Abstract

The upwelling radiance field beneath the ocean surface and the emerging radiance field are not generally isotropic. Their bidirectional structure depends on the illumination conditions (the Sun’s position in particular) and on the optical properties of the water body. In oceanic case 1 waters, these properties can be related, for each wavelength λ, to the chlorophyll (Chl) concentration. We aim to quantify systematically the variations of spectral radiances that emerge from an ocean with varying Chl when we change the geometric conditions, namely, the zenith–Sun angle, the viewing angle, and the azimuth difference between the solar and observational vertical planes. The consequences of these important variations on the interpretation of marine signals, as detected by a satelliteborne ocean color sensor, are analyzed. In particular, the derivation of radiometric quantities, such as R(λ), the spectral reflectance, or [Lw(λ)]N, the normalized water-leaving radiance that is free from directional effects, is examined, as well as the retrieval of Chl. We propose a practical method that is based on the use of precomputed lookup tables to provide values of the f/Q ratio in all the necessary conditions [f relates R(λ) to the backscattering and absorption coefficients, whereas Q is the ratio of upwelling irradiance to any upwelling radiance]. The f/Q ratio, besides being dependent on the geometric configuration (the three angles mentioned above), also varies with λ and with the bio-optical state, conveniently depicted by Chl. Because Chl is one of the entries for the lookup table, it has to be derived at the beginning of the process, before the radiometric quantities R(λ) or [Lw(λ)]N canbe produced. The determination of Chl can be made through an iterative process, computationally fast, using the information at two wavelengths. In this attempt to remove the bidirectional effect, the commonly accepted view relative to the data-processing strategy is somewhat modified, i.e., reversed, as the Chl index becomes a prerequisite parameter that must be identified prior to the derivation of the fundamental radiometric quantities at all wavelengths.

© 1996 Optical Society of America

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  1. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  2. A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13,143–13,151 (1995).
    [CrossRef]
  3. K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
  4. H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of Coastal Zone Color Scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
    [CrossRef] [PubMed]
  5. A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanol. Acta 7, 33–50 (1987).
  6. J. M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanol. Acta 14, 3–22 (1991).
  7. C. Myrmehl, A. Morel, “Accounting for the marine reflectance bidirectionality when processing remotely sensed ocean colour data,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 870–878 (1994).
  8. H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery,” in Lecture Notes on Coastal and Estuarine Studies, R. T. Barber, C. N. K. Mooers, M. J. Bowman, B. Zeitzschel, eds., (Springer-Verlag, Berlin, 1983), Vol. 4.
  9. R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, San Diego, Calif., 317–344 (1974).
  10. 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]
  11. 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]
  12. 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]
  13. As discussed in Refs. 1 and 12, the unique nature of the VSF for particles limits the validity of the modeled inherent optical properties. With this VSF, when the chlorophyll levels are above 1.5 mg m−3, the backscattering efficiency becomes too high and contradicts the empirical relationship providing the backscatter coefficient as a function of Chl proposed in Ref. 18. Therefore, above this limit, results become dubious. Attempts to model the VSF of marine hydrosols from the VSF of several constituents already exist,28 even if data for these VSF’s and their respective roles are currently scarce.
  14. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  15. 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]
  16. A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
    [CrossRef]
  17. 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]
  18. The historical bio-optical algorithms that were developed during the CZCS era used the symbol C to designate the algal pigment concentration; C was supposed to be the sum of chlorophyll a and pheophytin a, as was determined by using the fluorometric method. It is now acknowledged that, because of the interference with Chl b, phaeopigments have been seriously overestimated. Therefore it is wise to return to the notation Chl, which also has the advantage of avoiding any confusion with the symbol C, for carbon, in papers in which both are involved.
  19. 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]
  20. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” Environmental Research Paper 285, AFCRL-68-0153. (Air Force Cambridge Research Laboratories, Bedford, Mass., 1968).
  21. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Environmental Research Paper 676, AFGL-TR-79-0214. (Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  22. C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).
  23. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994), p. 592.
  24. J. T. O. Kirk, “Dependence of the relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
    [CrossRef]
  25. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
    [CrossRef]
  26. W. W. Gregg, F. S. Platt, R. H. Woodward, “The simulated SeaWIFS data set, Version 2,” S. B. Hooker, E. R. Firestone, eds., Vol. 15 of NASA Tech. Memo. 104566 (1994), pp. 1–42.
  27. K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
    [CrossRef]
  28. S. Sathyendranath, F. E. Hoge, T. Platt, R. N. Swift, “Detection of phytoplankton pigments from ocean color: improved algorithms,” Appl. Opt. 33, 1081–1089 (1994).
    [CrossRef] [PubMed]
  29. A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).
  30. G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean 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. J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWIFS validation, Revision 1,” S. B. Hooker, E. R. Firestone, J. G. Acker, eds., Vol. 25 of NASA Tech. Memo. 104566 (1995), pp. 1–67.
  32. J. R. V. Zaneveld, “A theorical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13,135–13,142 (1991).
  33. 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]
  34. A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
    [CrossRef]

1995 (1)

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13,143–13,151 (1995).
[CrossRef]

1994 (3)

1993 (2)

1991 (5)

J. M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanol. Acta 14, 3–22 (1991).

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]

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[CrossRef]

A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

J. R. V. Zaneveld, “A theorical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13,135–13,142 (1991).

1989 (3)

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean 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. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[CrossRef]

1988 (2)

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]

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]

1987 (1)

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanol. Acta 7, 33–50 (1987).

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)

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

1981 (1)

1980 (1)

A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
[CrossRef]

1977 (1)

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

1975 (1)

1955 (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

Adams, C. N.

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

André, J. M.

J. M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanol. Acta 14, 3–22 (1991).

Antoine, D.

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

Austin, R. W.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWIFS validation, Revision 1,” S. B. Hooker, E. R. Firestone, J. G. Acker, eds., Vol. 25 of NASA Tech. Memo. 104566 (1995), pp. 1–67.

R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, San Diego, Calif., 317–344 (1974).

Baker, K. A.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[CrossRef]

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]

Bricaud, A.

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanol. Acta 7, 33–50 (1987).

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.

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]

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[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]

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]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of Coastal Zone Color Scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

Cox, C.

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

Davis, C. O.

Elterman, L.

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

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]

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Environmental Research Paper 676, AFGL-TR-79-0214. (Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Gentili, B.

Gordon, H. R.

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]

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[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]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of Coastal Zone Color Scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
[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]

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery,” in Lecture Notes on Coastal and Estuarine Studies, R. T. Barber, C. N. K. Mooers, M. J. Bowman, B. Zeitzschel, eds., (Springer-Verlag, Berlin, 1983), Vol. 4.

Gregg, W. W.

W. W. Gregg, F. S. Platt, R. H. Woodward, “The simulated SeaWIFS data set, Version 2,” S. B. Hooker, E. R. Firestone, eds., Vol. 15 of NASA Tech. Memo. 104566 (1994), pp. 1–42.

Hawes, S. K.

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]

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[CrossRef]

Hoge, F. E.

Jacobs, M. M.

Jin, Z.

Kattawar, G. W.

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]

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

Kirk, J. T. O.

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

Lee, Z. P.

Mitchell, B. G.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[CrossRef]

Mobley, C. D.

Morel, A.

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13,143–13,151 (1995).
[CrossRef]

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

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, 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. 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]

J. M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanol. Acta 14, 3–22 (1991).

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, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanol. Acta 7, 33–50 (1987).

A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
[CrossRef]

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

C. Myrmehl, A. Morel, “Accounting for the marine reflectance bidirectionality when processing remotely sensed ocean colour data,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 870–878 (1994).

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery,” in Lecture Notes on Coastal and Estuarine Studies, R. T. Barber, C. N. K. Mooers, M. J. Bowman, B. Zeitzschel, eds., (Springer-Verlag, Berlin, 1983), Vol. 4.

Mueller, J. L.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWIFS validation, Revision 1,” S. B. Hooker, E. R. Firestone, J. G. Acker, eds., Vol. 25 of NASA Tech. Memo. 104566 (1995), pp. 1–67.

Munk, W.

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

Myrmehl, C.

C. Myrmehl, A. Morel, “Accounting for the marine reflectance bidirectionality when processing remotely sensed ocean colour data,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 870–878 (1994).

Peacock, T. G.

Platt, F. S.

W. W. Gregg, F. S. Platt, R. H. Woodward, “The simulated SeaWIFS data set, Version 2,” S. B. Hooker, E. R. Firestone, eds., Vol. 15 of NASA Tech. Memo. 104566 (1994), pp. 1–42.

Platt, T.

Prieur, L.

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

Reinersman, P.

Sathyendranath, S.

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Environmental Research Paper 676, AFGL-TR-79-0214. (Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Smith, R. C.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[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]

Stamnes, K.

Stavn, R. H.

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. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

Steward, R. G.

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]

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[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]

Swift, R. N.

Voss, K. J.

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13,143–13,151 (1995).
[CrossRef]

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

Weidemann, A. D.

A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

Wilcox, M. R.

A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

Woodward, R. H.

W. W. Gregg, F. S. Platt, R. H. Woodward, “The simulated SeaWIFS data set, Version 2,” S. B. Hooker, E. R. Firestone, eds., Vol. 15 of NASA Tech. Memo. 104566 (1994), pp. 1–42.

Zaneveld, J. R. V.

A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

J. R. V. Zaneveld, “A theorical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13,135–13,142 (1991).

Appl. Opt. (7)

Boundary-Layer Meteorol. (1)

A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
[CrossRef]

J. Geophys. Res. (6)

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. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13,143–13,151 (1995).
[CrossRef]

A. D. Weidemann, R. H. Stavn, J. R. V. Zaneveld, M. R. Wilcox, “Error in predicting hydrosol backscattering from remotely sensed reflectance,” J. Geophys. Res. 100(C7), 13,163–13,177 (1991).

J. R. V. Zaneveld, “A theorical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13,135–13,142 (1991).

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]

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in presence of productivity degradation products,” J. Geophys. Res. 96, 20,599–20,611 (1991).
[CrossRef]

J. Mar. Res. (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

J. Phys. Oceanogr. (1)

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

Limnol. Oceanogr. (5)

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

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean 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]

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

Oceanol. Acta (2)

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanol. Acta 7, 33–50 (1987).

J. M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanol. Acta 14, 3–22 (1991).

Opt. Eng. (1)

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

Other (10)

As discussed in Refs. 1 and 12, the unique nature of the VSF for particles limits the validity of the modeled inherent optical properties. With this VSF, when the chlorophyll levels are above 1.5 mg m−3, the backscattering efficiency becomes too high and contradicts the empirical relationship providing the backscatter coefficient as a function of Chl proposed in Ref. 18. Therefore, above this limit, results become dubious. Attempts to model the VSF of marine hydrosols from the VSF of several constituents already exist,28 even if data for these VSF’s and their respective roles are currently scarce.

C. Myrmehl, A. Morel, “Accounting for the marine reflectance bidirectionality when processing remotely sensed ocean colour data,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 870–878 (1994).

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery,” in Lecture Notes on Coastal and Estuarine Studies, R. T. Barber, C. N. K. Mooers, M. J. Bowman, B. Zeitzschel, eds., (Springer-Verlag, Berlin, 1983), Vol. 4.

R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, San Diego, Calif., 317–344 (1974).

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

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Environmental Research Paper 676, AFGL-TR-79-0214. (Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

The historical bio-optical algorithms that were developed during the CZCS era used the symbol C to designate the algal pigment concentration; C was supposed to be the sum of chlorophyll a and pheophytin a, as was determined by using the fluorometric method. It is now acknowledged that, because of the interference with Chl b, phaeopigments have been seriously overestimated. Therefore it is wise to return to the notation Chl, which also has the advantage of avoiding any confusion with the symbol C, for carbon, in papers in which both are involved.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWIFS validation, Revision 1,” S. B. Hooker, E. R. Firestone, J. G. Acker, eds., Vol. 25 of NASA Tech. Memo. 104566 (1995), pp. 1–67.

W. W. Gregg, F. S. Platt, R. H. Woodward, “The simulated SeaWIFS data set, Version 2,” S. B. Hooker, E. R. Firestone, eds., Vol. 15 of NASA Tech. Memo. 104566 (1994), pp. 1–42.

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

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Figures (11)

Fig. 1
Fig. 1

Schematic geometry and symbols for radiances and angles. Note that θ is a zenith angle and θ′ is a nadir angle.

Fig. 2
Fig. 2

Variations of f [Eq. (10a)] as a function of solar zenith angle θ0 for various wavelengths and chlorophyll concentrations equal to 0.03, 0.1, 0.3, 1, and 3 mg m−3 from bottom to top.

Fig. 3
Fig. 3

For the wavelengths indicated, variation of Qn, the specific value of the Q factor when the radiance originates from nadir, as a function of the solar zenith angle θ0. The various curves in each panel are for chlorophyll concentrations of 0.03, 0.1, 0.3, 1, and 3 mg m−3 from bottom to top.

Fig. 4
Fig. 4

Qn plotted versus wavelength and for four specific values of θ0, as indicated. In the upper left panel where θ0 = 0°, Qn has the specific value of Q0.

Fig. 5
Fig. 5

Same as Figs. 2 and 3 except for the ratio f0)/Qn.

Fig. 6
Fig. 6

Selected examples of the ratio f/Q for some θ0 and Chl values as indicated and when θ′ varies from ±50° with respect to the vertical direction and within the principal plane containing the Sun (Δϕ = 0 or π) or within the perpendicular half-plane (Δϕ =0 π/2). The standard conditions for this figure are W = 0 ms−1 and τa = 0.20. Note that for RS applications and because of the sphericity of the Earth, a viewing angle θυ = 45°, from an altitude of 705 km (SeaWIFS), corresponds to θ = 52° and θ′ = 36°. With the scales adopted for these graphs, the curves corresponding to the various wavelengths are barely discernible except those for λ = 670 nm (dotted curves). They are actually approximately arranged with increasing wavelength (410–670 nm) from top to bottom.

Fig. 7
Fig. 7

Chlorophyll concentration (in mg m−3, log scale) within a scan line of SeaWIFS (bottom, solid line). The geometric conditions are those of the SeaWIFS sensor, computed for the vernal Equinox (day 80) and for a subsatellite point on the polar arctic circle (in descending mode, noon orbit26); θ0 is approximately 65° and Δϕ is between 85° and 92°, everywhere within the swath, and the swath corresponds to θ = ±52°. The dashed curve represents the retrieved Chl1 values after the first processing (see text). The relative error with respect to the input value (in percent) is also shown as a dashed curve in the upper panel; the dotted curve and solid line represent the relative errors after the first and second iterations, respectively.

Fig. 8
Fig. 8

Water-leaving radiances at all wavelengths have been computed in the same geometric conditions as for Fig. 7. Only three wavelengths and half of the swaths are displayed. These actual radiances are transformed into operational normalized water-leaving radiances [Appendix A, Eq. (A2)] and are shown as solid curves. They are also transformed into exact normalized water-leaving radiances (dashed lines) by way of Eq. (8) and by using the f/Q table after the chlorophyll concentration has been iteratively estimated (see text).

Fig. 9
Fig. 9

Same as Fig. 6 (for θ0 = 75° and λ = 555 nm) and for two other aerosol optical thicknesses (dashed and solid curves, respectively) and for two extreme values of the wind speed (filled and open symbols, respectively, for identification).

Fig. 10
Fig. 10

Variations of bb/a as a function of Chl for various wavelengths, and of some of their ratios, based on the bio-optical model summarized in Appendix C.

Fig. 11
Fig. 11

Variations of ℜ(θ), a term that merges all the reflection and refraction effects [Eq. (5)], with θ and for several wind speeds as indicated. In correspondence with the θ scale the θ′ and θυ scales are also given (θυ is the viewing angle from a satellite at an altitude of 705 km).

Equations (29)

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L w ( θ , ϕ ) = L u ( 0 , θ , ϕ ) [ 1 ρ ( θ , θ ) ] n 2 ,
R ( 0 ) = E u ( 0 ) E d ( 0 ) ,
E d ( 0 ) = Ξ d L d ( 0 , θ , ϕ ) cos θ d Ω ,
E u ( 0 ) = Ξ u L u ( 0 , θ , ϕ ) cos θ d Ω ,
Q = E u ( 0 ) / L u ( 0 , θ , ϕ ) ,
Q ( θ , θ 0 , Δ ϕ ) = E u / L u ( θ , θ 0 , Δ ϕ ) .
L w ( θ , θ 0 , Δ ϕ ) = E d ( 0 ) [ 1 ρ ( θ , θ ) ] ( 1 r ¯ R ) n 2 R ( θ 0 ) Q ( θ , θ 0 , Δ ϕ ) ,
L w ( θ , θ 0 , Δ ϕ ) = E d ( 0 + ) × { ( 1 ρ ¯ ) [ 1 ρ ( θ , θ ) ] ( 1 r ¯ R ) n 2 } R ( θ 0 ) Q ( θ , θ 0 , Δ ϕ ) ,
L w ( θ , θ 0 , Δ ϕ ) = [ F 0 ε t ( θ 0 ) μ 0 ] ( θ 0 ) R ( θ 0 ) Q ( θ , θ 0 , Δ ϕ ) .
( L w ) N = F 0 0 Q 0 R 0 ,
L w ( θ , θ 0 , Δ ϕ ) = [ ε t ( θ 0 ) μ 0 ] R ( θ 0 ) R 0 ( θ ) 0 Q 0 Q ( θ , θ 0 , Δ ϕ ) ( L w ) N .
Q [ θ , θ 0 , Δ ϕ , τ , W , ω ¯ ( λ ) , η b ( λ ) ]
Q n [ θ 0 , Δ ϕ , τ , W , ω ¯ ( λ ) , η b ( λ ) ]
Q 0 [ τ , W , ω ¯ ( λ ) , η b ( λ ) ] .
R = f b b a
R = f b b a + b b .
f [ θ 0 , τ , W , ω ¯ ( λ ) , η b ( λ ) ] ,
L w ( θ , θ 0 , Δ ϕ ) = E d ( 0 + ) ( θ ) f Q b b a .
( L w ) N = F 0 0 f ( 0 ) Q 0 b b a .
f ( θ 0 , λ , chl ) / Q ( θ , θ 0 , Δ ϕ , λ , chl )
[ L w ] N f = L w ( θ = 0 , θ 0 ) ε t ( θ 0 ) cos θ 0 ,
( L w ) N s = L w ( θ , θ 0 , Δ ϕ ) ε t ( θ 0 ) cos θ 0 .
( L w ) N ex = 0 ( θ ) R 0 R ( θ 0 ) Q ( θ , θ 0 , Δ ϕ ) Q 0 ( L w ) N s = R 0 R ( θ 0 ) Q n ( θ 0 ) Q 0 ( L w ) N f .
R RS = L w ( θ = 0 , θ 0 ) E d ( 0 + , θ 0 ) .
R RS = 0 Q n ( θ 0 ) R = ( L w ) N f F 0
R RS = ( L w ) N ex Q 0 Q n ( θ 0 ) R ( θ 0 ) R 0 1 F 0 .
ρ 443 555 = a ( 443 ) b b ( 555 ) a ( 555 ) b b ( 443 ) .
Y = n = 0 5 A n X n ,
A 0 = 0 . 71576 , A 1 = 2 . 48781 , A 2 = 0 . 71844 , A 3 = 0 . 60042 , A 4 = 0 . 29756 , A 5 = 0 . 08105 .

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