Howard R. Gordon, Tao Du, and Tianming Zhang, "Remote sensing of ocean color and aerosol properties: resolving the issue of aerosol absorption," Appl. Opt. 36, 8670-8684 (1997)
Current atmospheric correction and aerosol retrieval algorithms for ocean color sensors use measurements of the top-of-the-atmosphere reflectance in the near infrared, where the contribution from the ocean is known for case 1 waters, to assess the aerosol optical properties. Such measurements are incapable of distinguishing between weakly and strongly absorbing aerosols, and the atmospheric correction and aerosol retrieval algorithms fail if the incorrect absorption properties of the aerosol are assumed. We present an algorithm that appears promising for the retrieval of in-water biophysical properties and aerosol optical properties in atmospheres containing both weakly and strongly absorbing aerosols. By using the entire spectrum available to most ocean color instruments (412–865 nm), we simultaneously recover the ocean’s bio-optical properties and a set of aerosol models that best describes the aerosol optical properties. The algorithm is applied to simulated situations that are likely to occur off the U.S. East Coast in summer when the aerosols could be of the locally generated weakly absorbing Maritime type or of the pollution-generated strongly absorbing urban-type transported over the ocean by the winds. The simulations show that the algorithm behaves well in an atmosphere with either weakly or strongly absorbing aerosol. The algorithm successfully identifies absorbing aerosols and provides close values for the aerosol optical thickness. It also provides excellent retrievals of the ocean bio-optical properties. The algorithm uses a bio-optical model of case 1 waters and a set of aerosol models for its operation. The relevant parameters of both the ocean and atmosphere are systematically varied to find the best (in a rms sense) fit to the measured top-of-the-atmosphere spectral reflectance. Examples are provided that show the algorithm’s performance in the presence of errors, e.g., error in the contribution from whitecaps and error in radiometric calibration.
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Values of ω0 at 865 nm for the Candidate and Test Aerosol Models
Candidate Models at RH
Test Models at RH
Aerosols
50%
70%
90%
99%
80%
M
0.9814
0.9859
0.9953
0.9986
0.9934
C
0.9705
0.9768
0.9919
0.9974
0.9884
T
0.9295
0.9346
0.9698
0.9870
0.9528
U
0.6026
0.6605
0.8206
0.9419
0.7481
Table 2
Mean Values of Retrieved ω0′ (865) for the Seven Sun-Viewing Geometries and Each of Four Aerosol Modelsa
Models
C (mg/m3)
0.100
0.500
1.000
M80
τa(865) = 0.100
0.992 (0.43%)
0.996 (0.14%)
0.997 (0.10%)
ω0 = 0.993
τa(865) = 0.200
0.995 (0.10%)
0.995 (0.10%)
0.996 (0.05%)
τa(865) = 0.300
0.996 (0.05%)
0.996 (0.06%)
0.996 (0.10%)
C80
τa(865) = 0.100
0.980 (0.97%)
0.972 (1.60%)
0.965 (2.26%)
ω0 = 0.988
τa(865) = 0.200
0.983 (0.53%)
0.988 (0.31%)
0.989 (0.41%)
τa(865) = 0.300
0.987 (0.25%)
0.987 (0.27%)
0.987 (0.37%)
T80
τa(865) = 0.100
0.952 (0.78%)
0.935 (0.13%)
0.935 (0.00%)
ω0 = 0.953
τa(865) = 0.200
0.946 (0.34%)
0.936 (0.44%)
0.940 (1.41%)
τa(865) = 0.300
0.945 (0.31%)
0.934 (0.04%)
0.945 (1.82%)
U80
τa(865) = 0.100
0.793 (4.21%)
0.761 (4.51%)
0.769 (3.36%)
ω0 = 0.748
τa(865) = 0.200
0.730 (4.76%)
0.750 (8.25%)
0.712 (7.44%)
τa(865) = 0.300
0.730 (5.14%)
0.784 (2.56%)
0.699 (7.34%)
The standard deviation divided by the mean is listed in parentheses.
Table 3
Mean Values of Retrieved C′ for Seven Sun-Viewing Geometries and Four Aerosol Modelsa
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (1.90%)
0.528 (7.30%)
1.098 (11.7%)
τa(865) = 0.200
0.101 (4.56%)
0.547 (15.2%)
0.982 (23.9%)
τa(865) = 0.300
0.101 (4.42%)
0.612 (24.1%)
0.947 (31.3%)
The standard deviation divided by the mean is listed in parentheses.
Table 4
Mean Values of Retrieved C′ for Seven Sun-Viewing Geometries and Three Aerosol Models (M80, C80, T80) derived with the Gordon and Wang11 Algorithma
C (mg/m3)
0.10
0.47
0.91
τa(865) = 0.100
0.101 (1.6%)
0.466 (3.4%)
0.912 (9.1%)
τa(865) = 0.200
0.100 (3.1%)
0.470 (4.7%)
0.940 (12.8%)
τa(865) = 0.300
0.098 (5.5%)
0.493 (15.3%)
0.936 (25.3%)
The standard deviation divided by the mean is listed in parentheses.
Table 5
Percentage of Retrieved Pigment Concentration C′ Within Certain Error Limits for Aerosol Models M80, C80, T80, and U80
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
96%
100%
100%
100%
τa(865) = 0.200
89%
92%
100%
100%
τa(865) = 0.300
89%
92%
100%
100%
0.5
τa(865) = 0.100
32%
75%
92%
100%
τa(865) = 0.200
32%
50%
75%
89%
τa(865) = 0.300
25%
35%
64%
75%
1.0
τa(865) = 0.100
21%
50%
71%
96%
τa(865) = 0.200
28%
39%
57%
71%
τa(865) = 0.300
14%
25%
50%
60%
Table 6
Mean Values of Retrieved τa′(865) for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80)a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.102 (8.94%)
0.101 (10.2%)
0.102 (11.6%)
τa(865) = 0.200
0.201 (6.31%)
0.199 (8.53%)
0.199 (8.20%)
τa(865) = 0.300
0.300 (6.22%)
0.294 (8.79%)
0.300 (9.93%)
The standard deviation divided by the mean is listed in parentheses.
Table 7
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Three Aerosol Models (UU80, U280, U480)a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.103 (8.74%)
0.600 (29.11%)
1.054 (19.27%)
τa(865) = 0.200
0.114 (17.51%)
0.574 (39.12%)
1.026 (35.13%)
τa(865) = 0.300
0.125 (32.93%)
0.644 (57.33%)
0.863 (52.53%)
The standard deviation divided by the mean is listed in parentheses.
Table 8
Percentage of Retrieved Pigment Concentration C Within Certain Error Limits for Aerosol Models UU80, U280, and U480
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
85%
85%
95%
95%
τa(865) = 0.200
57%
57%
71%
80%
τa(865) = 0.300
57%
57%
61%
61%
0.5
τa(865) = 0.100
28%
52%
71%
90%
τa(865) = 0.200
38%
57%
66%
66%
τa(865) = 0.300
23%
38%
66%
66%
1.0
τa(865) = 0.100
47%
66%
71%
76%
τa(865) = 0.200
19%
38%
52%
61%
τa(865) = 0.300
4%
28%
52%
57%
Table 9
Mean Values of Retrieved ω0(865) for Seven Sun-Viewing Geometries of Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
U180
τa(865) = 0.100
0.764 (4.81%)
0.787 (6.82%)
0.787 (4.88%)
ω0 = 0.748
τa(865) = 0.200
0.737 (3.24%)
0.737 (8.84%)
0.723 (13.50%)
τa(865) = 0.300
0.736 (4.31%)
0.727 (4.39%)
0.714 (8.86%)
The standard deviation divided by the mean is listed in parentheses.
Table 10
Mean Values of Retrieved C for Seven Sun-Viewing Geometries of Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.00%)
0.556 (7.15%)
1.094 (8.53%)
τa(865) = 0.200
0.100 (0.00%)
0.544 (8.74%)
1.101 (16.12%)
τa(865) = 0.300
0.100 (0.00%)
0.566 (3.04%)
1.061 (15.11%)
The standard deviation divided by the mean is listed in parentheses.
Table 11
Percentage of Retrieved Pigment Concentration C Within Certain Error Limits for the Aerosol Model U180
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
100%
100%
100%
100%
τa(865) = 0.200
100%
100%
100%
100%
τa(865) = 0.300
100%
100%
100%
100%
0.5
τa(865) = 0.100
28%
42%
71%
100%
τa(865) = 0.200
14%
42%
100%
100%
τa(865) = 0.300
0%
14%
100%
100%
1.0
τa(865) = 0.100
28%
57%
85%
100%
τa(865) = 0.200
0%
28%
57%
100%
τa(865) = 0.300
28%
28%
71%
100%
Table 12
Mean Values of Retrieved τa(865) for Seven Sun-Viewing Geometries of the Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.102 (1.68%)
0.101 (3.62%)
0.099 (3.83%)
τa(865) = 0.200
0.206 (3.49%)
0.206 (2.89%)
0.209 (7.59%)
τa(865) = 0.300
0.305 (3.32%)
0.307 (2.52%)
0.304 (7.36%)
The standard deviation divided by the mean is listed in parentheses.
Table 13
Values of the Residual Radiometric Calibration Uncertainty After Affecting an In-orbit Calibration Adjustment45
λi (nm)
Uncertainty (%)
412
0.3
443
0.5
490
0.8
520
1.0
550
1.5
670
2.0
765
3.0
865
5.0
Table 14
Mean Values of the Retrieved C for the Seven Sun-Viewing Geometries and Each of Four Aerosol Models (M80, C80, T80, U80) for the Indicated Calibration Error (Table 13)a
Calibration Error
C (mg/m3)
0.100
0.500
1.000
Positive Error
0.102 (4.3%)
0.539 (15.1%)
0.976 (21.2%)
Zero Error
0.100 (3.1%)
0.470 (4.7%)
0.940 (12.8%)
Negative Error
0.100 (5.7%)
0.534 (15.9%)
1.029 (23.3%)
The standard deviation divided by the mean is listed in parentheses. τa(865) = 0.2.
Table 15
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80) for Δ[ρwc] = +0.002a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.00%)
0.455 (9.54%)
0.838 (19.89%)
τa(865) = 0.200
0.101 (4.68%)
0.485 (15.72%)
0.891 (23.44%)
τa(865) = 0.300
0.102 (6.97%)
0.526 (18.80%)
0.843 (25.55%)
The standard deviation divided by the mean is listed in parentheses.
Table 16
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80) for Δ[ρwc] = −0.002a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.94%)
0.647 (12.83%)
1.175 (18.21%)
τa(865) = 0.200
0.100 (2.32%)
0.644 (17.53%)
1.030 (24.13%)
τa(865) = 0.300
0.101 (4.96%)
0.699 (24.94%)
0.985 (31.03%)
The standard deviation divided by the mean is listed in parentheses.
Tables (16)
Table 1
Values of ω0 at 865 nm for the Candidate and Test Aerosol Models
Candidate Models at RH
Test Models at RH
Aerosols
50%
70%
90%
99%
80%
M
0.9814
0.9859
0.9953
0.9986
0.9934
C
0.9705
0.9768
0.9919
0.9974
0.9884
T
0.9295
0.9346
0.9698
0.9870
0.9528
U
0.6026
0.6605
0.8206
0.9419
0.7481
Table 2
Mean Values of Retrieved ω0′ (865) for the Seven Sun-Viewing Geometries and Each of Four Aerosol Modelsa
Models
C (mg/m3)
0.100
0.500
1.000
M80
τa(865) = 0.100
0.992 (0.43%)
0.996 (0.14%)
0.997 (0.10%)
ω0 = 0.993
τa(865) = 0.200
0.995 (0.10%)
0.995 (0.10%)
0.996 (0.05%)
τa(865) = 0.300
0.996 (0.05%)
0.996 (0.06%)
0.996 (0.10%)
C80
τa(865) = 0.100
0.980 (0.97%)
0.972 (1.60%)
0.965 (2.26%)
ω0 = 0.988
τa(865) = 0.200
0.983 (0.53%)
0.988 (0.31%)
0.989 (0.41%)
τa(865) = 0.300
0.987 (0.25%)
0.987 (0.27%)
0.987 (0.37%)
T80
τa(865) = 0.100
0.952 (0.78%)
0.935 (0.13%)
0.935 (0.00%)
ω0 = 0.953
τa(865) = 0.200
0.946 (0.34%)
0.936 (0.44%)
0.940 (1.41%)
τa(865) = 0.300
0.945 (0.31%)
0.934 (0.04%)
0.945 (1.82%)
U80
τa(865) = 0.100
0.793 (4.21%)
0.761 (4.51%)
0.769 (3.36%)
ω0 = 0.748
τa(865) = 0.200
0.730 (4.76%)
0.750 (8.25%)
0.712 (7.44%)
τa(865) = 0.300
0.730 (5.14%)
0.784 (2.56%)
0.699 (7.34%)
The standard deviation divided by the mean is listed in parentheses.
Table 3
Mean Values of Retrieved C′ for Seven Sun-Viewing Geometries and Four Aerosol Modelsa
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (1.90%)
0.528 (7.30%)
1.098 (11.7%)
τa(865) = 0.200
0.101 (4.56%)
0.547 (15.2%)
0.982 (23.9%)
τa(865) = 0.300
0.101 (4.42%)
0.612 (24.1%)
0.947 (31.3%)
The standard deviation divided by the mean is listed in parentheses.
Table 4
Mean Values of Retrieved C′ for Seven Sun-Viewing Geometries and Three Aerosol Models (M80, C80, T80) derived with the Gordon and Wang11 Algorithma
C (mg/m3)
0.10
0.47
0.91
τa(865) = 0.100
0.101 (1.6%)
0.466 (3.4%)
0.912 (9.1%)
τa(865) = 0.200
0.100 (3.1%)
0.470 (4.7%)
0.940 (12.8%)
τa(865) = 0.300
0.098 (5.5%)
0.493 (15.3%)
0.936 (25.3%)
The standard deviation divided by the mean is listed in parentheses.
Table 5
Percentage of Retrieved Pigment Concentration C′ Within Certain Error Limits for Aerosol Models M80, C80, T80, and U80
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
96%
100%
100%
100%
τa(865) = 0.200
89%
92%
100%
100%
τa(865) = 0.300
89%
92%
100%
100%
0.5
τa(865) = 0.100
32%
75%
92%
100%
τa(865) = 0.200
32%
50%
75%
89%
τa(865) = 0.300
25%
35%
64%
75%
1.0
τa(865) = 0.100
21%
50%
71%
96%
τa(865) = 0.200
28%
39%
57%
71%
τa(865) = 0.300
14%
25%
50%
60%
Table 6
Mean Values of Retrieved τa′(865) for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80)a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.102 (8.94%)
0.101 (10.2%)
0.102 (11.6%)
τa(865) = 0.200
0.201 (6.31%)
0.199 (8.53%)
0.199 (8.20%)
τa(865) = 0.300
0.300 (6.22%)
0.294 (8.79%)
0.300 (9.93%)
The standard deviation divided by the mean is listed in parentheses.
Table 7
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Three Aerosol Models (UU80, U280, U480)a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.103 (8.74%)
0.600 (29.11%)
1.054 (19.27%)
τa(865) = 0.200
0.114 (17.51%)
0.574 (39.12%)
1.026 (35.13%)
τa(865) = 0.300
0.125 (32.93%)
0.644 (57.33%)
0.863 (52.53%)
The standard deviation divided by the mean is listed in parentheses.
Table 8
Percentage of Retrieved Pigment Concentration C Within Certain Error Limits for Aerosol Models UU80, U280, and U480
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
85%
85%
95%
95%
τa(865) = 0.200
57%
57%
71%
80%
τa(865) = 0.300
57%
57%
61%
61%
0.5
τa(865) = 0.100
28%
52%
71%
90%
τa(865) = 0.200
38%
57%
66%
66%
τa(865) = 0.300
23%
38%
66%
66%
1.0
τa(865) = 0.100
47%
66%
71%
76%
τa(865) = 0.200
19%
38%
52%
61%
τa(865) = 0.300
4%
28%
52%
57%
Table 9
Mean Values of Retrieved ω0(865) for Seven Sun-Viewing Geometries of Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
U180
τa(865) = 0.100
0.764 (4.81%)
0.787 (6.82%)
0.787 (4.88%)
ω0 = 0.748
τa(865) = 0.200
0.737 (3.24%)
0.737 (8.84%)
0.723 (13.50%)
τa(865) = 0.300
0.736 (4.31%)
0.727 (4.39%)
0.714 (8.86%)
The standard deviation divided by the mean is listed in parentheses.
Table 10
Mean Values of Retrieved C for Seven Sun-Viewing Geometries of Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.00%)
0.556 (7.15%)
1.094 (8.53%)
τa(865) = 0.200
0.100 (0.00%)
0.544 (8.74%)
1.101 (16.12%)
τa(865) = 0.300
0.100 (0.00%)
0.566 (3.04%)
1.061 (15.11%)
The standard deviation divided by the mean is listed in parentheses.
Table 11
Percentage of Retrieved Pigment Concentration C Within Certain Error Limits for the Aerosol Model U180
C (mg/m3)
ΔC/C
<5%
<10%
<20%
<30%
0.1
τa(865) = 0.100
100%
100%
100%
100%
τa(865) = 0.200
100%
100%
100%
100%
τa(865) = 0.300
100%
100%
100%
100%
0.5
τa(865) = 0.100
28%
42%
71%
100%
τa(865) = 0.200
14%
42%
100%
100%
τa(865) = 0.300
0%
14%
100%
100%
1.0
τa(865) = 0.100
28%
57%
85%
100%
τa(865) = 0.200
0%
28%
57%
100%
τa(865) = 0.300
28%
28%
71%
100%
Table 12
Mean Values of Retrieved τa(865) for Seven Sun-Viewing Geometries of the Aerosol Model U180a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.102 (1.68%)
0.101 (3.62%)
0.099 (3.83%)
τa(865) = 0.200
0.206 (3.49%)
0.206 (2.89%)
0.209 (7.59%)
τa(865) = 0.300
0.305 (3.32%)
0.307 (2.52%)
0.304 (7.36%)
The standard deviation divided by the mean is listed in parentheses.
Table 13
Values of the Residual Radiometric Calibration Uncertainty After Affecting an In-orbit Calibration Adjustment45
λi (nm)
Uncertainty (%)
412
0.3
443
0.5
490
0.8
520
1.0
550
1.5
670
2.0
765
3.0
865
5.0
Table 14
Mean Values of the Retrieved C for the Seven Sun-Viewing Geometries and Each of Four Aerosol Models (M80, C80, T80, U80) for the Indicated Calibration Error (Table 13)a
Calibration Error
C (mg/m3)
0.100
0.500
1.000
Positive Error
0.102 (4.3%)
0.539 (15.1%)
0.976 (21.2%)
Zero Error
0.100 (3.1%)
0.470 (4.7%)
0.940 (12.8%)
Negative Error
0.100 (5.7%)
0.534 (15.9%)
1.029 (23.3%)
The standard deviation divided by the mean is listed in parentheses. τa(865) = 0.2.
Table 15
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80) for Δ[ρwc] = +0.002a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.00%)
0.455 (9.54%)
0.838 (19.89%)
τa(865) = 0.200
0.101 (4.68%)
0.485 (15.72%)
0.891 (23.44%)
τa(865) = 0.300
0.102 (6.97%)
0.526 (18.80%)
0.843 (25.55%)
The standard deviation divided by the mean is listed in parentheses.
Table 16
Mean Values of Retrieved C for Seven Sun-Viewing Geometries and Four Aerosol Models (M80, C80, T80, U80) for Δ[ρwc] = −0.002a
C (mg/m3)
0.100
0.500
1.000
τa(865) = 0.100
0.100 (0.94%)
0.647 (12.83%)
1.175 (18.21%)
τa(865) = 0.200
0.100 (2.32%)
0.644 (17.53%)
1.030 (24.13%)
τa(865) = 0.300
0.101 (4.96%)
0.699 (24.94%)
0.985 (31.03%)
The standard deviation divided by the mean is listed in parentheses.