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

60 Chapter 3
where I ram,app and I ray,app are approximate radiance spectra and I ray,vec is the corresponding radiance
spectrum simulated with the vector model. Figure 3.8 shows the errors in the single scattering Ring
spectra R I,ssc , R Q,ssc , and R U,ssc . As expected, below 300 nm Ring structures are reproduced well by
this approximation due to the small fraction of multiple scattering events at these wavelengths. With
the increase of multiple scattering toward longer wavelengths also the error in the single scattering
Ring spectra increases. For the radiance component the absolute error in the Ring spectra is generally
less than 4% but can reach 7% at the Ca II lines for ϑ 0 =70 ◦ . Keeping in mind that the filling-in of this
Fraunhofer lines is about 12%, this represents a clear bias of more than a factor of 2 in the simulation
of Ring spectra. For the polarization components relatively large errors occur in R Q,ssc for a solar
zenith angle ϑ 0 =10 ◦ . This fact confirms the interpretation that for this particular case Ring structures
are mainly produced by elastic scattering processes following a Raman scattering event. Obviously,
this effect cannot be simulated in the single scattering approximation. For the other polarization Ring
spectra, where this propagation effect is of minor importance, the differences are much smaller and
generally below 0.2%.
Another widely used approximation method, if only radiances need to be simulated, is the scalar
radiative transfer approach. The advantage of this approach is that it takes into account multiple
scattering of light but at the same time greatly simplifies the calculations, which reduces the computational
cost. However, neglecting polarization can cause errors in the modeled radiance of up to
10% [Chandrasekhar, 1960, Mishchenko et al., 1994, Lacis et al., 1998, Hasekamp et al., 2002]. The
upper panel of Fig. 3.9 shows the error in the radiance component I. In the single scattering domain
below approximately 300 nm the error is very small. For singly scattered light the scalar approximation
yields the same radiance as the vector approach, because the incoming sunlight can be assumed
unpolarized [Hansen and Travis, 1974a]. However, if a second scattering process takes place, which
is very likely for wavelengths longer than 300 nm (see Fig. 3.7), the incoming light for this process
is strongly polarized (see e.g. Mishchenko et al. [1994]). The radiance of this second order scattered
light does not depend only on the radiance component of the incoming light but also on its Stokes
parameters Q and U. Hence, a neglect of polarization leads to an incorrect value of the modeled radiance.
The same is true for higher order scattering but here the effect is smaller. In Fig. 3.9 magnitude
and sign of the error in the scalar radiative transfer depend additionally on the scattering geometry
and on the orientation of successive scattering processes [Mishchenko et al., 1994].
For the simulation of Ring spectra R I,sca the scalar approach is much more exact than for simulations
of the continuum. The errors, shown in Fig. 3.9 are mostly below 0.1% and reach their maximum
of 0.14% for the Ca II lines for ϑ 0 = 70 ◦ . Again, compared with the filling-in of the Fraunhofer line
of 12% this represents a bias of only a factor of about 1.01. The high accuracy can be explained by
the fact that Raman scattered light is less polarized and so the coupling of the Stokes parameters due
to scattering processes is of minor importance for the simulation of Ring spectra in I.