Backscatter in energetically-constrained Leith parameterizations

This paper combines two strains in the literature on subgrid-scale parameterizations for eddying ocean models to develop six new parameterizations and test them in an idealized quasigeostrophic model. The first strain develops nonlinear, Smagorinsky-like Leith scalings for the viscous coefficient based on reasoning about the turbulent forward enstrophy cascade of geophysical turbulence. The second introduces backscatter whose amplitude is scaled to re-inject a portion of the energy dissipated by other parameterizations. In the new parameterizations developed here the backscatter and viscous coefficients depend on each other and are set to simultaneously absorb the forward enstrophy (or potential enstrophy) cascade and backscatter a portion of the dissipated energy. The addition of backscatter to Leith-scaled nonlinear viscosity improves the simulations at resolutions from 4 km to 24 km by increasing the total kinetic energy and by reducing the fraction of the total energy dissipation rate associated with the net effect of viscosity and backscatter. Versions that use biharmonic viscosity to absorb the enstrophy cascade perform better than versions using a harmonic viscosity, and purely viscous closures perform better than closures that dissipate both kinetic and potential energy. Stochastic and deterministic backscatter schemes are developed, and though similar, the deterministic schemes perform slightly better.