Stability of subglacial sediment systems

Glacier surges are quasiperiodic episodes of fast ice flow that occur principally due to increased slip at the ice-bed interface. However, mechanisms that trigger glacier surges are poorly understood. We study deformable subglacial sediment systems by drawing on earthquake literature to formulate a rate-and-state description of subglacial sediment and coupling it to an overlying viscous ice layer. Our framework models saturated sediment and accounts for the evolution of water pressure. The formulation is shown to produce a positive feedback process between the dynamics of the granular sediment and the viscous flow of the glacier, revealing an instability mechanism. We explore the stability of the purely time-dependent system, constructing a full regime diagram showing the conditions for stability. On incorporating vertical dependence into the system, we find that the sediment layer deepens, and sediment flux is enhanced during surge events, corresponding to observations of surging glaciers.