Bathymetry-aware mesoscale eddy parameterizations across upwelling slope fronts: A machine learning-augmented approach

Mesoscale eddy buoyancy fluxes across continental slopes profoundly modulate the boundary current dynamics and shelf-ocean exchanges, but have yet to be appropriately parameterized via the Gent-McWilliams (GM) scheme in predictive ocean models. In this work, we test the prognostic performance of multiple GM variants in non-eddying simulations of upwelling slope fronts that are commonly found along the subtropical continental margins. The tested GM variants range from a set of constant eddy buoyancy diffusivities to recently developed energetically-constrained, bathymetry-aware diffusivities, whose implementation is augmented by an artificial neural network (ANN) serving to predict the mesoscale eddy energy based on the topographic and mean flow quantities online. In addition, an ANN is employed to parameterize the cross-slope eddy momentum flux (EMF) that maintains a barotropic flow field analogous to that in an eddy-resolving model. Our tests reveal that non-eddying simulations employing the bathymetry-aware forms of the Rhines scale-based scheme and GEOMETRIC scheme (Wang and Stewart, 2020; https://doi.org/10.1016/j.ocemod.2020.101579) can most accurately reproduce the heat contents and along-slope baroclinic transports as those in the eddy-resolving simulations. Further analyses reveal certain degrees of physical consistency in the ANN-inferred eddy energy, which tends to grow (decay) as isopycnal slopes are steepened (flattened), and in the parameterized EMF, which exhibits the correct strength of shaping the flow baroclinicity if a bathymetry-aware GM variant is jointly used. These findings provide a recipe of GM variants for use in non-eddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes.