Scaling laws for parametrizations of subgrid interactions in simulations of oceanic circulations.

Parametrizations of the subgrid eddy-eddy and eddy-meanfield interactions are developed for the simulation of baroclinic ocean circulations representative of an idealized Antarctic Circumpolar Current. Benchmark simulations are generated using a spectral spherical harmonic quasi-geostrophic model with maximum truncation wavenumber of T=504, which is equivalent to a resolution of 0.24° globally. A stochastic parametrization is used for the eddy-eddy interactions, and a linear deterministic parametrization for the eddy-meanfield interactions. The parametrization coefficients are determined from the statistics of benchmark simulations truncated back to the large eddy simulation (LES) truncation wavenumber, TR<T. A stochastic technique is used to determine the eddy-eddy coefficients, and a new least-squares regression method for the eddy-meanfield terms. Truncations are repeated for various TR, and the resolution dependence of the subgrid coefficients is identified. The mean jet structure and the kinetic and potential energy spectra resulting from the LESs closely agree with those from the benchmark simulations.