Elastic response of a grounded ice sheet coupled to a floating ice shelf

An ice sheet that spreads into an ocean is forced to bend owing to its buoyancy and detaches from the bedrock to form a floating ice shelf. The location of the transition between the grounded sheet and the floating shelf, defined as the grounding line, behaves as a free boundary. We develop a model of an elastic grounded sheet resting on a deformable elastic bed and coupled to an elastic floating shelf. We find that the grounding-line position is determined by the geometry of the bed and the bending-buoyancy length scale of the system. These two contributions depend on the reaction modulus of the bed in opposite ways. We show that the structure of the floating shelf depends on the bending-buoyancy length scale only, allowing us to calculate the bending stiffness of the elastic sheet independently of the properties of the bed. Relations between the structure of the floating shelf and the grounding-line position are also developed. Our theoretical predictions agree with laboratory experiments made using thick elastic sheets and a dense salt solution. Our findings may provide new insights into the dynamics near grounding lines, as well as methods to infer the bending stiffness of ice sheets and the grounding-line position from satellite altimetery that can be applied to elastic sheets in general.