Tidal Grounding‐Line Migration Modulated by Subglacial Hydrology

Abstract

Abstract 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. Plain Language Summary The grounding zone, where the ice sheet transitions from contact with the bed to floating on the ocean, plays an important role in understanding the contribution of polar ice sheets to sea level rise. This model explores how ocean water can be pumped through the grounding zone to the region underneath ice sheets as the ocean tides go in and out. Water present underneath ice sheets can make the ice flow faster. We show that the difference between how quickly the water flows into and out of the grounding zone could explain some observations of tidal variations in glacier speed and raises questions for the amount of melting happening underneath ice sheets. Key Points Hydraulic resistance of the subglacial environment limits the speed of grounding‐line migration Speed of grounding‐line migration may differ between incoming and outgoing tides Asymmetric response of the grounding zone can act as a nonlinear filter on the tidal forcing