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

A vector radiative transfer model using the perturbation theory approach 41
ization can vary significantly with wavelength [Aben et al., 1999, Stam et al., 2001, Schutgens and
Stammes, 2002]. Here, not only atmospheric absorption (e.g. by ozone and molecular oxygen) but
also atmospheric Raman scattering is of relevance. So any attempt to reconstruct the polarization
information at the required spectral resolution of the instrument using broadband polarization measurements
introduces errors in the polarization corrected spectrum and thus can bias significantly the
interpretation of the measurements. To overcome this problem, Hasekamp et al. [2002] suggested
to simulate directly the polarization sensitive measurement taken by the instrument. This requires
a vector radiative transfer model, which simulates the Stokes vectors of the reflected sunlight in the
viewing direction of the instrument. For radiative transfer simulations at fine spectral resolution this
model has to account for inelastic Raman scattering in the atmosphere.
The simulation of radiative transfer including inelastic rotational Raman scattering becomes complicated
due to the coupling of radiation at different wavelengths. A first numerical approach was
proposed by Kattawar et al. [1981]. Their computational technique is based on a separation of single
and multiple scattering using a scalar Monte Carlo model for a Rayleigh scattering atmosphere (by
which we mean a model atmosphere where atmospheric scattering is described by Rayleigh scattering
only). For both the single and multiple scattering component a correction is proposed for polarization
effects and inelastic Raman scattering contributions. A more rigorous approach is presented by
Joiner et al. [1995]. They utilize a successive order of scattering model of scalar radiative transfer
for a Rayleigh scattering atmosphere. Here, each scattering contribution is corrected for one order of
Raman scattering, where the spectral dependence of Raman scattering is taken fully into account. The
approach contains an exact solution for singly scattered light. To ease the correction for multiple scattering
it is assumed that the incoming radiation field of a Raman scattering process is isotropic. The
work of Vountas et al. [1998] represents an alternative approach to treat inelastic Raman scattering in
scalar radiative transfer. The radiative transfer equation, which describes Cabannes and Raman atmospheric
scattering, is divided into two parts, the radiative transfer equation for a Rayleigh scattering
atmosphere and a perturbation term, which describes the additional inelastic scattering contribution.
The effect of Raman scattering on the radiation field is described by a Picard iteration series that uses
the radiance field for a Rayleigh scattering atmosphere as a first guess. This technique represents
a sound treatment of the problem in its scalar approximation, because it iterates toward the correct
solution. Vountas et al. [1998] presents numerical results for a first iteration of this approach.
For the first time Humphreys et al. [1984] presented a vector radiative transfer model, which simulates
the effect of inelastic Raman scattering on the full Stokes vector. Here the frequency variation
of individual rotational Raman lines is described in a simplified form. This effect is described fully
in the model of Aben et al. [2001] and Stam et al. [2002]. They demonstrated that differential fine
structures in polarization measurements could be simulated already by a second order of scattering
model. However, for a proper simulation of the continuum of the radiation signal higher orders of
scattering must be included. Recently, Sioris and Evans [2002a] have improved on the earlier effort
of Joiner et al. [1995] with a successive order of scattering model including polarization. The underlying
assumption of their approach is that for scattering events of second order and higher only
the scattering phase matrix determines the angular distribution of the outgoing radiation field. So
the angle distribution of the incoming radiation is neglected. This is not entirely valid for scattering