Transient response of glacier slip to velocity or effective stress perturbations

Abstract:

Most glacier slip laws directly depend on subglacial effective stress but are generally formulated in terms of only steady-state relationships. In reality, a sudden change in sliding velocity or effective stress produces a transient response in which the basal drag adjusts to the new basal slip condition (i.e., state) over a period of time. As changes in subglacial hydrology can alter basal effective stress on short timescales (hours-days), the transient adjustment of glacier slip in response to these changes may be important, or even dominate, the basal drag and slip velocity in certain circumstances.

To quantify the transient response to basal sliding perturbations, we conducted a series of velocity-stepping experiments in which ice at the pressure melting point was slid over a hard, bumpy bed. Experiments were conducted using a ring shear apparatus that slides a ring of temperate ice over a rigid bed under an applied vertical stress. The sliding speed at the ice ring’s centerline was varied between 0.8—324 m/yr. The instantaneous slip resistance and dilation (contraction) resulting from a speed perturbation were measured. Based on these laboratory observations we develop a set of rate-and-state-like equations that describe the transient response. We then apply these laboratory findings to field observations from Greenland to test their applicability for large-scale glacier slip.

All velocity increases resulted in a sudden, transient increase in slip resistance before slip resistance evolved to a new steady state, which required days in some cases. For a rigid bed where cavities formed, the duration and form of the transient stress evolution was found to depend on the effective stress, the original and new sliding speeds, and the state of the ice-bed contact (i.e., the extent of basal cavities) prior to velocity stepping. The timescale for these transient responses in the laboratory was on the order of days (1-15 days), whereas field observations of transient variations in water pressure varied on shorter timescales, in some instances even diurnally. This implies that for sufficiently large variations in effective stress occurring over short durations, basal drag and slip velocity could be in a state of continual adaptation to transient conditions.