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A Monte Carlo procedure, designated as FLASH, was developed for use in computing the intensity and polarization of the radiation emerging from spherical-shell atmospheres and is especially useful for investigating the sunlit sky at twilight time. The procedure utilizes the backward Monte Carlo method and is capable of computing the Stokes parameters for discrete directions at the receiver position. Both molecular and aerosol scattering are taken into account as well as ozone, aerosol, water vapor, and carbon dioxide absorption within the atmosphere. The curvature of the light path due to the changing index of refraction with altitude is taken into account. Some comparisons are made between FLASH calculations for a pure Rayleigh atmosphere, a combined Rayleigh and aerosol atmosphere, and calculations reported by other authors for plane-parallel atmospheres. The comparisons show that the FLASH calculations for spherical-shell atmospheres are in good agreement with those for plane-parallel atmospheres within the range of zenith angles for which no differences could be attributed to the difference in the geometries of the two atmospheric models.
Collins et al. (1972) studied this question.