Parameterizing eddy buoyancy fluxes across prograde shelf/slope fronts using a slope-aware GEOMETRIC closure

Accurate parameterizations of eddy fluxes across prograde, buoyant shelf and slope currents are crucial to faithful predictions of the heat transfer and water mass transformations in high-latitude ocean environments in ocean climate models. In this work we evaluate several parameterization schemes of eddy buoyancy fluxes in predicting the mean state of prograde current systems using a set of coarse-resolution non-eddying simulations, the solutions of which are compared against those of fine-resolution eddy-resolving simulations with nearly identical model configurations. It is found that coarse-resolution simulations employing the energetically-constrained GEOMETRIC parameterization can accurately reconstruct the prograde mean flow state, provided that the suppression of eddy buoyancy diffusivity over the continental slope is accounted for. The prognostic subgrid-scale eddy energy budget in the GEOMETRIC parameterization scheme effectively captures the varying trend of the domain-wide eddy energy level in response to environmental changes, even though the energy budget is not specifically designed for a sloping-bottomed ocean. Local errors of the predicted eddy energy are present but do not compromise the predictive skill of the GEOMETRIC parameterization for prograde current systems. This work lays a foundation for improving the representation of prograde current systems in coarse-resolution ocean climate models.