Parameterizing mesoscale eddy buoyancy fluxes using small neural networks

Mesoscale eddies are the energetically dominant flow structures in the ocean, and play a central role in transporting tracers and setting the stratification. The Gent-McWilliams (GM) and Redi parameterizations represent the impacts of these eddies in ocean models, which are unable or only partially able to resolve these eddies. The major advantage of these parameterizations is that they cast the mesoscale fluxes in an adiabatic framework, which is important for correctly representing these processes in the interior of the ocean. However, these parameterizations are a considerable source of uncertainty, as the eddy diffusivities associated with these parameterizations are hard to diagnose and prescribe, and also because these parameterizations are not designed to accurately capture the spatial and temporal structure of the eddy fluxes.

In this work, done under the umbrella of the M2LInES project, we take an alternative approach. We build a parameterization with the help of machine learning, which retains the adiabatic nature of the GM parameterization but models the mesoscale fluxes with the help of small neural networks (~1000 parameters) that are trained using high-resolution simulation output. This physics-based machine learning approach provides a good candidate to replace the existing GM parameterization in ocean models, and is able to accurately capture the spatial structure and the mean effect of the eddy fluxes. Here we will present a few different physics based neural network architectures that we considered for this task, and discuss their pros and cons. More importantly, we show that this approach has superior skill relative to conventional GM, in both offline and online settings, where the online skill is evaluated by implementing this parameterization in MOM6.