Subgrid parameterizations of the eddy-eddy, eddy-mean field, eddy-topographic, mean field-mean field, and mean field-topographic interactions in atmospheric models

Parameterizations are developed for each of the subgrid turbulence interaction classes in fully three-dimensional global atmospheric flows over topography, typical of January and July climate states. Stochastic and deterministic parameterizations are developed for the eddy-eddy interactions and deterministic parameterizations for eddy- mean field, eddy-topographic, mean field-mean field, and mean field-topographic interactions. All parameterizations are calculated from the statistics of higher-resolution reference direct numerical simulations (DNSs) truncated into resolved and subgrid scales and employed without tuning coefficients. This parameterization framework is validated by performing large-eddy simulations (LESs) that closely agree with the reference DNSs in terms of time-averaged kinetic energy spectra, zonal jet structure, and nonzonal streamfunction fields. Both the DNSs and LESs are formulated in such a way that the usual problem of a long artificial dissipation range does not occur. Successful LESs are produced with truncation wavenumbers 31 and 15, using, respectively, only 11.9% and 1.3% of the DNS computational effort at truncation wavenumber 63. The lower-resolution LESs show that the parameterizations are successful even when the energy injection due to baroclinic instability is not completely resolved. The contribution of each of the parameterized interaction classes to the quality of the LES is identified. The best agreement is achieved when all subgrid components are included. There is a very high level of agreement between the LESs and DNSs with typical streamfunction pattern correlations of r 5 0.962 for the nonzonal components and r 5 0.999 for the total fields when the complete sets of parameterizations are used.