Ice streams: thermal and hydraulic pattern formation in ice sheets

Abstract:

"Pure" ice streams, not confined to topographic troughs, are likely to be spontaneously generated patterns in ice sheets. We study two mechanisms that can cause their formation through feedbacks between enhanced dissipation and faster sliding. The first relies on enhanced dissipation raising basal temperatures where the bed is subtemperate, with a subtemperate sliding law that assumes reduced basal shear stress at warmer bed temperatures, leading to faster sliding and more dissipation. This mechanism has received minimal attention in the literature. The second, better-known mechanism considers basal effective pressure rather than temperature as the dynamical degree of freedom involved: increased dissipation produces additional meltwater, whose drainage requires a higher drainage capacity and therefore (depending on the drainage model) a lower effective pressure. That in turn leads to faster sliding. Both mechanisms can operate independently of each other, and either can cause patterning. Using a novel, hybrid `shallow/"full Stokes" flow' model derived from first principles, we are able to resolve fully how accelerated flow due to either feedback leads to advection of cold ice to the bed. Downward advection occurs both along the axis of the incipient ice stream, and in the transverse plane, where a significant secondary flow towards the ice stream centre develops. We show how that advection as a negative feedback controls the onset of instability for both mechanisms. These can be understood as "spatial" instabilities in which small-scale structure is amplified in the downflow direction, and we give a simple criterion for the onset of instability for the first, subtemperate feedback mechanism. Our model self-consistently predicts the formation of a sharply-defined ice stream margin separating a very cold, frozen-bedded ice ridge from a fully established ice stream over a relatively short downstream distance from the onset of patterning for both mechanisms. The model also shows how englacial dissipation in the margin leads to appreciable stream widening in the downstream direction. We demonstrate additionally that the emergent patterns can be unstable in time, identifying conditions under which stable steady states are impossible, potentially forcing oscillatory behaviour in the ice stream.