Lattice Boltzmann model for multidimensional polarized radiative transfer: theory and application

Polarimetric observations of planets are providing increasing details of the three-dimensional (3D) atmospheric structure. The one-dimensional plane-parallel approximation model neglects horizontally polarized radiative transfer. Multidimensional polarized radiative transfer models, especially 3D models, are required to contain the horizontal polarization mechanism. Here, we propose a lattice Boltzmann (LB) model for multidimensional polarized radiative transfer, which enables a simple solution of the multidimensional vector radiative transfer equation (VRTE) by performing collision and streaming processes. Through the Chapman–Enskog analysis, we rigorously derive the multi-dimensional VRTE from the proposed LB model. 2D and 3D numerical tests demonstrate that the proposed LB model is effective and accurate for simulating multidimensional polarized radiative transfer. Furthermore, we apply the proposed LB model to investigate the effects of multiple scattering on radiation intensity and degree of polarization in a 3D case and find that multiple scattering enhances the radiation intensity but dampens the degree of polarization throughout almost the whole angular space in multidimensional polarized radiative transfer. This work is expected to provide a simple and effective mesoscopic tool for multidimensional polarized radiative transfer.