When this research was done both authors were with the Center for Climate System Research, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153, Japan.
F. Zhao is now with the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China.
Fengsheng Zhao and Teruyuki Nakajima, "Simultaneous determination of water-leaving reflectance and aerosol optical thickness from Coastal Zone Color Scanner measurements," Appl. Opt. 36, 6949-6956 (1997)
We present an iterative algorithm for the simultaneous determination of water-leaving reflectances and aerosol optical thickness from the total outgoing radiances measured in the Coastal Zone Color Scanner (CZCS) visible and near-infrared channels. Numerical experiments were carried out to investigate the feasibility of the algorithm. The results show that the errors in determined water-leaving reflectance at 0.443 µm are approximately
10% in most cases. The errors in determined water-leaving reflectance at 0.55 µm are in the 4.05–7.2% range. The errors in the simultaneously determined aerosol optical thickness for all CZCS visible and near-infrared channels are less than approximately 10%.
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Results of Water-Leaving Reflectance Measurementsa
θ0 (deg)
θ (deg)
δw (0.443) (%)
δw (0.55) (%)
20
21.5
0.0241
21.5
0.0156
7.2
48
0.217
9.67
0.0149
4.25
40
21.5
0.0218
10.7
0.0148
4.58
48
0.0212
8.25
0.0146
4.05
60
21.5
0.0215
9.68
0.0156
4.62
48
0.0221
12
0.0155
5.47
and
are the averaged values of the determined water-leaving reflectances at
0.443 and 0.55 µm, respectively,
δw(0.443) and
δw(0.55) are the standard deviations (for definition see the text). The true values of the water-leaving reflectances at 0.443 and 0.55 µm are 0.02 and 0.015, respectively.
Table 3
Errors in the Aerosol Optical Thickness
Mode Size Distribution
Standard Deviations (%)
δa (0.443)
δa (0.52)
δa (0.55)
δa (0.67)
δa (0.75)
1
7.86
3.22
2.64
4.49
6.31
2
10.89
6.41
4.87
1.46
2.32
3
7.03
5.48
5.19
5.53
6.80
4
6.40
5.37
5.09
4.73
5.11
5
8.80
4.01
3.18
4.53
6.50
6
7.83
3.74
3.11
4.28
6.25
7
4.88
1.07
1.95
6.58
8.14
8
8.10
3.80
3.37
4.75
6.35
9
3.99
7.55
8.58
9.94
9.49
10
0.91
0.40
0.32
0.92
1.42
Table 4
Water-Leaving Reflectance Values of Rw1 (0.443) Determined at
τao (0.44) = 0.4a
θ0 (deg)
θ (deg)
τao (0.55) = 0.15
τao (0.55) = 0.4
Rw1
(0.443)
Error in %
Rw1
(0.443)
Error in (%)
20
21.5
0.0245
22.5
0.0258
29.0
48
0.0207
3.8
0.0218
9.25
40
21.5
0.0212
6.12
0.0236
18.2
48
0.0212
5.8
0.0199
-0.3
60
21.5
0.0215
7.45
0.022
10.0
48
0.0230
15.0
0.0231
15.3
The true value of the water-leaving reflectance is 0.02. For comparison, the values of the water-leaving reflectance determined at τao(0.55) = 0.15 are also listed.
Table 5
Aerosol Optical Thickness Values of
τa1
(0.55) Determined at τao (0.55) = 0.4a
θ0 (deg)
θ (deg)
τao (0.55) = 0.15
τao (0.55) = 0.4
τa1 (0.55)
Error in %
τa1 (0.55)
Error in (%)
20
21.5
0.154
2.7
0.412
3.0
48
0.147
-2.0
0.384
-4.0
40
21.5
0.149
-0.7
0.392
-2.0
48
0.146
-2.7
0.375
-6.3
60
21.5
0.147
-2.0
0.378
-5.5
48
0.143
-4.7
0.365
-8.7
For comparison, the values of the aerosol optical thickness determined at
τao (0.55) = 0.15
are also listed.
Results of Water-Leaving Reflectance Measurementsa
θ0 (deg)
θ (deg)
δw (0.443) (%)
δw (0.55) (%)
20
21.5
0.0241
21.5
0.0156
7.2
48
0.217
9.67
0.0149
4.25
40
21.5
0.0218
10.7
0.0148
4.58
48
0.0212
8.25
0.0146
4.05
60
21.5
0.0215
9.68
0.0156
4.62
48
0.0221
12
0.0155
5.47
and
are the averaged values of the determined water-leaving reflectances at
0.443 and 0.55 µm, respectively,
δw(0.443) and
δw(0.55) are the standard deviations (for definition see the text). The true values of the water-leaving reflectances at 0.443 and 0.55 µm are 0.02 and 0.015, respectively.
Table 3
Errors in the Aerosol Optical Thickness
Mode Size Distribution
Standard Deviations (%)
δa (0.443)
δa (0.52)
δa (0.55)
δa (0.67)
δa (0.75)
1
7.86
3.22
2.64
4.49
6.31
2
10.89
6.41
4.87
1.46
2.32
3
7.03
5.48
5.19
5.53
6.80
4
6.40
5.37
5.09
4.73
5.11
5
8.80
4.01
3.18
4.53
6.50
6
7.83
3.74
3.11
4.28
6.25
7
4.88
1.07
1.95
6.58
8.14
8
8.10
3.80
3.37
4.75
6.35
9
3.99
7.55
8.58
9.94
9.49
10
0.91
0.40
0.32
0.92
1.42
Table 4
Water-Leaving Reflectance Values of Rw1 (0.443) Determined at
τao (0.44) = 0.4a
θ0 (deg)
θ (deg)
τao (0.55) = 0.15
τao (0.55) = 0.4
Rw1
(0.443)
Error in %
Rw1
(0.443)
Error in (%)
20
21.5
0.0245
22.5
0.0258
29.0
48
0.0207
3.8
0.0218
9.25
40
21.5
0.0212
6.12
0.0236
18.2
48
0.0212
5.8
0.0199
-0.3
60
21.5
0.0215
7.45
0.022
10.0
48
0.0230
15.0
0.0231
15.3
The true value of the water-leaving reflectance is 0.02. For comparison, the values of the water-leaving reflectance determined at τao(0.55) = 0.15 are also listed.
Table 5
Aerosol Optical Thickness Values of
τa1
(0.55) Determined at τao (0.55) = 0.4a
θ0 (deg)
θ (deg)
τao (0.55) = 0.15
τao (0.55) = 0.4
τa1 (0.55)
Error in %
τa1 (0.55)
Error in (%)
20
21.5
0.154
2.7
0.412
3.0
48
0.147
-2.0
0.384
-4.0
40
21.5
0.149
-0.7
0.392
-2.0
48
0.146
-2.7
0.375
-6.3
60
21.5
0.147
-2.0
0.378
-5.5
48
0.143
-4.7
0.365
-8.7
For comparison, the values of the aerosol optical thickness determined at
τao (0.55) = 0.15
are also listed.