Canals under sediment-based ice sheets

Abstract

AbstractClassical theories of channelized subglacial drainage identify a melting vs creep balance at the channel-ice boundary that is crucial in determining its steady flow properties, but this consideration neglects the role of erodible-deformable basal sediments, especially in controlling channel morphology. Here we present a mathematical model for channel/underneath ice sheets, which incorporates the detailed mechanics of sediment transport over a mobile till-bed interface, and which allows a variable, wide channel cross section also. The resulting drainage conditions depend on the sediment flux (q) as well as the water flux (Q) through the channel - these quantities being controlled by the rates at which sediment and meltwater are captured by the flow. An approximate analytical solution indicates a "canal"-type drainage law (Walder and Fowler, 1994) of the form where N2 is thε effective channel pτessUτe, n is the exponent in Glen’s flow law for ice, and Ψ is the imposed hydraulic gradient (due to topography). By solving the downstream problem numerically, the canal characteristic has been confirmed and found to be insensitive to upstream conditions. Thus, low effective pressures can result from high basal water flux or melt rates. This supports the contention that canals may be a central component in fast ice flow over soft beds The proposed model also establishes a fundamental link between the plumbing system of a glacier and its sediment budget.