Chebyshev collocation spectral method for vector radiative transfer equation and its applications in two-layered media

Abstract The Chebyshev collocation spectral method (CCSM) is developed for solving the vector radiative transfer equation (VRTE) in participating media and then extended to polarized radiative transfer problems in two-layered media. The derivation of the CCSM discretization for the VRTE is presented and the numerical performance of the CCSM is investigated. The accuracy of the CCSM for solving the VRTE is first verified by comparing the CCSM solutions for the polarized radiative transfer in a plane-parallel medium with published results. Afterward, the CCSM is applied to polarized radiative transfer problems in inhomogeneous media, including two-layered media with different scattering characteristics and two-layered media with different refractive indices. Finally, taking both effects of different medium properties and reflective/refractive interface into account, we investigated the polarized radiative transfer in a realistic atmosphere-ocean system via the CCSM and discussed the distributions of the Stokes vector components. Results show that the CCSM is accurate and efficient for solving the VRTE and the distributions of Stokes vector for a realistic atmosphere-ocean system are presented in detail.