An Embedded Boundary Algorithm for Ice Sheet Grounding Line Reconstruction

Projecting contributions from marine ice sheets to future sea level rise requires an accurate representation of the region of ice neighboring the grounding line. The grounding line marks the location where formerly grounded ice flows into floating ice shelves, making it an area of dynamic activity. It is critical that an ice sheet model be able to locate the grounding line with high precision in order to capture the distinct behavior of ice on either side of it. From a mathematical perspective, the grounding line represents a subgrid-scale moving boundary that divides the domain into regions with distinct sets of governing equations. However, the exact position of this boundary is unknown, as it is a function of values that are only known at discrete points in space or as local averages. Our algorithm locates this "embedded" boundary in space by reconstructing the discontinuity in the slope of the ice surface at the grounding line, then iteratively refining geometric moments on cut cells and conserving ice thickness. The reconstructed subgrid-scale representation of the grounding line will be incorporated into a higher-order velocity solve and ice thickness advection. The algorithm will be tested on a range of idealized and realistic problems in the BISICLES ice sheet model.