Dynamics of ice stream temporal variability: Modes, scales, and hysteresis

Abstract

[1] Understanding the mechanisms governing temporal variability of ice stream flow remains one of the major barriers to developing accurate models of ice sheet dynamics and ice-climate interactions. Here we analyze a simple model of ice stream hydrology coupled to ice flow dynamics and including drainage and basal cooling processes. Analytic and numerical results from this model indicate that there are two major modes of ice stream behavior: steady-streaming and binge-purge variability. The steady-streaming mode arises from friction-stabilized subglacial meltwater production, which may also activate and interact with subglacial drainage. The binge-purge mode arises from a sufficiently cold environment sustaining successive cycles of thinning-induced basal cooling and stagnation. Low prescribed temperature at the ice surface and weak geothermal heating typically lead to binge-purge behavior, while warm ice surface temperature and strong geothermal heating will tend to produce steady-streaming behavior. Model results indicate that modern Siple Coast ice streams reside in the binge-purge parameter regime near a subcritical Hopf bifurcation to the steady-streaming mode. Numerical experiments exhibit hysteresis in ice stream variability as the surface temperature is varied by several degrees. Our simple model simulates Heinrich event-like variability in a hypothetical Hudson Strait ice stream including dynamically determined purge time scale, till freezing and basal cooling during the binge phase. These findings are an improvement on studies of both modern and paleo-ice stream variability and provide a framework for interpreting complex ice flow models.Citation: Robel, A. A., E. DeGiuli, C. Schoof, and E. Tziperman (2013), Dynamics of ice stream temporal variability: Modes, scales, and hysteresis,

Sedimentary and structural evolution of a relict subglacial to subaerial drainage system and its hydrogeological implications: an example from Anglesey, north Wales, UK

“…Understanding the behaviour of subglacial meltwater systems is crucial because of their influence upon substrate rheology and ice-bed coupling (Boulton & Hindmarsh, 1987;Iverson et al, 1995;Boulton, 1996;Piotrowski et al, 2004Piotrowski et al, , 2006Evans et al, 2006;Kjaer et al, 2006;Lee & Phillips, 2008;Boulton et al, 2009), and in-turn, glacier dynamics that operate over a range of temporal and spatial scales (Kamb, 1987;Bartholomew et al, 2010;Sundal et al, 2011;Robel et al, 2013). Research now recognises that these processes act to drive the expansion, break-up and collapse of major ice streams and ice masses (MacAyeal, 1993;Clark, 1994;Tulaczyk et al, 2000;Bell et al, 2007;Stokes et al, 2007;Burke et al, 2012) thus linking subglacial drainage to collapsing ice masses, sea-level change and abrupt climate change (Goezler et al, 2011;King et al, 2012;Hanna et al, 2013;Fürst et al, 2014 and references therein).…”

Stochastic ice stream dynamics

“…This regime can be explained by thermal feedbacks that enhance basal meltwater production (24)(25)(26)(27). How meltwater modulates ice stream velocity depends on the nature of the ice−bed contact: If the ice stream is underlain by a layer of sediment, meltwater infiltrates the sediment, which, in turn, deforms more easily as a result of the shear stress imposed by the ice (27)(28)(29). If, instead, ice is in direct contact with bedrock, the lubrication provided by water at the ice−rock interface controls the rate at which ice slips over the bed (25).…”

“…Despite different levels of complexity, a common feature of ice stream models is oscillatory behavior in the form of stagnation and activation cycles (24-27, 29, 40). Recent work (29) has proven that this behavior emerges through a Hopf bifurcation in the dynamics of steady ice stream flow under changes in the control parameters, which noticeably include atmospheric temperature and snow recharge. This kind of bifurcation, which consists of a transition from a stable fixed point to a stable limit cycle, is widespread in environmental systems, and the literature suggests that it is sensitive to stochastic forcing (41,43).…”

“…The simplest model able to capture these dynamics is proposed by Robel et al (29). They develop a physically based, spatially lumped model where time is the only independent variable, to understand the physical processes underpinning temporal ice stream dynamics.…”

“…Robel et al (29) consider an ice stream of fixed width underlain by a layer of subglacial sediment (known as till). The key ingredients of the model are (i) the ice stream mass balance and (ii) the basal energy budget.…”