Numerical simulations of glacial-valley longitudinal profile evolution

Glaciers shape alpine landscapes. They broaden valley bottoms, enhance loca l valley relief, generate multiple steps, overdeepen valley floors, and cau se tributary valleys to hang. These distinctive glacial signatures result f rom 10(4)-10(5) yr of erosion, during which swings in climate drive advance s and retreats of alpine glaciers. We use a numerical model of glacial eros ion to explore the development of the longitudinal profiles of glaciated va lleys. The model is driven by the past 400 k.y. of variable climate. Becaus e both sliding speed, which dictates abrasion rate, and water-pressure fluc tuations, which strongly modulate quarrying rate, should peak at the equili brium-line altitude (ELA), we expect the locus of most rapid erosion to fol low the transient ELA. Simulations of a single glacial valley show rapid fl attening of the longitudinal profile. Inclusion of a tributary glacier crea tes a step immediately downvalley of the tributary junction that persists o ver multiple glaciations and commonly leaves the tributary valley hanging. Steps and overdeepenings result from an increase in ice discharge immediate ly below the tributary junction, which is accommodated primarily by increas ed ice thickness and hence sliding rate. The size of the step increases wit h the ratio of tributary to trunk ice discharge, while the height of a hang ing valley reflects the difference in the time-integrated ice discharge in tributary and trunk valleys and therefore increases as the discharge ratio decreases.