Abstract

A radiative transfer code termed OSOA for the ocean–atmosphere system that is able to predict the total and the polarized signals has been developed. The successive-orders-of-scattering method is used. The air–water interface is modeled as a planar mirror. Four components grouped by their optical properties, pure seawater, phytoplankton, nonchlorophyllose matter, and yellow substances, are included in the water column. Models are validated through comparisons with standard models. The numerical accuracy of the method is better than 2%; high computational efficiency is maintained. The model is used to study the influence of polarization on the detection of suspended matter. Polarizing properties of hydrosols are discussed: phytoplankton cells exhibit weak polarization and small inorganic particles, which are strong backscatterers, contribute appreciably to the polarized signal. Therefore the use of the polarized signal to extract the sediment signature promises good results. Also, polarized radiance could improve characterization of aerosols when open ocean waters are treated.

© 2001 Optical Society of America

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    [CrossRef]
  2. G. N. Plass, G. W. Kattawar, “Color of the ocean,” Appl. Opt. 17, 1432–1446 (1978).
    [CrossRef] [PubMed]
  3. H. R. Gordon, O. B. Brown, “Irradiance reflectivity of a flat ocean as a function of the optical properties,” Appl. Opt. 12, 1549–1551 (1973).
    [CrossRef] [PubMed]
  4. M. Viollier, “Contribution à l’étude du rayonnement rétrodiffusé par l’océan. Application à la télédétection de la chlorophylle,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1976).
  5. H. Gordon, “A bio-optical model describing the distribution of irradiance at the sea surface resulting from a point source embedded in the ocean,” Appl. Opt. 26, 4133–4148 (1987).
    [CrossRef] [PubMed]
  6. C. D. Mobley, B. Gentili, H. R. Gordon, J. Zhonghai, 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]
  7. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  8. C. D. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
    [CrossRef]
  9. G. N. Plass, G. W. Kattawar, “Radiative transfer in an atmosphere–ocean system,” Appl. Opt. 8, 455–466 (1969).
    [CrossRef] [PubMed]
  10. E. Raschke, “Multiple scattering calculation of the transfer of solar radiation in an atmosphere–ocean system,” Contrib. Atmos. Phys. 45, 1–19 (1972).
  11. G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere–ocean system. I. Flux in the atmosphere and the ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
    [CrossRef]
  12. Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media such as the atmosphere–ocean system,” Appl. Opt. 33, 431–443 (1994).
    [CrossRef] [PubMed]
  13. H. R. Gordon, T. Zhang, “How well can radiance reflected from the ocean–atmosphere system be predicted from measurements at the sea surface?,” Appl. Opt. 35, 6527–6543 (1996).
    [CrossRef] [PubMed]
  14. J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
    [CrossRef]
  15. C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).
  16. J. L. Deuzé, “Etude de la polarisation du rayonnement par les milieux diffusants. Application à la polarisation localisée de Venus,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1974).
  17. E. Dilligeard, “Télédétection des eaux du cas II. Caractérisation des sédiments marins,” Ph.D. dissertation (Université du Littoral Côte d’Opale, Wimereux, France, 1997).
  18. A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
    [CrossRef]
  19. A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
    [CrossRef]
  20. H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery. A Review, Vol. 4 of Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983).
  21. H. Bader, “The hyperbolic distribution of particle sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
    [CrossRef]
  22. C. H. Whitlock, L. R. Poole, J. W. Usry, W. M. Houghton, W. G. Witte, W. D. Morris, E. A. Gurganus, “Comparison of reflectance with backscatter and absorption parameters for turbid waters,” Appl. Opt. 20, 517–522 (1981).
    [CrossRef] [PubMed]
  23. Y. H. Ahn, “Propriétés optiques de particules biologiques et minérales présentes dans l’océan. Application: inversion de la réflectance,” Ph.D. dissertation (Université Pierre et Marie Curie, Paris, 1990).
  24. A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, N. E. Steemann eds. (Academic, San Diego, Calif., 1974).
  25. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
  26. J. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
    [CrossRef]
  27. J. Lenoble, ed., Standard Procedures To Compute Atmospheric Radiative Transfer in a Scattering Atmosphere (International Association of Meteorology and Atmospheric Physics Radiation Commission, 1974), Vols. I and II.
  28. T. J. Petzold, “Volume scattering functions for selected natural waters,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsberg, Pa., 1977), pp. 150–174.
  29. J. Lenoble, Atmospheric radiative transfer (Deepak, Hampton, Va., 1993).
  30. G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean system with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
  31. K. J. Voss, E. S. Fry, “Measurements of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984).
    [CrossRef] [PubMed]
  32. T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
    [CrossRef] [PubMed]
  33. P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).
  34. B. Fougnie, “Contribution à l’observation de la couleur de l’océan à partir du capteur spatial POLDER,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1998).
  35. K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
    [CrossRef]
  36. R. Santer, “Contribution à l’étude de la polarisation du rayonnement solaire diffusé par Vénus,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1977).

1997 (1)

1996 (1)

1994 (2)

Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media such as the atmosphere–ocean system,” Appl. Opt. 33, 431–443 (1994).
[CrossRef] [PubMed]

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

1993 (2)

1989 (3)

C. D. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
[CrossRef]

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean system with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

1988 (1)

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

1987 (1)

1985 (1)

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

1984 (1)

1981 (2)

C. H. Whitlock, L. R. Poole, J. W. Usry, W. M. Houghton, W. G. Witte, W. D. Morris, E. A. Gurganus, “Comparison of reflectance with backscatter and absorption parameters for turbid waters,” Appl. Opt. 20, 517–522 (1981).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

1978 (1)

1973 (1)

1972 (2)

E. Raschke, “Multiple scattering calculation of the transfer of solar radiation in an atmosphere–ocean system,” Contrib. Atmos. Phys. 45, 1–19 (1972).

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere–ocean system. I. Flux in the atmosphere and the ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

1970 (2)

H. Bader, “The hyperbolic distribution of particle sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
[CrossRef]

J. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

1969 (1)

1954 (2)

Adams, C. N.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean system with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Ahn, Y. H.

Y. H. Ahn, “Propriétés optiques de particules biologiques et minérales présentes dans l’océan. Application: inversion de la réflectance,” Ph.D. dissertation (Université Pierre et Marie Curie, Paris, 1990).

Bader, H.

H. Bader, “The hyperbolic distribution of particle sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
[CrossRef]

Bréon, F. M.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Bricaud, A.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Brown, O. B.

Buriez, J. C.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Carder, K. L.

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

Cox, C.

Deschamps, P. Y.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Deuzé, J. L.

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
[CrossRef]

J. L. Deuzé, “Etude de la polarisation du rayonnement par les milieux diffusants. Application à la polarisation localisée de Venus,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1974).

Dilligeard, E.

E. Dilligeard, “Télédétection des eaux du cas II. Caractérisation des sédiments marins,” Ph.D. dissertation (Université du Littoral Côte d’Opale, Wimereux, France, 1997).

Fougnie, B.

B. Fougnie, “Contribution à l’observation de la couleur de l’océan à partir du capteur spatial POLDER,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1998).

Fry, E. S.

Gentili, B.

Gordon, H.

Gordon, H. R.

Gurganus, E. A.

Herman, M.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
[CrossRef]

Houghton, W. M.

Jin, Z.

Kattawar, G. W.

C. D. Mobley, B. Gentili, H. R. Gordon, J. Zhonghai, 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]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean system with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Color of the ocean,” Appl. Opt. 17, 1432–1446 (1978).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere–ocean system. I. Flux in the atmosphere and the ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Radiative transfer in an atmosphere–ocean system,” Appl. Opt. 8, 455–466 (1969).
[CrossRef] [PubMed]

Lenoble, J.

J. Lenoble, Atmospheric radiative transfer (Deepak, Hampton, Va., 1993).

Leroy, M.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Mobley, C. D.

C. D. Mobley, B. Gentili, H. R. Gordon, J. Zhonghai, 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]

C. D. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
[CrossRef]

C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).

Morel, A.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

C. D. Mobley, B. Gentili, H. R. Gordon, J. Zhonghai, 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. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, N. E. Steemann eds. (Academic, San Diego, Calif., 1974).

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery. A Review, Vol. 4 of Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983).

Morris, W. D.

Munk, W.

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected natural waters,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsberg, Pa., 1977), pp. 150–174.

Plass, G. N.

G. N. Plass, G. W. Kattawar, “Color of the ocean,” Appl. Opt. 17, 1432–1446 (1978).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere–ocean system. I. Flux in the atmosphere and the ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Radiative transfer in an atmosphere–ocean system,” Appl. Opt. 8, 455–466 (1969).
[CrossRef] [PubMed]

Podaire, A.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Poole, L. R.

Pope, R. M.

Potter, J.

J. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

Prieur, L.

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Raschke, E.

E. Raschke, “Multiple scattering calculation of the transfer of solar radiation in an atmosphere–ocean system,” Contrib. Atmos. Phys. 45, 1–19 (1972).

Reinersman, P.

Santer, R.

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
[CrossRef]

R. Santer, “Contribution à l’étude de la polarisation du rayonnement solaire diffusé par Vénus,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1977).

Sèze, G.

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

Stamnes, K.

Stavn, R. H.

Steward, R. G.

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

Usry, J. W.

Viollier, M.

M. Viollier, “Contribution à l’étude du rayonnement rétrodiffusé par l’océan. Application à la télédétection de la chlorophylle,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1976).

Voss, K. J.

Waterman, T. H.

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef] [PubMed]

Whitlock, C. H.

Witte, W. G.

Zhang, T.

Zhonghai, J.

Appl. Opt. (11)

H. Gordon, “A bio-optical model describing the distribution of irradiance at the sea surface resulting from a point source embedded in the ocean,” Appl. Opt. 26, 4133–4148 (1987).
[CrossRef] [PubMed]

C. D. Mobley, B. Gentili, H. R. Gordon, J. Zhonghai, 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. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Color of the ocean,” Appl. Opt. 17, 1432–1446 (1978).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “Irradiance reflectivity of a flat ocean as a function of the optical properties,” Appl. Opt. 12, 1549–1551 (1973).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Radiative transfer in an atmosphere–ocean system,” Appl. Opt. 8, 455–466 (1969).
[CrossRef] [PubMed]

Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media such as the atmosphere–ocean system,” Appl. Opt. 33, 431–443 (1994).
[CrossRef] [PubMed]

H. R. Gordon, T. Zhang, “How well can radiance reflected from the ocean–atmosphere system be predicted from measurements at the sea surface?,” Appl. Opt. 35, 6527–6543 (1996).
[CrossRef] [PubMed]

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

C. H. Whitlock, L. R. Poole, J. W. Usry, W. M. Houghton, W. G. Witte, W. D. Morris, E. A. Gurganus, “Comparison of reflectance with backscatter and absorption parameters for turbid waters,” Appl. Opt. 20, 517–522 (1981).
[CrossRef] [PubMed]

K. J. Voss, E. S. Fry, “Measurements of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984).
[CrossRef] [PubMed]

Contrib. Atmos. Phys. (1)

E. Raschke, “Multiple scattering calculation of the transfer of solar radiation in an atmosphere–ocean system,” Contrib. Atmos. Phys. 45, 1–19 (1972).

IEEE Trans. Geosci. Remote Sens. (1)

P. Y. Deschamps, M. Herman, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 3598–3615 (1994).

J. Atmos. Sci. (1)

J. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

J. Geophys. Res. (2)

H. Bader, “The hyperbolic distribution of particle sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere–ocean system. I. Flux in the atmosphere and the ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

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

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 483–494 (1989).
[CrossRef]

Limnol. Oceanogr. (4)

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

C. D. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean system with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

Science (1)

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef] [PubMed]

Other (12)

B. Fougnie, “Contribution à l’observation de la couleur de l’océan à partir du capteur spatial POLDER,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1998).

R. Santer, “Contribution à l’étude de la polarisation du rayonnement solaire diffusé par Vénus,” Ph.D. dissertation (Université des Sciences et Techniques de Lille, Lille, France, 1977).

Y. H. Ahn, “Propriétés optiques de particules biologiques et minérales présentes dans l’océan. Application: inversion de la réflectance,” Ph.D. dissertation (Université Pierre et Marie Curie, Paris, 1990).

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, N. E. Steemann eds. (Academic, San Diego, Calif., 1974).

J. Lenoble, ed., Standard Procedures To Compute Atmospheric Radiative Transfer in a Scattering Atmosphere (International Association of Meteorology and Atmospheric Physics Radiation Commission, 1974), Vols. I and II.

T. J. Petzold, “Volume scattering functions for selected natural waters,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsberg, Pa., 1977), pp. 150–174.

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Figures (18)

Fig. 1
Fig. 1

Geometric parameters: θ, zenith angle; 0, v, and a, w, solar and viewing angles and air and water, respectively. The angular relationship between air and water follows the Descartes–Snell law. ϕ is the difference in azimuth between the viewing and the solar planes.

Fig. 2
Fig. 2

(a) Schematic description of primary scattering for atmospheric upward radiance: (1) primary scattering atmospheric radiance [see Eq. (3)], (2) forward scattering of the reflected solar beam [see Eq. (12)], (3) reflection by the air–water interface of the primary scattering of atmospheric radiance, and (4) water-leaving radiance. (b) Schematic description of primary scattering for in-water downward radiance: (1) primary scattering of the in-water radiance, (2) transmitted primary scattering of the atmospheric radiance, and (3) backward atmospheric scattering.

Fig. 3
Fig. 3

Schematic description of sources for secondary scattering. (a) In the atmosphere: (1) upward radiance as described in Fig. 2(a), (2) primary scattering from the upper atmosphere, (3) Lambertian reflection of the direct solar beam by the sea surface (foam), and (4) Lambertian reflection of the direct solar beam by the sea bottom; (b) in the water: (1) downward radiance as described in Fig. 2(b), (2) primary scattering from the lower ocean, and (3) Lambertian reflection of the direct solar beam by the sea bottom.

Fig. 4
Fig. 4

Fit of the Petzold phase function28 by a phase function obtained with particles modeled as being distributed according to a Junge size with a slope ν = -4 and a refractive index m = 1.23–0.162j. The retrieval of the fitted function with a Legendre polynomial expansion is plotted for NB = 800 terms and NB = 80 terms. If the Legendre polynomial expansion is limited to NB = 80, the phase function oscillates.

Fig. 5
Fig. 5

Truncation of the Legendre polynomial expansion of the marine particle phase function measured by Petzold.28 Truncation improves the accuracy of the Legendre phase function at angles far from the forward peak.

Fig. 6
Fig. 6

Degree of polarization resulting from three chlorophyll contents (0.5, 1, and 2 mg m-3) for the exact scattering matrix and the truncated matrix, as predicted by the OSOA. Results are reported for an observation point just beneath the sea surface (0-1). The solar zenith angle is θ0 = 0°, and the wavelength is λ = 560 nm. Atmospheric effects are ignored.

Fig. 7
Fig. 7

Geometric series convergence of the upwelling radiance at the top of the uppermost layer for a nadir view. The solar zenith angle is θ0 = 30°. Results are plotted for the cases enumerated in Subsection 3.C. The radiance is normalized to extraterrestrial irradiance E 0, so L normalized = L(π/E 0) [sr-1]. A geometric series convergence is obtained when the radiance values are lined up on the y log scale.

Fig. 8
Fig. 8

(a) Reflected radiance, (b) degree of polarization, and (c) Stokes parameters Q and (d) U for models studied by Kattawar and Adams30 (their Figs. 6 and 7). The results presented here were computed with the OSOA code for conservative scattering (single-scattering albedo, ω0 = 1), with molecularly scattering atmospheres with optical depths τ = 0.1, 0.25, 0.5, 1.0, 3.0, and 5.0. The solar zenith angle (denoted S) is 10.24°. The results were averaged over the intervals 0° < Φ < 30° (left) and 150° < Φ < 180° (right).

Fig. 9
Fig. 9

(1) Upwelled and downwelled radiances and (b) degree of polarization for models studied by Kattawar and Adams30 (their Figs. 11 and 15). The results presented here were computed with the OSOA code for an ocean–atmosphere system separated by an interface of refractive index n w = 1.338. The atmosphere has an optical depth of 0.15, and the ocean has an optical depth of 4.85. Molecular scattering is used in each layer, and the single-scattering albedo is set to ω a = 0.8. Observations are made just above and just below the air–water interface. The solar zenith angle is 10.24°.

Fig. 10
Fig. 10

Polarized water-leaving radiance for various concentrations of phytoplankton (here, 0, 1, 5, 10, and 20 mg m-3) homogeneously distributed in the water column for the wavelength λ = 670 nm, as predicted by OSOA. The radiance is normalized to extraterrestrial irradiance E 0, so L normalized= L(π/E 0) [sr-1; plotted data, 10-2 sr-1]. The solar angle is θ0 = 30°, and atmospheric effects were ignored for the computations.

Fig. 11
Fig. 11

Polarized water-leaving radiance computed in the principal plane for various phytoplankton concentrations homogeneously distributed in the water column (a) at 443 nm and (b) at 560 nm. Results are reported for an observation point above the sea surface (0+). The solar zenith angle is θ0 = 30°, and atmospheric effects are ignored. Computational aspects for phytoplankton are enumerated in Subsection 4.A.

Fig. 12
Fig. 12

Same as Fig. 11 but here a Gaussian distribution in the water column is selected for phytoplankton, with a deep chlorophyll maximum at z max = 80 m.

Fig. 13
Fig. 13

Polarized TOA radiance for a phytoplankton concentration of 1 mg m-3 at (a) 443 nm and (b) 560 nm as predicted by the OSOA code. A Gaussian vertical profile (z max = 80 m) is used for the phytoplankton. A pure molecular atmosphere and a standard aerosol model were computed. Aerosols were modeled as being distributed according to a Junge power law with a slope of ν = -4, the refractive index is m = 1.33–0.000j, and the visibility is 23 km. The solar zenith angle is 30°.

Fig. 14
Fig. 14

Polarized water-leaving radiance resulting from various concentrations of sediment at λ = 670 nm, as predicted by the OSOA code. The radiance is normalized to extraterrestrial irradiance E 0, so L normalized = L(π/E 0) [sr-1; plotted data, units of 10-2 sr-1]. The solar angle is θ0 = 30°, and atmospheric effects were ignored for the computations. Computational conditions for sediments are enumerated in Subsection 4.A. The refractive index is m = 1.20–0.001j, and slope ν is -3.2.

Fig. 15
Fig. 15

Relationship between sediment concentration and slope ν of sediment size distribution for several sediment refractive indices. The total Rrs was computed by the OSOA code for a scattering angle θ = 100°, for an observation point above the sea surface (0+), and for a solar zenith angle of 30°. Atmospheric effects were ignored. A sediment reference model was selected. In this reference model, sediment is distributed according to a Junge power law size distribution with a slope of ν = -4, the refractive index is m = 1.16–0.001j, and the concentration is C = 10 mg/l (filled diamond). Only sediment models that successfully retrieved the total reference Rrs are plotted.

Fig. 16
Fig. 16

Polarized remote-sensing reflectance Rrs that correspond to the sediment models that permit retrieval of the total reference Rrs (Fig. 15) as computed by the OSOA code. Computational conditions are similar to those for Fig. 15. The horizontal bar indicates the polarized Rrs value obtained with the reference sediment model. The polarized component enables one to select from among the numerous models that retrieve the total Rrs signal.

Fig. 17
Fig. 17

Same as Fig. 14, except that atmospheric effects are included. The aerosol was modeled as being distributed according to a Junge power law with a slope of ν = -4, the refractive index is m = 1.50–0.001j, and the visibility is 8 km. The polarized water-leaving radiance plotted here has been corrected for the sky reflection on the sea surface.

Fig. 18
Fig. 18

Ratio of polarized water-leaving radiance when atmospheric effects are accounted for (Fig. 17) and ignored (Fig. 14) for several sediment concentrations in the specular plane. Briefly, the existence of the atmosphere modifies the downward incoming ocean irradiance (extinction of direct solar beam, diffuse flux). The effect on the polarized water-leaving radiance is observed here.

Tables (5)

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Table 1 Computation of Diffuse Downward and Upward Irradiances Just Below the Surface by Use of the Actual Petzold Phase Function and the Corresponding Truncated Function for Three Chlorophyll Contents for Case I Watersa

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Table 2 Order of Convergence for the Scattering Order of the Zeroth Order (s = 0) Fourier Series Term and for the Fourier Series Expansion (θ 0 = 30°) a

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Table 3 Bidirectional Reflectance (in percent) Above the Ocean Surface, ρw (0 + ), for a Solar Zenith Angle of θ 0 = 30° and a Nadir View a

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Table 4 Computations of Diffuse Irradiance for Conservative Casesa

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Table 5 Bidirectional Reflectance (in percent) Above the Ocean Surface, ρw (0 + ), for a Solar Zenith Angle of θ 0 = 30° and a Nadir View a

Equations (38)

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Lμ0, μν, ϕ=s=02-δ0sLsμ0, μνcossϕ=s=02-δ0sLsμ0, μvsinsϕ,
δ0s=1s=00s0.
M11μ=l=0NB βlPlμ,
βl=2l+12-11 M11μPlμdμ,
Lsτ, μν, μ0=ωaE˜0τlτexp+tμ0×exp-t-τμνM˜st, μν, μ04πμνdt,
Lsτ, μν, μs=ωaE˜00τexp+tμ0×exp+τ-tμνM˜st, μν, μ04πμνdt,
Lnsτ, μν, μ0=ωaτlτexp-tμν-1+1 Ln-1st, μν, μ×M˜st, μν, μ4πμνdμdt.
Lnsi=0n-1 Lis<10-5.
LnsLn-1s-Ln-1sLn-2s<10-2.
r=sin2θa-θwsin2θa+θw  perpendicular plane,
r//=tan2θa-θwtan2θa+θw  parallel plane,
R=12r//2+r2r//2-r20r//2-r2r//2+r20002rr//,
T=12nw cos θwcos θat//2+t2t//2-t20t//2-t2t//2+t20002t//t,
t//=2 sin θw cos θasinθa+θwcosθa-θw, t=2 sin θw cos θasinθa+θw.
Lsτ, μν, μ0=ωaRθ0E˜0 expτlμ0τlτexpτl-tμ0×exp- t-τμνM˜st, μν, μ04πμνdt,
Lsτ, μν, μ0=ωaRθ0E˜0 expτlμ00τexpτl-tμ0×exp+τ-tμνM˜st, μν, μ04πμνdt.
Lsτ, μν, μ0=ωaTθ0E˜0 exp+τlμ0×τl+τwτ exp+t-τlμ0wexp- t-τμνw×M˜wst, μνw, μ0w4πμνwdt,
La=TθwLw/nw2.
Lw=Tθanw2La.
b=b×1-f,
M12θM11θ=M12*θM11*θ,
M33θM11θ=M33*θM11*θ,
Lμ0, μ, ϕ=180=s=02-δ0sLsμ0, μ.
2Ls/L<10-3.
ρwθ0, θν, Φ=πLwθ0, θν, ΦEd,
ψ=bdVE04π02π-1+1 M11μdμdϕ,
ψ=bdVE04π02π-1+1M11μ-M11*μdμdϕ.
A=-1+1M11μ-M11*μdμ,
ψ=bdVE0A/2.
dE=-bdVE01-A2.
b*=b1-f,
ωa*=ωa1-f1-ωaf,
τ*=τ1-ωaf.
ψ*=b*dVE04π02π-1+1 M11tμdμdϕ,
-1+1 M11tμdμ=2.
M˜=M11=l=0NB βlPlμM12=l=2NB γlPl2μ0M12=l=2NB γlPl2μM11=l=0NB βlPlμ000M33=l=0NB δlPlμ,
l=2NB γlPl2μl=0NB βlPlμ=l=2NB* γl*Pl2μl=0NB* βl*Plμ.
M33μM11μ=M33*μM11*μ,

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