A glacier slip law incorporating debris-bed friction

In fast-flowing regions of the Antarctic and Greenland ice sheets, most motion occurs through slip at the boundary between ice and its substrate. Glaciologists have developed “slip laws” that describe basal motion as a function of resistive stress (e.g. basal drag) and effective pressure. When implemented in ice sheet models, the choice of slip law affects predictions of grounding-line migration and sea-level rise. Slip laws implemented in ice sheet models assume that the base of the glacier is “clean” (without rock debris) and separated from the bed by a thin frictionless water film, implying that the only source of basal drag is viscous flow and regelation around bed obstacles. However, observations of basal ice indicate that it is “dirty” (debris or sediment-rich) in most glacial environments, suggesting an additional source of drag due to friction between debris-laden basal ice and the bed. Incorporating debris-bed friction into a slip law may lead to significantly different predictions of the magnitude of basal drag and alter the functional form of the slip law.

Here, we report results of laboratory experiments using a geomechanical apparatus (cryogenic ring shear) to slide ice over a rigid bed composed of inclined marble steps at realistic glaciological conditions (e.g. slip velocity, effective pressure, temperature). We conduct a control experiment by sliding clean ice at a range of velocities and recording the resistance to basal motion. We then slide debris-laden basal ice to determine how debris affects the magnitude and functional form of the basal slip law. Our results suggest that slip in clean ice conditions is well described by the commonly used regularized Coulomb slip law. However, debris-bed friction is a significant source of basal drag, raising measured shear stress by ~50-75% despite a sparse areal debris concentration of ~5%. We derive a slip law incorporating debris-bed friction that fits our experimental data within measurement uncertainty with two tuning parameters. The debris-bed friction slip law is composed of three terms: a clean ice term (equivalent to regularized Coulomb), a pressure-dependent debris friction term, and a velocity-dependent debris-friction term. We further validate this slip law for realistic 3-D bed topographies using a finite-element ice flow model (Elmer/Ice). Finally, we implement a parameterized form of the slip law in an ice sheet model (MPAS-Albany Land Ice) and assess the sensitivity of grounding-line migration and ice-mass loss to the choice of slip law.