The zonal atmospheric structure: A heuristic theory

Abstract

A heuristic theory of the zonally averaged structure of the atmosphere is formulated on the spherical Earth using parameterization of the influence of the eddies on the zonal structure. The principal influences of the eddies are the meridional transports of heat and momentum. These transports are expressed in terms of zonally averaged quantities by using the assumption that the transports of quasi-conservative quantities may be parameterized by a diffusion process with a constant value of the coefficient. The principle is used on the transports of potential vorticity and of potential temperature, where after it is shown that the momentum transport may be obtained indirectly. The theory is formulated for the quasi-geostrophic two-level model with heating and dissipation using an expansion of the dependent zonally averaged variables in Legendre polynomials. The quasi-geostrophic equations supplemented by a linear balance equation are sufficient to satisfy the parity relations valid on the sphere. Applications of the theory are carried out using zonally averaged heating based on calculations from observations or on simple specifications. In the first case it is shown that the theory, in a qualitatively correct way, can account for the meridional profiles of the zonal winds at the various levels, for the mean meridional circulation and for the meridional transports of momentum derived from the meridional transport of vorticity. Solutions for various values of the coefficient determining the transport of potential vorticity show that the energy conversion from eddy to zonal kinetic energy is particularly sensitive to the strength of the potential vorticity transport. If the transport is decreased, it turns out that the conversion becomes negative in such a way that the conversion goes from the zonal to the eddy kinetic energy. It is known that this situation corresponds to intense cases of blocking. A simple specification of the heating, simulating heating in the lower and cooling in the higher latitudes is insufficient to give a qualitatively correct picture of the mean meridional circulation.