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

A vector radiative transfer model using the perturbation theory approach 65
can be interpreted as a measure of the conversion bias. Obviously, b mean depends on the selected
spectral range of the measurement. In the following we consider two examples: (a) the spectral range
290–313 nm, which can be used for ozone profile retrieval (see e.g. Hasekamp and Landgraf [2001])
and (b) two detector bins related to the center of the Ca II K and H Fraunhofer lines at 393.5 and
396.8 nm, which contain information on the cloud distribution of the observed ground scene [Joiner
and Bhartia, 1995]. In the case of ozone profile retrieval the mean relative bias b mean due to the neglect
of Raman scattering in the polarization correction is 0.3 and 0.7 for the error scenarios e max and e min ,
respectively. This indicates that the mean bias is below the instrument noise for this application.
However, at the center of the Ca II Fraunhofer lines b mean reaches values of 10.0 and 11.34 for both
error scenarios. So in this case the bias is 10 times as large as the instrument noise, which can cause
serious problems for the interpretation of the filling-in of these Fraunhofer lines.
For retrieval purposes the polarization correction can be avoided, if one attempts to reproduce the
polarization sensitive measurement I pol,i instead of a polarization corrected radiance measurement.
For GOME this requires the simulation of Stokes parameters I i and Q i of the backscattered sunlight.
Hasekamp et al. [2002] have demonstrated that this approach provides a clear improvement for ozone
profile retrieval from GOME reflectance measurements, compared to a retrieval approach using polarization
corrected radiances. The retrieval approach utilizes measurement simulations, which are
performed for a Rayleigh scattering atmosphere. To include Ring structures in the simulations one
may introduce Ring spectra in the different Stokes parameters of the polarization sensitive GOME
measurement in Eq. (3.60), viz.
I pol = (1 + R I,vec )I ray,vec + m 12 (1 + R Q,vec )Q ray,vec . (3.65)
To simplify matters we omit the pixel index i on the spectra.
For an efficient simulation of polarization sensitive GOME measurements one can try to approximate
the Ring structures of I pol by a simplified calculation scheme. The results of the previous section
suggest to neglect the Ring spectrum R Q,vec in Eq. (3.65) because of its small value. Thus we first
consider the approximation
I app1 = (1 + R I,vec )I ray,vec + m 12 Q ray,vec . (3.66)
Subsequently, we replace the Ring spectrum R I,vec by the respective scalar and single scattering spectra,
which yields the approximations
I app2 = (1 + R I,sca )I ray,vec + m 12 Q ray,vec , (3.67)
I app3 = (1 + R I,ssc )I ray,vec + m 12 Q ray,vec . (3.68)
In the context of GOME measurement simulations the goodness of these approximations can be assessed
using the mean relative bias b mean in Eq. (3.64) with b i = I app,i − I pol,i . Again we consider
the mean bias for the spectral range 290-313 nm as well as at the center of the Ca II Fraunhofer lines.
Figure 3.12 shows b mean for the spectral window of ozone profile retrieval as functions of the solar
zenith angle, of the viewing zenith angle and of the relative azimuthal angle for a fixed model atmosphere.
The dependence on atmospheric parameters is demonstrated in Fig. 3.13, which shows the