Abstract

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.

© 2002 Optical Society of America

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2002 (1)

B. Sturm, G. Zibordi, “SeaWiFS atmospheric correction by an approximate model and vicarious calibration,” Int. J. Remote Sens. 23, 489–501 (2002).
[CrossRef]

2000 (1)

S. B. Hooker, C. R. McClain, “The calibration and validation of SeaWiFS data,” Prog. Oceanogr. 45, 427–465 (2000).
[CrossRef]

1999 (2)

G. Zibordi, J. P. Doyle, S. B. Hooker, “Offshore tower shading effects on in-water optical measurements,” J. Atmos. Oceanic Technol. 16, 1767–1779 (1999).
[CrossRef]

B. Bulgarelli, V. Kisselev, L. Roberti, “Radiative transfer in the atmosphere-ocean system: the finite-element method,” Appl. Opt. 38, 1530–1542 (1999).
[CrossRef]

1998 (1)

J. P. Doyle, H. Rief, “Photon transport in three-dimensional structures treated by random walk techniques: Monte Carlo benchmark of ocean colour simulations,” Math. Comput. Simul. 47, 215–241 (1998).
[CrossRef]

1997 (1)

1996 (1)

H. Rief, “Stochastic perturbation analysis applied to neutral particle transport,” Adv. Nucl. Sci. Technol. 23, 69–140 (1996).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

1991 (1)

1987 (1)

1985 (1)

1984 (1)

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

1980 (2)

1978 (1)

B. Leckner, “The spectral distribution of solar radiation at the Earth’s surface: elements of a model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

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, 93–111 (1977).
[CrossRef]

1975 (1)

1974 (1)

A. A. Lacis, J. E. Hansen, “Parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

1969 (3)

W. A. Margraaf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of the solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–477 (1969).
[CrossRef]

A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1969).

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1969).
[CrossRef]

1957 (1)

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

1956 (1)

C. Cox, W. Munk, “Slopes of the sea surface deduced from photographs of Sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–488 (1956).

1953 (1)

E. Vigroux, “Contribution a l’etude experimentale de l’absorption de l’ozone,” Ann. Phys. 8, 709–762 (1953).

1941 (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1910 (1)

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” (“Theoretical aspects of the opalescence of homogeneous fluids and liquid mixtures near the critical state”), Ann. Phys. (Leipzig) 33, 1275–1298 (1910).

1871 (1)

Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120, (1871), reprinted in Scientific Papers by Lord Rayleigh, Vol I: 1869–1881 (Dover, New York, 1964).

Alberotanza, L.

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Ångström, A.

A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1969).

Austin, R. W.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Project Technical Report Series, NASA Tech. Memo. 104566, Vol. 25, S. B. Hooker, E. R. Firestone, J. G. Acker, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1995).

Berthon, J. F.

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Brown, O. B.

Buiteveldt, H.

H. Buiteveldt, J. H. M. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Bulgarelli, B.

Case, K. M.

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

Cashwell, E. D.

E. D. Cashwell, C. J. Everett, Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, New York, 1959).

Castaño, D. J.

Cox, C.

C. Cox, W. Munk, “Slopes of the sea surface deduced from photographs of Sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–488 (1956).

Ding, K.

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Donze, M.

H. Buiteveldt, J. H. M. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Doyle, J. P.

G. Zibordi, J. P. Doyle, S. B. Hooker, “Offshore tower shading effects on in-water optical measurements,” J. Atmos. Oceanic Technol. 16, 1767–1779 (1999).
[CrossRef]

J. P. Doyle, H. Rief, “Photon transport in three-dimensional structures treated by random walk techniques: Monte Carlo benchmark of ocean colour simulations,” Math. Comput. Simul. 47, 215–241 (1998).
[CrossRef]

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. P. Doyle is preparing a Ph.D. dissertation called “Monte Carlo modelling of radiative transfer in a 3-D ocean-atmosphere system: ocean colour simulations,” (Imperial College of Science, Technology, and Medicine, University of London, London, UK, 2002).

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Edwards, G. D.

K. J. Voss, J. W. Nolten, G. D. Edwards, “Ship shadow effects on apparent optical properties,” in Ocean Optics VIII, M. A. Blizard, ed., Proc. SPIE637, 186–190 (1986).
[CrossRef]

Einstein, A.

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” (“Theoretical aspects of the opalescence of homogeneous fluids and liquid mixtures near the critical state”), Ann. Phys. (Leipzig) 33, 1275–1298 (1910).

Elterman, L.

L. Elterman, “UV, visible and IR attenuation for altitudes to 50 km,” Environmental Research Papers 285, AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratories, L. G. Hanscom Field, Bedford, Mass., 1968).

Everett, C. J.

E. D. Cashwell, C. J. Everett, Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, New York, 1959).

Ferrari, M.

Firestone, E. R.

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Frölich, C.

Fry, E. S.

Gelbard, E. M.

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

Gentili, B.

Gordon, H. R.

Greenstein, J. L.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Griggs, M.

W. A. Margraaf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of the solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–477 (1969).
[CrossRef]

Grossi, S.

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Hakvoort, J. H. M.

H. Buiteveldt, J. H. M. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Hansen, J. E.

A. A. Lacis, J. E. Hansen, “Parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

Helliwell, W. S.

W. S. Helliwell, G. N. Sullivan, B. MacDonald, K. J. Voss, “Ship shadowing: model and data comparisons,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 55–71 (1990).
[CrossRef]

Henyey, L. C.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hooker, S. B.

S. B. Hooker, C. R. McClain, “The calibration and validation of SeaWiFS data,” Prog. Oceanogr. 45, 427–465 (2000).
[CrossRef]

G. Zibordi, J. P. Doyle, S. B. Hooker, “Offshore tower shading effects on in-water optical measurements,” J. Atmos. Oceanic Technol. 16, 1767–1779 (1999).
[CrossRef]

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Jacobs, M. M.

Jin, Z.

Jodai, Y.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

Kadokura, K.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

Kattawar, G. W.

Kearns, E.

E. Kearns, R. Riley, C. Woody, “Bio-optical time series collected in coastal waters for SeaWiFS calibration and validation: large structure shadowing considerations,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 697–702 (1996).

Kishino, M.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

Kisselev, V.

Koblinger, L.

I. Lux, L. Koblinger, Monte Carlo Transport Methods; Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

Labs, D.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Lacis, A. A.

A. A. Lacis, J. E. Hansen, “Parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

Leckner, B.

B. Leckner, “The spectral distribution of solar radiation at the Earth’s surface: elements of a model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

Lux, I.

I. Lux, L. Koblinger, Monte Carlo Transport Methods; Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

MacDonald, B.

W. S. Helliwell, G. N. Sullivan, B. MacDonald, K. J. Voss, “Ship shadowing: model and data comparisons,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 55–71 (1990).
[CrossRef]

Margraaf, W. A.

W. A. Margraaf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of the solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–477 (1969).
[CrossRef]

McClain, C. R.

S. B. Hooker, C. R. McClain, “The calibration and validation of SeaWiFS data,” Prog. Oceanogr. 45, 427–465 (2000).
[CrossRef]

Menzies, D. W.

C. T. Weir, D. A. Siegel, A. F. Michaels, D. W. Menzies, “In situ evaluation of a ship’s shadow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 815–821 (1994).

Michaels, A. F.

C. T. Weir, D. A. Siegel, A. F. Michaels, D. W. Menzies, “In situ evaluation of a ship’s shadow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 815–821 (1994).

Mobley, C. D.

Morel, A.

Mueller, J. L.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Project Technical Report Series, NASA Tech. Memo. 104566, Vol. 25, S. B. Hooker, E. R. Firestone, J. G. Acker, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1995).

Munk, W.

C. Cox, W. Munk, “Slopes of the sea surface deduced from photographs of Sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–488 (1956).

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, 93–111 (1977).
[CrossRef]

Neckel, H.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Nolten, J. W.

K. J. Voss, J. W. Nolten, G. D. Edwards, “Ship shadow effects on apparent optical properties,” in Ocean Optics VIII, M. A. Blizard, ed., Proc. SPIE637, 186–190 (1986).
[CrossRef]

Oishi, T.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected natural waters,” SIO Ref. 72-78 (Visibility Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, Calif., 1972).

Pope, R. M.

Potter, J. F.

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1969).
[CrossRef]

Rayleigh,

Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120, (1871), reprinted in Scientific Papers by Lord Rayleigh, Vol I: 1869–1881 (Dover, New York, 1964).

Reinersman, P.

Rief, H.

J. P. Doyle, H. Rief, “Photon transport in three-dimensional structures treated by random walk techniques: Monte Carlo benchmark of ocean colour simulations,” Math. Comput. Simul. 47, 215–241 (1998).
[CrossRef]

H. Rief, “Stochastic perturbation analysis applied to neutral particle transport,” Adv. Nucl. Sci. Technol. 23, 69–140 (1996).
[CrossRef]

Riley, R.

E. Kearns, R. Riley, C. Woody, “Bio-optical time series collected in coastal waters for SeaWiFS calibration and validation: large structure shadowing considerations,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 697–702 (1996).

Roberti, L.

Saruya, Y.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

Shaw, G. E.

Siegel, D. A.

C. T. Weir, D. A. Siegel, A. F. Michaels, D. W. Menzies, “In situ evaluation of a ship’s shadow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 815–821 (1994).

Spanier, J.

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

Stamnes, K.

Stavn, R. H.

Sturm, B.

B. Sturm, G. Zibordi, “SeaWiFS atmospheric correction by an approximate model and vicarious calibration,” Int. J. Remote Sens. 23, 489–501 (2002).
[CrossRef]

Sullivan, G. N.

W. S. Helliwell, G. N. Sullivan, B. MacDonald, K. J. Voss, “Ship shadowing: model and data comparisons,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 55–71 (1990).
[CrossRef]

Tanaka, A.

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

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, 93–111 (1977).
[CrossRef]

Targa, C.

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

van der Linde, D.

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Vigroux, E.

E. Vigroux, “Contribution a l’etude experimentale de l’absorption de l’ozone,” Ann. Phys. 8, 709–762 (1953).

Voss, K. J.

W. S. Helliwell, G. N. Sullivan, B. MacDonald, K. J. Voss, “Ship shadowing: model and data comparisons,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 55–71 (1990).
[CrossRef]

K. J. Voss, J. W. Nolten, G. D. Edwards, “Ship shadow effects on apparent optical properties,” in Ocean Optics VIII, M. A. Blizard, ed., Proc. SPIE637, 186–190 (1986).
[CrossRef]

Weir, C. T.

C. T. Weir, D. A. Siegel, A. F. Michaels, D. W. Menzies, “In situ evaluation of a ship’s shadow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 815–821 (1994).

Woody, C.

E. Kearns, R. Riley, C. Woody, “Bio-optical time series collected in coastal waters for SeaWiFS calibration and validation: large structure shadowing considerations,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 697–702 (1996).

Young, A. T.

Zibordi, G.

B. Sturm, G. Zibordi, “SeaWiFS atmospheric correction by an approximate model and vicarious calibration,” Int. J. Remote Sens. 23, 489–501 (2002).
[CrossRef]

G. Zibordi, J. P. Doyle, S. B. Hooker, “Offshore tower shading effects on in-water optical measurements,” J. Atmos. Oceanic Technol. 16, 1767–1779 (1999).
[CrossRef]

G. Zibordi, M. Ferrari, “Instrument self-shading in underwater optical measurements: experimental data,” Appl. Opt. 34, 2750–2754 (1995).
[CrossRef] [PubMed]

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

Adv. Nucl. Sci. Technol. (1)

H. Rief, “Stochastic perturbation analysis applied to neutral particle transport,” Adv. Nucl. Sci. Technol. 23, 69–140 (1996).
[CrossRef]

Ann. Phys. (1)

E. Vigroux, “Contribution a l’etude experimentale de l’absorption de l’ozone,” Ann. Phys. 8, 709–762 (1953).

Ann. Phys. (Leipzig) (1)

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” (“Theoretical aspects of the opalescence of homogeneous fluids and liquid mixtures near the critical state”), Ann. Phys. (Leipzig) 33, 1275–1298 (1910).

Appl. Opt. (10)

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, 417–427 (1975).
[CrossRef] [PubMed]

H. R. Gordon, “Ship perturbation of irradiance measurements at sea. 1. Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
[CrossRef]

G. Zibordi, M. Ferrari, “Instrument self-shading in underwater optical measurements: experimental data,” Appl. Opt. 34, 2750–2754 (1995).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

B. Bulgarelli, V. Kisselev, L. Roberti, “Radiative transfer in the atmosphere-ocean system: the finite-element method,” Appl. Opt. 38, 1530–1542 (1999).
[CrossRef]

C. Frölich, G. E. Shaw, “New determination of Rayleigh scattering in the terrestrial atmosphere,” Appl. Opt. 19, 1773–1775 (1980).
[CrossRef]

H. R. Gordon, D. J. Castaño, “The Coastal Zone Color Scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
[CrossRef]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Int. J. Remote Sens. (1)

B. Sturm, G. Zibordi, “SeaWiFS atmospheric correction by an approximate model and vicarious calibration,” Int. J. Remote Sens. 23, 489–501 (2002).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

G. Zibordi, J. P. Doyle, S. B. Hooker, “Offshore tower shading effects on in-water optical measurements,” J. Atmos. Oceanic Technol. 16, 1767–1779 (1999).
[CrossRef]

J. Atmos. Sci. (3)

W. A. Margraaf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of the solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–477 (1969).
[CrossRef]

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1969).
[CrossRef]

A. A. Lacis, J. E. Hansen, “Parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[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, 93–111 (1977).
[CrossRef]

Limnol. Oceanogr. (1)

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Math. Comput. Simul. (1)

J. P. Doyle, H. Rief, “Photon transport in three-dimensional structures treated by random walk techniques: Monte Carlo benchmark of ocean colour simulations,” Math. Comput. Simul. 47, 215–241 (1998).
[CrossRef]

Philos. Mag. (1)

Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120, (1871), reprinted in Scientific Papers by Lord Rayleigh, Vol I: 1869–1881 (Dover, New York, 1964).

Prog. Oceanogr. (1)

S. B. Hooker, C. R. McClain, “The calibration and validation of SeaWiFS data,” Prog. Oceanogr. 45, 427–465 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

Scripps Inst. Oceanogr. Bull. (1)

C. Cox, W. Munk, “Slopes of the sea surface deduced from photographs of Sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–488 (1956).

Sol. Energy (1)

B. Leckner, “The spectral distribution of solar radiation at the Earth’s surface: elements of a model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

Sol. Phys. (1)

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Tellus (1)

A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1969).

Other (17)

L. Elterman, “UV, visible and IR attenuation for altitudes to 50 km,” Environmental Research Papers 285, AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratories, L. G. Hanscom Field, Bedford, Mass., 1968).

H. Buiteveldt, J. H. M. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.

T. J. Petzold, “Volume scattering functions for selected natural waters,” SIO Ref. 72-78 (Visibility Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, Calif., 1972).

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, L. Alberotanza, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 1: A long-term measurement program,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689219, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. P. Doyle is preparing a Ph.D. dissertation called “Monte Carlo modelling of radiative transfer in a 3-D ocean-atmosphere system: ocean colour simulations,” (Imperial College of Science, Technology, and Medicine, University of London, London, UK, 2002).

E. D. Cashwell, C. J. Everett, Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, New York, 1959).

I. Lux, L. Koblinger, Monte Carlo Transport Methods; Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, “Coastal Atmosphere and Sea Time Series (CoASTS). Part 2: Data analysis,” in SeaWiFS Project Technical Report Series, NASA Tech. Memo. TM-2002-20689220, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

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

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Project Technical Report Series, NASA Tech. Memo. 104566, Vol. 25, S. B. Hooker, E. R. Firestone, J. G. Acker, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1995).

K. J. Voss, J. W. Nolten, G. D. Edwards, “Ship shadow effects on apparent optical properties,” in Ocean Optics VIII, M. A. Blizard, ed., Proc. SPIE637, 186–190 (1986).
[CrossRef]

W. S. Helliwell, G. N. Sullivan, B. MacDonald, K. J. Voss, “Ship shadowing: model and data comparisons,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 55–71 (1990).
[CrossRef]

C. T. Weir, D. A. Siegel, A. F. Michaels, D. W. Menzies, “In situ evaluation of a ship’s shadow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 815–821 (1994).

E. Kearns, R. Riley, C. Woody, “Bio-optical time series collected in coastal waters for SeaWiFS calibration and validation: large structure shadowing considerations,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 697–702 (1996).

Y. Saruya, T. Oishi, M. Kishino, Y. Jodai, K. Kadokura, A. Tanaka, “Influence of ship shadow on underwater irradiance fields,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 760–765 (1996).

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Figures (17)

Fig. 1
Fig. 1

Ship-shadowed E d relative errors (log of percentage), estimated with the pho-tran MC code as a function of θ0, for three ϕ0 angles (ϕ0 = 0°, circles; 45°, squares; 90°, triangles) and uniform incident radiance distribution (sky). Other parameters are d = 30 m, X = 4.5 m, ω0 = 0.9, and c = 0.1 m-1. To be compared with Fig. 3 in Gordon’s work.1 Vertical error bars centered on the points indicate the ±1σ estimated statistical uncertainty of the pho-tran MC computations (error bars might not be visible if contained within the plotted symbol).

Fig. 2
Fig. 2

Instrument self-shadowed L u relative errors (percentage), estimated with the pho-tran MC code as a function of cR for different ω0 values (ω0 = 0.5, circles; 0.7, squares; 0.9, triangles; 0.95, diamonds). Solar zenith is θ0 = 30°. This figure is to be compared with Fig. 2 in the Gordon and Ding paper.9 Vertical error bars centered on the points indicate the ±3σ estimated statistical uncertainty of the pho-tran MC computations (error bars might not be visible if contained within the plotted symbol).

Fig. 3
Fig. 3

Ship-shadowed E d relative errors (log of percentage), estimated with the pho-tran MC code as a function of in-water sensor depth d, for three solar azimuth angles ϕ00 = 0°, circles; 45°, squares; 90°, triangles) and a uniform incident radiance distribution (sky, diamonds). Values for the other parameters used in these simulations are X = 4.5 m, θ0 = 40°, ω0 = 0.9, and c = 0.1 m-1. The filled symbols and continuous curves identify the results that were obtained when photon interactions with the sea surface and with the ship’s hull were completely ignored, whereas additional simulations that allow for photons to interact with the sea surface and with the submerged ship’s hull are overplotted with open symbols and dashed curves, at 1-m-deep increments within the 10-m top ocean layer. Horizontal error bars that indicate the ±1σ estimated statistical uncertainty of the pho-tran MC computations are not visible because they are completely enclosed within the plotted symbol.

Fig. 4
Fig. 4

AAOT schematic 3-D geometry as modeled within the pho-tran MC code; distances are shown in meters and surfaces are assumed black. The south-north direction intersects two opposite angular AAOT pillars as shown by the N arrow that points to the north. Optical radiometers are deployed at 7.5 m from the tower legs (along the vertical line through the indicated Radiometer). The orthogonal x-y-z axes origin is placed on the sea surface and between the southern and southeastern tower legs. Radiometers are placed at X 0 = (x 0, y 0, z 0).

Fig. 5
Fig. 5

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of θ0 with ϕ0 = 0°, i.e., the Sun projection on a horizontal plane moves along the AAOT deployment platform axis (ϕ0 is measured on the pho-tran AAOT coordinate reference system).

Fig. 6
Fig. 6

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of ϕ0 with θ0 = 75°, i.e., a low Sun moves along an imaginary circular trajectory (open circles), and with θ0 = 30°, i.e., a high Sun moves along an imaginary circular trajectory (filled circles). Computations for θ0 = 30° stop at ϕ0 = -90° because the Sun never exceeds such a solar azimuth angle for the given θ0 = 30° at the AAOT latitude.

Fig. 7
Fig. 7

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of variable ϕ0 (and covarying θ0) along two real solar path orbits, and resolved at 0.5-h increments. The ∊ for a boreal summer (high Sun) orbit are shown as open circles; the filled circles represent a boreal winter (low Sun) orbit.

Fig. 8
Fig. 8

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of λ.

Fig. 9
Fig. 9

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u (c) ∊ L u on in-depth E d , E u , and L u for the standard case as a function of sensor depth z0 in a homogeneous water column.

Fig. 10
Fig. 10

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of sensor distance along the x axis (x 0 is a component of sensor position X 0).

Fig. 11
Fig. 11

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of sensor distance along the y axis (y 0 is a component of sensor position X 0).

Fig. 12
Fig. 12

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of τaer. The filled circles to the left of the plots represent an atmosphere that contains virtually no aerosol, i.e., τaer = 0. The filled circles to the right of the plots represent a totally diffuse above-water illumination (i.e., for an isotropic water-incident photon flux, a condition approached asymptotically when τaer → ∞).

Fig. 13
Fig. 13

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of a hyd. The a hyd = 0-m-1 value corresponds to a hyd = 10-4 m-1.

Fig. 14
Fig. 14

AAOT tower-shading percentage relative errors (a) ∊ E d , (b) ∊ E u , (c) ∊ L u on subsurface E d , E u , and L u for the standard case as a function of b hyd.

Fig. 15
Fig. 15

AAOT ηℜ̃(λ) correction factors as a function of sampling time (between October 1995 and February 2001) for the shadowed subsurface downwelling irradiance d at λ = (a) 443, (b) 555, (c) 665 nm. The dots represent average campaign values, crosses indicate single measurement values (a single campaign can include as much as one week of data).

Fig. 16
Fig. 16

As in Fig. 15 but for η u (λ).

Fig. 17
Fig. 17

As in Fig. 15 but for η u (λ).

Tables (9)

Tables Icon

Table 1 Comparison of the Gordon and the pho-tran MC Estimatesa

Tables Icon

Table 2 Comparison of the Gordon and the pho-tran Backward MC Simulationsa

Tables Icon

Table 3 Comparison of the Gordon and the pho-tran Backward MC Simulationsa

Tables Icon

Table 4 Standard Sun-Atmosphere-Ocean-AAOT-Detector Reference Systema

Tables Icon

Table 5 AAOT Tower-Shading Percentage Relative Errorsa

Tables Icon

Table 6 AAOT Tower-Shading Percentage Relative Errorsa

Tables Icon

Table 7 Parameters and Their Discretized Valuesa

Tables Icon

Table 8 Spectrally Linked Parameters (All Dimensionless)a

Tables Icon

Table 9 Average and Standard Deviation of Subsurface Tower-Shadowing Percentage Relative Errorsa

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

==Δ/×100,
σ=σ=var1/2Δ/×100.
η˜=/˜
pescτf=exp-τf1-exp-τesc-1,
varΔf=varf+varf-2 covf, f,
varΔf=varf+varf.
limΔ0 varΔf/Δ=varf+varfΔ2.
limΔ0varΔf/Δ=varf+varf-2 covf, fΔ2κ<,
2 covf, fvarf+varf,
31+cos2 ψ16π
31+q cos2 ψ4π3+q

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