Atmospheric correction of ocean color imagery: use of the Junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption
Roman M. Chomko and Howard R. Gordon, "Atmospheric correction of ocean color imagery: use of the Junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption," Appl. Opt. 37, 5560-5572 (1998)
When strongly absorbing aerosols are present in the atmosphere, the
usual two-step procedure of processing ocean color data—(1)
atmospheric correction to provide the water-leaving reflectance
(ρw), followed by (2) relating
ρw to the water constituents—fails and
simultaneous estimation of the ocean and aerosol optical properties is
necessary. We explore the efficacy of using a simple model of the
aerosol—a Junge power-law size distribution consisting of homogeneous
spheres with arbitrary refractive index—in a nonlinear optimization
procedure for estimating the relevant oceanic and atmospheric
parameters for case 1 waters. Using simulated test data generated
from more realistic aerosol size distributions (sums of log-normally
distributed components with different compositions), we show that the
ocean’s pigment concentration (C) can be retrieved with
good accuracy in the presence of weakly or strongly absorbing
aerosols. However, because of significant differences in the
scattering phase functions for the test and power-law distributions,
large error is possible in the estimate of the aerosol optical
thickness. The positive result for C suggests that the
detailed shape of the aerosol-scattering phase function is not relevant
to the atmospheric correction of ocean color sensors. The relevant
parameters are the aerosol single-scattering albedo and the spectral
variation of the aerosol optical depth. We argue that the
assumption of aerosol sphericity should not restrict the validity of
the algorithm and suggest an avenue for including colored aerosols,
e.g., wind-blown dust, in the procedure. A significant advantage of
the new approach is that realistic multicomponent aerosol models are
not required for the retrieval of C.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Tabulated are mean values of retrieved
ω0 for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
b0 for seven Sun-viewing geometries and each of
four hypothetical atmospheric aerosols (M80, C80, T80,
U80). Also provided are the standard deviations over viewing
geometries divided by the mean (Sd) as well
as the deviations from given parameters (D).
Table 6
Mean SLSQ and its Standard
Deviation σS (both in %), over all
Values of τa(865), C, and
Sun-Viewing Geometries
Model
σS
M80
0.27
22
C80
0.28
19
T80
0.36
23
U80
0.15
16
U280
1.57
27
U480
5.58
27
UU80
133.48
68
Table 7
Values of the Residual Radiometric Calibration Uncertainty
after Effecting an In-Orbit Calibration
Adjustmenta
Retrieval of Ocean’s Pigment Concentration with Negative
Calibration Errora
C (mg/m3)
0.100
0.500
1.000
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
M80
τa(865) = 0.10
0.094
2.3
6.00
0.479
2.3
4.20
1.004
0.8
0.40
ω0 = 0.993
τa(865) = 0.20
0.091
4.0
9.00
0.463
4.6
7.40
1.005
2.2
0.50
τa(865) = 0.30
0.090
4.7
3.00
0.452
6.1
9.60
0.998
4.0
0.20
C80
τa(865) = 0.10
0.094
2.6
6.00
0.476
2.5
4.80
0.997
0.9
0.30
ω0 = 0.988
τa(865) = 0.20
0.090
4.7
10.0
0.455
5.2
9.00
0.983
2.2
1.70
τa(865) = 0.30
0.088
5.3
12.0
0.438
6.5
12.4
0.964
4.4
3.60
T80
τa(865) = 0.10
0.086
10.0
5.00
0.437
9.5
12.6
1.038
14.0
3.80
ω0 = 0.953
τa(865) = 0.20
0.078
14.0
22.0
0.377
19.0
24.6
0.836
3.4
16.4
τa(865) = 0.30
0.081
12.0
19.0
0.337
15.0
32.6
0.640
26.0
36.0
U80
τa(865) = 0.10
0.098
1.5
2.00
0.496
0.2
0.80
1.021
2.7
2.10
ω0 = 0.748
τa(865) = 0.20
0.099
2.7
1.00
0.507
1.9
1.40
1.033
3.5
3.30
τa(865) = 0.30
0.104
3.2
4.0
0.530
4.7
6.00
1.056
4.1
5.60
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Table 9
Retrieval of Ocean’s Pigment Concentration with Positive
Calibration Errora
C (mg/m3)
0.100
0.500
1.000
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
M80
τa(865) = 0.10
0.098
1.6
2.00
0.494
2.7
1.20
1.011
4.2
1.10
ω0 = 0.993
τa(865) = 0.20
0.097
2.2
3.00
0.487
5.0
2.60
0.999
8.5
0.10
τa(865) = 0.30
0.097
2.2
3.00
0.485
6.2
3.00
0.991
11.0
0.90
C80
τa(865) = 0.10
0.098
1.6
2.00
0.490
3.6
2.00
0.995
6.3
0.50
ω0 = 0.988
τa(865) = 0.20
0.097
2.2
3.00
0.478
7.1
4.40
0.966
12.0
3.40
τa(865) = 0.30
0.097
2.6
3.00
0.471
10.0
5.80
0.940
17.0
6.00
T80
τa(865) = 0.10
0.095
4.7
5.00
0.487
2.4
2.60
1.037
4.9
3.70
ω0 = 0.953
τa(865) = 0.20
0.093
1.3
7.00
0.470
4.0
6.00
0.935
3.0
6.50
τa(865) = 0.30
0.096
4.4
4.0
0.469
2.1
6.20
0.943
2.7
5.70
U80
τa(865) = 0.10
0.103
0.8
3.00
0.519
1.1
3.80
1.043
2.3
4.30
ω0 = 0.748
τa(865) = 0.20
0.109
2.8
9.00
0.543
3.8
8.60
1.062
2.9
6.20
τa(865) = 0.30
0.116
5.7
16.0
0.573
6.4
14.6
1.089
3.6
8.90
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80. Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tables (10)
Table 1
Characteristics of the Test Aerosol Models used in the
Study
Aerosol Model
Size Distribution
Refractive Index
Ni
Di
σi
412 nm
865 nm
M80
0.990000
0.06548
0.35
1.446-i
3.309
E-3
1.436-i
6.107
E-3
0.010000
0.63600
0.40
1.359-i
5.165
E-9
1.348-i
1.381
E-6
C80
0.995000
0.06548
0.35
1.446-i
3.309
E-3
1.436-i
6.107
E-3
0.005000
0.63600
0.40
1.359-i
5.165
E-9
1.348-i
1.381
E-6
T80
1.000000
0.06548
0.35
1.446-i
3.309
E-3
1.436-i
6.107
E-3
U80
0.999875
0.07028
0.35
1.423-i
3.473
E-2
1.414-i
3.412
E-2
0.000125
1.16200
0.40
1.415-i
3.151
E-2
1.406-i
3.095
E-2
Table 2
Values of Single-Scattering Albedo at λ = 412 and 865 nm
for the Test Aerosol Models used in the Study
Tabulated are mean values of retrieved
ω0 for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
b0 for seven Sun-viewing geometries and each of
four hypothetical atmospheric aerosols (M80, C80, T80,
U80). Also provided are the standard deviations over viewing
geometries divided by the mean (Sd) as well
as the deviations from given parameters (D).
Table 6
Mean SLSQ and its Standard
Deviation σS (both in %), over all
Values of τa(865), C, and
Sun-Viewing Geometries
Model
σS
M80
0.27
22
C80
0.28
19
T80
0.36
23
U80
0.15
16
U280
1.57
27
U480
5.58
27
UU80
133.48
68
Table 7
Values of the Residual Radiometric Calibration Uncertainty
after Effecting an In-Orbit Calibration
Adjustmenta
Retrieval of Ocean’s Pigment Concentration with Negative
Calibration Errora
C (mg/m3)
0.100
0.500
1.000
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
M80
τa(865) = 0.10
0.094
2.3
6.00
0.479
2.3
4.20
1.004
0.8
0.40
ω0 = 0.993
τa(865) = 0.20
0.091
4.0
9.00
0.463
4.6
7.40
1.005
2.2
0.50
τa(865) = 0.30
0.090
4.7
3.00
0.452
6.1
9.60
0.998
4.0
0.20
C80
τa(865) = 0.10
0.094
2.6
6.00
0.476
2.5
4.80
0.997
0.9
0.30
ω0 = 0.988
τa(865) = 0.20
0.090
4.7
10.0
0.455
5.2
9.00
0.983
2.2
1.70
τa(865) = 0.30
0.088
5.3
12.0
0.438
6.5
12.4
0.964
4.4
3.60
T80
τa(865) = 0.10
0.086
10.0
5.00
0.437
9.5
12.6
1.038
14.0
3.80
ω0 = 0.953
τa(865) = 0.20
0.078
14.0
22.0
0.377
19.0
24.6
0.836
3.4
16.4
τa(865) = 0.30
0.081
12.0
19.0
0.337
15.0
32.6
0.640
26.0
36.0
U80
τa(865) = 0.10
0.098
1.5
2.00
0.496
0.2
0.80
1.021
2.7
2.10
ω0 = 0.748
τa(865) = 0.20
0.099
2.7
1.00
0.507
1.9
1.40
1.033
3.5
3.30
τa(865) = 0.30
0.104
3.2
4.0
0.530
4.7
6.00
1.056
4.1
5.60
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Table 9
Retrieval of Ocean’s Pigment Concentration with Positive
Calibration Errora
C (mg/m3)
0.100
0.500
1.000
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
Result
Sd (%)
D (%)
M80
τa(865) = 0.10
0.098
1.6
2.00
0.494
2.7
1.20
1.011
4.2
1.10
ω0 = 0.993
τa(865) = 0.20
0.097
2.2
3.00
0.487
5.0
2.60
0.999
8.5
0.10
τa(865) = 0.30
0.097
2.2
3.00
0.485
6.2
3.00
0.991
11.0
0.90
C80
τa(865) = 0.10
0.098
1.6
2.00
0.490
3.6
2.00
0.995
6.3
0.50
ω0 = 0.988
τa(865) = 0.20
0.097
2.2
3.00
0.478
7.1
4.40
0.966
12.0
3.40
τa(865) = 0.30
0.097
2.6
3.00
0.471
10.0
5.80
0.940
17.0
6.00
T80
τa(865) = 0.10
0.095
4.7
5.00
0.487
2.4
2.60
1.037
4.9
3.70
ω0 = 0.953
τa(865) = 0.20
0.093
1.3
7.00
0.470
4.0
6.00
0.935
3.0
6.50
τa(865) = 0.30
0.096
4.4
4.0
0.469
2.1
6.20
0.943
2.7
5.70
U80
τa(865) = 0.10
0.103
0.8
3.00
0.519
1.1
3.80
1.043
2.3
4.30
ω0 = 0.748
τa(865) = 0.20
0.109
2.8
9.00
0.543
3.8
8.60
1.062
2.9
6.20
τa(865) = 0.30
0.116
5.7
16.0
0.573
6.4
14.6
1.089
3.6
8.90
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80). Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).
Tabulated are mean values of retrieved
C for seven Sun-viewing geometries and each of four
hypothetical atmospheric aerosols (M80, C80, T80, U80. Also
provided are the standard deviations over viewing geometries divided by
the mean (Sd) as well as the deviations from
given parameters (D).