Modeling thermodynamic ice-ocean interactions at the base of an ice shelf

Models of ocean circulation beneath ice shelves are driven primarily by the heat and freshwater fluxes that are associated with phase changes at the ice-ocean boundary. Their behavior is therefore closely linked to the mathematical description of the interaction between ice and ocean that is included in the code. An hierarchy of formulations that could be used to describe this interaction is presented. The main difference between them is the treatment of turbulent transfer within the oceanic boundary layer. The computed response to various levels of thermal driving and turbulent agitation in the mixed layer is discussed, as is the effect of various treatments of the conductive heat flux into the ice shelf. The performance of the different formulations that have been used in models of sub-ice-shelf circulation is assessed in comparison with observations of the turbulent heat flux beneath sea ice. Formulations that include an explicit parameterization of the oceanic boundary layer give results that lie within about 30% of observation. Formulations that use constant bulk transfer coefficients entail a definite assumption about the level of turbulence in the water column and give melt/freeze rates that vary by a factor of 5, implying very different forcing on the respective ocean models.