Analytical calculation of Stokes parameters Q and U of atmospheric radiation

For polarisation correction of the radiances measured by polarisation-sensitive satellite instruments like GOME, SCIAMACHY and GOME-2, both the Stokes parameters Q and U are of interest. Below a wavelength of about 300 nm, single Rayleigh scattering is the only mechanism contributing to the TOA reflectances. The single Rayleigh scattering polarisation therefore provides, next to these instruments' own polarisation measurements, an extra data point for their Polarisation Correction Algorithms. However, the Polarisation Correction Algorithm also needs the (single scattering) direction of polarisation for a proper correction of a large part of the visible spectrum. This makes the polarisation correction very sensitive to possible errors in the single scattering polarisation. This report presents a calculation of the single Rayleigh scattering Stokes parameters, and their verification using a radiative transfer code as well as POLDER data. The single scattering model is furthermore extended by including also Lambertian surface reflection.