Basal mechanics of Ice Stream B, West Antarctica 2. Undrained plastic bed model

Abstract

Based on the results of our studies of the physical conditions beneath Ice Stream B, we formulate a new analytical ice stream model, the undrained plastic bed model (henceforth the UPB model). Mathematically, the UPB model is represented by a non-linear system of four coupled equations which express the relationships among ice sliding velocity, till strength, water storage in till, and basal melt rate. We examine this system of equations for conditions of ice stream stability over short timescales that permit holding ice stream geometry constant (less than hundreds of years). Temporal variability is introduced into the UPB model only by the direct dependence of till void ratio changes (ė = ∂e/∂t) on the basal melting rate mr. Since till strength τb{e} and ice stream velocity Ub{τb} change as long as till void ratio varies, the first condition for ice stream stability is that of constant till water storage ė = 0. The second condition for ice stream stability arises from the feedback between ice stream velocity, till strength, and the basal melting rate which depends on shear heating mr{Ubτb}. This is the "weak till" condition which requires that in a steady state till strength is a small fraction of the gravitational driving stress τb