P. Y. Deschamps, M. Herman, and D. Tanre, "Modeling of the atmospheric effects and its application to the remote sensing of ocean color," Appl. Opt. 22, 3751-3758 (1983)
The effect of atmospheric scattering on ocean color measurements from space is considered. It is shown that modeling of the atmospheric effects can be improved by taking into account not only the direct but also the diffuse component of atmospheric transmittance and by a more precise formulation of the interaction between molecular and aerosol scattering in the calculation of atmospheric reflectance. This method, necessitating two near-infrared channels, should be used in future ocean color experiments to better correct for variable aerosol reflectance. The relative accuracy of the aerosol reflectance correction would then be to within 5%, as opposed to the more than 10% obtained with previous modelings.
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Optical Thicknesses of the Three Scattering Model Atmospheres Calculated from the Aerosol Optical Properties13a
λ = 400 nm
λ = 450 nm
λ = 550 nm
λ = 650 nm
λ = 850 nm
τR
0.3510
0.2157
0.0948
0.0481
0.0163
τR(V23)
0.3083
0.2801
0.2348
0.2011
0.1550
τR(V5)
1.0241
0.9305
0.7801
0.6681
0.5151
(R) contains no aerosols and would correspond to the best achievable conditions; (V23) and (V5) correspond to ground visibilities of 23 and 5 km, i.e., mean and extreme atmospheric conditions.
Table II
Influence of Atmospheric Scattering T(λ1,θ0)/T(λ2,θ0) on the Ratio of Water Leaving Radiances at (λ1 = 450 nm; λ2 = 550 nm) and (
; λ2 = 550 nm)
θ0 (deg)
λ1,λ2 (in nm)
R
V23
V5
0
450; 550
0.945
0.931
0.935
60
450; 550
0.903
0.901
0.898
0
400; 550
0.889
0.886
0.878
60
400; 550
0.815
0.816
0.822
Table III
Diffuse Molecular Transmittance E′R(θ) and Spherical Molecular Albedo S′R for Unit Irradiance with an Angular Dependence 1/μ
θυ (deg)
λ = 400 nm
λ = 450 nm
2.84
0.1639
0.1182
17.64
0.1733
0.1257
32.48
0.1981
0.1458
Function E′R(θ)
λ = 400 nm
λ = 450 nm
0.3115
0.2340
Function S′R
Table IV
Computed Atmospheric Reflectances at λ = 450 nm for a Moderate Aerosol Content [(V23) Model]
θυ,φυ
Solar zenith angle = 15°
Solar zenith angle - 60°
(1)
(2)
(3)
(1)
(2)
(3)
2.84; 0
0.1054
−0.0010
−0.008
0.1271
0.0022
−0.0006
17.64; 0
0.0966
0.0015
−0.0011
0.1260
−0.0011
0.0002
17.64; 90
0.1057
−0.0001
−0.0010
0.1353
0.0028
−0.0001
17.64;180
0.1194
−0.0041
−0.0009
0.1588
0.0034
0.0000
32.48; 0
0.0946
0.0028
−0.0007
0.1504
−0.0101
0.0021
32.48; 90
0.1058
0.0022
−0.0006
0.1512
0.0028
0.0010
32.48;180
0.1236
−0.0013
−0.0005
0.2051
0.0007
0.0017
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
Table V
Same as Table IV but for a High Aerosol Content [(V5) Model]
θυ,φυ
Solar zenith angle = 15°
Solar zenith angle = 60°
(1)
(2)
(3)
(1)
(2)
(3)
2.84; 0
0.1599
−0.0058
−0.0034
0.2022
−0.0104
−0.0006
17.64; 0
0.1487
−0.0008
−0.0034
0.2144
−0.0224
0.0010
17.64; 90
0.1607
−0.0041
−0.0033
0.2140
−0.0105
0.0002
17.64;180
0.1817
−0.0123
−0.0033
0.2338
−0.0067
0.0002
32.48; 0
0.1522
−0.0001
−0.0027
0.2676
−0.0515
0.0047
32.48; 90
0.1633
−0.0008
−0.0028
0.2423
−0.0151
0.0025
32.48;180
0.1867
−0.0076
−0.0026
0.2929
−0.0139
0.0032
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
Table VII
Relative Accuracy
of the Modeling of the Atmospheric Reflectance by Eqs. (4) and (12)
Optical Thicknesses of the Three Scattering Model Atmospheres Calculated from the Aerosol Optical Properties13a
λ = 400 nm
λ = 450 nm
λ = 550 nm
λ = 650 nm
λ = 850 nm
τR
0.3510
0.2157
0.0948
0.0481
0.0163
τR(V23)
0.3083
0.2801
0.2348
0.2011
0.1550
τR(V5)
1.0241
0.9305
0.7801
0.6681
0.5151
(R) contains no aerosols and would correspond to the best achievable conditions; (V23) and (V5) correspond to ground visibilities of 23 and 5 km, i.e., mean and extreme atmospheric conditions.
Table II
Influence of Atmospheric Scattering T(λ1,θ0)/T(λ2,θ0) on the Ratio of Water Leaving Radiances at (λ1 = 450 nm; λ2 = 550 nm) and (
; λ2 = 550 nm)
θ0 (deg)
λ1,λ2 (in nm)
R
V23
V5
0
450; 550
0.945
0.931
0.935
60
450; 550
0.903
0.901
0.898
0
400; 550
0.889
0.886
0.878
60
400; 550
0.815
0.816
0.822
Table III
Diffuse Molecular Transmittance E′R(θ) and Spherical Molecular Albedo S′R for Unit Irradiance with an Angular Dependence 1/μ
θυ (deg)
λ = 400 nm
λ = 450 nm
2.84
0.1639
0.1182
17.64
0.1733
0.1257
32.48
0.1981
0.1458
Function E′R(θ)
λ = 400 nm
λ = 450 nm
0.3115
0.2340
Function S′R
Table IV
Computed Atmospheric Reflectances at λ = 450 nm for a Moderate Aerosol Content [(V23) Model]
θυ,φυ
Solar zenith angle = 15°
Solar zenith angle - 60°
(1)
(2)
(3)
(1)
(2)
(3)
2.84; 0
0.1054
−0.0010
−0.008
0.1271
0.0022
−0.0006
17.64; 0
0.0966
0.0015
−0.0011
0.1260
−0.0011
0.0002
17.64; 90
0.1057
−0.0001
−0.0010
0.1353
0.0028
−0.0001
17.64;180
0.1194
−0.0041
−0.0009
0.1588
0.0034
0.0000
32.48; 0
0.0946
0.0028
−0.0007
0.1504
−0.0101
0.0021
32.48; 90
0.1058
0.0022
−0.0006
0.1512
0.0028
0.0010
32.48;180
0.1236
−0.0013
−0.0005
0.2051
0.0007
0.0017
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
Table V
Same as Table IV but for a High Aerosol Content [(V5) Model]
θυ,φυ
Solar zenith angle = 15°
Solar zenith angle = 60°
(1)
(2)
(3)
(1)
(2)
(3)
2.84; 0
0.1599
−0.0058
−0.0034
0.2022
−0.0104
−0.0006
17.64; 0
0.1487
−0.0008
−0.0034
0.2144
−0.0224
0.0010
17.64; 90
0.1607
−0.0041
−0.0033
0.2140
−0.0105
0.0002
17.64;180
0.1817
−0.0123
−0.0033
0.2338
−0.0067
0.0002
32.48; 0
0.1522
−0.0001
−0.0027
0.2676
−0.0515
0.0047
32.48; 90
0.1633
−0.0008
−0.0028
0.2423
−0.0151
0.0025
32.48;180
0.1867
−0.0076
−0.0026
0.2929
−0.0139
0.0032
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
(1) Atmospheric reflectance ρa with an aerosol layer below a molecular layer, referred to below as the exact atmospheric reflectance.
(2) Difference between the exact value and the result given by Eq. (4).
(3) Difference between the exact value and the result given by Eq. (12).
Table VII
Relative Accuracy
of the Modeling of the Atmospheric Reflectance by Eqs. (4) and (12)