Vector radiative transfer in a multilayer medium by natural element method

The vector radiative transfer problem in a vertically multilayer scattering medium with spatial changes in the index of refraction is solved by the natural element method (NEM). The top boundary of the multilayer medium is irradiated by a collimated beam. In our model, the angular space is discretized by the discrete ordinates approach, and the spatial discretization is conducted by the Galerkin weighted residuals approach. In the solution procedure, the collimated component for the Stokes parameters is first solved by NEM, and then it is embedded into the vector radiative transfer equation for the diffuse component as a source term. To keep the consistency of the directions in all the layers, angular interpolation of the Stokes parameters at the interfaces is adopted. The NEM approach for the collimated component is first validated. Then, the classical coupled atmosphere–water system irradiated by different states of collimated beam is examined to verify the numerical performance of the method. Numerical results show that the NEM is accurate, flexible, and effective in solving polarized radiative transfer in a multilayer medium. Finally, polarized radiative transfer in a four-layer system is investigated and analyzed.