J. P. Doyle (j.doyle@ic.ac.uk) is with the Department of Computational Physics and Geophysics, T. H. Huxley School, Imperial College of Science, Technology, and Medicine, University of London, London SW7 2BP, UK.
G. Zibordi (giuseppe.zibordi@jrc.it) is with the Marine Environment Unit, Space Applications Institute, Joint Research Centre of the European Commission, I-21020 Ispra (Va), Italy.
John P. Doyle and Giuseppe Zibordi, "Optical propagation within a three-dimensional shadowed atmosphere–ocean field: application to large deployment structures," Appl. Opt. 41, 4283-4306 (2002)
Estimation of optical shadowing effects that occur on in situ submerged radiance and irradiance measurements conducted in the proximity of a large and complex three-dimensional deployment structure is addressed by use of Monte Carlo simulations. We have applied backward Monte Carlo techniques and variance reduction schemes in three-dimensional radiative transfer computations of in-water light field perturbations by taking into account relevant geometric, environmental, and optical parameters that describe a realistic atmosphere-ocean system. Significant parameters, determined by a sensitivity analysis study, have then been systematically varied for the computation of an extensive set of correction factors, included in look-up tables designed for operational removal of tower-shading uncertainties, which typically induce an ∼1–10% decrease in absolute radiometric data values near a specific oceanographic tower located in the northern Adriatic Sea. In principle, the proposed correction methodology can be transferred to other deployment systems, instrument casings, and measurement sites if a comprehensive description is provided for the system parameters and their variability.
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Comparison of the Gordon and the pho-tran MC Estimatesa
Radiometric Quantity (at 0-)
g = 0
g = 0.750
g = 0.875
g = 0.950
KA
KA′
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Lu
0.08122
0.08119
0.02019
0.02021
0.00825
0.00855
0.00256
0.00251
0.01113
0.01069
0.01045
0.01022
Lu:σ
0.00132
0.00014
0.00100
0.00015
0.00115
0.00018
0.00197
0.00022
0.00348
0.00060
0.00061
0.00014
Lu:SRE
0.01630
0.00180
0.04950
0.00710
0.13940
0.02160
0.76950
0.08840
0.31260
0.05570
0.05830
0.01360
(Lu - L̃u)
0.01016
0.01013
0.00249
0.00257
0.00096
0.00103
0.00029
0.00030
0.00157
0.00102
0.00102
0.00098
(Lu - L̃u):σ
0.00049
0.00006
0.00044
0.00006
0.00059
0.00007
0.00068
0.00008
0.00187
0.00010
0.00026
0.00006
(Lu - L̃u):SRE
0.04820
0.00600
0.17670
0.00240
0.61450
0.07120
2.34480
0.26670
1.19100
0.09800
0.25490
0.02330
(Lu - L̃u)/Lu in %
12.50
12.48
12.30
12.72
11.60
12.10
11.30
12.03
14.10
9.53
9.70
9.59
(Eu - Ẽu)/Eu in %
21.30
21.27
14.50
13.74
12.20
12.55
14.20
14.94
14.70
14.90
14.20
14.14
The estimates are of absolute values (means, standard deviations σ, and SRE) of unperturbed and ship-shadow perturbed radiometric quantities. Results are given as a function of the in-water Henyey-Greenstein phase function (variable asymmetry parameters g) and for two separate phase functions (KA and KA′).
Table 2
Comparison of the Gordon and the pho-tran Backward MC Simulationsa
MC Simulation
ϕ0 =
∊Ed (5 m)
∊Ed (40 m)
0°
45°
90°
0°
45°
90°
I Gordon
1.27
1.43
2.36
3.98
5.80
15.88
I pho-tran
1.33
1.52
2.47
3.83
5.76
15.69
III Gordon
0.43
0.60
1.57
4.01
5.71
15.71
III pho-tran
0.40
0.58
1.55
4.05
5.62
16.04
Included are percentage relative error values for ship-shadowed Ed at 5- and 40-m depth and variable solar azimuth. Two simulation techniques were adopted: I, ship’s hull in the water; III ship’s hull above the water and no surface interactions allowed.
Table 3
Comparison of the Gordon and the pho-tran Backward MC Simulationsa
MC Simulation
ϕ0 =
∊Eu (0- m)
∊Lu (0- m)
0°
45°
90°
0°
45°
90°
I Gordon
7.74
8.13
8.95
3.33
4.30
8.96
I pho-tran
8.40
8.78
9.92
3.61
4.57
9.97
III Gordon
7.81
8.22
9.01
3.17
3.98
8.83
III pho-tran
7.90
8.17
9.16
3.22
3.95
8.90
Included are percentage relative error values for ship-shadowed Eu and Lu at 0--m depth and at variable solar azimuths. The same simulation techniques as in Table
2 were adopted.
Table 4
Standard Sun-Atmosphere-Ocean-AAOT-Detector Reference Systema
The values were allowed to vary within the simplified atmosphere-ocean system and were used to compute indexed AAOT subsurface tower-shading correction factors ηℜ̃(λ)[i,j,k,l,m]
included in the look-up tables.
The →∞ represents the overcast situation and is taken as the limiting parameter value for high (≫1.00) τaer values.
Their spectrally fixed values were allowed to covary with λ within the simplified atmosphere-ocean system and were used to compute AAOT tower-shading correction factors included in the look-up tables.
Table 9
Average and Standard Deviation of Subsurface Tower-Shadowing Percentage Relative Errorsa
Parameter
Unit
412 nm
443 nm
490 nm
510 nm
555 nm
665 nm
∊Ẽd
—
4.37 [1.42]
3.49 [1.19]
2.43 [0.86]
2.06 [0.73]
1.40 [0.50]
0.98 [0.22]
∊Ẽu
—
4.58 [1.05]
4.32 [1.03]
4.14 [1.03]
3.76 [1.07]
3.20 [1.13]
0.71 [0.34]
∊L̃u
—
4.28 [1.31]
3.67 [1.04]
3.19 [1.04]
2.87 [0.87]
2.35 [0.77]
0.55 [0.30]
ahyd
m-1
0.217 [0.084]
0.100 [0.066]
0.098 [0.036]
0.067 [0.026]
0.037 [0.014]
0.032 [0.028]
w0
—
0.795 [0.069]
0.823 [0.066]
0.858 [0.055]
0.856 [0.060]
0.847 [0.068]
0.508 [0.162]
Ir
—
0.844 [0.369]
0.671 [0.307]
0.499 [0.254]
0.438 [0.247]
0.336 [0.186]
0.223 [0.148]
∊ℜ values for Ẽd, Ẽu, and L̃u AAOT data, and the average and standard deviation of the relevant parameters used to retrieve the subsurface ηℜ̃ values from the look-up tables. Measurements were taken with solar zenith θ0 varying between 22° and 77° (48° average), and compass solar azimuth ϕ0′ varying between 87° and 245° (163° average). The numbers within brackets represent the standard deviation.
Tables (9)
Table 1
Comparison of the Gordon and the pho-tran MC Estimatesa
Radiometric Quantity (at 0-)
g = 0
g = 0.750
g = 0.875
g = 0.950
KA
KA′
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Gordon
pho-tran
Lu
0.08122
0.08119
0.02019
0.02021
0.00825
0.00855
0.00256
0.00251
0.01113
0.01069
0.01045
0.01022
Lu:σ
0.00132
0.00014
0.00100
0.00015
0.00115
0.00018
0.00197
0.00022
0.00348
0.00060
0.00061
0.00014
Lu:SRE
0.01630
0.00180
0.04950
0.00710
0.13940
0.02160
0.76950
0.08840
0.31260
0.05570
0.05830
0.01360
(Lu - L̃u)
0.01016
0.01013
0.00249
0.00257
0.00096
0.00103
0.00029
0.00030
0.00157
0.00102
0.00102
0.00098
(Lu - L̃u):σ
0.00049
0.00006
0.00044
0.00006
0.00059
0.00007
0.00068
0.00008
0.00187
0.00010
0.00026
0.00006
(Lu - L̃u):SRE
0.04820
0.00600
0.17670
0.00240
0.61450
0.07120
2.34480
0.26670
1.19100
0.09800
0.25490
0.02330
(Lu - L̃u)/Lu in %
12.50
12.48
12.30
12.72
11.60
12.10
11.30
12.03
14.10
9.53
9.70
9.59
(Eu - Ẽu)/Eu in %
21.30
21.27
14.50
13.74
12.20
12.55
14.20
14.94
14.70
14.90
14.20
14.14
The estimates are of absolute values (means, standard deviations σ, and SRE) of unperturbed and ship-shadow perturbed radiometric quantities. Results are given as a function of the in-water Henyey-Greenstein phase function (variable asymmetry parameters g) and for two separate phase functions (KA and KA′).
Table 2
Comparison of the Gordon and the pho-tran Backward MC Simulationsa
MC Simulation
ϕ0 =
∊Ed (5 m)
∊Ed (40 m)
0°
45°
90°
0°
45°
90°
I Gordon
1.27
1.43
2.36
3.98
5.80
15.88
I pho-tran
1.33
1.52
2.47
3.83
5.76
15.69
III Gordon
0.43
0.60
1.57
4.01
5.71
15.71
III pho-tran
0.40
0.58
1.55
4.05
5.62
16.04
Included are percentage relative error values for ship-shadowed Ed at 5- and 40-m depth and variable solar azimuth. Two simulation techniques were adopted: I, ship’s hull in the water; III ship’s hull above the water and no surface interactions allowed.
Table 3
Comparison of the Gordon and the pho-tran Backward MC Simulationsa
MC Simulation
ϕ0 =
∊Eu (0- m)
∊Lu (0- m)
0°
45°
90°
0°
45°
90°
I Gordon
7.74
8.13
8.95
3.33
4.30
8.96
I pho-tran
8.40
8.78
9.92
3.61
4.57
9.97
III Gordon
7.81
8.22
9.01
3.17
3.98
8.83
III pho-tran
7.90
8.17
9.16
3.22
3.95
8.90
Included are percentage relative error values for ship-shadowed Eu and Lu at 0--m depth and at variable solar azimuths. The same simulation techniques as in Table
2 were adopted.
Table 4
Standard Sun-Atmosphere-Ocean-AAOT-Detector Reference Systema
The values were allowed to vary within the simplified atmosphere-ocean system and were used to compute indexed AAOT subsurface tower-shading correction factors ηℜ̃(λ)[i,j,k,l,m]
included in the look-up tables.
The →∞ represents the overcast situation and is taken as the limiting parameter value for high (≫1.00) τaer values.
Their spectrally fixed values were allowed to covary with λ within the simplified atmosphere-ocean system and were used to compute AAOT tower-shading correction factors included in the look-up tables.
Table 9
Average and Standard Deviation of Subsurface Tower-Shadowing Percentage Relative Errorsa
Parameter
Unit
412 nm
443 nm
490 nm
510 nm
555 nm
665 nm
∊Ẽd
—
4.37 [1.42]
3.49 [1.19]
2.43 [0.86]
2.06 [0.73]
1.40 [0.50]
0.98 [0.22]
∊Ẽu
—
4.58 [1.05]
4.32 [1.03]
4.14 [1.03]
3.76 [1.07]
3.20 [1.13]
0.71 [0.34]
∊L̃u
—
4.28 [1.31]
3.67 [1.04]
3.19 [1.04]
2.87 [0.87]
2.35 [0.77]
0.55 [0.30]
ahyd
m-1
0.217 [0.084]
0.100 [0.066]
0.098 [0.036]
0.067 [0.026]
0.037 [0.014]
0.032 [0.028]
w0
—
0.795 [0.069]
0.823 [0.066]
0.858 [0.055]
0.856 [0.060]
0.847 [0.068]
0.508 [0.162]
Ir
—
0.844 [0.369]
0.671 [0.307]
0.499 [0.254]
0.438 [0.247]
0.336 [0.186]
0.223 [0.148]
∊ℜ values for Ẽd, Ẽu, and L̃u AAOT data, and the average and standard deviation of the relevant parameters used to retrieve the subsurface ηℜ̃ values from the look-up tables. Measurements were taken with solar zenith θ0 varying between 22° and 77° (48° average), and compass solar azimuth ϕ0′ varying between 87° and 245° (163° average). The numbers within brackets represent the standard deviation.
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