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

42 Chapter 3
contributions of lower order.
In this work, we present a vector radiative transfer model, where inelastic Raman scattering is
taken into account using the radiative transfer perturbation theory approach. Similar to the work of
Vountas et al. [1998], the vector radiative transfer equation is separated in an unperturbed radiative
transfer problem describing radiative transfer in a Rayleigh scattering atmosphere, and a perturbation
term for additional Raman scattering (Section 3.2). In Section 3.3, the effect of this perturbation on
the measurement simulation is described by a classical perturbation series using the Green’s function
formalism. In this approach the n-th order perturbation term can be interpreted as a correction to the
simulated measurement for n orders of Raman scattering. To first order the numerical implementation
of the perturbation can be eased significantly by the adjoint formulation of radiative transfer, which is
also discussed in Section 3.3. Section 3.4 shows numerical simulations for the Stokes parameters I,
Q and U of the reflected sunlight. Here the effect of one order of Raman scattering on the polarization
components is considered in detail. Furthermore, the accuracy of both the single scattering approximation
and the scalar approach of radiative transfer is studied for the simulation of Ring structures
in the reflectance spectra. Finally, in Section 3.5 we investigate the suitability of the single scattering
and scalar radiative transfer approximation for the simulation of Ring structures in polarization sensitive
measurements of GOME within the error margins of the instrument. Here, we focus on both
the spectral range 290–313 nm, which contains information on the vertical ozone distribution in the
probed atmosphere, and the filling-in of the Ca II Fraunhofer lines, which can be used to retrieve
cloud properties.
3.2 The radiative transfer problem
3.2.1 The radiative transfer equation including both elastic Cabannes scattering
and inelastic Raman scattering
The radiance and state of polarization of light can be described by an intensity vector I, which has the
Stokes parameters I, Q, U, and V as its components (see e.g. Chandrasekhar [1960], Hovenier and
van der Mee [1983])
I = [I,Q,U,V ] T . (3.1)
Here, the superscript T indicates the transposed vector. The intensity vector is defined with respect
to a certain reference plane, which in this paper is given by the local meridian plane. In general, the
intensity vector is a function of altitude z, of wavelength λ and of direction Ω = (µ,ϕ), where ϕ is the
azimuthal angle measured clockwise when looking downward and µ is the cosine of the zenith angle
(µ < 0 for downward directions and µ > 0 for upward directions). The domain of these variables
define the so-called phase space of the radiative transfer problem.
In the following, we consider a plane-parallel, macroscopically isotropic atmosphere bounded
from below by a Lambertian reflecting surface. For such an atmosphere the equation of transfer for