A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media

We calculate the reflection matrix for the first two orders of scattering in a vertically inhomogeneous, scattering-absorbing medium. We take full account of polarization and perform a complete linearization (analytic differentiation) of the reflection matrix with respect to both the inherent optical properties of the medium and the surface reflection condition. Further, we compute a scalar-vector correction to the total intensity due to the effect of polarization; this correction is also fully linearized. The solar beam attenuation has been computed for a pseudo-spherical atmosphere. Results from the two orders of scattering (2OS) model have been tested against scalar intensities for an inhomogeneous atmosphere, and against Stokes vector results for a homogeneous atmosphere. We have also performed backscatter simulations of reflected sunlight in the O(2) A band for a variety of geometries, and compared our results with those from a full vector multiple scattering code. Our results are exact in the center of strong lines and most inaccurate in the continuum, where polarization is least significant. The s- and p-polarized radiances are always computed very accurately. The effect of gas absorption optical depth, solar zenith angle, viewing geometry, surface albedo and wind speed (in the case of ocean glint) on the intensity, polarization and corresponding weighting functions have been investigated. It is shown that the 2OS model provides fast and reliably accurate polarization corrections to the scalar-model radiance and weighting function fields. The model can be implemented in operational retrieval algorithms as an adjunct radiative transfer code to deal with polarization effects. (c) 2007 Elsevier Ltd. All rights reserved.