Modeling of inelastically scattered radiation: Rotational Raman scattering in the spherical Earth’s atmosphere

•Rotational Raman scattering in a spherical atmosphere is accounted for.•The solution method is based on the forward-adjoint perturbation theory.•Filling-in of solar Fraunhofer lines is strongly dependent on the spectral resolution.•Sensitivity to atmospheric and surface parameters is illustrated.•Relevance for the limb-scatter retrievals is discussed. This study presents an approximative approach to solve the radiative transfer equation accounting for the rotational Raman scattering in a spherical atmosphere. The solution is obtained employing the method of characteristics in combination with the discrete-ordinates technique and the forward-adjoint perturbation theory. For a non-limb observational geometry, impact of the atmospheric sphericity on the filling-in of solar Fraunhofer lines is discussed. For a limb viewing geometry, the dependence of the filling-in on the surface elevation, surface albedo, and cloudiness below the instrument line of sight as well as the effect of the multiple scattering in the spatial domain is analyzed. A comparison of modeled and measured Ring spectra for a limb-viewing geometry is shown. The considered solution technique is implemented in the radiative transfer model SCIATRAN and is ready to use for atmospheric applications.