Abstract

Ocean color is determined by spectral variations in reflectance at the sea surface, which in turn result from both elastic and inelastic processes. We extend an elastic-scattering model of sea surface reflectance to deal with Raman scattering, which is an inelastic process. The analytic solutions are derived for a vertically homogeneous and optically deep water column. The model presented here is based on the quasi-single-scattering approximation of Gordon [Appl. Opt. 12, 2803 (1973)] and is an extension of the model of Sathyendranath and Platt [Appl. Opt. 36, 2620 (1997)]. The Raman-scattering model includes a first-order Raman-scattering term and four second-order terms. Two of the second-order terms result from a combination of an elastic and a Raman-scattering event, whereas the other two second-order terms result from two Raman-scattering events. We show that the contribution to reflectance from these last two terms is typically of the order of 1% of the first-order Raman-scattering term. Therefore these terms and higher-order terms can be neglected for most applications. Issues related to the implementation of the model are discussed, with special reference to remote-sensing applications. Results from the analytic model are compared with Monte Carlo simulations of reflectance at the sea surface.

© 1998 Optical Society of America

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  1. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
    [CrossRef] [PubMed]
  2. S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
    [CrossRef] [PubMed]
  3. J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
    [CrossRef] [PubMed]
  4. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
    [CrossRef]
  5. S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
    [CrossRef]
  6. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  7. H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18, 1161–1166 (1979).
    [CrossRef] [PubMed]
  8. R. A. Neville, J. F. R. Gower, “Passive remote sensing of phytoplankton via chlorophyll a fluorescence,” J. Geophys. Res. 82, 3487–3493 (1977).
    [CrossRef]
  9. J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Boundary-Layer Meteorol. 18, 235–245 (1980).
    [CrossRef]
  10. S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
    [CrossRef]
  11. R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
    [CrossRef] [PubMed]
  12. B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29, 71–84 (1990).
    [CrossRef] [PubMed]
  13. V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5356–5367 (1993).
    [CrossRef] [PubMed]
  14. R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. 32, 6853–6863 (1993).
    [CrossRef] [PubMed]
  15. Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
    [CrossRef] [PubMed]
  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, 417–427 (1975).
    [CrossRef] [PubMed]
  17. H. R. Gordon, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975).
    [CrossRef] [PubMed]
  18. E. Aas, “Two-stream irradiance model for deep waters,” Appl. Opt. 26, 2095–2101 (1987).
    [CrossRef] [PubMed]
  19. J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
    [CrossRef]
  20. S. Sathyendranath, T. Platt, “Angular distribution of the submarine light field: modification by multiple scattering,” Proc. R. Soc. London Ser. A 433, 287–297 (1991).
    [CrossRef]
  21. S. Sathyendranath, T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
    [CrossRef]
  22. J. T. O. Kirk, “Monte Carlo study of the nature of the underwater light field in, and the relationship between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
    [CrossRef]
  23. J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
    [CrossRef]
  24. 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]
  25. H. R. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds., of Oxford Monographs on Geology and Geophysics (Oxford U. Press, New York, 1994), pp. 3–39.
  26. H. R. Gordon, K. J. Voss, K. A. Kilpatrick, “Angular distribution of fluorescence from phytoplankton,” Limnol. Oceanogr. 38, 1582–1586 (1993).
    [CrossRef]
  27. A. Morel, “Optical properties of pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, New York, 1974), pp. 1–24.
  28. R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
    [CrossRef] [PubMed]
  29. O. Ulloa, S. Sathyendranath, T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
    [CrossRef] [PubMed]
  30. Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
    [PubMed]
  31. A. Morel, “In-water and remote measurement of ocean color,” Boundary-Layer Meteorol. 18, 177–201 (1980).
    [CrossRef]
  32. 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]
  33. L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
    [CrossRef]
  34. T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, San Diego, 1972), p. 79.
  35. K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13,151–13,161 (1995).
    [CrossRef]
  36. G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
    [CrossRef]
  37. G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
    [CrossRef]
  38. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, San Diego, 1994), p. 592.
  39. J. S. Bartlett, K. L. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. (to be published).

1997 (2)

1995 (1)

K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13,151–13,161 (1995).
[CrossRef]

1994 (2)

1993 (4)

1991 (2)

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]

S. Sathyendranath, T. Platt, “Angular distribution of the submarine light field: modification by multiple scattering,” Proc. R. Soc. London Ser. A 433, 287–297 (1991).
[CrossRef]

1990 (1)

1989 (2)

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

1988 (3)

S. Sathyendranath, T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
[CrossRef] [PubMed]

1987 (1)

1984 (2)

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

1982 (1)

1981 (3)

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

J. T. O. Kirk, “Monte Carlo study of the nature of the underwater light field in, and the relationship between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

1980 (2)

A. Morel, “In-water and remote measurement of ocean color,” Boundary-Layer Meteorol. 18, 177–201 (1980).
[CrossRef]

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Boundary-Layer Meteorol. 18, 235–245 (1980).
[CrossRef]

1979 (1)

1977 (2)

R. A. Neville, J. F. R. Gower, “Passive remote sensing of phytoplankton via chlorophyll a fluorescence,” J. Geophys. Res. 82, 3487–3493 (1977).
[CrossRef]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

1975 (2)

1973 (1)

1969 (1)

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

1967 (1)

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

Aas, E.

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

Bartlett, J. S.

J. S. Bartlett, K. L. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. (to be published).

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

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]

Carder, K. L.

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Davis, C. O.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Fry, E. S.

Ge, Y.

Gentili, B.

Gordon, H. R.

Gower, J. F. R.

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Boundary-Layer Meteorol. 18, 235–245 (1980).
[CrossRef]

R. A. Neville, J. F. R. Gower, “Passive remote sensing of phytoplankton via chlorophyll a fluorescence,” J. Geophys. Res. 82, 3487–3493 (1977).
[CrossRef]

Haltrin, V. I.

Hawes, S. K.

Jacobs, M. M.

Kattawar, G. W.

Kilpatrick, K. A.

H. R. Gordon, K. J. Voss, K. A. Kilpatrick, “Angular distribution of fluorescence from phytoplankton,” Limnol. Oceanogr. 38, 1582–1586 (1993).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

J. T. O. Kirk, “Monte Carlo study of the nature of the underwater light field in, and the relationship between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

Kishino, M.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

Lee, Z. P.

Marshall, B. R.

McCluney, W. R.

Mobley, C. D.

C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, San Diego, 1994), p. 592.

Morel, A.

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]

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

A. Morel, “In-water and remote measurement of ocean color,” Boundary-Layer Meteorol. 18, 177–201 (1980).
[CrossRef]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

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

Neville, R. A.

R. A. Neville, J. F. R. Gower, “Passive remote sensing of phytoplankton via chlorophyll a fluorescence,” J. Geophys. Res. 82, 3487–3493 (1977).
[CrossRef]

Okami, N.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

Peacock, T. G.

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, San Diego, 1972), p. 79.

Platt, T.

S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
[CrossRef] [PubMed]

O. Ulloa, S. Sathyendranath, T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef] [PubMed]

S. Sathyendranath, T. Platt, “Angular distribution of the submarine light field: modification by multiple scattering,” Proc. R. Soc. London Ser. A 433, 287–297 (1991).
[CrossRef]

S. Sathyendranath, T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
[CrossRef]

Pope, R. M.

Prieur, L.

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Sathyendranath, S.

S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
[CrossRef] [PubMed]

O. Ulloa, S. Sathyendranath, T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef] [PubMed]

S. Sathyendranath, T. Platt, “Angular distribution of the submarine light field: modification by multiple scattering,” Proc. R. Soc. London Ser. A 433, 287–297 (1991).
[CrossRef]

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

S. Sathyendranath, T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

J. S. Bartlett, K. L. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. (to be published).

Smith, R. C.

Stavn, R. H.

Steward, R. G.

Sugihara, S.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

Ulloa, O.

Vodacek, A.

J. S. Bartlett, K. L. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. (to be published).

Voss, K. J.

Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
[PubMed]

H. R. Gordon, K. J. Voss, K. A. Kilpatrick, “Angular distribution of fluorescence from phytoplankton,” Limnol. Oceanogr. 38, 1582–1586 (1993).
[CrossRef]

Voss, K. L.

J. S. Bartlett, K. L. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. (to be published).

Walrafen, G. E.

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

Waters, K. J.

K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13,151–13,161 (1995).
[CrossRef]

Weidemann, A. D.

Zaneveld, J. R. V.

Appl. Opt. (17)

H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
[CrossRef] [PubMed]

S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
[CrossRef] [PubMed]

J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
[CrossRef] [PubMed]

H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18, 1161–1166 (1979).
[CrossRef] [PubMed]

R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
[CrossRef] [PubMed]

B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29, 71–84 (1990).
[CrossRef] [PubMed]

V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5356–5367 (1993).
[CrossRef] [PubMed]

R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. 32, 6853–6863 (1993).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

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, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975).
[CrossRef] [PubMed]

E. Aas, “Two-stream irradiance model for deep waters,” Appl. Opt. 26, 2095–2101 (1987).
[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]

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

O. Ulloa, S. Sathyendranath, T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef] [PubMed]

Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
[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]

Aust. J. Mar. Freshwater Res. (1)

J. T. O. Kirk, “Monte Carlo study of the nature of the underwater light field in, and the relationship between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

Boundary-Layer Meteorol. (2)

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Boundary-Layer Meteorol. 18, 235–245 (1980).
[CrossRef]

A. Morel, “In-water and remote measurement of ocean color,” Boundary-Layer Meteorol. 18, 177–201 (1980).
[CrossRef]

Int. J. Remote Sensing (1)

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

J. Chem. Phys. (2)

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

J. Geophys. Res. (4)

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S. Sathyendranath, T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
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Figures (5)

Fig. 1
Fig. 1

Schematic diagram showing the geometry of the first-order Raman-scattering term considered (term 1). The inverse of the cosines of angles θ S and (π - θ R ) determine, respectively, the path lengths of the downwelling light stream and the upwelling light stream per unit vertical distance.

Fig. 2
Fig. 2

Schematic diagram showing the geometry of a second-order scattering term (term 2). A downward Raman-scattering event at depth z′ is followed by an upward elastic-scattering event at z.

Fig. 3
Fig. 3

Schematic diagram showing the geometry of a second-order scattering term (term 3). An elastic-upward-scattering event (at z) is followed by an upward Raman-scattering event at z′.

Fig. 4
Fig. 4

Schematic diagram showing the geometry of a second-order Raman-scattering term (term 4). A downward Raman-scattering event at z′ is followed by an upward Raman-scattering event at z. Note that, if we assume the source wavelength is the same as in the previous cases considered, the resultant upward Raman flux at the sea surface will be at a wavelength other than λ.

Fig. 5
Fig. 5

Reflectance at 520 nm computed with Monte Carlo simulations (filled circles) and with the simplified analytic model (continuous curve), plotted as a function of chlorophyll concentration. The elastic and Raman components of reflectance are plotted separately.

Tables (1)

Tables Icon

Table 1 Components of Reflectance at the Sea Surfacea

Equations (27)

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R λ ,   z = E u λ ,   z E d λ ,   z .
R λ ,   0 = s λ b b λ μ d λ K λ + κ λ ,
K λ = a λ + b b λ μ d ,
κ λ = a λ + b b λ μ u ,
R λ ,   0 = μ u λ s λ μ u λ + μ d λ b b λ a λ + b b λ .
E d λ ,   z = E d λ ,   0 exp - K λ z ,
d E u R λ ,   z = E d λ ,   z s R λ b b R λ μ d λ d z ,
d E u R λ ,   z = E d λ ,   0 b b R λ μ d λ exp - K λ z d z .
d E u R λ ,   z ,   0 = E d λ ,   0 b b R λ μ d λ exp - K λ z × exp - κ R λ z d z ,
E u R λ ,   0 = E d λ ,   0 b b R λ μ d λ 0 exp - K λ + κ R λ z d z , = E d λ ,   0 b b R λ μ d λ 1 K λ + κ R λ .
R R λ ,   0 = E u R λ ,   0 E d λ ,   0 .
d E d R λ ,   z = E d λ ,   z b b R λ μ d λ d z = E d λ ,   0 b b R λ μ d λ exp - K λ z d z .
d E d R λ ,   z ,   z = E d λ ,   0 b b R λ μ d λ exp - K λ z × exp - K R λ z - z d z ,
E d R λ ,   z = E d λ ,   0 b b R λ μ d λ 0 z exp - K λ z × exp - K R λ z - z d z , = E d λ ,   0 b b R λ μ d λ exp - K R λ z K λ - K R λ × 1 - exp - K λ - K R λ z .
d E u RE λ ,   z = E d R λ ,   z s E λ b b E λ μ d R λ d z .
E u RE λ ,   0 = 0 d E u RE λ ,   z exp - κ RE λ z d z .
E u RE λ ,   0 = E d λ ,   0 s E λ b b E λ μ d R λ b b R λ μ d λ × 1 K λ + κ RE λ K R λ + κ RE λ ,
R RE λ ,   0 = E u RE λ ,   0 E d λ ,   0 .
d E u E λ ,   z = E d λ ,   0 s E λ b b E λ μ d λ exp - K λ z d z .
d E u ER λ ,   z ,   0 = d E u E λ ,   z b b R λ μ u E λ 0 z exp - κ E λ × z - z exp - κ ER λ z d z .
d E u ER λ ,   z ,   0 = d E u E λ ,   z b b R λ μ u E λ exp - κ E λ z κ ER λ - κ E λ × 1 - exp - κ ER λ - κ E λ z .
E u ER λ ,   0 = E d λ ,   0 s E λ b b E λ μ d λ b b R λ μ u E λ × 1 K λ + κ E λ K λ + κ ER λ ,
R ER λ ,   0 = E u ER λ ,   0 E d λ ,   0 .
R 1 RR λ ,   0 = E d λ ,   0 E d λ ,   0 b b R λ μ d λ b b R λ μ d R λ × 1 K λ + κ RR λ K R λ + κ RR λ .
R 2 RR λ ,   0 = E d λ ,   0 E d λ ,   0 b b R λ μ d λ b b R λ μ u R λ × 1 K λ + κ R λ K λ + κ RR λ .
R λ ,   0 = R E λ ,   0 + R R λ ,   0 1 + b b E λ κ E λ + b b E λ 0.5 K λ + κ E λ .
λ   b b R λ ,   λ d λ = λ   b b R λ ,   λ d λ = b b R λ ,

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