Derivation of Phase Functions from Multiply Scattered Sunlight Transmitted Through a Hazy Atmosphere

J. A. Weinman Department of Meteorology, University of Wisconsin, Madison 53706

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J. T. Twitty Department of Meteorology, University of Wisconsin, Madison 53706

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S. R. Browning Department of Atmospheric Physics, University of Arizona, Tucson 85701

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B. M. Herman Department of Atmospheric Physics, University of Arizona, Tucson 85701

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Abstract

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few percent.

The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Abstract

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few percent.

The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

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