Vector Radiative Transfer in a Vertically Inhomogeneous Scattering and Emitting Atmosphere. Part I: A New Discrete Ordinate Method

The original vector discrete ordinate radiative transfer (VDISORT) model takes into account Stokes radiance vector but derives its solution assuming azimuthal symmetric surface reflective matrix and atmospheric scattering phase matrix, such as the phase matrix derived from spherical particles or randomly oriented non-spherical particles. In this study, a new VDISORT is developed for general atmospheric scattering and boundary conditions. Stokes vector is decomposed into both sinusoidal and cosinusoidal harmonic modes, and the radiance at arbitrary viewing geometry is solved directly by adding two zero-weighted points in the Gaussian quadrature scheme. The complex eigenvalues in homogeneous solutions are also taken into full consideration. The accuracy of VDISORT model is comprehensively validated by four cases: Rayleigh scattering case, the spherical particle scattering case with the Legendre expansion coefficients of 0th–13th orders of the phase matrix (hereinafter L13), L13 with a polarized source, and the random-oriented oblate particle scattering case with the Legendre expansion coefficients of 0th–11th orders of the phase matrix (hereinafter L11). In all cases, the simulated radiances agree well with the benchmarks, with absolute biases less than 0.0065, 0.0006, and 0.0008 for Rayleigh, unpolarized L13, and L11, respectively. Since a polarized bidirectional reflection distribution function (pBRDF) matrix is used as the lower boundary condition, VDISORT is now able to handle fully coupled atmospheric and surface polarimetric radiative transfer processes.