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  1. Abstract

    The flow speed of the Greenland Ice Sheet changes dramatically in inland regions when surface meltwater drains to the bed. But ice-sheet discharge to the ocean is dominated by fast-flowing outlet glaciers, where the effect of increasing surface melt on annual discharge is unknown. Observations of a supraglacial lake drainage at Helheim Glacier, and a consequent velocity pulse propagating down-glacier, provide a natural experiment for assessing the impact of changes in injected meltwater, and allow us to interrogate the subglacial hydrological system. We find a highly efficient subglacial drainage system, such that summertime lake drainage has little net effect on ice discharge. Our results question the validity of common remote-sensing approaches for inferring subglacial conditions, knowledge of which is needed for improved projections of sea-level rise.

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  2. Grounding lines exist where land-based glacial ice flows on to a body of water. Accurately modelling grounding-line migration at the ice–ocean interface is essential for estimating future ice-sheet mass change. On the interior of ice sheets, the shores of subglacial lakes are also grounding lines. Grounding-line positions are sensitive to water volume changes such as sea-level rise or subglacial-lake drainage. Here, we introduce numerical methods for simulating grounding-line dynamics in the marine ice sheet and subglacial-lake settings. Variational inequalities arise from contact conditions that relate normal stress, water pressure and velocity at the base. Existence and uniqueness of solutions to these problems are established using a minimisation argument. A penalty method is used to replace the variational inequalities with variational equations that are solved using a finite-element method. We illustrate the grounding-line response to tidal cycles in the marine ice-sheet problem and filling–draining cycles in the subglacial-lake problem. We introduce two computational benchmarks where the known lake volume change is used to measure the accuracy of the numerical method. 
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