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

66 Chapter 3
dependence on the vertically integrated ozone column, on the Lambertian ground albedo, and on the
truncation height for the lower model boundary. The latter combined with a high Lambertian albedo
of A=0.8 simulates the effect of different cloud top heights.
The different scenarios show that in average the neglect of polarization Ring spectra between
290–313 nm insignificantly biases the simulation of GOME measurements with a mean bias of about
two orders of magnitude below the instrument noise level. Also the approximation in Eq. (3.67),
which employs scalar radiance Ring spectra, shows a small bias with b mean < 0.1. Therefore, the bias
is overwhelmed mostly by instrument noise. Contrary to that, the single scattering approximation
produces a clear bias in the simulation with 1 < b mean < 4. Here, the dependence on the different
parameters is related to the amount of multiple scattered light contributing to the detected signal.
This becomes obvious for the increase of b mean with increasing ground albedo. A change of the
lower boundary height of the model atmosphere shows a similar effect, where the smallest b mean
values are related to the highest truncation height, which corresponds to a high cloud top. In this
case the optically dense troposphere is cut off and the radiative transfer becomes dominated by single
scattering.
The error assessment differs, if one considers the bias for the Ca II Fraunhofer lines only. Figure
3.14 shows the corresponding relative mean bias b mean as functions of solar zenith angle. For
the single scattering approximation I app3 we obtain a large bias with 40 < b mean < 70. Also the
approximations I app1 and I app2 are clearly biased in this case. For I app1 the relative mean bias b mean
increases toward larger solar zenith angles and reaches the level of the instrument noise at ϑ 0 = 70 ◦ .
This dependence is caused by the increase of the degree of polarization of the reflected sunlight for
large solar zenith angles (see e.g. Fig. 3.2). The approximation I app2 has its largest bias for ϑ 0 = 0 ◦
with b mean ≈ 1. Here, the bias decreases toward larger solar zenith angle because of the cancellation
of errors due to both the scalar simulation of the radiance Ring spectrum and the neglect of the
polarization Ring spectrum R Q . We achieve similar results for different viewing zenith angles and
for different relative azimuthal angles as well as for a change of atmospheric parameters (not shown).
Thus the simulation of the filling-in of the Ca II Fraunhofer lines in GOME radiance measurements,
which uses the approximations I app1 and I app2 , can causes biases in the order of the instrument noise.
Overall, the suitability of the proposed approximation techniques depends clearly on the specific
application. Here, we have considered two examples: For ozone profile retrieval from GOME
polarization sensitive measurements an efficient simulation can be achieved using the approach of
Eq. (3.67). This includes (a) the calculation of Ring spectra with a scalar radiative transfer approach
and (b) the use of a vector radiative transfer model to determine the continuum spectra of Stokes parameters
I and Q for a Rayleigh scattering atmosphere. Contrary, for the retrieval of cloud properties
from the filling-in of the Ca II H and K Fraunhofer lines, an accurate simulation of the Ring structures
within the bounds of the instrument noise can only be achieved using a vector radiative transfer
simulation of both the Ring spectra R I and R Q .