The Editor,
Journal of Glaciology
Sir,
The determination of temperature and flow in an ice mass undergoing subsolidus creep is a coupled thermomechanical problem. Both quantities must be found simultaneously and self-consistently; temperature affects flow because the effective viscosity of ice is highly temperature-dependent and flow affects temperature because shear in the flow leads to frictional heating. One of the major purposes of our paper (Reference Yuen and SchubertYuen and Schubert, 1979) was to explore the properties of self-consistent solutions to a tractable mathematical model of the deformation of an ice mass. It was found that the family of mathematical solutions is multiple-valued in that two (or three) values of surface velocity or basal temperature can correspond to one value of ice thickness. The existence of mathematical multiple steady states does not imply, of course, the existence of physical multiple steady states for real ice masses (Reference FowlerFowler, 1980). Environmental circumstances, including the integrated mass flux arising from the net of accumulation and ablation, will determine a particular value of ice thickness. However, while such environmental factors remove the indeterminacy of the steady state, they do not help us to understand how the ice mass will evolve when environmental conditions undergo sudden and dramatic changes. The determination of steady state and the stability of the steady state are distinct issues. To decide whether a steady state is stable, one must subject the steady state to finite-amplitude changes in the environmental factors such as accumulation- and ablation-rates and follow the temporal evolution of the ice mass in a self-consistent thermomechanical calculation. We believe that thermal runaway can be shown to occur in idealized mathematical models of ice-sheet deformation when the ice is subject to finite-amplitude changes in certain environmental factors. However, thermal runaway may not in fact occur in a real ice mass because the appropriate changes in environmental conditions may not be realizable. Caution is certainly required in attributing such phenomena as glacial surges to the thermal runaway instability.
