In recent years, the method of obtaining a direct solution of the spherical harmonics approximation to the equation of radiative transfer has been shown to be a very efficient and powerful one for the evaluation of diffuse fluxes at various levels of a plane-parallel, nonhomogeneous atmosphere containing arbitrary height distributions of absorbing gases, aerosol particles, and cloud water drops. In this report, we attempt to provide (a) a detailed de¬rivation of the spherical harmonics equations starting with the basic transfer equation, and (b) a description of the method for the numerical solution of the resultant system of linear equations.nThis report is written with the hope that any person with a moderate background in atmospheric radiative transfer, matrix algebra, and computer programming would be able to understand and use the described method.
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