A statistical-dynamical model of the zonally averaged steady-state of the general circulation of the atmosphere

Abstract

A statistical-dynamical model of the zonally averaged steady state of the atmosphere is presented, which aims at an examination of the response of the general circulation to changes in the forcing functions. The basic equations of the model are the equations of horizontal motion, the thermodynamic energy equation, the mass continuity equation, and the prediction equations for the eddy kinetic energy, the variance of temperature, the northward transport of temperature and westerly momentum and for the eastward transport of temperature. The components of the mean motion, the 600-mb temperature, the surface pressure are treated as variables in the model as are some eddy statistics like the eddy kinetic energy, the northward eddy transport of sensible heat and westerly momentum and the upward eddy transport of heat and momentum. The system is closed essentially by assuming that all central moments of third order vanish. It is, however, necessary to introduce further assumptions on eddy statistics to make the system numerically tractable. These assumptions do not rely upon an Austausch approach or on baroclinic wave theory. They are based partly on observations, but some are dictated by modelling reasons. The vertical structure and the parameterization of friction and radiation is that of the Mintz-Arakawa two-level general circulation model. Convective processes and the hydrological cycle are not treated explicitly. A numerical solution of the complete set of nonlinear equations is achieved by use of Newton's method. A first guess of the solution, which is needed for an application of this iterative scheme, is obtained by solving a subset of the complete system where the annual mean temperature and the mean surface pressure are prescribed. This preliminary solution reproduces fairly well the observed meridional distribution of the variables in the atmosphere. Then, the response of the complete system to changes of the parameters in the forcing functions, as are the surface drag coefficient, or the albedo of the earth's surface, is investigated. In particular, the model simulates fairly realistically the sensitivity of the time-dependent two-level general circulation model of Smagorinsky to the surface drag coefficient. DOI: 10.1111/j.2153-3490.1975.tb01684.x