Modes of Operation of Thermo-Mechanically Coupled Ice Sheets

Abstract

A dimensionless model of thermo-mechanically coupled ice sheets is used to analyse the operation of the system. Three thermal processes are identified: (i) dissipation, having a maximum time-scale of thousands of years; (ii) advection, having a time-scale of tens of thousands of years; and (iii) conduction, having a time-scale of 100000 years. Kinematical processes occur on two time-scales: (i) a marginal advective time-scale of thousands of years; and (ii) a diffusive time-scale of tens of thousands of years dominant in the divide area. The coupling with the temperature field in the bed produces fluctuations to the depth of a few kilometres, which means that horizontal conduction in the bed can be ignored except perhaps in the marginal area. The thermal inertia of the bed could produce significant fluctuations in the geothermal heat gradient. The operation of the thermo-mechanically coupled system is explored with a time-dependent thermo-mechanically coupled numerical algorithm. Dependence of the basal friction on temperature is introduced heuristically, and an enthalpy method is used to represent the effect of latent heat. The marginal area is shown to be dissipation-driven, and always reaches melting point. The divide area can show two modes of behaviour: a warm-based mode where the ice sheet is thin, and a cold-based mode where the ice sheet is thick. Which mode operates depends upon the applied temperature field and the amount of heat conducted from the bed. Calculations where sliding is limited were not found to be possible owing to problems with the reduced model which resulted in a violation of the approximation conditions at the margin. Cases which did work required a substantial sliding component; as a result, a significant coupling between geometry and temperature can only be demonstrated when sliding is made temperature-dependent.