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

TL;DR

This paper introduces a discrete spherical harmonics method for analyzing polarized radiative transfer in inhomogeneous atmospheres, accurately predicting radiance and polarization without linearization, validated against benchmark results.

Contribution

The paper presents a novel discrete spherical harmonics approach that expands the Stokes vector and phase matrix, enabling precise radiative transfer analysis in inhomogeneous polarized atmospheres.

Findings

Predictions agree well with benchmark results, deviations less than 0.9%.

Method accurately predicts radiance and polarization for Rayleigh and Mie scattering.

Deviations are minimal for directions with polar angles greater than 0.1.

Abstract

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for absolue value of the polar directions greater than 0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10 % for Rayleigh and Mie scattering, respectively.