Most numerical models of present ice-sheet dynamics predict basal thermal conditions for an assumed geothermal heat flux and measured ice thickness, surface temperature, and snow precipitation. These models are not ideally suited for reconstructing former ice sheets because what is known for present ice sheets is unknown for former ones, and vice versa. In particular, geothermal heat fluxes are immeasurable at an ice-sheet bed but can be measured after the ice sheet is gone, and the thermal conditions predicted at an ice-sheet bed can be inferred from the glacial-geological–topographic record after the ice sheet is gone. The Maine CLIMAP ice-sheet reconstruction model uses these inferred basal thermal conditions to compute ice thicknesses from basal shear stresses.

Basal shear stress is assumed to reflect the degree of ice–bed coupling which, in turn, is assumed to reflect the amount and distribution of basal water under the ice sheet. Under the ice-sheet interior, basal water exists in a thin film of constant thickness covering the low places on the bed. This film expands for a melting bed and contracts for a freezing bed. Along the ice-sheet margin, basal water exists in narrow channels of varying thickness corresponding to troughs on the bed. These water channels become deeper for a melting bed and shallower for a freezing bed. In areas covered by the Laurentide and Scandinavian ice sheets, myriads of interconnected lakes in regions of greatest postglacial rebound are interpreted as evidence suggesting the interior basal water distribution, whereas eskers pointed toward terminal moraines and troughs across continental shelves are interpreted as evidence suggesting the basal water distribution toward the margins. Continental-shelf troughs were assumed to correspond to former ice streams, by analogy with observations in Greenland and Antarctica.

Three modes of glacial erosion are considered to be responsible for the lakes, eskers, troughs, and associated topography. Quarrying is by a freeze-thaw mechanism which occurs where the melting-point isotherm intersects bedrock, so it is important only for freezing or melting beds because high places on the bed are frozen, low places are melted, and minor basal temperature fluctuations shift the isotherm separating them. Crushing results when rocks at the ice-bed interface are ground against each other and the bed by glacial sliding, so it occurs where the bed is melted and is most important when the entire bed is melted. Abrasion of bedrock occurs when rock cutting tools imbedded in the ice at the ice–rock interface are moved across the interface by glacial sliding, so it is also most important when the entire bed is melted. If basal melting continued after the entire bed is melted, abrasion-rates drop because the basal water layer thickens and drowns bedrock projections otherwise subjected to abrasion. Basal freezing reduces both crushing and abrasion-rates by coating quarried rocks with a sheath of relatively soft ice and transporting them upward from the ice–rock interface.

An initially flat subglacial topography will develop depressions where glacial erosion is greatest and deposition is least, and ridges where the opposite conditions prevail. We interpret the central depressions represented today by Hudson Bay and the Gulf of Bothnia as caused by erosion on a melting bed under the Laurentide and Scandinavian ice sheets, respectively. The arc of lakes, gulfs, and shallow seas surrounding these depressions are interpreted as resulting from a freezing bed under the former ice sheets. The present watershed separating the depressions from the arcs marks the approximate former basal equilibrium line where the bed was melted. The Canadian and Baltic continental shields beyond these arcs are blanketed by material eroded from within the arcs, and represent areas having a frozen bed where evidence for abrasion is missing and a second zone having a melting bed where evidence for abrasion is present. This basic pattern was assumed to be imprinted on the bed during the steady-state period of maximum ice-sheet extent, and maintained in varying degrees during growth and shrinkage of these ice sheets.