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

34 Chapter 2
f. Differences occur at wavelengths where filling-in of solar Fraunhofer lines and/or atmospheric
absorption lines takes place (see Fig. 2.4). For example at the Ca II K and H line, approach A leads
to an underestimation of the filling-in, whereas approach B leads to an overestimation of the filling of
these Fraunhofer lines. The latter seems surprising at first: on might expect that a model like PTB,
which does not take all Raman scattering processes into account, would show a weaker filling-in than
DA. In other words, the more Raman scattering is allowed, the more filling-in is expected. This is not
the case and the explanation of the overestimation can be found in the way how perturbation theory
works. Due to the fact that the perturbation theory approach does not account for changes in light
propagation succeeding the perturbation, an overestimation or an underestimation is possible depending
on the specific application. This effect has to be considered in addition to the underestimation of
the filling-in due to the neglect of multiple Raman scattering.
To explain this in more detail, Fig. 2.6 shows the difference of the reflectivity due to inelastic
scattering for incoming sunlight at one particular wavelength, i.e. λ = 395 nm, as it is simulated with
the different models. The PTA model underestimates the reflectivity at any wavelength of the outgoing
light. The propagation effect in this model is of minor importance and the neglect of multiple inelastic
scattering processes dominates the simulation. Overall, this results in an underestimation of the fillingin.
The situation is different for PTB, which shows three different groups of lines. The elastic line
is clearly underestimated. Here, the perturbation ∆L means to replace a Rayleigh scattering event
by a Cabannes scattering event. The inelastic lines are caused by a perturbation ∆L, which adds a
Raman process to the Rayleigh scattering solution. This causes an overestimation of Raman lines
because too much light is built up in the inelastic lines due to multiple Rayleigh scattering before
and after the perturbation. However, also multiple inelastic scattering leads to more light arriving at
the Raman lines. Due to both effects PTB overestimates the lines close to the elastic component and
underestimates the weaker outer lines. Overall, the differences add up to zero, which has to be the
case for a perturbation of this type. This is consistent with getting the correct continuum height of the
radiance. Applying a solar spectrum to the reflectivity gives the backscattered intensity of the model
atmosphere, which demonstrates that PTB generates a too strong filling-in of the Ca II K and H line
compared to DA. For the same reason we get an exaggeration of the filling-in amplitudes in the range
300-330 nm.
In conclusion, approach B is successful in compensating for neglecting multiple inelastic scattering
when it comes to reaching the correct continuum radiance. However, at wavelengths where
filling-in occurs, the filling-in amplitudes are noticeably exaggerated. Fig. 2.5 shows that the fillingin
amplitudes in a filling-in spectrum are overestimated with approximately 0.2% in the range 320–
330 nm, and with about 0.6% at the Ca II H and K lines. These differences with respect to the
continuum seem slightly larger than when approach A is used, which produces differences of about
0.1% in the range 320–330 nm and about -0.5% at the Ca II H and K lines.