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, where 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 hyperviscosity, which is shown to cause a significant amount of energy dissipation. However, geostrophic turbulence exhibits a forward enstrophy cascade but an inverse energy cascade. This phenomenology suggests that enstrophy should be dissipated below the grid-scale, whereas energy dissipation should occur only in boundary layers.

To obtain a closure that is in agreement with this basic physical principle, we propose to combine a standard bi-harmonic hyperviscous closure with a representation of energy “backscatter”, which ensures the conservation of energy. The parameterization of energy backscatter is formulated 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 Laplacian viscosity, which returns energy at somewhat larger scales than the hyperviscous dissipation, thus ensuring dissipation of enstrophy. The general idea has been demonstrated in idealized models, where the parameterization greatly improves simulations at typical eddy-permitting resolutions. First sucessfull tests have also been performed using GFDL’s MOM6 ocean model in a global configuration with an eddy permitting resolution of 1/4 degree. Kinetic energy levels are enhanced and more closely match the observations, and the representation of various eddying currents is improved.