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

70 Chapter 3
3.6 Summary
A vector radiative transfer model is presented that includes the simulation of inelastic rotational Raman
scattering in addition to elastic Cabannes scattering. The model describes the reflectance properties
of a vertically inhomogeneous, plane-parallel model atmosphere bounded below by a Lambertian
surface. Rotational Raman scattering is treated as a perturbation to Rayleigh scattering. This perturbation
is presented by a classical perturbation series using the Green’s function formalism of the
unperturbed problem. The n-th contribution of the perturbation series describes the effect of n orders
of Raman scattering. The model is worked out in more detail for first order perturbations. In this case
the forward and the adjoint solutions of the radiative transfer problem replace the expensive calculation
of the corresponding Green’s function, which provides a significant reduction in the numerical
requirements. Based on this a numerical vector radiative transfer model is presented including one
order of Raman scattering. For the calculation of the perturbation effect any vector radiative transfer
model can be used that calculates the internal forward and adjoint intensity vector field of the
atmosphere. In this paper the Gauss-Seidel iteration method is employed, which provides efficient
simulations for cloud-free atmospheres.
Simulations of Ring spectra are presented for the spectral range 290-405 nm and the effect of
Raman scattering on the the polarization components Q and U is discussed. Here, Ring structures
in the Stokes parameters Q and U originate both from the polarization of light by Raman scattering
itself and from the polarization by Cabannes scattering following a Raman scattering process. In
general, polarization Ring spectra of Q and U are much weaker than those of the radiance component
due to the low polarization of Raman scattered light. Only for a low polarization of the reflected
sunlight pronounced Ring structures occur in the polarization spectra. Those are mainly caused by
the propagation of Ring structures from the radiance component to the polarization components by
Cabannes scattering processes. However, because of the small degree of polarization of the reflected
light, this effect is of minor importance for most applications.
The accuracy of two common approximation techniques is investigated for an efficient simulation
of Ring spectra: the single scattering approximation and the scalar approximation. The single scattering
approach shows a clear bias in the simulation of Ring structures. For example, the filling-in of the
Ca II Fraunhofer lines near 395 nm is underestimated by more than a factor of 2. The corresponding
filling-in simulated with the scalar approach is only biased with a factor of about 1.01. The relevance
of biases depends on the spectral range of the measurement and on the specific application. For example,
for ozone profile retrieval from GOME polarization sensitive radiance measurements between
290–313 nm the combination of both a vector radiative transfer model, which simulates the measurement
for a Rayleigh scattering atmosphere, with a scalar radiative transfer approach to account for
the effect of inelastic Raman scattering on the measurement provides an efficient simulation of the
measurement with only a minor bias. However, for the retrieval of cloud properties using the filling-in
of the Ca II Fraunhofer lines of GOME radiance measurements we recommend comprehensive vector
radiative transfer simulations of the Ring spectra in both Stokes parameters I and Q.