Analytical Method of Inverse Problem Solution for Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 203

Analytical Method of Inverse Problem Solution
for Cloudy Atmospheres

6.1
Single Scattering Albedo and Optical Thickness Retrieval
fromData of Radiative Observation

The approach of the numerical solving of the inverse problem of atmospheric
optics has been presented in Chaps. 4 and 5. In addition, the direct problem
solution compared with the values of the observed radiative characteristics
has been obtained with the universal numerical Monte-Carlo method. In some
cases we succeeded to find the solution of the direct problem in the analytical
form (Sects. 2.2 and 2.3), then the procedure of computing the derivatives of
the irradiances with respect to the atmospheric parameters becomes faster and
simpler. Moreover, the possibility of the analytical expressions of the radiative
characteristics suggest an idea to convert these expressions and to obtain the
inverse formulas for the retrieval of the desired parameters after substituting
themeasuredvalues of the radiative characteristics. The first studies in this field
assumed either the infinitely thick or the conservative scattering atmosphere
toexcludeoneoftheunknownparameters.Thus,wearecitinghereonly
the studies, which have presented some analytical expression for finding the
optical parameters but not the studies where the optical parameters have been
obtained with a simple comparison of calculations and observational results.
The authors of the study by Rozenberg et al. (1974) took the first step
by using the observation of the reflected solar radiation from satellites for
obtaining the small parameter connected with the single scattering albedo ω 0

of the cloud while assuming its infinite optical thickness and the expansion
analogous to (2.29). Only the first power of the expansion was taken into
account, and the optical thickness of the cloud layer was not analyzed. In the
study by Yanovitskij (1972), the expression for spherical albedo of the infinite
atmosphere was inferred and applied to the clouds of Venus for defining the
single scattering albedo with the same assumption about the optically infinite
atmosphere (proven to be more correct than the assumption of the study
by Rozenberg (1974) for terrestrial clouds). The spectral values of

ω 0 for six
wavelengths from the data of the astronomical observations of the atmosphere
of Venus were evaluated there as well.
The expressions for the retrieval of optical thickness from the radiance
observations above the cloud layer and within it were firstly proposed in