Shrinkage of the ice sheets in Antarctica and Greenland in response to climate warming and the sea-level rise associated with that ice loss depends on the speed at which ice is shed into the oceans by glacier flow. Over much longer time scales, glacier flow erodes rock and shapes the topography of Earth's most spectacular mountain belts. Slip of glaciers over their beds is the principal process that both conveys ice within ice sheets to the oceans and shapes glacial landscapes. Building physically-based numerical models of these processes requires a "slip law" that describes the relationship between the stresses at the bases of glaciers and the speeds at which they slide over rough bedrock surfaces. This research resulted in the first slip law computed for topographies of actual glacier beds. Results will streamline efforts of numerical modelers to estimate the speeds of glaciers and their associated contributions to sea-level rise and shaping of glacial topography.

With ground-based LiDAR and drone-based photogrammetry, we surveyed proglacial areas of receding mountain glaciers in the Canadian Rockies and Swiss Alps to create high-resolution digital elevation models of their former beds. Their topographies were analyzed statistically to isolate small areas (100 m²) with topography most representative of each proglacial area. We then built a three-dimensional, mathematical representation of debris-free ice near the bed of a glacier slipping over the representative bedrock topographies of each area. This allowed the numerical modeling of slip across the bed, with associated separation of ice from the bed in the lees of bedrock bumps--a key process controlling stresses that resist glacier slip. Modeling slip of ice across the bed at different speeds and different subglacial water pressures allowed associated stresses resisting slip to be calculated, resulting in slip laws for various proglacial areas with contrasting morphologies.

Slip laws indicate acute sensitivity of slip velocity to slip resistance, in agreement with slip laws used in some ice-sheet models. The form of the computed slip laws also agrees with slip laws determined experimentally for the other common bed condition, in which glaciers rest on deformable sediment rather than on bedrock. This finding suggests that basal slip may be governed by a slip law with a form that is independent of the bed type, which would simplify glacier modeling efforts.

Ice at the beds of glaciers, however, is not debris-free; it contains rock particles that are in frictional contact with the bed. The associated friction also resists slip at glacier beds. To study this process we conducted the most realistic laboratory experiments to date in which melting ice, under pressure and containing rock clasts, was slid across a rock bed. Results indicate that the friction associated with particles in ice pressing on the bed is not related to the ice pressure. Rather friction depends on the component of ice movement towards the bed on upglacier-facing bedrock surfaces beneath glaciers. This convergence of ice with the bed pushes particles against the bed and thereby controls friction. These results provide clear guidance for how particle-bed friction can be added to our numerical model for computing slip laws. Adding such friction to a simpler, two-dimensional mathematical model of glacier slip indicates that particle-bed friction can significantly add to stresses resisting glacier slip, thereby decreasing slip velocity. However, this modeling also indicates that the form of the relationship between resisting stress at the bed and slip velocity is insensitive to particle-bed friction. 

More broadly our results show that the slip velocities of glaciers are more sensitive to changes in stress at their beds than is assumed in most numerical models aimed at estimating glacier and ice sheet flow velocities. This result is, therefore, directly relevant to estimating sea level rise from climate warming over the next century and building more accurate models of glacial landscape evolution.

Last Modified: 10/19/2020
Modified by: Neal R Iverson