Explosive Growth of Shear-Heating Instabilities in the Down-Slope Creep of Ice Sheets

Abstract

The time-scale for the onset of the explosive growth of a finite-amplitude shear-heating instability in the down-slope creep of a thick ice sheet is determined by integrating the equation for the temporal evolution of the temperature-depth profile subsequent to a sudden change in ice thickness. All instabilities eventually grow explosively after a prolonged period of simmering or relatively slow monotonic growth. Though times for explosive growth depend on initial and final ice thicknesses, surface temperature, accumulation rate, basal heat flux, and ice rheological parameters, the explosion times are extremely sensitive to the activation energy and the pre-exponential constant of the ice-creep law. Sudden increases in ice-sheet thickness of 1–2 km due to a rapid climatic deterioration can lead to explosive instability and melting of the basal shear layer in only thousands of years if ice-creep activation energies are lower than about 60 kJ mol ^-1.