Ice stream formation

Ice streams are the arteries through which a large fraction of the ice lost from Antarctica is discharged. With the introduction of "higher order" mechanics, the representation of ice streams in ice sheet models appears to have become more robust, eliminating previously ubiquitous grid effects. The detailed processes that control ice stream formation --- and the minimal ingredients that a model requires to represent them faithfully --- remain incompletely explored. Here we focus on "pure" ice streams, not confined to topographic troughs. We study two mechanisms that can cause their formation through feedbacks between enhanced dissipation and faster sliding, and study the minimal model capable of reproducing both mechanisms. In the first mechanism, increased dissipation raises basal temperature before the melting point is reached, and subtemperate sliding is in turn facilitated by these higher temperatures, leading to yet more dissipation. This mechanism has received very limited attention in the literature, and is not fully incorporated in at least some commonly used ice sheet model. The second, better-studied mechanism involves basal effective pressure rather than temperature as the degree of freedom that creates a positive feedback: increased dissipation produces additional meltwater. Draining that excess water requires a lower effective pressure in typical "distributed" draiange ssytems. Reduced effective pressure in turn leads to faster sliding, and yet more dissipation. The two mechanisms are distinct and one can operate in the absence of the other, but both can cause the formation of ice streams whose trunks have very similar features. Using a novel, hybrid `shallow/"full Stokes" flow' model derived from first principles, we show how accelerated flow due to either feedback leads to advection of cold ice to the bed, and demonstrate that this is the key negative feedback that controls ice steam formation due to its role in cooling the bed. Downward advection occurs both along the axis of the incipient ice stream, and in the transverse plane. There, a significant secondary flow towards the ice stream centre develops, which is of equal importance to along-flow advection in controlling heat transport. Our model is unique in its ability to fully resolve that secondary flow while still using the "shallowness" of the flow to simplify computations of ice stream physics. The formation of ice streams can be understood as "spatial" instabilities in which small-scale structure is amplified in the downflow direction, for which we derive an analytical criterion. Our model self-consistently predicts the formation of a sharply-defined ice stream margin and very cold-bedded ice ridges over a relatively short downstream distance from the onset of patterning for both mechanisms. The model also shows how basal dissipation in the margin leads to appreciable stream widening in the downstream direction, while englacial dissipation in combination with advection can lead to a pronounced peak in basal water supply some distance inside the margins. We demonstrate additionally that the emergent patterns can be unstable in time, and identify the properties required of a model that can handle such temporal instabilities.