Premelting dynamics on the boundary between glaciological and hydrological systems

The effective stress N, rate of basal freeze-on (or melting) V, heat flow, and rates of frictional and viscous dissipation control how glaciers interact with sub-glacial hydrological systems at the glacier/sediment interface. Interactions between ice and porous media are well understood from studies of ground-freezing in subaerial environments. Though the overburden beneath glaciers is much larger, N is often within the typical range that is considered by models for frost-heaving behavior in fine-grained sediments. Adapting these models to the subglacial environment, thermodynamic and mechanical considerations require that a fringe of partially frozen sediment extend beneath soft-bedded glaciers when N>pf≈1.1 (Tm- Tf) MPa/°C, where Tm-Tf is larger for sediments with finer grain sizes, and is equal to the temperature drop below the pressure-melting point that is needed for ice to infiltrate the pore space. Coupling between the glaciological and hydrological systems determines the fringe thickness h (sometimes 0) as a function of the local effective stress N, the basal energy balance, and sediment properties. Typically, pf=O(104) Pa and fringe thicknesses of several decimeters to meters in scale are predicted. The rate V that water can be transported through the fringe and frozen onto or melted from the glacier base can achieve a steady-state that is in balance with the rate that latent heat is transported to or from the basal interface. This water transport can represent a primary source or sink in the hydrological system, and the latent heat transport can make a leading-order contribution to the basal energy balance. For a glacier that is perched above a given sediment, larger h is predicted with higher N and the lower frictional heat input that accompanies slower sliding rates Ws. Unsteady behavior can lead to large changes in h when there is a mismatch between the rate that latent heat can be extracted and the rate that fluid is supplied to the ice--liquid boundary. Changes in N or Ws are expected to cause transient behavior, with the freezing rate V adjusting rapidly to satisfy force-balance constraints, and h relaxing on the time scale for conduction of latent heat. This can cause the integrated pattern of sediment deformation to be distributed over a finite depth range even when shear is perfectly localized at any given instant in time. Channelized subglacial flow implies spatial variations in N that require h and V to vary laterally in a predictable fashion that might be tested against field observations. An improved understanding of the coupled glacio-hydraulic system can be achieved with a more accurate parameterization of conditions on their common boundary.