Leveraging machine learning to parameterise ocean mesoscale eddies

The dynamics of the ocean are dictated by processes that occur over a wide spectrum of scales. Of particular importance are the motions that occur at and around the Rossby radius of deformation, between approximately 10 and 1000 km, so called mesoscale eddies. Mesoscales exchange energy with large-scale ocean currents, thus influencing global ocean circulation. Mesoscale eddies extract potential energy (PE) from the large scale via baroclinic instability, and transfer kinetic energy (KE) upscale via the backscatter effect (inverse cascade). Accurately capturing the global ocean circulation, and the role of mesoscale eddies, is imperative in the development of reliable climate models. However, the resolution required to resolve mesoscales and their contribution to the global ocean energy cycle is far too computationally expensive, particularly for long climate integrations or large ensembles. Thus, the contributions of mesoscale eddies to the energy cycle must be parameterised in terms of the coarse-resolution flow variables of climate models. 

Most parameterisations of mesoscale eddies have focussed on resolving individual aspects of the energy cycle. Our approach aims to simultaneously address the downscale transfer of PE and the upscale transfer of KE by leveraging high-resolution simulations and machine learning. This endeavour relies on a theoretical framework that projects the buoyancy flux onto the momentum equations, resulting in an eddy forcing captured by the divergence of the Eliassen-Palm (EP) flux tensor. We develop our parameterisation using the idealised two-layer double-gyre (DG) configuration of MOM6 (ocean component of GFDL + NCAR model). High-resolution DG data is used to train an artificial neural network offline on the correlation between spatially-filtered (large scale) flow features with EP fluxes (subgrid-scale forcing). This parameterisation is shown to improve the representation of the eddy energy cycle in a DG configuration of MOM6. Our results are part of an ongoing effort towards a comprehensive parameterisation capable of capturing the entirety of the mesoscale eddy energy cycle.