Theory of Equilibrium Temperatures in Radiative-Turbulent Atmospheres

Kuo-Nan Liou Department of Meteorology, University of Utah, Salt Lake City 84112

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Szu-Cheng S. Ou Department of Meteorology, University of Utah, Salt Lake City 84112

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Abstract

We have developed a thermodynamic model for the determination of the temperature profile based on the balance of radiative and turbulent fluxes. In the context of a one-dimensional case, we show that the temperature field is governed by a first-order differential-integro equation involving temperature to the fourth power. In conjunction with the temperature profile determination, parameterization programs for the transfer of broadband thermal infrared and solar fluxes in inhomogeneous atmospheres are developed. In addition, the vertical transport is parameterized using a first-order closure scheme with the eddy thermal diffusion coefficients derived either from known theories or from available data. By virtue of an efficient perturbation technique devised for the solution of the thermal equilibrium temperature, we show that the simulated temperatures compare well with those of a standard atmosphere employing climatological water vapor, ozone and cloud profiles. Simulations using the steady-state one-dimensional model also reveal that high clouds will produce warming everywhere in the atmosphere whereas middle and low clouds will generate cooling as noted by several previous investigators, Moreover, extension of the model to a two-dimensional case is accomplished by incorporating empirical data for the horizontal heat transport. Simulated temperature profiles for the tropics (0–30°) and midlatitude (30–60°) compare closely with the climatological data except in the vicinity of the tropopause. For the subarctic case (60–90°), simulated temperatures are colder than the climatological values within about 5 K in the troposphere. Finally, two-dimensional heat budget analyses reveal that there is a slight gain of energy in the tropical region of the Northern Hemisphere.

Abstract

We have developed a thermodynamic model for the determination of the temperature profile based on the balance of radiative and turbulent fluxes. In the context of a one-dimensional case, we show that the temperature field is governed by a first-order differential-integro equation involving temperature to the fourth power. In conjunction with the temperature profile determination, parameterization programs for the transfer of broadband thermal infrared and solar fluxes in inhomogeneous atmospheres are developed. In addition, the vertical transport is parameterized using a first-order closure scheme with the eddy thermal diffusion coefficients derived either from known theories or from available data. By virtue of an efficient perturbation technique devised for the solution of the thermal equilibrium temperature, we show that the simulated temperatures compare well with those of a standard atmosphere employing climatological water vapor, ozone and cloud profiles. Simulations using the steady-state one-dimensional model also reveal that high clouds will produce warming everywhere in the atmosphere whereas middle and low clouds will generate cooling as noted by several previous investigators, Moreover, extension of the model to a two-dimensional case is accomplished by incorporating empirical data for the horizontal heat transport. Simulated temperature profiles for the tropics (0–30°) and midlatitude (30–60°) compare closely with the climatological data except in the vicinity of the tropopause. For the subarctic case (60–90°), simulated temperatures are colder than the climatological values within about 5 K in the troposphere. Finally, two-dimensional heat budget analyses reveal that there is a slight gain of energy in the tropical region of the Northern Hemisphere.

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