Polarized Radiative Transfer Simulations: A Tutorial Review and Upgrades of the Vector Discrete Ordinate Radiative Transfer Computational Tool - Lin, Zhenyi; Stamnes, Snorre; Li, Wei; Hu, Yongxiang; Laszlo, Istvan; Tsay, Si-Chee; Berk, Alexander; van den Bosch, Jeannette; Stamnes, Knut (Frontiers in Remote Sensing, 2022)
We present an overview and several important upgrades to the Vector Discrete Ordinate Radiative Transfer (VDISORT) code. VDISORT is a polarized (vector) radiative transfer code that can be applied to a wide range of research problems including the Earth's atmosphere and ocean system. First, a solution is developed to the complex algebraic eigenvalue problem resulting when the $b_2$ component of the Stokes scattering matrix is non-zero. This solution is needed to compute the $V$ component of the Stokes vector ${\bf I} = [I_\parallel, I_\perp, U, V]^T$. Second, a significant improvement in computational efficiency is obtained by reducing the dimension of the algebraic eigenvalue by a factor of 2 resulting in a speed increase of about $2^3 = 8$. Third, an important upgrade of the VDISORT code is obtained by developing and implementing a method to enable output at arbitrary polar angles by the integration of the source function (ISF) method for partially reflecting Lambertian as well as general non-Lambertian surfaces. Fourth, a pseudo-spherical treatment has been implemented to provide important corrections for Earth curvature effects at near horizontal solar zenith and observation (viewing) polar angles. Fifth, a post-processing single-scattering correction procedure has been developed to enhance the accuracy and speed for strongly forward-peaked scattering. With these significant improvements the results from the upgraded version of the VDISORT code match published benchmark results for Rayleigh scattering, Mie scattering, and scattering by non-spherical cirrus particles. The performance of VDISORT for a polarized incident beam source is equally satisfactory. The VDISORT vector radiative transfer code is made public and freely available for use by the growing polarimetric research community including the space-borne polarimeters on the future NASA PACE and AOS missions.