An energetically consistent backscatter parameterization for eddy permitting ocean models

Increasing computational resources are starting to allow global ocean simulations at so-called “eddy permitting” resolutions, where the largest meso-scale eddies can be resolved explicitly, but an adequate parameterization of sub-grid eddy effects remains necessary. Most eddy-permitting models presently employ some kind of hyperviscosity, which is shown to cause a significant amount of energy dissipation. However, geostrophic turbulence exhibits a forward enstrophy- but not energy-cascade, suggesting that enstrophy but little or no energy should be dissipated at the grid-scale. As a result of the spurious energy dissipation associated with hyperviscous closures, eddy permitting models tend to have too little mesoscale eddy kinetic energy (EKE). We propose to counteract the spurious energy dissipation with an additional forcing term, which represents “backscatter” of energy from the unresolved scales to the resolved flow. The proposed parameterization makes use 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 larger scales than the hyperviscous dissipation, thus ensuring the 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.