A Theoretical Study of the Efficiency of the General Circulation

Lloyd L. Schulman Department of Melerology, Massachusetts institute of Technology, Cambridge 02139

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Abstract

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 diabatic heating generates available potential energy (APE), which can be estimated independently of any frictional processes. Since diabatic heating includes long- and shortwave 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.

Observational studies indicate that the actual rate of generation of APE is from 2–6 W m−2, which corresponds to an atmospheric efficiency of about 1–2%. Experiments with a 5-level, 5-latitude model yield a maximum generation of APE near 12 W m−2. A higher resolution 5-level, 9-latitude model leads to a maximum generation near 10 W 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 nearly its maximum efficiency.

Abstract

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 diabatic heating generates available potential energy (APE), which can be estimated independently of any frictional processes. Since diabatic heating includes long- and shortwave 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.

Observational studies indicate that the actual rate of generation of APE is from 2–6 W m−2, which corresponds to an atmospheric efficiency of about 1–2%. Experiments with a 5-level, 5-latitude model yield a maximum generation of APE near 12 W m−2. A higher resolution 5-level, 9-latitude model leads to a maximum generation near 10 W 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 nearly its maximum efficiency.

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