 125000 B.P. increase in air temperature might have melted the confined ice shelves which now buttress this ice sheet. A Maine CLIMAP ice-sheet disintegration model was developed to couple with the Maine CLIMAP ice-sheet reconstruction model to treat disintegration of marine ice sheets by means of surging ice streams. This model was then applied to the West Antarctic ice sheet, as reconstructed for the CLIMAP 18000 years B.P. experiment, and disintegration was allowed to proceed to completion for the 125 000 B.P. sea-level and air-temperature boundary conditions.

In the Maine CLIMAP ice-sheet reconstruction model (Hughes, in press), ice-stream grounding lines are across the tops of sills at the seaward end of fore-deepened channels on the floor of continental shelves formerly covered by marine ice sheets. Isostatic sinking of continental shelves underneath these ice sheets is assumed to be zero at ice-stream grounding lines, ice streams have a concave surface profile above the channels, and a zone of converging ice flow may exist at the landward end of these channels, particularly if they continue as fiords through coastal mountain ranges. Ice–bed uncoupling obeys a damped cosine function in the channel, with complete uncoupling at the sill.

In the Maine CLIMAP ice-sheet disintegration model (Stuiver and others, in press), an ice-stream surge law related to ice-bed uncoupling represents the driving force for ice-stream flow along the channel, and the hydrostatic potential difference between ice and water columns represents the driving force for ice-stream flow across the sill. Grounding-line retreat during the surge is caused by decreasing the difference between the heights of the ice and water columns at the sill. This decrease can be triggered by a negative mass balance in the ice-stream drainage basin, isostatic depression of the sill, a rise in sea-level, or a rise in air temperature. In our disintegration model, mass balance changes mainly by changing areas of ice-stream drainage basins rather than changing snow accumulation-rates over them, isostatic depression of the sill is not allowed, sea-level rises as all ice sheets disintegrate before 125000 B.p. but as only the West Antarctic ice sheet disintegrates during that interglaciation, and air temperature rises only enough to ablate the ice-shelf fringe of West Antarctica during disintegration. Isostatic rebound lags ice-sheet disintegration by prescribed amounts. Fast and slow disintegration models are derived. In the fast model, calving bays closely follow the grounding lines retreating along evacuated ice-stream channels. In the slow model, the ice-shelf fringe expands southward as the grounding line retreats. Both models pinpoint Pine Island Bay in the Amundsen Sea as the site where the present-day West Antarctic ice sheet is most vulnerable to collapse, provided that Thwaites and Pine Island Glaciers have no high bedrock sills.