AUTHOR=Lin Zhenyi , Stamnes Snorre , Li Wei , Hu Yongxiang , Laszlo Istvan , Tsay Si-Chee , Berk Alexander , van den Bosch Jeannette , Stamnes Knut 

TITLE=Polarized Radiative Transfer Simulations: A Tutorial Review and Upgrades of the Vector Discrete Ordinate Radiative Transfer Computational Tool

JOURNAL=Frontiers in Remote Sensing

VOLUME=3

YEAR=2022

URL=https://www.frontiersin.org/journals/remote-sensing/articles/10.3389/frsen.2022.880768

DOI=10.3389/frsen.2022.880768

ISSN=2673-6187

ABSTRACT=<p>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 <italic>b</italic><sub>2</sub> component of the Stokes scattering matrix is non-zero. This solution is needed to compute the <italic>V</italic> component of the Stokes vector <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="bold">I</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mo>∥</mml:mo></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mo>⊥</mml:mo></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mi>V</mml:mi></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>. 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<sup>3</sup> = 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.</p>