On the computation of angular distributions of radiation in planetary atmospheres

The discrete ordinate approximation to the radiative transfer equation is used to derive simple analytic expressions for the intensity in a vertically inhomogeneous plane parallel atmosphere. This approach allows one to compute the intensity at arbitrary depths and angles. The merit and soundness of these expressions, which are interpolatory in nature, are discussed and it is conjectured that they are superior to any other standard interpolation scheme as far as accuracy is concerned. The computational time also compares favorably with that of standard interpolation schemes such as cubic splines.