A power-based abrasion law for use in landscape evolution models

Subglacial abrasion drives erosion for many glaciers, inundating forefields and proglacial marine environments with glaciogenic sediments. Theoretical treatments of this process suggest that bedrock abrasion rates scale linearly with the energy expended through rock-on-rock friction during slip, but this assumption lacks an empirical basis for general implementation. To test this approach, we simulated abrasion by sliding debris-laden ice over rock beds under subglacial conditions in a cryo-ring shear and a direct shear device. Miniscule volumes of erosion that occurred during each run were mapped with a white-light profilometer, and we measured the rock mechanical properties needed to constrain the energy expended through abrasion. We find that abraded volume per unit area increases linearly with average shear force at the bed and that abrasion rates increase linearly with basal power for plane beds. Lastly, only a small percentage (1%) of the energy partitioned to basal slip is dissipated by abrasion. These results confirm the basal-power abrasion rule is viable to implement in landscape evolution models.