Impact of Parameterized Isopycnal Diffusivity on Shelf‐Ocean Exchanges Under Upwelling‐Favorable Winds: Offline Tracer Simulations Augmented by Artificial Neural Network.

Isopycnal eddy mixing across continental slopes profoundly modulates the ocean circulation and biogeochemistry. Yet this process must be parameterized in coarse‐resolution ocean models via an isopycnal eddy diffusivity prescribed with the Redi scheme. In this work, we evaluate the skill of physics‐based and data‐driven Redi variants in predicting the cross‐slope exchanges using a suite of offline‐mode parameterized tracer simulations for wind‐driven upwelling continental slope fronts, which commonly arise around the margins of subtropical gyres. The tested physics‐based Redi variants range from a constant eddy diffusivity to a recently proposed, bathymetry‐aware diffusivity augmented by the artificial neural network (ANN) that infers the mesoscale eddy kinetic energy from the mean flow and topographic quantities. Moreover, a purely data‐driven eddy diffusivity is learned by the ANN from the output data set of an eddy‐resolving model, whose solutions serve as the ground truth against which the parameterized tracer simulations are compared. Among all tested Redi variants, the ANN‐learned diffusivity and the bathymetry‐aware diffusivity outperform others in reproducing the tracer solutions of the eddy‐resolving model. However, a physics‐based Redi variant with local deficiencies can introduce global errors in the predicted tracer distribution, which calls for ongoing efforts in constraining the shelf‐to‐ocean transition of the isopycnal eddy diffusivity. A purely data‐driven diffusivity can nearly reproduce the diagnosed diffusivity from the eddy‐resolving model, which highlights the efficacy of machine learning techniques for parameterizing eddy processes across steep topography. This work serves as a key step toward parameterizing the isopycnal eddy mixing in ocean models with continental slopes. Plain Language Summary: Turbulent eddies across continental slopes drive the exchanges between shelf seas and open oceans, which are essential for coastal ecosystems and the global climate. These eddies are characterized by length scales smaller than the grid spacing of today's ocean climate models, resulting in unresolved eddy‐induced exchanges. This issue is usually remedied by eddy parameterizations that infer eddy fluxes from properties explicitly resolved in climate models. In this work, we evaluate extant parameterizations in constraining cross‐slope exchanges of oceanic tracers (such as salt and nutrients) by comparing simulations that utilize parameterizations with simulations that can explicitly resolve mesoscale eddies. Our results reveal the necessity to adopt more sophisticated parameterizations in non‐eddying simulations for cross‐slope eddy tracer exchanges than those currently used in climate models. Moreover, machine learning techniques are found to be effective in parameterizing cross‐slope eddy exchanges. Key Points: Data‐driven and physics‐based parameterizations of isopycnal eddy diffusivity across continental slopes are tested prognosticallyArtificial neural network‐inferred diffusivities and bathymetry‐aware diffusivities outperform previously tested variants over steep slopesMachine learning techniques effectively augment physics‐based mesoscale eddy parameterizations [ABSTRACT FROM AUTHOR]

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