Abstract

Most in-water irradiance and radiance measurements at sea are carried out by suspending an instrument from a hydrocable located relatively close to the ship, the presence of which can severely perturb the in-water light field. This paper describes Monte Carlo techniques which have been developed specifically to assess such perturbations. Sample computations of the perturbation to the upward and downward irradiances due to the presence of the ship are presented for the case of a homogeneous ocean. The results reveal situations in which the downward irradiance, in the case of collimated illumination, is relatively unperturbed, while large effects are observed in the case of diffuse illumination. Conversely, the upwelled irradiance just beneath the surface is seen to be strongly influenced by the ship’s presence for both types of illumination.

© 1985 Optical Society of America

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References

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  1. D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres,” Appl. Opt. 11, 2684 (1972).
    [CrossRef] [PubMed]
  2. C. A. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres 1. Rayleigh Scattering,” Icarus 35, 139 (1978).
    [CrossRef]
  3. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
  4. K. M. Case, “Transfer Problems and the Reciprocity Principle,” Rev. Mod. Phys. 29, 651 (1957).
    [CrossRef]
  5. P. Moon, D. E. Spencer, “Illumination from a Non-Uniform Sky,” Illum. Eng. N.Y. 37, 707 (1942).
  6. S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950).
  7. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  8. M. H. Kalos, “On the Estimation of Flux at a Point by Monte Carlo,” Nucl. Sci. Eng. 16, 111 (1963).
  9. G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix Operator Theory of Radiative Transfer. 1: Raleigh Scattering,” Appl. Opt. 12, 314 (1973).
    [CrossRef] [PubMed]
  10. G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).
  11. J. Spanier, E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, Reading, Mass., 1969).
  12. J. E. Hansen, “Exact and Approximate Solution for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres,” J. Atmos. Sci. 26, 478 (1969).
    [CrossRef]
  13. J. F. Potter, “The Delta Function Approximation in Radiative Transfer Theory,” J. Atmos. Sci. 27, 943 (1970).
    [CrossRef]
  14. H. R. Gordon, “Simple Calculation of the Diffuse Reflectance of the Ocean,” Appl. Opt. 12, 2803 (1973).
    [CrossRef] [PubMed]
  15. M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
    [CrossRef]
  16. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed Relationships Between the Inherent and Apparent Optical Properties of a Flat Homogeneous Ocean,” Appl. Opt. 14, 417 (1975).
    [CrossRef] [PubMed]
  17. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Visible Satellite Imagery: A Review (Springer-Verlag, New York, 1983).
  18. H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary Layer Meteorol. 18, 299 (1980).
    [CrossRef]
  19. D. K. Clark, “Phytoplankton Pigment Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 227–237.
    [CrossRef]
  20. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton Pigment Concentrations in the Middle Atlantic Bight: Comparison of Ship Determinations and CZCS Estimates,” Appl. Opt. 22, 20 (1983).
    [CrossRef] [PubMed]
  21. R. C. Smith, C. R. Booth, J. L. Star, “Oceanographic Biooptical Profiling System,” Appl. Opt. 23, 2791 (1984).
    [CrossRef] [PubMed]

1984 (1)

1983 (1)

1980 (1)

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary Layer Meteorol. 18, 299 (1980).
[CrossRef]

1978 (2)

C. A. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres 1. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).

1977 (1)

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

1975 (1)

1973 (2)

1972 (1)

1970 (1)

J. F. Potter, “The Delta Function Approximation in Radiative Transfer Theory,” J. Atmos. Sci. 27, 943 (1970).
[CrossRef]

1969 (1)

J. E. Hansen, “Exact and Approximate Solution for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres,” J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

1963 (1)

M. H. Kalos, “On the Estimation of Flux at a Point by Monte Carlo,” Nucl. Sci. Eng. 16, 111 (1963).

1957 (1)

K. M. Case, “Transfer Problems and the Reciprocity Principle,” Rev. Mod. Phys. 29, 651 (1957).
[CrossRef]

1942 (1)

P. Moon, D. E. Spencer, “Illumination from a Non-Uniform Sky,” Illum. Eng. N.Y. 37, 707 (1942).

Adams, C. A.

C. A. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres 1. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

Blattner, W. G.

Booth, C. R.

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Case, K. M.

K. M. Case, “Transfer Problems and the Reciprocity Principle,” Rev. Mod. Phys. 29, 651 (1957).
[CrossRef]

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Catchings, F. E.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950).

Clark, D. K.

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton Pigment Concentrations in the Middle Atlantic Bight: Comparison of Ship Determinations and CZCS Estimates,” Appl. Opt. 22, 20 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary Layer Meteorol. 18, 299 (1980).
[CrossRef]

D. K. Clark, “Phytoplankton Pigment Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 227–237.
[CrossRef]

Collins, D. G.

Evans, R. H.

Gelbard, E. M.

J. Spanier, E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, Reading, Mass., 1969).

Gordon, H. R.

Hansen, J. E.

J. E. Hansen, “Exact and Approximate Solution for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres,” J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

Horak, H. G.

Humphreys, T. J.

G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).

Jacobs, M. M.

Kalos, M. H.

M. H. Kalos, “On the Estimation of Flux at a Point by Monte Carlo,” Nucl. Sci. Eng. 16, 111 (1963).

Kattawar, G. W.

C. A. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres 1. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).

G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix Operator Theory of Radiative Transfer. 1: Raleigh Scattering,” Appl. Opt. 12, 314 (1973).
[CrossRef] [PubMed]

Moon, P.

P. Moon, D. E. Spencer, “Illumination from a Non-Uniform Sky,” Illum. Eng. N.Y. 37, 707 (1942).

Morel, A. Y.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Visible Satellite Imagery: A Review (Springer-Verlag, New York, 1983).

Nakajima, T.

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

Plass, G. N.

G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).

G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix Operator Theory of Radiative Transfer. 1: Raleigh Scattering,” Appl. Opt. 12, 314 (1973).
[CrossRef] [PubMed]

Potter, J. F.

J. F. Potter, “The Delta Function Approximation in Radiative Transfer Theory,” J. Atmos. Sci. 27, 943 (1970).
[CrossRef]

Smith, R. C.

Spanier, J.

J. Spanier, E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, Reading, Mass., 1969).

Spencer, D. E.

P. Moon, D. E. Spencer, “Illumination from a Non-Uniform Sky,” Illum. Eng. N.Y. 37, 707 (1942).

Star, J. L.

Tanaka, M.

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

Wells, M. B.

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Appl. Opt. (6)

Boundary Layer Meteorol. (1)

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary Layer Meteorol. 18, 299 (1980).
[CrossRef]

Icarus (1)

C. A. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres 1. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

Illum. Eng. N.Y. (1)

P. Moon, D. E. Spencer, “Illumination from a Non-Uniform Sky,” Illum. Eng. N.Y. 37, 707 (1942).

J. Atmos. Sci. (2)

J. E. Hansen, “Exact and Approximate Solution for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres,” J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

J. F. Potter, “The Delta Function Approximation in Radiative Transfer Theory,” J. Atmos. Sci. 27, 943 (1970).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

Nucl. Sci. Eng. (1)

M. H. Kalos, “On the Estimation of Flux at a Point by Monte Carlo,” Nucl. Sci. Eng. 16, 111 (1963).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. W. Kattawar, T. J. Humphreys, G. N. Plass, “Radiative Transfer in an Atmosphere Ocean System: A Matrix Operator Approach,” Proc. Soc. Photo-Opt. Instrum. Eng. 160, 123 (1978).

Rev. Mod. Phys. (1)

K. M. Case, “Transfer Problems and the Reciprocity Principle,” Rev. Mod. Phys. 29, 651 (1957).
[CrossRef]

Other (6)

D. K. Clark, “Phytoplankton Pigment Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 227–237.
[CrossRef]

J. Spanier, E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, Reading, Mass., 1969).

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Visible Satellite Imagery: A Review (Springer-Verlag, New York, 1983).

S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950).

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

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Figures (10)

Fig. 1
Fig. 1

Schematic geometry defining the quantities used in the simulation.

Fig. 2
Fig. 2

Downwelling irradiance error as a function of depth for three solar azimuth angles (ϕ0) and a uniform incident radiance distribution (SKY). Values for the other parameters used in this simulation were c = 0.1 m−1, θ0 = 40°; ω0 = 0.9; and X = 4.5 m.

Fig. 3
Fig. 3

Downwelling irradiance error as a function of the solar zenith angle (θ0) for three solar azimuth angles (ϕ0) and a uniform incident radiance distribution (SKY). Values for the other parameters used in this simulation were c = 0.1 m−1; depth = 30 m; ω0 = 0.9; and X = 4.5 m.

Fig. 4
Fig. 4

Downwelling irradiance error as a function of depth for ϕ0 = 45°, and a uniform incident radiance distribution (SKY), and various values of ω0 (0.5, 0.7, and 0.9). Values for the other parameters used in this simulation were c = 0.1 m−1; θ0 = 40°; and X = 4.5 m.

Fig. 5
Fig. 5

Downwelling irradiance error as a function of depth for ϕ0 = 45°, and a uniform incident radiance distribution (SKY), and two values of the beam attenuation coefficient (0.1 and 0.3 m−1). Values for the other parameters used in this simulation were ω0 = 0.9; θ0 = 40°; and X = 4.5 m.

Fig. 6
Fig. 6

Downwelling irradiance error as a function of X for ϕ0 = 45°, and a uniform incident radiance distribution (SKY), and two values of the beam attenuation coefficient (0.1 and 0.3 m−1). Values for the other parameters used in this simulation were ω0 = 0.9; θ0 = 40°; and depth = 30 m.

Fig. 7
Fig. 7

Upwelling irradiance error at the surface as a function of the solar zenith angle (θ0) for three solar azimuth angles (ϕ0 = 0, 45°, and 90°) and three values of the beam attenuation coefficient (0.1, 0.3, and 0.5 m−1). For a given beam attenuation coefficient the curve with the smallest error is ϕ0 = 0 and the curve with the largest error is ϕ0 = 90°. Values for the other parameters used in this simulation were ω0 = 0.9 and X = 4.5 m.

Fig. 8
Fig. 8

Upwelling radiance error at the surface as a function of the solar zenith angle (θ0) for three solar azimuth angles (ϕ0 = 0, 45°, and 90°) and three values of the beam attenuation coefficient (0.1, 0.3, and 0.5 m−1). For a given beam attenuation coefficient the curve with the smallest error is ϕ0 = 0 and the curve with the largest error is ϕ0 = 90°. Values for the other parameters used in this simulation were ω0 = 0.9 and X = 4.5 m.

Fig. 9
Fig. 9

Upwelling irradiance error at the surface as a function of X for θ0 = 0 and three values of the beam attenuation coefficient (0.1, 0.3, and 0.5 m−1). The single scattering albedo (ω0) was 0.9.

Fig. 10
Fig. 10

Upwelling radiance error at the surface as a function of X for θ0 = 0 and three values of the beam attenuation coefficient (0.1, 0.3, and 0.5 m−1). The single scattering albedo (ω0) was 0.9.

Tables (5)

Tables Icon

Table I Q1(r,ξ) Required to Extract the Desired Quantity from Eq. (5); in Each Case L1(inc)(ρ,ξ) = 0

Tables Icon

Table II Comparison Between Exact and Backward Monte Carlo Computations of the Radiance and Irradiance Reflected from a Semi-Infinite Medium with ω0 = 0.8 and ξ0 · n = 0.5

Tables Icon

Table III Means and Standard Deviations for Lu in the Absence (L) and the Presence (L′) of the Ship as a Function of the Henyey-Greenstein Asymmetry Parameter g for ω0 = 0.8 and ξ0 · n = 1a

Tables Icon

Table IV Comparison of Three Different Techniques for Treating the Ship’s Hull and the Interface on Downwelling Irradiancea

Tables Icon

Table V Comparison of Three Different Techniques for Treating the Ship’s Hull and the Interface on the Upwelled Irradlance and Radiance Just Beneath the Surfacea

Equations (37)

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( ξ · ) L ( r , ξ ) + c ( r ) L ( r , ξ ) = Ω β ( r , ξ ξ ) L ( r , ξ ) d Ω ( ξ ) + Q ( r , ξ ) ,
c ( r ) = a ( r ) + b ( r ) ,
b ( r ) Ω β ( r , ξ ξ ) d Ω ( ξ ) .
β ( r , ξ ξ ) = β ( r , ξ ξ ) ,
ξ · n < 0 d Ω d S | n · ξ | [ L 2 ( ρ , ξ ) L 1 ( ρ , ξ ) L 1 ( ρ , ξ ) L 2 ( ρ , ξ ) ] = d Ω d V [ L 2 ( r , ξ ) Q 1 ( r , ξ ) L 1 ( r , ξ ) Q 2 ( r , ξ ) ] ,
Q 2 ( r , ξ ) = 0 and L 2 ( inc ) ( ρ , ξ ) = L 0 .
E d 2 ( r 0 ) = ξ · n < 0 ξ · n L 2 ( r 0 , ξ ) d Ω
Q 1 ( r , ξ ) = [ ξ · n δ ( r r 0 ) J 0 for ξ · n > 0 , 0 for ξ · n < 0 ,
ξ · n < 0 d Ω | ξ · n | L 0 L 1 ( ρ , ξ ) d S = J 0 E d 2 ( r 0 ) / m 2 .
L 0 E u 1 ( ρ ) d S ,
E u 1 ( ρ ) = ξ · n > 0 ( ξ · n ) L 1 ( ρ , ξ ) d Ω ,
P 1 = d V d Ω Q 1 ( r , ξ ) ,
E d 2 ( r 0 ) / E d 2 ( ρ ) = [ m 2 / P 1 ] E d 1 ( ρ ) d S .
L 2 ( ρ , ξ ) = ( 3 / 7 π ) E d 2 ( ρ ) [ 1 + 2 | ξ · n | ] .
E d 2 ( r , 0 ) / E d 2 ( ρ ) = ( 3 m 2 / 7 P 1 ) d S [ E u 1 ( ρ ) + 2 E u 1 ( ρ ) ] ,
E u 1 ( ρ ) = ξ · n < 0 d Ω | ξ · n | 2 L 1 ( ρ , ξ ) .
L 0 | ξ 0 · n | L 1 ( ρ , ξ 0 ) Δ Ω ( ξ 0 ) d S = J 0 E d 2 ( r 0 ) / m 2 ,
E d 2 ( ρ ) = | ξ 0 · n | L 0 Δ Ω ( ξ 0 ) ,
E d 2 ( r 0 ) E d 2 ( ρ ) = [ m 2 π / P 1 ] L 1 ( ρ , ξ 0 ) d S ,
m 2 | ξ 0 · n | Δ Ω ( ξ 0 ) = | ξ 0 · n | Δ Ω ( ξ 0 ) .
E u 1 ( ρ , ξ 0 ) L 1 ( ρ , ξ 0 ) | ξ 0 · n | Δ Ω ( ξ 0 )
E d 2 ( r 0 ) E d 2 ( ρ ) = π P 1 | ξ 0 · n | Δ Ω ( ξ 0 ) E u 1 ( ρ , ξ 0 ) d S .
t ( ξ 0 ) exp [ 0 1 c ( l ) d l ] ,
P i j = ω 0 ( r ) t ( ξ 0 ) P ( r , ξ ξ 0 ) Δ Ω ( ξ ) exp [ 0 l c ( l ) d l ] ,
i j W i P i j .
E d 2 ( r 0 ) E d 2 ( ρ ) = i j W i P i j P 1 | ξ 0 · n | Δ Ω ( ξ 0 ) + t ( ξ 0 ) exp [ 0 1 c ( l ) d l ] .
E u 2 ( r 0 ) = ξ · n > 0 ξ · n L 2 ( r 0 , ξ ) d Ω ,
E 0 ( r 0 ) = L ( r 0 , ξ ) d Ω ,
P ( θ ) = ( 1 g 2 ) / [ 4 π ( 1 + g 2 2 g cos θ ) 3 / 2 ] ,
var ( x x ) = var ( x ) + var ( x ) .
var ( x x ) = var ( x ) + ( x ) 2 cov ( x , x ) ,
2 cov ( x , x ) var ( x ) + var ( x ) .
β ( cos α ) = b F 2 π δ ( 1 cos α ) + β ( cos α ) ,
F = 1 b b .
b = 4 π β d Ω ,
[ P P = β / b , ω 0 ω 0 ( 1 F ) / ( 1 ω 0 F ) c c ( 1 ω 0 F ) . ,
irradiance error = [ ( E true E meas ) / E true ] × 100 % ,

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