Numerical and physical instability of subglacial water flow

Abstract

The sliding speed of glaciers depends strongly on the water pressure at the ice-sediment interface, which is controlled by the efficiency of water transport through a subglacial hydrological system. The least efficient component of the system is a `distributed' uniform sheet flow everywhere beneath the ice, whereas the `channelised' drainage through large, thermally eroded conduits is more efficient. To understand the conditions under which the subglacial network channelises, we perform a linear stability analysis of distributed flow, considering competition between thermal erosion and viscous ice collapse. We derive a stability criterion and determine the minimum subglacial meltwater flux needed for channels to form. We demonstrate the need to include lateral heat diffusion when modeling melt incision to resolve channel widths. We also show that low numerical resolution can suppress channel formation and lead to overestimates of water pressure. We demonstrate the applicability of linear stability results to predicting the character of subglacial hydrological networks without recourse to numerical modeling.