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over, the authors have not presented yet any example of the application of this
approach.
It should be emphasized that these assumptions are very often used because
it is believed in the model of the pure water clouds that nothing is absorbing
solarradiationoutofthemolecularbands.However,theexistenceofsignificant
absorption follows even from the results of the study by Rozenberg et al. (1974).
Note, that introducing the atmospheric aerosols to the cloud model provides
certain radiation absorption in the calculations of the radiative characteristics
(direct problem solving), but this is rather weak. Hence, many investigators
have been still assuming the conservative scattering of solar radiation in clouds
within the VD spectral region, though these assumptions strongly restrict the
problem solution. Further, in Chap. 7 it will be shown that both assumptions
(the conservative scattering in the VD spectral region, the invariant optical
thicknesswithrespecttowavelength)arefalseinmostcasesofextended
clouds.
Let us return to Sects. 2.2-2.5, where the optical model of the extended
cloudiness and radiative characteristics observed during the experiments have
been considered. The radiation scattering in the layers above and below the
cloud is neglected at the first stage. In this chapter, we will derive the for-
mulas for the cloud optical parameters from the observed solar radiances or
irradiances values. Expansions (2.29), (2.30), and (2.44) over small parame-
ter
s
=
(1 −
ω
0
)
|
(3 − 3
g
) that is characterized the radiation absorption and
phase function influence are substituted to (2.24), (2.26), (2.41) (2.43), and
(2.45) describing the diffused radiation in the cloudy atmosphere. Then op-
erations of multiplying and dividing are to be accomplished by exploiting the
rules of algebra of series while taking into account the terms till the second
power of the small parameter. Only the observed values of solar irradiances
F
↑
and
F
↓
or radiance
I
and values of functions
K
0
(
µ
0
)for
the fixed incident and viewing (for radiance) angles are included to the final
equations.
The approach for obtaining the cloud optical parameters, presented here is
useful for the interpretation of the airborne, ground and satellite observational
data, but it needs careful analysis of the accuracy of the desired parameters
retrieval, using the numerical models. This analysis has been accomplished
for the set of single scattering albedo
µ
0
),
K
2
(
µ
0
)and
a
2
(
ω
0
and optical thickness
τ
0
(Melnikova
1991, 1992) and will be briefly presented in Sect. 6.3.
Relation
κ
=
τ
|∆
s
2
z
expresses the absorption volume coefficient and no
assumption concerning the phase function is needed. Obtaining scattering
volume coefficient
α
=
τ
(3−3
g
)
|∆
κ
demands the assignment of phase
function parameter
g
or its determining using an independent methodology.
Fortunately, the phase function parameter does not vary strongly with wave-
length within the stratus clouds; hence, we assume the spectral values of mean
cosine of the scattering angle
g
in accordance with the results of the study
by Stephens (1979). If geometrical thickness
z
−
∆
z
stays unknown then it is only
possible to determine the optical thickness and single scattering albedo, but
not the scattering and absorption volume coefficients.
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