Tidal forcing of ice stream subglacial drainage and the potential for delivery of ocean heat into an ice stream interior

Ocean tides at a range of time scales are observed to cause surface displacement up to 100 km upstream of the grounding line. In narrow ice streams, a viscoelastic ice stream response alone cannot explain such far-reaching tidal influence due to the strong resistance provided by lateral shear stresses. One potential mechanism for transmitting tidal forcing far upstream of the grounding line is a pressure wave in the subglacial drainage system. In this study, we discuss a simple 1D model of subglacial drainage and water temperature. Our approach resembles that used in modeling Jokulhlaups, where increasing water pressure due to the filling of a lake at the upstream end of a glacier leads to rapid drainage channel widening and discharge. In our case, tidally-driven pressure variations at the grounding line drive flow of warm sub-shelf water into the drainage system, slowly widening channels further up into the ice stream over time. We discuss the effectiveness of this process for different tidal amplitudes and periods and the prescribed ambient temperature of seawater at the grounding line. We also show how the modeled pressure wave can potentially explain the extent of tidal velocity variations in one ice stream. We also discuss the implications for propagating an ocean warming signal into the ice sheet interior.