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suitable for applying the approach developed here. The principal restrictions
are put on space homogeneity and the temporal stability of cloud fields.
It should be pointed out that the interpretation of the radiation observations
based on the monochromatic radiative transfer theory is available with the
spectral measurements only. Applying the methodology to the observational
data of total radiation needs the special analysis of uncertainties appearing,
whileintegratingtheformulasoverwavelength.Thevaluesandfunctionsin
the asymptotic formulas of the radiative transfer theory depend on single
scattering albedo and optical thickness, which in their turn are greatly varying
with wavelength. Regretfully, this fact is neither mentioned nor analyzed in
the many studies dealing with the observational data of total radiation.
The data of both the radiance and irradiance observations could be used for
retrieval of the optical parameters. Interpretation of the irradiance data needs
no high azimuthal harmonics of reflected radiances and the calculating errors
of these harmonics neither included to the result.
The reflected and transmitted solar irradiance for the optically thick and
weakly absorbing cloud layer are described by formulas (2.25). Consider these
expressions for two values of cosine of the incident solar angle
µ
0,2
corre-
sponding to the observations accomplished at two moments. The expressions
for parameter
s
2
and for scaled optical thickness
µ
0,1
,
τ
0
(1 −
g
)areeasytode-
rive taking the ratios of the reflected (transmitted) irradiances for two different
values of the cosine of the incident solar angle as has been shown inMelnikova
and Domnin (1997) and Melnikova et al. (1998, 2000). Here they are:
τ
=
3
-forthereflectedirradiance
(
a
(
0,1
)
−1
0,1
)−
F
1
)
K
0
(
µ
µ
0,2
)
0,2
)−
F
2
)
K
0
(
µ
µ
(
a
(
s
2
=
,
µ
0,1
)−
w
(
µ
0,2
))
n
2
(
w
(
(6.11)
ln
mnlK
(
µ
0,
i
)−
F
↑
+
ll
,
µ
0,
i
)
1
2
s
τ
=
a
(
µ
µ
where function
w
(
) is defined with (2.34) for function
K
2
(
), and sub-
µ
0,2
could be substituted to
the second of (6.11). It is convenient to apply these expressions for the
data processing of satellite observations of the reflected solar irradiance.
- and for transmitted irradiance:
µ
0,1
,
script
i
indicates that any of two values
F
1
K
0
(
0,1
)
−1
µ
0,2
)
F
2
K
0
(
µ
s
2
=
,
µ
0,1
)−
w
(
µ
0,2
))
n
2
(
w
(
(6.12)
(4
F
↓
2
ll
+
m
2
n
2
K
(
⎡
⎤
µ
0,
i
)
2
)+
mnK
(
µ
0,
i
)
τ
=
⎣
⎦
,
s
−1
ln
2
F
↓
ll
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