In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions.
We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (601), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function.
We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector ½I; Q ; U; V as well as the more practical use of only ½I; Q ; U. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes vector remains practically constant for all azimuthal planes, while that associated with intensity-only measurements falls as we approach the plane perpendicular to the principal plane. The ½I; Q ; U vector is equivalent to the full Stokes vector in the principal plane, but its information content drops towards the perpendicular plane, albeit less sharply than I-only measurements.