Constraining a generalized glacier slip relationship using high spatiotemporal resolution data of a surging glacier

Abstract:

Basal sliding is an essential component of ice dynamics. The relationship between glacier slip and basal shear stress in glaciological theory is commonly formulated for either a deformable (sediment) or rigid (bedrock) bed, while the general shape of the relationship remains the same. The maximum resistive stress that can be produced by the glacier bed is capped and depends mainly on bed geometry, water pressure and sediment shear strength. Where the shear stress applied by the glacier remains lower than the maximum resistive stress of the bed, basal shear stresses increase non-linearly with sliding velocity. Once that threshold is reached, sliding can become independent of shear stress and even show a rate-weakening behavior. These results are supported by laboratory experiments and theoretical work, but verification in the field is still lacking.

We combine slip relationships for deformable and rigid beds into a single generalized equation, from which we identify four key parameters: maximum resistive stress, threshold velocity, and two empirical exponents. To constrain this relationship, we use estimates of calculated basal stresses and sliding velocities for Shisper glacier, Pakistan, before and during its recent surge. We approximate basal stresses using pre- and syn-surge DEMs, and available estimates of ice thickness. Sliding velocity estimates are calculated based on a velocity timeseries with a high spatio-temporal resolution (60m pixels and time windows as short as 5 days) extracted from optical images between 2013 and 2019 (see Delaney et al., AGU abstract 753171 submitted to C027). We find that when velocities increase significantly, the stress versus slip relationships are characterized by stresses that are either independent of or decrease with slip rate, consistent with the generalized slip relation. The details of this relationship appear to vary for individual regions of the glacier, and to change in time. These results suggest that a single set of parameters is inadequate to reproduce the slip behavior across the entire glacier bed. Finally, by fitting the parameters of the slip relationship to an entire glacier over a six-year period, we can further constrain their plausible ranges. Applying this method to glacier globally would enable large-scale assessment of adequate parameters for glacier slip relationships.