Design and Implementation of a Data‐Driven Parameterization for Mesoscale Eddy‐Induced Transport: Idealized Two‐Layer Configurations

Abstract

Mesoscale eddies contribute to ocean transport and are a major sink of available potential energy (APE). When unresolved or only partially resolved, their effects must be parameterized to simulate a realistic large‐scale state. Traditionally, this is achieved via the Gent‐McWilliams (GM) parameterization, which represents the eddy‐induced transport as an adiabatic advection built from a downgradient diffusive closure for the horizontal flux. While effective at capturing the bulk APE removal by eddies, the downgradient diffusive framework limits the structural accuracy of the parameterized fluxes, which in reality can contain significant upgradient and cross‐gradient components. Additionally, at eddy permitting resolutions, GM can negatively impact the resolved eddies, and is often turned off in regions where eddies are partially resolved. Here we present a novel data‐driven parameterization that is not constrained to be diffusive, and can capture the full structure of the eddy‐induced thickness fluxes while extracting APE and without overly negative impacts on the resolved flow. It is both flow‐aware and scale‐aware, and its magnitude can be tuned using an O(1) non‐dimensional number. Features like non‐dimensional inputs/outputs, lateral non‐locality, flow‐dependent coordinates, and range limitation improve the generalization of the data‐driven scheme. A small neural network is used, ensuring low cost and ease of implementation. The parameterization performs skillfully in offline evaluation, especially at scales smaller than the largest eddies. It is implemented in NOAA GFDL′ ${\text{GFDL}}^{\prime }$ s MOM6 and is skillful in online tests in two‐layer idealized simulations of a zonal channel and a wind‐driven gyre, at eddy‐permitting and non‐eddying resolutions.