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
