N-Stream Approximations to Radiative Transfer

Charles Acquista Department of Physics and Atmospheric Science, Drexel University, Philadelphia, PA 19104

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Frederick House Department of Physics and Atmospheric Science, Drexel University, Philadelphia, PA 19104

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James Jafolla Department of Physics and Atmospheric Science, Drexel University, Philadelphia, PA 19104

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Abstract

Schuster's two-stream approximation is first derived from Chandrasekhar's radiative transfer equation, and then generalized to an arbitrary number of streams. The resulting technique for solving the transfer equation that is similar to the discrete ordinate and spherical harmonic methods, is found to be especially useful for modeling atmospheres with complicated phase functions and moderate optical depths. To illustrate the method, a four-stream approximation is evaluated for a Henyey-Greenstein phase function with asymmetry factor g = 0.5.

Abstract

Schuster's two-stream approximation is first derived from Chandrasekhar's radiative transfer equation, and then generalized to an arbitrary number of streams. The resulting technique for solving the transfer equation that is similar to the discrete ordinate and spherical harmonic methods, is found to be especially useful for modeling atmospheres with complicated phase functions and moderate optical depths. To illustrate the method, a four-stream approximation is evaluated for a Henyey-Greenstein phase function with asymmetry factor g = 0.5.

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