The Friction Law Stress Exponent under Pine Island Glacier from 15 Years of Surface Elevation and Velocity Measurements

Abstract:

Polar the ice-sheets mass balance largely depends on the flow of ice-streams. Rapid basal motion generally accounts for most of the velocities. In flow models, the conditions at the base of the ice in contact with the bedrock are generally parameterised using a friction law that relates the sliding velocity to the basal shear stress. The most common law has two poorly constrained parameters, the basal slipperiness c and the stress exponent m. The basal slipperiness is expected to depend on local unobservable quantities and is routinely tuned from observed surface velocities using inverse methods. Different values for m are expected depending on the processes, from hard-bed sliding to soft bed deformation, and no consensus has emerged so far for its value that range from 1 to infinity. However, several studies have shown that the transient response of the ice-sheet models to external forcing is highly sensitive to m. Therefore, the uncertainty attached to the friction law is an important limit to our ability to evaluate future dynamical evolution of coastal regions.

Calibrating m can be done only if either basal stresses and/or velocities have changed significantly while c can be assumed constant in time. Here, we use Elmer/Ice to model the flow of Pine Island Glacier (PIG), Antarctica, sufficiently far upstream of the grounding line so that we can assume no change in c. Observations show an increase of surface velocities by up to 50% between 1996 and 2010, associated with an important dynamical thinning. Using a control inverse method and different values of m, we tune a spatially varying basal slipperiness field that best fit, in the same time, observed surface velocities for years 1996, 2007, 2008, 2009 and 2010. These years correspond to the MeaSUREs project velocity datasets that have the best spatial coverage for our model domain. Surface elevations for the corresponding years are constructed using ERS and Envisat radar altimetry data.

We show that the substantial ice flow acceleration shown by the data can be reproduce by the model only for high values of m. We interpret this result as the sign that basal motion in the upstream part of PIG is mostly govern by plastic deformation of the underlying sediments. This means that the bedrock can not deliver higher resistive stresses to compensate increased longitudinal and driving stresses.