How ice shelf morphology controls basal melting

The response of ice shelf basal melting to climate is a function of ocean temperature, circulation, and mixing in the open ocean and the coupling of this external forcing to the sub-ice shelf circulation. Because slope strongly influences the properties of buoyancy-driven flow near the ice shelf base, ice shelf morphology plays a critical role in linking external, subsurface heat sources to the ice. In this paper, the slope-driven dynamic control of local and area-integrated melting rates is examined under a wide range of ocean temperatures and ice shelf shapes, with an emphasis on smaller, steeper ice shelves. A 3-D numerical ocean model is used to simulate the circulation underneath five idealized ice shelves, forced with subsurface ocean temperatures ranging from -2.0°C to 1.5°C. In the sub-ice shelf mixed layer, three spatially distinct dynamic regimes are present. Entrainment of heat occurs predominately under deeper sections of the ice shelf; local and area-integrated melting rates are most sensitive to changes in slope in this "initiation" region. Some entrained heat is advected upslope and used to melt ice in the "maintenance" region; however, flow convergence in the "outflow" region limits heat loss in flatter portions of the ice shelf. Heat flux to the ice exhibits (1) a spatially nonuniform, superlinear dependence on slope and (2) a shape- and temperature-dependent, internally controlled efficiency. Because the efficiency of heat flux through the mixed layer decreases with increasing ocean temperature, numerical simulations diverge from a simple quadratic scaling law.