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

A vector radiative transfer model using the perturbation theory approach 63
m 12 ≈ 0.5 below 315 nm, which belongs to channel 1 of the instrument. In the second instrument
channel m 12 changes approximately linearly from 0.30 to 0.46 in the spectral range 315-405 nm.
An additional calibration step of the standard GOME data processing is the so-called polarization
correction, which aims to eliminate the polarization dependence of I pol,i in Eq. (3.60). In other words,
I pol,i has to be converted to a corresponding radiance spectrum, viz.
I conv,i = C conv I pol,i (3.61)
with a conversion factor
C conv =
1
1 + m 12 q i
. (3.62)
Here, q i is the relative Stokes parameter Q i /I i . In case of an unbiased conversion the spectrum I conv,i
is identical to I i in Eq. (3.60). This conversion requires polarization measurements to determine q i
at the spectral resolution of the measurement I pol,i . However, GOME only performs broadband polarization
measurements and so polarization spectra have to be reconstructed from measurements at
lower spectral resolution. Here, errors of the order of 10% may be introduced in the converted radiances,
in particular in parts of the spectrum with strong variation of q i due to atmospheric absorption
[Aben et al., 1999, Stam et al., 2001, Schutgens and Stammes, 2002]. Additionally, q i is affected by
Raman scattering. Ring lines in q i are mainly caused by corresponding Ring structures in the radiance
component I i and only to a minor extent by Ring structures in Q i . Figure 3.10 shows that the neglect
of the Ring structures in q i can cause errors of up to 1.4% in the converted radiance spectrum I conv,i ,
depending on the degree of polarization.
To investigate the relevance of this error, we consider the instrument noise of GOME reflectance
spectra r = I conv /F 0 between 290–405 nm, at 12 geo-locations (±60 ◦ and ±20 ◦ latitude, 0 ◦ , 120 ◦
and 240 ◦ longitude) for the period April, 1996 - March, 1998. Figure 3.11 shows the frequency
distribution of the mean error ε for these measurements, where ε is defined by
ε = √ 1 N
N∑
i=1
[
ei
r i
] 2
. (3.63)
Here e i denotes the absolute 1 σ error of a reflectance measurement r i for a detector pixel i, and
N is the total number of detector pixels of the considered spectral range. For about 97% of all
measurements the mean error lies between 0.19–0.43%. From this distribution we select two spectra
e min with ε = 0.19% and e max with ε = 0.43%, representing a lower and an upper error margin of
GOME. The error spectra are shown in the right panel of Fig. 3.11.
Using these error scenarios, we consider the relative bias b i /e i , where b i = I conv,i − I i is the
absolute difference between the polarization corrected radiances and the unbiased radiance spectrum.
The mean relative bias
b mean = 1 ∣ N∑
b i∣∣∣
N ∣
(3.64)
e i
i=1