Abstract
AbstractThis paper examines the effect of basal topography and strength on the grounding-line position, flux and stability of rapidly-sliding ice streams. It does so by supposing that the buoyancy of the ice stream is small, and of the same order as the longitudinal stress gradient. Making this scaling assumption makes the role of the basal gradient and accumulation rate explicit in the lowest order expression for the ice flux at the grounding line and also provides the transcendental equation for the grounding-line position. It also introduces into the stability condition terms in the basal curvature and accumulation-rate gradient. These expressions revert to well-established expressions in circumstances in which the thickness gradient is large at the grounding line, a result which is shown to be the consequence of the non-linearity of the flow. The behaviour of the grounding-line flux is illustrated for a range of bed topographies and strengths. We show that, when bed topography at a horizontal scale of several tens of ice thicknesses is present, the grounding-line flux and stability have more complex dependencies on bed gradient than that associated with the ‘marine ice-sheet instability hypothesis’, and that unstable grounding-line positions can occur on prograde beds as well as stable positions on retrograde beds.
Highlights
The discovery that sections of the West Antarctic Ice Sheet are losing mass to the oceans (Wingham and others, 1998; Rignot, 1998; Shepherd and others, 2018) with significant implications for global sea levels (e.g. Shepherd and others, 2018) has given practical importance to understanding the evolution of the grounding line – the boundary between the grounded and floating parts – of marine ice sheets
Since the original framing of Weertman (1974), the matter has received continuous theoretical attention (e.g. Chugunov and Wilchinsky, 1996; Hindmarsh and Le Meur, 2001; Schoof, 2007a, 2007b, 2012; Nowicki and Wingham, 2008; Robel and others, 2014; Tsai and others, 2015; Robel and others, 2016; Kowal and others, 2016; Schoof and others, 2017; Haseloff and Sergienko, 2018; Pegler, 2018), principally arising from the contention of Weertman (1974) that a marine ice sheet cannot exist in steady state on a retrograde bed, a hypothesis that has become known as the ‘marine ice-sheet instability hypothesis’
This, in turn, depends on the assumption that the thickness gradient in the momentum equation is large in comparison with the basal gradient. While this is a reasonable description of ice streams flowing over smooth beds offering considerable resistance to the flow, ice streams can experience a variety of frictional resistance at their beds and flow over bed topography that contains a wide range of spatial scales as Figure 1 illustrates
Summary
The discovery that sections of the West Antarctic Ice Sheet are losing mass to the oceans (Wingham and others, 1998; Rignot, 1998; Shepherd and others, 2018) with significant implications for global sea levels (e.g. Shepherd and others, 2018) has given practical importance to understanding the evolution of the grounding line – the boundary between the grounded and floating parts – of marine ice sheets. This, in turn, depends on the assumption that the thickness gradient in the momentum equation is large in comparison with the basal gradient While this is a reasonable description of ice streams flowing over smooth beds offering considerable resistance to the flow, ice streams can experience a variety of frictional resistance at their beds and flow over bed topography that contains a wide range of spatial scales as Figure 1 illustrates. The effect of the basal gradient in the momentum equation naturally occurs in the lowest order relation between ice flux and thickness at the grounding line, which supplies the transcendental equation for the steady grounding-line locations, assuming these exist. We consider the stability of the steady-state grounding line locations, and find that this depends on the basal curvature in addition to the basal gradient and the simple relationship between basal gradient no longer holds. The stability condition that informs the ‘marine ice-sheet instability hypothesis’ no longer generally applies
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