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these parameters are known with sufficient accuracy. Concerning the second
reason, we present the following consideration. According to the topic byMinin
(1988), the part of diffused radiation in the cloudless atmosphere depends on
solar incident angle and wavelength, and this part is approximately equal to
0.3 of the total flux. Function K 0 (
µ 0 )transformstovalue n and function a 2 (
µ 0 )
transforms to value 12 q =
8.5 for the fully diffused radiation, that yields
µ 0 =
K 0
0.03 and
a 2
0.25, and these values are minimal for
0.6−0.7.
This condition should be provided during observations.
Relative uncertainty
∆τ 0 0 is definedmainly by uncertainties of the retrieval
|
|
(1 − g ) as per (6.43), because the first item could be rather small
in the case of large cloud optical thickness and could weakly influence the
uncertainty. The value of
s
s and
g
|
(1 − g ) is caused by the second uncertainty source
and it depends on the consistency of the model value of parameter g to the real
cloud property. In accordance with the results of the study by Stephens (1979)
where the spectral values of g have been calculated with Mie theory for eight
cloud models, assuming g
g
=
0.85, it is possible to conclude that the variations
of parameter g in the short wavelength region are not exceeding 2%.
Uncertainty
|
|
s
s provided by (6.3)-(6.5) yields
s
s
0.05 after calculating
|
m 2 .Therelative
the corresponding derivatives and substituting
F
1−3W
ω 0 is derived from expression 1 −
ω 0 =
uncertainty of single scattering albedo
3 s 2 (1 − g ):
ω 0 )
|
ω 0 )
=
|
g |
(1 −
(1 −
2
s
s +
(1 − g ) .
(6.44)
ω 0 )
|
ω 0 ) 0.12.
Assuming value s
0.05, we have:
(1 −
(1 −
∆τ 0 0 provided by (6.6)-(6.8) is estimated according
to the following expression (Melnikova and Mikhailov 2001):
Relative uncertainty
F
s ( F F )(1 − g ) +
∆τ 0 0 2
|
|
s
s +
g
(1 − g ) .
(6.45)
Thevaluesofthetwofirstitemsinthesumdefinedbytheobservational
uncertainty and by the uncertainty of the retrieval of parameter s is about 15%,
the third item adds 2%, thus
∆τ 0 0 17%.
The error analysis in the case of using the reflected or transmitted irradiance
with (6.11) and (6.12) shows that the temporal stability of the cloud layer during
observations is necessary. As has been demonstrated in Sect. 1.5, the existence
of the overcast cloudiness during one hour is rather probable (about 80%).
Uncertainties
∆τ 0 0 are calculated in the case of using the reflected
irradiance by the following expressions:
|
s
s and
µ 2 )(
K 0 ( a F )+ K 0 (
s
a +
F )
=
µ 1 )− F 1 )− K 0 (
µ 2 )− F 2 )
s
µ 2 )( a (
µ 1 )( a (
K 0 (
(6.46)
+
K 0 ( a F )+ K 0 (
µ 1 )+
a +
F )
2
w (
n 2
+
µ 1 )− w (
µ 2 )) n 2
µ 2 )− F 2 )
( w (
µ 11 )( a (
2 K 0 (
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