An improved pseudo-spherical shell algorithm for modeling vector radiative transfer

The radiative transfer for the plane-parallel geometry has been widely used in remote sensing applications of the Earth system, even though the Earth atmosphere is essentially in the shape of spherical shell. The main reason is that it is much simpler and efficient to solve radiative transfer in plane-parallel geometries using the deterministic approaches, for instance, discrete ordinates (DISORT), successive order of scattering (SOS), matrix operator, etc. Moreover, the plane-parallel solution approximates the Earth geometry well for solar and viewing zenith angles smaller than 60 degrees, as the Earth Radius is quite large (~6371 km). However, the plane parallel solution does not provide satisfying accuracy for large solar/viewing zenith angles, which is frequently observed in polar regions. To mitigate this difficulty, the traditional pseudo-spherical approximation solves the single scattering solution by attenuating the solar beam properly. The higher order scattering solution is excited by this single scattering solution albeit still follows the plane-parallel geometry. The pseudo-spherical treatment can better simulate the nadir radiance field at the Top of the Atmosphere for larger solar zenith angles. However, for off-nadir radiances the pseudo spherical shell approximation still results in large errors (8%-20%) for solar zenith angles around 84 degrees. In this paper we will present an efficient new algorithm which improves the off-nadir radiance significantly by preserving the single to multiple scattering ratio and use the exact single scattering solution to the spherical shell system. The percentage error is reduced to be smaller than 1% and without obvious viewing zenith angle dependence. The polarization of the radiance field in the Earth atmosphere can also be calculated accurately. This new algorithm has a great potential to significantly improve the remote sensing of aerosol, cloud, surface or ocean color properties for polar regions.