Viscous response of ice sheet dynamics to water lubrication at the bed

Surface meltwater on the Greenland Ice Sheet, a viscous gravity current, can penetrate to the bed and lubricate the ice-bed interface. This reduction in basal friction leads to perturbations in the velocity, strain rate, and stress fields that are felt laterally away from the location of the basal lubrication as well as through the thickness of the ice column to the surface. It is therefore important to understand the dominant physical parameters which control the magnitude and spatial extent (i.e. the coupling lengthscale) of stress perturbations induced by basal lubrication. We investigate the effects of ice surface slope and thickness as controls on this stress response using (1) a 2D simulation of Stokes flow over a slippery patch simulating the presence of meltwater lubrication and (2) a reduced-order boundary layer model near the boundary condition transition. We found that the coupling length scales linearly with ice thickness whereas the surface stress increases with surface slope, and that the reduced-order model accurately captures depth-independent quantities such as the coupling lengthscale but cannot capture depth-dependent quantities such as the surface stress. These results indicate that inland ice may experience a weaker but longer-range stress perturbation in response to basal water lubrication.