Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

- We derived the radiative transfer equation accounting for rotational Raman scattering.
- Different approximate radiative transfer approaches with first order scattering were used.
- Rigorous and approximate approaches are shown to derive particular integrals.
- An alternative forward-adjoint technique is suggested as well.
- An additional spectral binning scheme which speeds up the calculations is presented.

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes-Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently.