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 noneddying 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.