Data-driven parameterisation of mesoscale eddies using the Eliassen-Palm flux

Parameterisations of mesoscale eddies have often focused on resolving individual aspects of the energy cycle characteristic of two-dimensional turbulence. To capture the full energy cycle of mesoscale eddies in a single parameterisation, we leverage data-driven methodologies. Our approach aims to simultaneously address the downscale transfer of potential energy (PE) and the upscale transfer of kinetic energy (KE). This endeavour relies on a theoretical framework that projects buoyancy fluxes onto the momentum equations, resulting in an eddy forcing represented by the divergence of the Eliassen-Palm (EP) flux tensor. High-resolution two-layer double-gyre data is used to train an artificial neural network (ANN) offline to correlate spatially-filtered (large scale) flow features with EP fluxes (subgrid-scale behaviours). This parameterisation is tested online in a double-gyre configuration of MOM6 (ocean component of GFDL + NCAR model) and assessed against the performance of a Gent-McWilliams parameterisation. Our results represent the first step towards a comprehensive parameterisation capable of capturing the entirety of the mesoscale eddy energy cycle.