PARAMETERIZATION OF DYNAMICAL SUBGRID-SCALE PROCESSES IN A SPECTRAL GCM

The resolution of general circulation and other numerical mq;lels is u sually 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 atm ospheric analyses 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 circulatio n models. The nonlinear interactions among scales are calculated in te rms of a spectral decomposition on the sphere. A spectral empirical in teraction function (EIF) is obtained from data that, when applied to l arger scales (corresponding to resolved scales in a numerical model), recovers the effects of small scales (corresponding to unresolved, sub grid 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 l arge scales. It is positive and increases sharply with wavenumber ther eafter. The EIF qualitatively (but not quantitatively) resembles the s pectral diffusion function proposed by Leith, obtained in a very diffe rent fashion from two-dimensional turbulence considerations. The EIF d iffers in spectral form from the hyperdiffusion operator del(2n) Often used in models, since the latter is inherently positive at all wavenu mbers (i.e., dissipates energy and enstrophy at all scales). The forme r is also height dependent. The effect of parameterized subgrid horizo ntal interactions, F-H, on the kinetic energy is evaluated by calculat ing the source/sink term v . F-H. For hyperdiffusion or a version of t he EIF that is non-negative, v . F-H is everywhere dissipative, while for the complete EIF regions of kinetic energy generation are seen. Th e effect of the EIF on the simulated climate of the Canadian Climate C entre General Circulation Model is investigated as is a simulation wit h a restricted version of the function, for which the negative values are set to zero. As expected, the results obtained using the full empi rical function show increased levels of kinetic energy at relatively s mall wavenumbers, where models have often been deficient.