Comparison of reflection function r 1 (m,m 0 ) calculation results accounting
coefficients r 2 (m,m 0 ) and r 3 (m,m 0 ) with numerical computing results yields the
errors shown in Table 11.6. Equation 11.8 for functions r 2 (m,m 0 ) and r 3 (m,m 0 )
allow computing the corresponded values with rather small error as far as
o 0 ¼ 0.9. Therefore, the solar radiance reflected from the cloud layer in the
shortwave spectral range is possible to calculate with the analytical formulas, and
this fact is useful for the interpretation of the satellite radiation data.
11.6.1 Optical Model of the Cloud Layer
The input of optical parameters is necessary for calculating radiative characteristics
Ranges of cloud optical parameters are presented below:
1. The optical thickness 100 ! t 0 ! 5;
2. The optical depth within the layer t is automatically assumed with dividing the
layer to five parts;
3. The single scattering albedo 1 ! o 0 ! 0.992;
4. The asymmetry parameter of the phase function g ¼ 0.5–0.85;
5. The surface albedo A ¼ 0–0.95
6. Solar and viewing zenith angles (degrees) 0–80
7. The azimuth angle relative to the Sun ’ (degrees) for radiance calculating 0–180
Table 11.5 Uncertainty of the escape function K(m) calculation,%
o 0
0.999
0.995
0.990
0.980
g
0.5
0.9
0.5
0.9
0.5
0.9
0.5
0.75
0.9
s
0.0258 0.05774 0.05774 0.1291 0.08165 0.18257 0.1155 0.1633 0.2582
m
0.1 0.1
0.2
0.4
1.0
0.5
2.0
10
33
127
0.5 0.1
0.4
0.1
2.0
0.1
4.0
6.0
29
79
0.7 0.3
0.5
0.3
0.8
0.4
3.0
5.0
25
64
1.0 0.2
0.6
0.6
2.0
1.0
4.0
2.5
12
45
Table 11.6 Uncertainty of calculating the reflection function r 1 (m,m 0 ) of the semi-infinite layer
o 0
0.999
0.995
0.990
g
0.5
0.9
0.5
0.9
0.5
0.9
s
0.0258
0.05774
0.05774
0.1291
0.08165
0.18257
m
0.1
0.2
0.6
0.2
1.0
0.3
2.6
0.5
0.2
0.3
0.4
1.0
1.0
3.0
1.0
0.2
0.3
0.5
1.0
0.7
3.0
116
11 Calculating Solar Radiative Characteristics in Clouds with Asymptotic
coefficients r 2 (m,m 0 ) and r 3 (m,m 0 ) with numerical computing results yields the
errors shown in Table 11.6. Equation 11.8 for functions r 2 (m,m 0 ) and r 3 (m,m 0 )
allow computing the corresponded values with rather small error as far as
o 0 ¼ 0.9. Therefore, the solar radiance reflected from the cloud layer in the
shortwave spectral range is possible to calculate with the analytical formulas, and
this fact is useful for the interpretation of the satellite radiation data.
11.6.1 Optical Model of the Cloud Layer
The input of optical parameters is necessary for calculating radiative characteristics
Ranges of cloud optical parameters are presented below:
1. The optical thickness 100 ! t 0 ! 5;
2. The optical depth within the layer t is automatically assumed with dividing the
layer to five parts;
3. The single scattering albedo 1 ! o 0 ! 0.992;
4. The asymmetry parameter of the phase function g ¼ 0.5–0.85;
5. The surface albedo A ¼ 0–0.95
6. Solar and viewing zenith angles (degrees) 0–80
7. The azimuth angle relative to the Sun ’ (degrees) for radiance calculating 0–180
Table 11.5 Uncertainty of the escape function K(m) calculation,%
o 0
0.999
0.995
0.990
0.980
g
0.5
0.9
0.5
0.9
0.5
0.9
0.5
0.75
0.9
s
0.0258 0.05774 0.05774 0.1291 0.08165 0.18257 0.1155 0.1633 0.2582
m
0.1 0.1
0.2
0.4
1.0
0.5
2.0
10
33
127
0.5 0.1
0.4
0.1
2.0
0.1
4.0
6.0
29
79
0.7 0.3
0.5
0.3
0.8
0.4
3.0
5.0
25
64
1.0 0.2
0.6
0.6
2.0
1.0
4.0
2.5
12
45
Table 11.6 Uncertainty of calculating the reflection function r 1 (m,m 0 ) of the semi-infinite layer
o 0
0.999
0.995
0.990
g
0.5
0.9
0.5
0.9
0.5
0.9
s
0.0258
0.05774
0.05774
0.1291
0.08165
0.18257
m
0.1
0.2
0.6
0.2
1.0
0.3
2.6
0.5
0.2
0.3
0.4
1.0
1.0
3.0
1.0
0.2
0.3
0.5
1.0
0.7
3.0
116
11 Calculating Solar Radiative Characteristics in Clouds with Asymptotic