Models for surface reflection of radiance and polarized radiance: Comparison with airborne multi-angle photopolarimetric measurements and implications for modeling top-of-atmosphere measurements

In this paper, we investigate the surface-atmosphere radiative interaction in application to the problem of aerosol satellite remote sensing over land. First, we test different models of the Bidirectional Reflectance and Polarization Distribution Function (BRDF and BPDF) for bare soil and vegetation surfaces using multi-angle, multi-spectral photopolarimetric airborne measurements of the Research Scanning Polarimeter (RSP). Then, we investigate the performance of different models of BRDF and BPDF for modeling top-of-atmosphere measurements. We have found that different BRDF models can describe the RSP measurements equally well. However, for soil surfaces, the different BRDF models show a different dependence on illumination geometry (solar zenith and azimuth angles), as well as a different dependence on viewing angle outside the range of RSP measurements. This implies that different models describe the surface-atmosphere interaction differently, leading for soil surfaces to differences in the top-of-atmosphere reflectance up to 4-5%, whereas at surface level the models agree within 2% for RSP illumination and measurement geometry. For vegetation, the different BRDF models show more similar dependence on illumination geometry, meaning that, in general, the differences in top-of-atmosphere reflectances are smaller than the differences in surface total reflectances. For the BPDF, we compare the empirical model of Nadal and Breon (1999) and the model developed by Maignan et al. (2009) with a newly developed model. The latter model compares better with RSP measurements. It was shown that, though all models have essentially different angular profiles at different illumination and viewing geometries, the difference of the top-of-atmosphere degree of linear polarization is less or is of the same order as the degree of linear polarization difference at the surface level taken at RSP illumination and measurement geometry. For the considered models, it can be up to 0.015 but is mostly below 0.005.