Landmark back-to-back papers by Ronald Shreve and Hans Röthlisberger in a 1972 issue of the Journal of Glaciology opened the way for quantitative analysis of eskers, using a combination of field data and numerical modeling. Shreve showed that deviations of eskers from expected paths in valley bottoms could be used to calculate the slope of the glacier surface beneath which the esker formed. Ice-surface slopes can also be estimated from numerical models that simulate the advance and retreat of ice sheets. Knowing the surface slope and making use of the equilibrium condition that melting on walls of subglacial conduits is balanced by closure of the conduits due to the small excess of the pressure in the ice over that in the water, one can determine the potential gradient driving the flow. Grain size measurements in an esker then provide an estimate of the water velocity, and by assuming a conduit roughness, one can calculate the minimum cross sectional area of the conduit required to obtain that velocity. One can then determine the length of time necessary to build an esker of a given size as a function of the sediment concentration in the basal ice.

Numerical modeling also constrains thermal conditions in the basal ice, and in particular the temperature gradient. High gradients can conduct upward into the ice all of the heat produced by viscous dissipation in water flowing in a small developing conduit. This inhibits enlargement of the conduit to a size in which an esker can form. During the deglaciation of Maine, our model suggests that basal temperature gradients increased rapidly with distance from the margin. This may explain why eskers commonly seem to form near the margin and are typically segmented, with later segments lapping onto earlier ones like shingles.