Examining the Fidelity of Leith Subgrid Closures for Parameterizing Mesoscale Eddies in Idealized and Global (NEMO) Ocean Models

Eddy-permitting models struggle to simulate accurate Southern Ocean (SO) circulation. In particular, the medium resolution Hadley Center Global Coupled model in CMIP6 exhibits a warm SO bias and weak Antarctic Circumpolar Current (ACC) transport. These issues are attributed to a poor representation of mesoscale eddies, which also impair the simulated transport of heat and carbon. To rectify these problems, two momentum closures (harmonic and biharmonic) are implemented in the Nucleus for European Modeling of the Ocean general circulation model: 2D Leith and Quasi-Geostrophic Leith. These Leith closures aim to capture the correct cascades of energy and enstrophy in quasi two-dimensional models. Additionally, the harmonic Leith viscosity coefficients can replace the traditional Gent-McWilliams and Redi diffusivity coefficients. In this work we explore Leith closures in an eddy-resolving channel model and an eddy-permitting forced global ocean sea-ice model, Global Ocean Sea-Ice 9 (GOSI9). The idealized model shows the Leith implementation functions as intended. In the GOSI9 configuration, the harmonic Leith schemes increase the ACC transport by $10-17$%. This is in response to isopycnal flattening across Drake Passage that reduces a strong Westward flow at $60°$S. This increase in ACC transport coincides with reduced warming around Antarctica and reduction of cold biases in the Atlantic. Both viscosity schemes also lead to a warm model drift. Swapping biharmonic with quasi-geostrophic Leith viscosity in GOSI9 results in one of the strongest ACC transports, along with improvements to some biases in the Atlantic.