An enthalpy method for subglacial frozen fringe

Fast glacier flow over soft beds account for a significant fraction of the uncertainty in future sea level rise. Failure of the subglacial sediments facilitates the fast flow and the strength of the sediments is tied to the effective pressure, i.e. the difference between overburden and pore water pressure. Depending on the effective pressure and the thermodynamic state, the boundary between the ice and sediment can be clean (i.e. debris free) or dirty, where the ice has infiltrated into the till sediments (i.e. a frozen fringe). Here we derive an enthalpy formulation for characterizing the infiltration of ice into subglacial sediments. Our model accounts for premelting at ice-sediment contacts, partial ice saturation of the pore space, water flow through the fringe, the thermodynamics of the ice-water-sediment interface, and vertical force balance. A significant advance of our enthalpy model over prior treatments, is that we can explicitly account for the formation of ice lenses, regions of pure ice that cleave the fringe at the depth where the interparticle force vanishes. Using this model, we find significant zones of ice infiltration for parameters choices typical for ice streams and we examine the spacing of ice lenses, which we will compare to borehole images of sediment freeze-on beneath ice streams. Our model results allow us to determine the thickness of frozen sediment at the base of ice streams for given parameters, further highlighting the need for techniques to characterize relevant parameters in the ice stream environment and better constrain the effects of frozen sediment on basal friction.