Use of a rate- and state-dependent friction law to parameterize subglacial tills

Recent studies show that small-amplitude stress changes associated with ocean tidal variations can control large-scale ice stream motion and trigger subglacial stick-slip behavior. The forcing of ice stream flow by the tides is observed under a surprisingly varied set of glacial and subglacial conditions. Ice stream basal seismicity, modulated by ocean tides, is present beneath the ice plain of rapidly flowing ice stream B; ice stream B has been hypothesized to be underlain by a plastic till which is actively freezing. Basal seismicity (also modulated by the tide) is present beneath much of ice stream C, which is slow-flowing and hypothesized to have a linear-viscous substrate. Ice stream D has a more-continuous rather than a stick-slip response to tidal forcing, with the flow speed of the ice stream changing by a factor of three over the course of a tidal cycle. Ice stream D is hypothesized to be underlain by a linear-viscous till similar to that beneath ice stream C and beneath the upstream segments of ice stream B. Reconciling these various observations is necessary to develop a sliding law for ice stream flow that can be generally applied. We propose the use of a rate- and state-dependent friction law to describe the behavior of the subglacial till layer. We suggest that subglacial tills can be classified as ``velocity-weakening'' (steady-state frictional strength decreases with increasing slip velocity, which is a necessary condition for stick-slip instability) or ``velocity-strengthening'' (steady-state frictional strength increases with increasing slip velocity, which results in inherently stable sliding). Whether a subglacial system is ``weakening'' or ``strengthening'' appears to be related to the hydrologic system and whether basal water is freezing-on (ice streams B & C which exhibit stick-slip) or not (ice stream D, no stick-slip). This model could also reconcile observations of the presence of pervasive subglacial till deformation (ice stream D, upper parts of ice stream B) and thin-layer plastic deformation at the boundary between the ice and till (ice stream B and C). A layer that exhibits velocity-strengthening would be expected to exhibit pervasive deformation whereas a weakening layer would fail on discrete slip planes.