Ice stream onset at a cold/temperate bed transition

Ice streams are corridors of fast flowing ice within an ice sheet. In some cases, their position is not constrained by bed topography, which suggests that patterning in the ice sheet velocity field can emerge spontaneously, in the form of a fingering instability. Previous research in this area has shown that subglacial hydrology and a feedback between strain heating, viscosity and flow rate can provide a recipe for the instability. Here, we pursue a slightly different angle and investigate whether an instability in the position of the cold-temperate transition at the bed can generate ice streams. Observations suggest that the marked contrast in velocity between ice streams and surrounding ice is due to a transition from cold, sticky bed underneath slow flowing regions, to temperate, well lubricated bed under ice streams. We treat this transition as a free boundary, whose position is constrained by basal thermal conditions. As in other models of ice stream formation, a positive feedback results from the fact that faster flowing ice dissipates more heat and therefore favours the formation of basal conditions that permit sliding. To understand how this positive feedback interacts with the evolution of the cold-temperate bed transition location, we develop a boundary layer model for dissipation and heat transport around the transition, which allows the transition migration rate to be computed. This enables us to include the contact line dynamics in a shallow ice model and to investigate the onset of streaming. Our results show that the background thermal structure of the ice sheet is key to the formation of ice streams: when the interior of the ice sheet is cold-based and the edges are warm-based, our model predicts the formation of regularly spaced though somewhat unrealistically wide ice streams. The reverse case of a warm interior and a cold edge results in an instability at wavelengths comparable to ice thickness, which is not resolved in most continental-scale ice sheet models.