A coupled model of rapidly-evolving subglacial hydrology with ice dynamics

The presence of subglacial water can have a significant effect on the motion of an ice sheet. The rate at which the ice slides over the bedrock is mediated by subglacial water pressure. Meltwater on the surface of the sheet can drain through cracks and moulins; drastically increasing the amount of water under the sheet. This source of water fluctuates seasonally and diurnally, much faster than the timescale associated with large-scale glacier evolution. We are interested in the effect that this short-term variation in the subglacial hydrology, and therefore water pressure, has on the long-term behaviour of the ice sheet.  In particular, we are interested in how important it is to resolve the short-timescale variations in ice sliding speed.

 

We use a mathematical model to study the response of the subglacial drainage system to time-varying surface melt input. By coupling this subglacial hydrology through an effective-pressure-dependent sliding law to the momentum equation for the overlying ice sheet, we study the impact of short-term meltwater fluctuations on the ice velocity.  We study these interactions using a one-dimensional (1D) flowline model representing a confined glacier, allowing us to explore a range of couplings between the ice flow and hydrology.  This enables us to assess the influence of the fluctuating meltwater input on the long-term behaviour of the ice sheet. We find that using a time-averaged effective pressure with an asynchronous coupling to the momentum equation gives a reasonable estimate for the time-averaged ice-sheet velocity, despite the nonlinearity of the governing equations. We use the results to suggest how hydrological coupling might be achieved in larger-scale models where resolving the short-term fluctuations is likely to be infeasible.