No abstract

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 ( b = c3e/c3t) on the basal melting rate m,.. Since till strength 'cb{e} and ice stream velocity Ub{'Cb} change as long as till void ratio varies, the first condition for ice stream stability is that of constant till water storage b = 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,.{ U6'c6}. This is the "weak till" condition which requires that in a steady state till strength is a small fraction of the gravitational driving stress 'c6<(n + 1)-•'ca. 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.

[1] We have produced a map of velocity covering much of the Siple Coast ice streams. The map confirms earlier estimates of deceleration on Whillans Ice Stream. Comparison with bed elevation data indicates that subglacial topography and the location of consolidated sediment play a strong role in determining the location of the tributaries feeding the ice streams. Force balance estimates based on these data indicate that the tributaries have beds nearly an order of magnitude stronger than those beneath many of the ice streams. We have used a theoretical analysis to examine the controls on fast flow. This analysis suggests that ice plains (very wide ice streams) are inherently unstable. This instability may be responsible for the current deceleration on the Ice Plain of Whillans Ice Stream and the shutdown of Ice Stream C 150 years ago. Thinning-induced reductions indriving stress may also explain some of the observed deceleration, particularly in upstream areas. The active portions of Ice Stream C coincide well with the areas where we estimate that melt should be taking place. Current topography and inferences of large thickening following a shutdown suggest the upstream migration of a stagnation front that initiated at the ice plain. Uncertainty remains about the basal conditions on Ice Stream D, while the basal resistance on Ice Stream E is large enough to ensure basal melting.

[1] We have constructed a high-resolution numerical model of heat, water, and solute flows in sub-ice stream till subjected to basal freeze-on. The model builds on quantitative treatments of frost heave in permafrost soils. The full version of the Clapeyron equation is used. Hence, ice-water phase transition depends on water pressure, osmotic pressure, and surface tension. The two latter effects can lead to supercooling of the ice base. This supercooling, in turn, induces hydraulic gradients that drive upward flow of pore water, which feeds the growth of segregation ice onto the freezing interface. This interface may progress into the till and form ice lenses if supercooling is sufficiently strong. Hence, the ice segregation process develops a stratified basal ice layer. In our model, a high basal temperature gradient ($0.054°C m À1 ) triggers ice stream stoppage, and the loss of basal shear heating leads to relatively high basal freeze-on rates ($3-5 mm a À1 ). In response, the subglacial till experiences comparatively rapid consolidation. Till porosity can decrease from 40% to <25%, and till strength can increase from $3 kPa to >120 kPa, approximately within one century. Basal supercooling arising from redistribution of solutes and ice-water interfacial effects amounts to ca. À0.35°C below the pressuremelting point. Fine-grained till is in our model associated with widely spaced, thick ice lenses. Coarse-grained till yields thinner ice lenses that are more closely spaced. Our model results compare favorably, although not in all details, with available observational evidence from borehole studies of West Antarctic ice streams.

[1] Ross ice streams supply over 90% of the ice volume flowing out of the Ross sector of the West Antarctic ice sheet (WAIS). Stoppage of Ice Stream C (ISC) ca. 150 years ago appears to have pushed this sector of WAIS from negative into positive mass balance [Joughin and Tulaczyk, 2002]. We propose an explanation for the unsteady behavior of ISC using a new numerical ice-stream model, which includes an explicit treatment of a subglacial till layer. When constrained by initial conditions emulating prestoppage geometry, dynamics, and mass balance of ISC, the model yields a rapid ($100 years) stoppage of the main ice-stream trunk. The stoppage is triggered by basal freeze-on, which consolidates and strengthens the subglacial till. Our numerical simulations produce results consistent with a number of existing observations, for example, continuing activity of the two tributaries of ISC. The model always yields rapid stoppage unless we specify icestream width that is smaller than its prestoppage values (maximum of $80 km). We conjecture that if ISC was active for at least a few thousand years before slowdown, its width was significantly smaller than today to sustain the long active phase. Ice-stream width is a key control that helps determine whether ice-stream flow is sustainable over a long term. Our work indicates that the recent stoppage of Ice Stream C could have been part of inherent ice-stream cyclicity, and it leaves open the possibility that other active ice streams may evolve in the future toward rapid shutdowns.