Discrete-ordinate radiative transfer in a stratified medium with first-order rotational Raman scattering

Rotational Raman scattering (RRS) by air molecules in the Earth's atmosphere is predominantly responsible for the Ring effect: Fraunhofer and absorption-feature filling-in observed in UV/visible backscatter spectra. Accurate determination of RRS effects requires detailed radiative transfer (RT) treatment. In this paper, we demonstrate that the discrete-ordinate RT equations may be solved analytically in a multi-layer multiple scattering atmosphere in the presence of RRS treated as a first-order perturbation. Based on this solution, we develop a generic pseudo-spherical RT model LIDORT-RRS for the determination of backscatter radiances with RRS included; the model will generate output at arbitrary viewing geometry and optical thickness. Model comparisons with measured RRS filling-in effects from OMI observations show very good agreement. We examine telluric RRS filling-in effects for satellite-view backscatter radiances in a spectral range covering the ozone Huggins absorption bands. The model is also used to investigate calcium H and K Fraunhofer filling-in through cloud layers in the atmosphere.