Investigation of creep instability as a mechanism for glacier surges

Creep instability was investigated by considering a simple slab model which includes the effect of ice advection normal to the surface. Whether a steady-state solution of the heat transfer equation exists depends on the value of a stability parameter proportional to the ratio of the rate of deformational heat production to the rate at which this heat is conducted away. If the parameter exceeds a certain critical value, instability occurs and basal ice eventually reaches melting point. The ice mass can then start to slide over its bed. If the stability parameter exceeds a second higher critical value, a layer of basal ice at melting point will form. The critical values depend on geothermal heat flux and strongly on advection. Upward advection as in the ablation area, decreases stability whereas downward advection (accumulation) increases it. On the other hand, if unstable conditions exist, accumulation increases the growth rate of the instability while ablation decreases it. Calculations suggest that certain natural ice masses may be unstable. The time for the instability to develop, however, is of the order of 100 to 10,000 yr., whereas the residence time of the ice in many glaciers is less than 10,000 yr.