Tidal Grounding-Line Migration Modulated by Subglacial Hydrology

We present a mathematical model of the hydrology of grounding-line migration on tidal timescales, in which the ice acts elastically, overlying a connected hydrological network, with the ocean tides modelled by an oscillating far-field fluid height. The upstream grounding-line migration is driven by a fluid pressure gradient through the grounding zone, while the downstream migration is limited by fluid drainage through the till. The two processes are described using separate travelling-wave solutions, based on a model of fluid flow under an elastic sheet. The asymmetry between the up- and downstream motion allows the grounding line to act as a non-linear filter on the tidal forcing as the pressure signal propagates upstream, and this frequency modulation is discussed in the context of velocity data from ice streams across Antarctica to provide a novel constraint on till permeability

Shear dilation of subglacial till results in time-dependent sliding laws

The dynamics of glacial sliding over water-saturated tills are poorly constrained and difficult to capture realistically in large-scale models. Experiments characterize till as a plastic material with a pressure-dependent yield stress, but the subglacial water pressure may fluctuate on annual to daily timescales, leading to transient adjustment of the till. We construct a continuum two-phase model of coupled fluid and solid deformation, describing the movement of water through the pore space of a till that is itself dilating and deforming. By forcing the model with time-dependent effective pressure at the ice-till interface, we infer the resulting relationships between basal traction, solid fraction and rate of deformation. We find that shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials. The result is a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the slidingspeed. This deviation from traditional steady-state sliding laws may play an important role in a wide range of transient ice-sheet phenomena, from glacier surges to the tidal response of ice streams

A shallow approximation for ice streams sliding over strong beds

Ice streams are regions of rapid ice sheet flow characterised by a high degree of sliding over a deforming bed. The shallow shelf approximation (SSA) provides a convenient way to obtain closed-form approximations of the velocity and flux in a rapidly sliding ice stream when the basal drag is much less than the driving stress. However, the validity of the SSA approximation breaks down when the magnitude of the basal drag increases. Here we find a more accurate expression for the velocity and flux in this transitional regime before vertical deformation fully dominates, in agreement with numerical results. The closed-form expressions we derive can be incorporated into wider modelling efforts to yield a better characterisation of ice stream dynamics, and inform the use of the SSA in large-scale simulations

Numerical model supporting "Tidal grounding-line migration modulated by subglacial hydrology"

This code implements the reduced model of grounding line migration derived and used in the Warburton 2020 - "Tidal grounding line migration modulated by subglacial hydrology". Given tidal height over time, bedslope, and hydraulic permittivity, it returns the height of the grounding line

Shear dilation of subglacial till results in time-dependent sliding laws

Peer reviewed: TrueThe dynamics of glacial sliding over water-saturated tills are poorly constrained and difficult to capture realistically in large-scale models. Experiments characterize till as a plastic material with a pressure-dependent yield stress, but the subglacial water pressure may fluctuate on annual to daily timescales, leading to transient adjustment of the till. We construct a continuum two-phase model of coupled fluid and solid deformation, describing the movement of water through the pore space of a till that is itself dilating and deforming. By forcing the model with time-dependent effective pressure at the ice–till interface, we infer the resulting relationships between basal traction, solid fraction and rate of deformation. We find that shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials. The result is a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the slidingspeed. This deviation from traditional steady-state sliding laws may play an important role in a wide range of transient ice-sheet phenomena, from glacier surges to the tidal response of ice streams.</jats:p