Statistical dynamical subgrid-scale parameterizations for geophysical flows

Simulations of both atmospheric and oceanic circulations at given finite resolutions are strongly dependent on the form and strengths of the dynamical subgrid-scale parameterizations (SSPs) and in particular are sensitive to subgrid-scale transient eddies interacting with the retained scale topography and the mean flow. In this paper, we present numerical results for SSPs of the eddy-topographic force, stochastic backscatter, eddy viscosity and eddy-mean field interaction using an inhomogeneous statistical turbulence model based on a quasi-diagonal direct interaction approximation (QDIA). Although the theoretical description on which our model is based is for general barotropic flows, we specifically focus on global atmospheric flows where large-scale Rossby waves are present. We compare and contrast the closure-based results with an important earlier heuristic SSP of the eddy-topographic force, based on maximum entropy or statistical canonical equilibrium arguments, developed specifically for general ocean circulation models (Holloway 1992 J. Phys. Oceanogr. 22 1033-46). Our results demonstrate that where strong zonal flows and Rossby waves are present, such as in the atmosphere, maximum entropy arguments are insufficient to accurately parameterize the subgrid contributions due to eddy-eddy, eddy-topographic and eddy-mean field interactions. We contrast our atmospheric results with findings for the oceans. Our study identifies subgrid-scale interactions that are currently not parameterized in numerical atmospheric climate models, which may lead to systematic defects in the simulated circulations.