Analytical Method of Inverse Problem Solution for Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 204

several studies (King 1987, 1993; King et al. 1990). Regretfully the authors of the
mentioned studies applied the formulas for the case of conservative scattering
only to obtain the optical thickness in the VD spectral region. As the radiation
absorption of the cloud layer was not accounted for, the significant errors
(the unknown a priori ones) could occur if there was radiation absorption
in the clouds. The problem of optical thickness retrieval from solar radiance
measurements in several wavelength channelswithin the cloud layerwas solved
in the study by King et al. (1990) again with the assumption of the conservative
scattering.
The important exact expression for scaled optical thickness τ 0

through the reflected radiancewas derived in the studybyKing (1987) as a result
of transforming the first of (2.24). Regretfully the author of the study (King
1987) continued the further application of the obtained formula assuming the
conservative scattering of radiation only.
The approach based on using the ratio of the radiances or irradiances at dif-
ferent levels within the cloud layer was proposed in several studies (Duracz and
McCormick 1986; McCormick and Leathers 1996) and the corresponding ana-
lytical formulas was derived for the realization of the approach. Unfortunately,
wehavefoundnoresultsofitsapplicationtotheanalysisoftheobservational
data.
The parameters of the optically thick atmosphere were determined on the
basis of applying the irradiance gradients to the observations of automatic in-
terplanetary station “Venera” in the atmosphere of Venus. The high accuracy
of the measurements (1) and sufficiently high variations of the correspon-
dent radiative characteristics with altitude (2) are readily needed to reach the
acceptable accuracy of the retrieval of optical parameters. While the second
condition is fulfilled in the atmosphere of Venus due to its large optical thick-
ness, the high observational accuracy is easier to reach in Earth's atmosphere.
Anyway, calculating the derivative of the radiative characteristics with respect
to altitude with high accuracy is difficult. Various studies (Germogenova et al
1977; Ustinov 1977; Konovalov and Lukashevitch 1981; Konovalov 1982) have
considered the approach of retrieving the optical parameters of the atmosphere
of Venus from irradiance observations basing on the asymptotic formulas of
the transfer theory.
In this connection the study by Zege and Kokhanovsky (1994) should be
mentioned, where the relations for optical parameters of the cloudy atmosphere
were deduced. The expansions over the parameter similar to the parameter
used in the study by Rozenberg (1974), (with taking only the first power of
the expansion), were convoluted together with the asymptotic formulas with
respect to

τ = 3(1 − g )

τ 0 . This approach provided certain advantages but impeded the anal-
ysis of its applicability region to the single scattering albedo and to the optical
thickness separately. The algorithm of the cloud retrieval for this method was
presented in the study by Kohanovsky et al. (2003). In spite of the advantages
of the method itself, the algorithm was elaborated with certain shortcoming
assumptions: the conservative scattering in the VD spectral region, the invari-
ant optical thickness with respect to wavelength, together with the usage of
the insufficient number of the expansion terms (only the first power). More-