Energy budget-based backscatter in an eddy permitting primitive equation model

Increasing computational resources are starting to allow global ocean simulations at so-called "eddy-permitting" resolutions, at which the largest mesoscale eddies can be resolved explicitly. However, an adequate parameterization of the interactions with the unresolved part of the eddy energy spectrum remains crucial. Hyperviscous closures, which are commonly applied in eddy-permitting ocean models, cause spurious energy dissipation at these resolutions, leading to low levels of eddy kinetic energy (EKE) and weak eddy induced transports. It has recently been proposed to counteract the spurious energy dissipation of hyperviscous closures by an additional forcing term, which represents "backscatter" of energy from the un-resolved scales to the resolved scales. This study proposes a parameterization of energy backscatter based on an explicit sub-grid EKE budget. Energy dissipated by hyperviscosity acting on the resolved flow is added to the sub-grid EKE, while a backscatter term transfers energy back from the sub-grid EKE to the resolved flow. The backscatter term is formulated deterministically via a negative viscosity, which returns energy at somewhat larger scales than the hyperviscous dissipation, thus ensuring dissipation of enstrophy. The parameterization is tested in an idealized configuration of a primitive equation ocean model, and is shown to significantly improve the solutions of simulations at typical eddy-permitting resolutions.