A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres

Mathematics

Scientific paper

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Atmospheric Scattering, Discrete Functions, Eigenvalues, Radiative Transfer, Angular Distribution, Approximation, Integral Equations, Linear Equations, Matrices (Mathematics), Planetary Atmospheres, Spherical Harmonics

Scientific paper

Difficulties inherent in the solution of radiative transfer equations with conventional numerical implementation of the discrete ordinate method are discussed, and a matrix formulation is developed to overcome these difficulties. It is shown that the order of the algebraic eigenvalue problem can be reduced by a factor of two, and, by appealing to the reciprocity principle, that substantial computational shortcuts are possible if only such integrated qualities as albedo and transmissivity are required. Comparison of sample flux calculations with those of other methods demonstrates that low order, discrete approximate formulations yield accurate results, so that the approach is efficient, reliable, and lends itself to the solution of a variety of radiative transfer problems in realistic planetary atmospheres.

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