Geoscience Reference
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µ
Tab l e 2 . 5 .
Uncertainty of the calculation of escape function
K
(
), %
ω
0.999
0.995
0.990
0.980
0
g
0.5
0.9
0.5
0.9
0.5
0.9
0.5
0.75
0.9
s
0.02580 0.05774 0.05774 0.12910 0.08165 0.18257 0.11550 0.16330 0.25820
µ
=
0.1 0.1
0.2
0.4
1.0
0.5
2.0
10
33
127
µ
=
0.5 0.1
0.4
0.1
2.0
0.1
4.0
6.0
29
79
µ
=
0.7 0.3
0.5
0.3
0.8
0.4
3.0
5.0
25
64
µ
=
1.0 0.2
0.6
0.6
2.0
1.0
4.0
2.5
12
45
ρ
∞
(
µ
µ
Tab l e 2 . 6 .
Uncertainty of the calculation of reflection function
,
) of the semispherical
layer
ω
0
0.999
0.995
0.990
g
0.5
0.9
0.5
0.9
0.5
0.9
s
0.02580
0.05774
0.05774
0.12910
0.08165
0.18257
µ
=
0.1
0.2
0.6
0.2
1.0
0.3
2.6
µ
=
0.5
0.2
0.3
0.4
1.0
1.0
3.0
µ
=
1.0
0.2
0.3
0.5
1.0
0.7
3.0
cal methods and presented in Yanovitskij (1997) and Dlugach and Yanovitskij
(1974). The relative uncertainties of the escape functioncomputedwithapprox-
imations (2.31) are presented in Table 2.5. It has been found that uncertainties
are rather small as far as
ω
0
=
=
µ
>
0.2.
Table 2.5 illustrates that the errors of the escape function calculation do not
exceed 6% for value
s<
0.12.
Comparison of the results of the reflection function
0.98 for magnitudes
g
0.5 and
ρ
∞
(
µ
µ
0
)calculation
,
µ
0
) of expansion (2.30) with the
numerical computing results of studies by Yanovitskij (1997) and Dlugach and
Yanovitskij (1974) yields the errors shown in Table 2.6. Equation (2.31) for
functions
ρ
2
(
µ
µ
0
)and
ρ
3
(
µ
accounting for coefficients
,
,
µ
0
)allowthecomputingofcorrespondingvalues
with a rather small error as far as
ρ
2
(
µ
µ
0
)and
ρ
3
(
µ
,
,
ω
0
=
0.9. Therefore, it is possible to calculate
the solar radiance reflected from the cloud layer in the shortwave spectral
range with the analytical formulas, and this fact is useful for the interpretation
of the satellite radiation data.
The accuracy of the formulas in the case of an arbitrary optical thickness
has been tested by comparison with the results of the numerical calculations
using the following methods: double and adding method, delta-Eddington
method andMonte-Carlomethod. Awide set of parameters has been analyzed:
τ
0
=
ω
0
=
=
0.25−0.75 (Melnikova and Solovjeva
2000). The results of all four methods have turned out to coincide with the
variationsfrom0.1to5%independentofthemagnitudesof
0.1−5.0;
0.99−0.9999 and
g
ω
0
and
g
.
Thus, it can be thought that all tested magnitudes of the parameters are in the
τ
0
,
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