Representing grounding line migration in synchronous coupling between a marine ice sheet model and a z-coordinate ocean model

Synchronous coupling is developed between an ice sheet model and a $z$-coordinate ocean model (the MITgcm). A previously-developed scheme to allow continuous vertical movement of the ice-ocean interface of a floating ice shelf (``vertical coupling'') is built upon to allow continuous movement of the grounding line, or point of floatation of the ice sheet (``horizontal coupling''). Horizontal coupling is implemented through the maintenance of a thin layer of ocean ($\sim$1 m) under grounded ice, which is inflated into the real ocean as the ice ungrounds. This is accomplished through a modification of the ocean model's nonlinear free surface evolution in a manner akin to a hydrological model in the presence of steep bathymetry. The coupled model is applied to a number of idealized geometries and shown to successfully represent ocean-forced marine ice sheet retreat while maintaining a continuous ocean circulation.