Polarized reflectances of natural surfaces: Spaceborne measurements and analytical modeling

The PARASOL instrument provides polarization measurements of the Earthʹs reflectance. Data processing of these measurements leads to a large and representative dataset of Bidirectional Polarization Distribution Functions (BPDF) for a wide range of surface cover. All surfaces show a similar pattern of the polarized reflectances, with very little polarization at backscattering and a general increase with the phase angle. The largest polarized reflectances are observed facing the sun, with large sun and view angles and amount to 0.02–0.04 depending on the surface type. Simple BPDF models available in the literature predict the correct order of magnitude as well as the main features of its directional signatures. However, these models also show significant biases for some viewing geometries. We propose a new model for the BPDF of natural surfaces, based on theoretical development as well as empirical fit to the PARASOL measurements. This linear model with only one free parameter allows a similar fit to the measurements as a previously published one (Nadal and Bréon, 1999), non-linear with two parameters. Because the BPDF of natural surfaces appears to vary very little, a fixed model (i.e. with a priori biome-specific values for the parameter) is defined and may be sufficient for most applications.