A Statistical-Dynamical Model of the General Circulation of the Atmosphere

Abstract

A statistical-dynamical, two-layer model of the atmosphere is constructed for the simulation of the climatic state of the global circulation. The meteorological variables, velocity, temperature and pressure, are decomposed into their zonal mean parts and eddy parts or deviations. The state of circulation is expressed by the zonal mean parts as well as eddy statistics which are the zonal averages of the product of the deviations. Eddy statistics such as the amount of eddy kinetic energy, and eddy transfer of heat and angular momentum are longitudinally integrated measures of the intensity and structure of individual synoptic-scale disturbances. The equations for the zonal means of wind, temperature and pressure and that of eddy kinetic energy are obtained from the equations of motion, the thermodynamical equation, and the continuity equation, and include the terms depending on the eddy statistics. The prediction equation for the horizontal eddy transfer of heat, as well as an estimate of the vertical eddy transfer of heat and angular momentum, are derived under the quasi-geostrophic assumption. The horizontal eddy transfer of momentum is estimated by a diagnostic formula similar to the one used by Smagorinsky. The results of theoretical studies of long waves are utilized to determine the pressure interaction term, the characteristic size of eddies, and the phase speed which are involved in certain of the equations. The model atmosphere expressed by the closed system of equations thus established is controlled by insulation, parameters for radiative heat transfer, static stability, lower boundary conditions for the exchange of momentum and heat, and parameters for horizontal stress and for the lateral diffusion of heat in the free atmosphere due to small-scale eddies. The present model does not include the effect of lateral transfer of latent energy. A numerical experiment is performed for a fixed annual mean insulation and a given specification of other control factors. The model consists of two layers, each having 48 zonal rings between the north and south poles. Starting from rest and a constant temperature at the middle level, the integration is done for the first 50 days without eddies. A small amount of eddy kinetic energy is superimposed on the axially symmetric flow at 50 days. Then, the primary features of the actual circulation, such as the jet stream, the Ferrel cell in mean meridional circulation, and the poleward eddy transport of heat, evolve, and a quasi-equilibrium state with a mode of fluctuation is attained.