Seasonal-scale abrasion and quarrying patterns from a two-dimensional ice-flow model coupled to distributed and channelized subglacial drainage

Field data and numerical modeling show that glaciations have the potential either to enhance relief or to dampen topography. We aim to model the effect of the subglacial hydraulic system on spatiotemporal patterns of glacial erosion by abrasion and quarrying on time scales commensurate with drainage system fluctuations (e.g., seasonal to annual). We use a numerical model that incorporates a dual-morphology subglacial drainage system coupled to a higher-order ice-flow model and process-specific erosion laws. The subglacial drainage system allows for a dynamic transition between two morphologies: the distributed system, characterized by an increase in basal water pressure with discharge, and the channelized system, which exhibits a decrease in equilibrium water pressure with increasing discharge. We apply the model to a simple synthetic glacier geometry, drive it with prescribed meltwater input variations, and compute sliding and erosion rates over a seasonal cycle. When both distributed and channelized systems are included, abrasion and sliding maxima migrate ~ 20% up-glacier compared to simulations with distributed drainage only. Power-law sliding generally yields to a broader response of abrasion to water pressure changes along the flowline compared to Coulomb-friction sliding. Multi-day variations in meltwater input elicit a stronger abrasion response than either diurnal- or seasonal variations alone for the same total input volume. An increase in water input volume leads to increased abrasion. We find that ice thickness commensurate with ice sheet outlet glaciers can hinder the up-glacier migration of abrasion. Quarrying patterns computed with a recently published law differ markedly from calculated abrasion patterns, with effective pressure being a stronger determinant than sliding speeds of quarrying rates. These variations in calculated patterns of instantaneous erosion as a function of hydrology-, sliding-, and erosion-model formulation, as well as model forcing, may lead to significant differences in predicted topographic profiles on long time scales.