The Role of Meltwater Advection in the Formulation of Conservative Boundary Conditions at an Ice–Ocean Interface

Abstract

Upper boundary conditions for numerical models of the ocean are conventionally formulated under the premise that the boundary is a material surface. In the presence of an ice cover, such an assumption can lead to nonconservative equations for temperature, salinity, and other tracers. The problem arises because conditions at the ice?ocean interface differ from those in the water beneath. Advection of water with interfacial properties into the interior of the ocean therefore constitutes a tracer flux, neglect of which induces a drift in concentration that is most rapid for those tracers having the lowest diffusivities. If tracers are to be correctly conserved, either the kinematic boundary condition must explicitly allow advection across the interface, or the flux boundary condition must parameterize the effects of both vertical advection and diffusion in the boundary layer. In practice, the latter alternative is often implemented, although this is rarely done for all tracers.