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However, in spite of the simplicity of (6.34), there is a problem in applying it. It
is impossible to obtain parameter
g
from the reflected or transmitted radiance
because the system of (6.34) with (6.11) or (6.12) for irradiance (6.13) or (6.20)
forradianceturnsouttobehomogeneous.Thereisawaytoobtainparameter
s
2
with another approach for example from the airborne observations with (6.1)
or (6.2). Then difference
K
2
(
µ
2
) is expressed through
parameter
s
2
and through the observational data of the transmitted irradiance
or radiance using (6.34). Finally, parameter
g
is estimated using one of the
following expressions:
µ
1
)
|
K
0
(
µ
1
)−
K
2
(
µ
2
)
|
K
0
(
(
1
)
−1
σ
1
K
0
(
1
)
−1
ρ
ρ
µ
µ
0
−
1
)
K
0
(
2
)
2
)
ρ
ρ
µ
σ
2
K
0
(
µ
(
0
−
2
)
K
0
(
=
=
g
g
(6.35)
µ
1
−
µ
2
)
s
2
]
µ
1
−
µ
2
)
s
2
]
[5. 57(
[5. 57(
Heretheexpressionsarewrittenforthecaseoftheradianceobservational
data with demand of the horizontal homogeneity of the cloud field. The ir-
radiance data need the temporal stability because of using the two-moment
observations, and the formulas of the irradiances are almost likewise, excluding
value
F
↓
, which is substituted with value
σ
µ
0
)−
F
↑
), which is substi-
,and(
a
(
ρ
0
−
ρ
tuted with (
). The evident advantages and disadvantages are seen, while
using the reflected or transmitted radiance, or the irradiance observations.
Thus, value
µ
0
) strongly depends on phase function. The dependence
of the plane albedo is weaker so using the reflected irradiance or transmit-
ted radiance is more preferable than using the reflected radiance. Using the
transmitted radiance is strongly influenced by the ground albedo, thus the
transmitted irradiance provides the better accuracy for the cloud above the
snow surface.
Now obtain the cloud optical parameters using the numerical model of the
radiative characteristics, calculated with the doubling and adding method.
Va l u e
s
2
and scaled optical thickness
ρ
∞
(
µ
,
τ
are retrieved from
F
↓
and
F
↑
data.
Then parameter
g
is obtained for the pair of radiances with (6.35), and single
scattering albedo and optical thickness are calculated. Table 6.2 presents the
obtained results.
Tab l e 6 . 2 .
Retrieval of the optical parameters of the cloud layer from the model values of the
radiative characteristics
Value
Model magnitudes
Retrieved magnitudes
Uncertainty (%)
F
↓
0.3051
F
↑
0.6398
τ
0
25
28.55
14
ω
0
0.99900
0.99919
0.2
g
0.850
0.872
2.5
s
2
0.002222
0.002227
0.2
µ
1.0
0.846
µ
I
↓
(
)
0.3866
0.3499
µ
K
0
(
)
1.272
1.153
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