Parameterizing subgrid-scale eddy effects using energetically consistent backscatter

In the near future we expect the resolution of many IPCC-class ocean models to enter the "eddy-permitting" regime. At this resolution models can produce reasonable eddy-like disturbances, but can still not properly resolve geostrophic eddies at all relevant scales. Adequate parameterizations representing sub-grid eddy effects are thus necessary. Most eddy-permitting models presently employ some kind of hyper-viscosity, which is shown to cause a significant amount of energy dissipation. However, comparison to higher resolution simulations shows that only enstrophy, but almost no energy, should be dissipated below the grid-scale. As a result of the artificial energy sink associated with viscous parameterizations, the eddy fields in eddy permitting models are generally not energetic enough. To overcome this problem, we propose a class of sub-grid parameterizations which dissipate enstrophy but little or no energy. The idea is to combine a standard hyperviscous closure with some mechanism to return dissipated energy to the resolved flow. Enstrophy dissipation remains ensured because the energy is returned at larger scales. Two simple ways to return the energy are proposed: one using a stochastic excitation and one using a negative Laplacian viscosity. Both approaches are tested in an idealized two-layer quasi-geostrophic model. Either approach is shown to greatly improve the solutions in simulations with typical eddy-permitting resolutions. The adaptation of the proposed parameterization for use in realistic ocean models is discussed.