Stick-slip Cycles and Tidal Modulation of Ice Stream Flow

The reactivation of a single dormant Antarctic ice stream would double the continent's mass imbalance. Despite importance of understanding the likelihood of such an event, direct observation of the basal processes that lead to the activation and stagnation of streaming ice are minimal. As the only ice stream undergoing stagnation, the Whillans Ice Plain (WIP) occupies a central role in our understanding of these subglacial processes. Complicating matters is the observation, from GPS records, that the WIP experiences most of its motion during episodes of rapid sliding. These sliding events are tidally modulated and separated by 12 hour periods of quiescence. We conduct numerical simulations of ice stream stick-slip cycles. Our simulations include rate- and state-dependent frictional sliding, tidal forcing, inertia, upstream loading in a cross-stream, thickness-averaged formulation. Our principal finding is that ice stream motion may respond to ocean tidal forcing with one of two end member behaviors. In one limit, tidally modulated slip events have rupture velocities that approach the shear wave speed and slip events have a duration that scales with the ice stream width divided by the shear wave speed. In the other limit, tidal modulation results in ice stream sliding velocities with lower amplitude variation but at much longer timescales, i.e. semi-diurnal and longer. This latter behavior more closely mimics the behavior of several active ice streams (Bindschadler, Rutford). We find that WIP slip events exist between these two end member behaviors: rupture velocities are far below the inertial limit yet sliding occurs only episodically. The continuum of sliding behaviors is governed by a critical ice stream width over which slip event nucleate. When the critical width is much longer than the ice stream width, slip events are unable to nucleate. The critical width depends on the subglacial effective pressure, ice thickness, and frictional and elastic constitutive parameters. One implication of our work is that, because the transition from steady to episodic sliding may occur by changing subglacial effective pressure, changing effective pressure may be responsible for the stagnation of the WIP.