Raman scattering in the earth’s atmosphere, part I: Optical properties

Abstract

Raman scattering in the Earth’s atmosphere is caused predominantly by its most abundant molecular components, N2 and O2. Modeling Raman scattering in the atmosphere is challenging for several reasons: the first challenge is the large number of molecular constants required for the computation of the wavelength/wavenumber shifts due to inelastic scattering by a given molecular species, and the corresponding variations in the scattering cross-sections and depolarization ratios depending on whether the scattering is rotational, vibrational or rovibrational. This is compounded by the lack of a consistent notation and uniform formalism across the seminal theoretical and experimental works that form the basis of our modeling effort.This work unifies the formalisms of Long (1977) and Chandrasekhar (1950), in order to make the quantum theoretical work of (Placzek, 1934) amenable to radiative transfer modeling using familiar quantities like the scattering cross-section and the scattering matrix. We also replace the form of key parameters like mean polarizability, α, the polarization anisotropy, γ, and their derivatives as introduced by Long (1977) for arbitrarily shaped molecules with the simplified formulations of Buldakov et al. (1996, 2000) for diatomic molecular species. The resulting scattering cross-sections and phase matrices for N2 and O2 are presented.In a companion paper, we provide the generalized radiative transfer formulation for the first fully polarized, exact simulations of inelastic scattering using the matrix operator method based RTM vSmartMOM, with optimizations for GPU runs to allow computationally competitive multi-wavelength radiative transfer computations of inelastic scattering. We subsequently use the formalism developed here to simulate key phenomena involving inelastic scattering in the Earth’s atmosphere, viz., the spectral response to a monochromatic light source as in Raman Lidar measurements, the Ring effect, the ghosting of Fraunhofer lines due to vibrational Raman scattering and the spectral impact of inelastic scattering on the O2 A-band.