Reliable reconstructions of paleoglaciers using topographic maps and aerial photographs allow calculation of effective basal shear stresses along the longitudinal profiles of these glaciers. Glacial flow theory applied to these shear stresses provides an estimate of the component of mass flux due to internal deformation. Assuming basal slip to be zero at the point where deformation mass flux is a maximum, minimum average accumulation gradients (above the equilibrium-line altitude (ELA)) and ablation gradients (below the ELA) can be calculated and minimum mass flux at the ELA can be estimated using the continuity equation. Average net winter accumulation can also be calculated by dividing the mass flux at the ELA by the accumulation area. Because local climate controls the mass balance of a glacier, and therefore the accumulation and ablation gradients, this model provides information on the climatic setting of these paleoglaciers.

This model also allows estimation of basal slip as a factor in point estimates of glacial flow. Application of the continuity model above and below the ELA generates additional estimates of mass flux at discrete points along the glacier. The difference between deformation mass flux and continuity flux at these points yields a first approximation of basal slip, which is highly variable along the glacier.

The model was tested on the Big Timber glacier of west-central Montana and applied to several other late Pleistocene glaciers in the northern Rocky Mountains of south-western Montana and north-eastern Idaho. Low ablation gradients (<4.0 mm m-1) suggest a climate during the late Pleistocene comparable to the present-day climate of the Brooks Range in Alaska. Calculated average net winter accumulation for the area is well below modern values, again indicating that the climate was much drier during the full glacial period. Basal sliding accounts for most (>90%) of the glacial flow near the terminus of each glacier but is variable along the rest of the glacier. While the mass-balance values are minima, they are assumed to be reasonable approximations of the actual values unless very high basal slip rates occurred along the entire length of each glacier.