Despite convergence of process-based theories on this slip law, nearly all large-scale models of glacier motion parameterize drag to increase monotonically with slip velocity, with varying degrees of nonlinearity bounded by Coulomb slip in which τ b/ N is independent of slip velocity ( Fig. The potential consequences of this slip law are severe: Weather or climate changes that increase slip velocity or decrease N would decrease resistance to slip, promoting faster flow and glacier instability, including glacier surge propagation ( 19, 25). Slip laws used in ice-sheet models (solid blue, dashed orange, and dotted purple) and a generalization of laws derived from process-based models of glacier slip that account for the effect of water-filled cavities at glacier beds (dashed light blue). Laboratory experiments confirm this drag relationship for a sinusoidal bed ( 24). Owing to bump convexity, this shift reduces slopes of stoss surfaces in contact with ice. The decrease in τ b/ N, called rate-weakening drag, is caused by cavity growth with increasing slip velocity that shifts shrinking zones of ice-bed contact toward the tops of bumps. Process-based models for hard-bedded slip with cavities indicate slip laws with a common form: With increasing slip velocity or decreasing N, τ b/ N increases, peaks at some fraction of m max, and then decreases at higher slip velocities ( Fig. Quasi-static equilibrium requires that for two-dimensional (2D) beds, the ratio, τ b/ N, cannot exceed the maximum slope, m max, of the up-glacier (stoss) sides of bed bumps ( 18). The cavity water pressure, subtracted from the ice-overburden pressure, yields an effective pressure, N, that also contributes to the balance of forces on the bed. Modeling studies indicate acute sensitivity of glacier response to the form of this relationship ( 2, 14– 16), which is affected by water-filled cavities that persist in the lees of bumps on the bed where ice pressure on the bed is low ( 17). Models of glacier flow in response to climate forcing ( 2, 10) and of orogen-scale glacial erosion and its effects ( 11, 12) therefore require a slip law for hard beds that relates drag at the bed, τ b, to slip velocity ( 13). Moreover, glacier slip over hard beds causes erosion of bedrock that modulates uplift rates in mountain belts ( 8) and rates of chemical weathering that alter climate ( 9). Where fast-flowing ice rests mostly on deformable till (“soft” beds), hard-bedded zones can have disproportionately large effects on modeled ice losses ( 7). Both slow-moving ( 3) and fast-moving ( 4– 6) parts of ice sheets can rest wholly or in part on hard beds that behave rigidly so that ice slips over them rather than deforming them. Major contributions of ice discharge to the oceans that result largely from rapid slip of glaciers over their beds are accelerating mass losses from ice sheets and associated sea-level rise ( 1, 2). Thus, these results may point to a universal slip law that would simplify and improve estimations of glacier discharges to the oceans. Computed slip laws have the same form as those indicated by experiments with ice dragged over deformable till, the other common bed condition. We find that consideration of actual glacier beds eliminates or makes insignificant rate-weakening drag, thereby uniting process-based models of slip with some ice-sheet model parameterizations. We present results of a process-based, three-dimensional model of glacier slip applied to measured bed topographies. Process-based models of glacier slip over idealized, hard (rigid) beds with water-filled cavities yield slip laws in which drag decreases with increasing slip velocity or water pressure (rate-weakening drag). Ice-sheet responses to climate warming and associated sea-level rise depend sensitively on the form of the slip law that relates drag at the beds of glaciers to their slip velocity and basal water pressure.
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