Abstract
The resolution of general circulation and other numerical models is usually characterized by their grid spacing or spectral truncation. In all models, some representation or parameterization of the effects of unresolved scales on those explicitly resolved is required. Global atmospheric analysts from several sources are used to infer the dynamical effects of smaller horizontal scales on larger horizontal scales for the purpose of parameterizing these interactions in general circulation models. The nonlinear interactions among scales are calculated in terms of a spectral decomposition on the sphere. A spectral empirical interaction function (EIF) is obtained from data that, when applied to larger scales (corresponding to resolved scales in a numerical model), recovers the effects of small scales (corresponding to unresolved, subgrid scales in a numerical model) on these larger scales in the data.
The EIF takes small negative values at low wavenumbers, implying that interactions with small scales provide energy and enstrophy to these large scales. It is positive and increases sharply with wavenumber thereafter. The EIF qualitatively (but not quantitatively) resembles the spectral diffusion function proposed by Leith, obtained in a very different fashion from two-dimensional turbulence considerations. The EIF differs in spectral form from the hyperdiffusion operator ∇2n often used in models, since the latter is inherently positive at all wavenumbers (i.e., dissipates energy and enstrophy at all scales). The former is also height dependent.
The effect of parameterized subgrid horizontal interactions, FH, on the kinetic energy is evaluated by calculating the source/sink term v·FH. For hyperdiffusion or a version of the EIF that is non-negative, v·FH is everywhere dissipative, while for the complete EIF regions of kinetic energy generation are seen.
The effect of the EIF on the simulated climate of the Canadian Climate Centre General Circulation Model is investigated as is a simulation with a restricted version of the function, for which the negative values are set to zero. As expected, the results obtained using the full empirical function show increased levels of kinetic energy at relatively small wavenumbers, where models have often been deficient.
