Strain heating and creep instability in glaciers and ice sheets

Abstract

Creep instability, the runaway increase of internal temperature and deformation rate, may affect the boundary condition at the base of glaciers and ice sheets and thus influence their flow and dimensions. We consider a simple slab model of heat transport in which three dimensionless parameters determine the relative importance of strain heating, ice advection normal to the surface, and boundary conditions. We find that an ice mass will be unstable if the strain‐heating parameter exceeds a critical value which depends strongly on advection and boundary conditions. Critical values over the range of parameters appropriate to natural ice masses are presented. Accumulation (downward advection) or ablation (upward advection) affects the critical value by up to 5 orders of magnitude: ablation tends to reduce stability, and accumulation increases it. For an ice mass frozen to its bed, instability eventually raises the basal ice to melting point. This can restore thermal stability, but the ice mass will start to slide over its bed. If the strain‐heating parameter exceeds a second, higher critical value, a layer of basal ice at melting point will form. We find that the conditions for instability are likely to exist in the accumulation and ablation zones of certain glaciers and ice sheets. However, times calculated for instability to develop are in the range 102–103 yr for glaciers and 103–104 yr for ice sheets. As these times exceed the normal residence time for ice in the ablation zone, it appears that instability is most likely to develop in the accumulation zone. This conclusion is reinforced by the fact that ablation increases the growth time for instability, whereas accumulation decreases it. The growth times quoted above are longer than the periods of most glacier surges, and thus creep instability is an unlikely surge mechanism. Unstable conditions may, however, obtain in East Antarctica and may have existed in the central part of ice age ice sheets. Surges of ice sheets triggered by creep instability may be possible.