Rotational Raman scattering in the Earth's atmosphere ... - SRON

10 Chapter 1
1974]. In this thesis we choose to calculate them. The rotational Raman scattering cross section,
which is a measure of the probability that light is scattered due to rotational Raman scattering, is
given for each transition J →J ′ (e.g. [Chance and Spurr, 1997, Sioris and Evans, 1999]):
σ ram (λ,λ in ) = 256π2
27 (λ)−4 [γ(λ in )] 2 f(T,J)b(J →J ′ ). (1.6)
Here, f is the fractional population of the initial energy states, T is the air temperature, γ is the
polarizability anisotropy of the molecule, and b are the Placzek-Teller coefficients for each energy
transition J →J ′ (See Appendix 3.A and 2.A and references therein for more details). The quantities
f, γ, and b are different for N 2 and O 2 . According to Sioris [2001] the modeled and measured line
strengths agree well within the experimental error of the measurements made by Penney et al. [1974]
with differences of ±0.4% for N 2 and ±2% for O 2 . To get the Raman cross sections for air the cross
sections of the different molecules have to be weighted according to their abundance, i.e. weighted
with 0.7809 and 0.2095 for N 2 and O 2 , respectively. Eq. 1.6 allows one to calculate the probability
ω(λ,λ in ) that light is scattered from a wavelength λ in to a different wavelength λ. Figure 1.4 shows
this probability distribution for λ in = 400 nm. The central line in the spectral scattering distribution
shown in Fig. 1.4 is called the Cabannes line. Fig. 1.4 shows that only a small fraction of the light,
approximately 4%, is scattered inelastically due to Raman scattering. The grey lines in Fig. 1.4 are
associated with N 2 and the black lines with O 2 . Due to their spherical symmetry Ar atoms are not
able to transfer rotational energy to the scattered light and hence show no Raman scattering.
At each wavelength sunlight is scattered according to a spectral distribution that is similar to one
that is shown in Fig. 1.4. Fig. 1.5 demonstrates how this leads to filling-in structures in a reflectivity
spectrum. At the center of a Fraunhofer line the scattered light is less intense than at a continuum
wavelength (Fig. 1.5 (a)). More light is scattered from the continuum into a Fraunhofer line than the
other way around. This results in filling-in structures in a reflectivity spectrum (Figs. 1.5 (b) and (c)).