A method is described for numerical solution with spherical harmonics of the equation of transfer for plane-parallel atmospheric models with arbitrary inhomogeneities in the vertical direction and with axially-symmetric phase functions. Our method has the following features: (1) high efficiency in finding eigenvalues and eigenvectors associated with characteristics of the scattering layer; (2) stable expressions for the condition linking the radiance at the top to the bottom of the layer; (3) economy in calculations for a multi-layer problem. A smoothing method to obtain reasonable intensity patterns is also discussed. Representative results are presented for monochromatic diffuse fluxes and for the intensity of the radiation emerging from a single layer. © 1988 Pergamon Press plc.
CITATION STYLE
Takeuchi, Y. (1988). Use of spherical harmonics in the solution of the radiation transfer problem. Journal of Quantitative Spectroscopy and Radiative Transfer, 39(3), 237–245. https://doi.org/10.1016/S0022-4073(88)90086-6
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