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A Numerical Model of Thermal Radiation in a Dusty Atmosphere

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  • 1 Solar Energy Laboratory and Dept. of Mechanical Engineering, The University of Wisconsin, Madison 53706
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Abstract

A method is presented for numerically calculating the infrared radiative fluxes in a dusty atmosphere: a multicomponent planar medium which absorbs, emits, and anisotropically scatters radiation. The method utilizes number of different solutions, depending on the particular monochromatic properties of the medium. The most general solution, including dust and gas absorption and dust scatter, is an iterative numerical integration of the system of simultaneous differential equations for the intensity. If scattering is relatively unimportant in a particular spectral region, the equations are uncoupled from one another and a non-iterative numerical integration is used. In spectral regions with very strong gaseous absorption, the optically thick limit is employed.

Elsasser's band-averaged gas transmissivities are represented by a weighted sum of exponential functions of optical path. This model provides gas absorption coefficients which may be treated as constant over specified fractions of a band. The dust, assumed to be quartz spheres of a known size distribution, absorbs, cants and scatters in all spectral regions, overlapping the gaseous absorption. A scattering model is developed which treats part of the scattered radiation as being transmitted, part as being scattered diffusely forward, and the remainder as being scattered diffusely backward.

The numerical solution is used to compute the infrared fluxes and cooling rates in the atmosphere above the Rajasthan Desert in northwestern India, where a heavy dust layer is present the year round. The computations show that the dust significantly decreases the upward flux, increases the downward flux, and increases the radiative cooling rate at lower levels, relative to values calculated when dust is assumed absent.

Abstract

A method is presented for numerically calculating the infrared radiative fluxes in a dusty atmosphere: a multicomponent planar medium which absorbs, emits, and anisotropically scatters radiation. The method utilizes number of different solutions, depending on the particular monochromatic properties of the medium. The most general solution, including dust and gas absorption and dust scatter, is an iterative numerical integration of the system of simultaneous differential equations for the intensity. If scattering is relatively unimportant in a particular spectral region, the equations are uncoupled from one another and a non-iterative numerical integration is used. In spectral regions with very strong gaseous absorption, the optically thick limit is employed.

Elsasser's band-averaged gas transmissivities are represented by a weighted sum of exponential functions of optical path. This model provides gas absorption coefficients which may be treated as constant over specified fractions of a band. The dust, assumed to be quartz spheres of a known size distribution, absorbs, cants and scatters in all spectral regions, overlapping the gaseous absorption. A scattering model is developed which treats part of the scattered radiation as being transmitted, part as being scattered diffusely forward, and the remainder as being scattered diffusely backward.

The numerical solution is used to compute the infrared fluxes and cooling rates in the atmosphere above the Rajasthan Desert in northwestern India, where a heavy dust layer is present the year round. The computations show that the dust significantly decreases the upward flux, increases the downward flux, and increases the radiative cooling rate at lower levels, relative to values calculated when dust is assumed absent.

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