The Dynamical Balance of a General Circulation Model

Abstract

A global, spectral model developed at the National Center for Atmospheric Research is investigated. It is first demonstrated that some of the model's normal modes tend toward an approximate dynamical balance. This is shown by presenting time series of a kind of mean frequency for the various types of modes. For the analyzed data investigated, almost all inertial-gravitational waves initially present are dissipated within two weeks. Most are dissipated much more quickly. The model is then used to determine which modes are balanced. Only the balance described byMachenhauer is investigated. The relative magnitudes of various diabatic and adiabatic forces (including advection as a "force"), as they act to drive each normal mode, are compared with the time tendency of each mode. A mode is considered balanced if the magnitude of its time tendency is significantly smaller than the magnitudes of some forces acting upon it, implying that those forces tend to cancel each other. Gravitational modes whose natural (i.e., resonant) periods are less than 20 h appear to be balanced; this balanced set includes modes of all vertical and horizontal scales, although not all combinations of such scales. That these modes are balanced implies that their amplitudes satisfy an approximate diagnostic relationship, although they are actually prognostically determined. Gravitational modes with longer natural periods appear to behave as forced waves. As expected, rotational modes are mostly driven by adiabatic, quasi-rotational dynamics, and exhibit neither balanced nor wavelike behavior to any great degree. The forces which are in balance include the inertial-gravitational force (expressed by linear terms in the model) and the forcing of the gravitational modes by the rotational modes (expressed by nonlinear terms). For shallow modes, surface drag also balances the inertial-gravitational force. For no modes does heating by any process appear to participate in a balance of forces. The force which includes the advection of gravitational modes by the rotational wind also participates in the balance of forces, although its participationis second-order. For the model investigated, initialization using Machenhauer's scheme seems most appropriate when applied only to modes whose natural periods are less than 20 h, and only to the adiabatic plus surface drag forces.