Energy balance of ice streams

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Abstract
Analysis of the cross-flow transmission of force from the central parts of a well-lubricated ice stream to its margins shows that there is a corresponding shift in the lateral location of motion-induced heat generation. The rate of basal heat generation in the center can be substantially smaller than the local rate of potential energy loss given by driving stress times the speed of downslope motion. The basal heating is a maximum for an intermediate level of lubrication for which speed is about 40% of the speed over a friction-less bed and base stress is about 25% of the driving stress. Stable and unstable balances between meltwater production and drainage on the bed are identified. A stable steady state with a speed less (more) than that giving maximum heat generation is termed drainage-(production-) limited, since an increase in speed would lead to increased (decreased) basal melting and must (need not) be balanced by increased drainage. It is shown that gradual evolution of the basal water drainage system and the factors affecting basal melting can cause discontinuous jumps between fast- and slow-moving states. A simplified analysis applied to six cross-sections of West Antarctic Ice Streams B, D, E and Rutford Ice Stream shows them to be diverse in the level of support from the sides and corresponding shift of mechanical heating sideward from their central parts. The cross-sections of Ice Stream B near “Upstream B” may be production-limited, because of especially high lubrication and related support from the sides. Cross-sections in the upper part of Ice Stream D, Ice Stream E and Rutford Ice Stream are in a drainage-limited condition. Substantial reduction of basal heat generation by side drag (in most cases) and expected high heat flow into the basal ice associated with low thickness (in some cases) tends to favor basal freezing. Nevertheless, all of the examined cross-sections except one are expected to experience basal melting with a modest geothermal heat-flux density of 60 m W m−1 or less in some cases. The lower part of Ice Stream B is an exception, where the analysis indicates that geothermal flux density must exceed 80–100 m W−1 m to maintain melting. If this high geothermal flux is not present, then the base of the lower part of Ice Stream B may be freezing, which would suggest continued deceleration of this part of Ice Stream B.