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A discrete spherical harmonics method is developed for the radiative transferproblem in inhomogeneous polarized planar atmosphere illuminated at the top bya collimated sunlight while the bottom reflects the radiation. The methodexpands both the Stokes vector and the phase matrix in a finite series ofgeneralized spherical functions and the resulting vector radiative transferequation is expressed in a set of polar directions. Hence, the polarizedcharacteristics of the radiance within the atmosphere at any polar directionand azimuthal angle can be determined without linearization and/orinterpolations. The spatial dependent of the problem is solved using thespectral Chebyshev method. The emergent and transmitted radiative intensity andthe degree of polarization are predicted for both Rayleigh and Mie scattering.The discrete spherical harmonics method predictions using 36 streams are foundin good agreement with benchmark literature results. The maximum deviationbetween the proposed method and literature results and for absolue value of thepolar directions greater than 0.1 is less than 0.5% and 0.9% for the Rayleighand Mie scattering, respectively. These deviations for directions close to zeroare about 3% and 10 % for Rayleigh and Mie scattering, respectively.

A Discrete Spherical Harmonics Method for Radiative Transfer Analysis in Inhomogeneous Polarized Planar Atmosphere