Modelling Subglacial Lakes: Quantifying Water Pressure Variations and Ice Surface Changes

Hundreds of subglacial lakes have been observed through satellite and aerogeophysical studies in Antarctica. Altimetry studies show that these lakes commonly inflate and deflate in response to water volume changes over time. Understanding how ice deformation above these lakes reflects changes in basal conditions is fundamental in assessing the state of the subglacial drainage system in many areas. However, the response of the ice surface to subglacial lake filling and draining has not been explored in sufficient detail with numerical models. Most modelling studies have utilized simplified models of subglacial lake drainage that assume the water pressure in the lake is always near the ice overburden pressure. The accuracy of this assumption for actively filling or draining lakes is unclear. Here we introduce a model for ice flow over a subglacial lake in order to characterize surface expressions of lake activity and quantify water pressure variations. We use a modified Stokes model where water volume is conserved via a Lagrange multiplier that in part determines the mean water pressure in the lake. Using this model, we study the evolution of the free surfaces over time for various lake sizes and volume change regimes. We quantify the departure of the mean water pressure from the ice overburden pressure in order to test the validity of an effective pressure approximation that has been used in simplified models of subglacial lake drainage. We compare the model results with ice altimetry data from both active and inactive Antarctic subglacial lakes to explore quantitatively the relationship between ice-surface deflection and changes in lake volume.