Polarized radiative transfer of a cirrus cloud consisting of randomly oriented hexagonal ice crystals: The 3×3 approximation for non-spherical particles

- Vector radiative transfer computations for a cirrus cloud (highly anisotropic scattering) are performed.
- Tests of the 3×3 approximation (setting b2=0) and the scalar approximation are made for reflected and transmitted polarized radiances.
- The computational efficiency of the vector discrete ordinate method is discussed.
- The input files and a database of the resulting Stokes parameters I, Q, U is available online.

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6×103 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling-adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen׳s conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error <2×10−6 for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.