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

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 m_r. Since till strength τ_b{e} and ice stream velocity U_b{τ_b} 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 m_r{ U_b τ_b}. This is the “weak till” condition which requires that in a steady state till strength is a small fraction of the gravitational driving stress τ_b < (n + 1)^(−1) τ_d. The salient feature of the UPB model is its ability to produce two thermo mechanically controlled equilibrium states, one with a strong bed and slow ice velocities (“ice sheet” mode) and one with a weak bed and fast ice velocities (“ice-stream” mode). This bimodality of basal conditions is consistent with the available observations of subglacial conditions beneath slow and fast moving ice in West Antarctica. Basal conditions that do not correspond to these two steady states may occur transiently during switches between the two stable modes. The UPB model demonstrates that ice streams may be prone to thermally triggered instabilities, during which small perturbations in the basal thermal energy balance grow, leading to generation or elimination of the basal conditions which cause ice streaming