A Theoretical Study of the Efficiency of the General Circulation

The hypothesis that the atmosphere may be constrained to operate at nearly maximum efficiency is examined. If atmospheric efficiency is defined as the ratio of the rate of production of kinetic energy to the rate at which solar energy reaches the top of the atmosphere, the problem becomes equivalent to finding the maximum rate at which dia-batic heating generates available potential energy (APE), which can be estimated independently of any frictional processes. Since diabatic heating includes long and short wave radiative heating, the vertical flux of sensible heat by the small scale eddies, and the release of latent heat, this would entail finding the maximizing fields of temperature , water vapor, carbon dioxide, ozone, cloudiness, and surface wind speed. By specifying the relative humidity to be constant and less than 100%, by ignoring ozone as an atmospheric constituent, and by using the observed mixing ratio of carbon dioxide as basic simplifying assumptions, the release of latent heat and clouds are eliminated, and for a specified solar forcing the efficiency becomes a function of the temperature field only. A series of numerical models, increasing in sophistication and resolution, are used to investigate the hypothesis. Fast but reliable calculations of the long and short wave radiative fluxes are obtained by modifying the techniques used in the NCAR general circulation model. Eddy diffusion is used to simulate the vertical flux of sensible heat. Maximization procedures include both graphical searching methods and gradient methods in phase space. Observational studies indicate that the actual rate of generation of APE is from 2-6 watts m-2 , which corresponds to an atmospheric efficiency of about 1-2%. Initial experiments with a 3-level, 2-latitude model in which the transfers of heat are accomplished only by long-wave radiative processes yield a maximum generation of APE near 2.5 watts m-2. Higher resolution models up to 5 levels and 9 latitudes, which also include atmospheric absorption of solar radiation and small scale sensible heat fluxes, lead to maximum generations near 10 watts m-2. The corresponding maximizing temperature fields show many qualitative agreements with the observed zonally averaged temperature field, including horizontal temperature gradients whose magnitudes decrease with height and the absence of superadiabatic lapse rates. The results are relatively insensitive to relative humidity, albedo, or surface wind speed, but do have a strong dependence on the sensible heat distribution scheme. These solutions suggest that the general circulation may indeed be operating at …