Polarized radiative transfer through terrestrial atmosphere accounting for rotational Raman scattering

- The vector radiative transfer equation is derived accounting for first-order source terms of rotational Raman scattering;
- Ring in-filling and degree of linear polarization in the Fraunhofer lines of Ca II and the oxygen A-band have been compared with independent results in literature;
- Dependence of reflectance, Ring in-filling and degree of linear polarization on non-spherical dust aerosols and two ice crystal habits above a polarizing bi-directional surface, has been investigated;
- Maps of reflectance, Ring in-filling and degree of linear polarization for realistic geometry of the UVN/Sentinel-4 mission have been computed.

This paper is devoted to the phenomenological derivation of the vector radiative transfer equation (VRTE) accounting for first-order source terms of rotational Raman scattering (RRS), which is responsible for the in-filling of Fraunhofer and telluric lines by inelastic scattered photons. The implementation of the solution of the VRTE within the framework of the forward-adjoint method is given. For the Ca II and the oxygen A-band (O2 A) spectral windows, values of reflectance, degree of linear polarization (DOLP) and in-filling, in zenith and nadir geometry, are compared with results given in literature. Moreover, the dependence of these quantities on the columnar loading and vertical layering of non-spherical dust aerosols is investigated, together with their changes as function of two habits of ice crystals, modeled as regular icosahedra and severely rough aggregated columns. Bi-directional effects of an underlying polarizing surface are accounted for. The forward simulations are performed for one selected wavelength in the continuum and one in the strong absorption of the O2 A, as their combination can be exploited for the spaceborne retrieval of aerosol and cloud properties. For this reason, we also mimic seasonal maps of reflectance, DOLP and in-filling, that are prototypical measurements of the Ultraviolet-Visible-Near Infrared (UVN) sensor, at a nominal spectral resolution of 0.12 nm. UVN is the core payload of the upcoming European Sentinel-4 mission, that will observe Europe in geostationary orbit for air quality monitoring purposes. In general, in the core of O2 A, depending on the optical thickness and altitude of the scatterers, we find RRS-induced in-filling values ranging from 1.3% to 1.8%, while DOLP decreases by 1%. Conversely, while negligible differences of RRS in-filling are calculated with different ice crystal habits, the severely rough aggregated column model can reduce DOLP by a factor up to 10%. The UVN maps of in-filling show values varying between 1% and 8%. These changes are mainly driven by surface type and seasonal observational geometry. However, accounting for RRS, differences in DOLP do not exceed ± 0.2% within the full instrumental field-of-view.