Constraints on the lake volume required for hydro-fracture through ice sheets

[1] Water-filled cracks are an effective mechanism to drive hydro-fractures through thick ice sheets. Crack geometry is therefore critical in assessing whether a supraglacial lake contains a sufficient volume of water to keep a crack waterfilled until it reaches the bed. In this study, we investigate fracture propagation using a linear elastic fracture mechanics model to calculate the dimensions of water-filled cracks beneath supraglacial lakes. We find that the cross-sectional area of water-filled cracks increases nonlinearly with ice sheet thickness. Using these results, we place volumetric constraints on the amount of water necessary to drive cracks through ∼1 km of sub-freezing ice. For ice sheet regions under little tension, lakes larger than 0.25-0.80 km in diameter contain sufficient water to rapidly drive hydro-fractures through 1-1.5 km of subfreezing ice. This represents ∼98% of the meltwater volume held in supraglacial lakes in the central western margin of the Gireenland Ice Sheet.