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 modeled 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 upstream and downstream motion allows the grounding line to act as a nonlinear 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.

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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.

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