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A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres. II: Intensity Computations

Knut Stamnes Geophysical Institute, University of Alaska, Fairbanks 99701

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Henri Dale Geophysical Institute, University of Alaska, Fairbanks 99701

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Abstract

The recently developed matrix method to solve the discrete ordinate approximation to the radiative transfer equation in plane parallel geometry (Stamnes and Swanson, 1981) is extended to compute the full azimuthal dependence of the intensity, Comparing computed intensifies with those obtained by other established methods, we find that for phase functions typical of atmospheric haze 32 streams are sufficient for better than 1% agreement, while 16 streams yield an accuracy of about 1–5% except for angles close to the forward and backward directions for which the error is about 10–15%. The results of the intensity computations are summarized by presenting three-dimensional “stack plots” of the intensity as a function of polar and azimuthal angles. We also show that for flux calculations four streams suffice to obtain 1% accuracy, while eight streams yield an accuracy better than 0.1%.

Abstract

The recently developed matrix method to solve the discrete ordinate approximation to the radiative transfer equation in plane parallel geometry (Stamnes and Swanson, 1981) is extended to compute the full azimuthal dependence of the intensity, Comparing computed intensifies with those obtained by other established methods, we find that for phase functions typical of atmospheric haze 32 streams are sufficient for better than 1% agreement, while 16 streams yield an accuracy of about 1–5% except for angles close to the forward and backward directions for which the error is about 10–15%. The results of the intensity computations are summarized by presenting three-dimensional “stack plots” of the intensity as a function of polar and azimuthal angles. We also show that for flux calculations four streams suffice to obtain 1% accuracy, while eight streams yield an accuracy better than 0.1%.

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