The steep-sided valleys and overdeepened basins of alpine landscapes are well-known products of glaciation, yet relatively little is known about how the dynamics of ice flow and glacial erosion interact to give rise to such landforms. By linking a finite-element model for ice flow through a glacier cross section with an erosion model, it is possible to investigate the development of one of the most striking glacial landforms, the U-shaped valley. In addition to providing a detailed understanding of landform development, such modeling provides a way to test current understanding of the controls on glacial sliding and erosion.
To simulate valley development, I first model flow through an initial glacier cross section and calculate the glaciological parameters that govern erosion. I then numerically simulate erosion to produce a modified transverse profile, for which a new flow field and erosion pattern are computed. A number of iterations permits examination of the progressive transformation of cross-section form, which can be compared with field data.
Model predictions of the cross-section flow field are in close accord with data from the Athabasca Glacier and include marked lateral variations in sliding velocity. With an erosion law dependent on basal velocity, the model predicts the rapid transformation of a V-shaped cross section into a recognizably glacial form over a time period on the order of 104 yr and the eventual development of a steady-state, quasi-parabolic glacier cross section. Better agreement with empirical data from glaciated valleys is obtained by including temporal variations in ice discharge, in order to mimic the characteristics of 100,000-yr glacial cycles. The high-discharge phase dominates form development, and, at low discharges, cross-section form is essentially inherited from the central part of the form that developed during the preceding high-discharge phase.