Abstract

The bidirectionality of the upward radiance field in oceanic case 1 waters has been reinvestigated by incorporation of revised parameterizations of inherent optical properties as a function of the chlorophyll concentration (Chl), considering Raman scattering and making the particle phase function shape (β̃p) continuously varying along with the Chl. Internal consistency is thus reached, as the decrease in backscattering probability (for increasing Chl) translates into a correlative change in β̃p. The single particle phase function (previously used) precluded a realistic assessment of bidirectionality for waters with Chl > 1 mg m-3. This limitation is now removed. For low Chl, Raman emissions significantly affect the radiance field. For moderate Chl (0.1–1 mg m-3), new and previous bidirectional parameters remain close. The ocean reflectance anisotropy has implications in ocean color remote-sensing problems, in derivation of coherent water-leaving radiances, in associated calibration–validation activities, and in the merging of data obtained under various geometrical configurations.

© 2002 Optical Society of America

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2002 (1)

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

2001 (4)

G. Zibordi, J.-F. Berthon, “Relationship between the Q-factor and seawater optical properties in a coastal region,” Limnol. Oceanogr. 46, 1130–1140 (2001).
[CrossRef]

H. Loisel, A. Morel, “Non-isotropy of the upward radiance field in typical coastal (Case 2) waters,” Int. J. Remote Sens. 22, 275–295 (2001).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

1999 (1)

E. Aas, N. K. Hojerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

1998 (2)

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[CrossRef]

1996 (3)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2248 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
[CrossRef] [PubMed]

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, 13143–13151 (1995).
[CrossRef]

1994 (1)

1993 (2)

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, 7884–7504 (1993).
[CrossRef]

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

1991 (2)

1990 (1)

W. W. Gregg, K. L. Carder, “A simple spectral solar model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

1989 (2)

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

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

1988 (2)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case 1 waters),” J. Geophys. Res. 93, 10749–10768 (1988).
[CrossRef]

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]

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

1981 (1)

1974 (1)

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

1973 (1)

1972 (1)

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

1960 (1)

J. E. Tyler, “Radiance distribution as a function of depth in a underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–412 (1960).

1955 (1)

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

Aas, E.

E. Aas, N. K. Hojerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2248 (1996).
[CrossRef]

Antoine, D.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Bartlett, J. S.

Berthon, J.-F.

G. Zibordi, J.-F. Berthon, “Relationship between the Q-factor and seawater optical properties in a coastal region,” Limnol. Oceanogr. 46, 1130–1140 (2001).
[CrossRef]

Boss, E.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Bricaud, A.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

O. B. Brown, H. R. Gordon, “Two component Mie scattering models of Sargasso Sea particles,” Appl. Opt. 12, 2461–2465 (1973).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

Carder, K. L.

W. W. Gregg, K. L. Carder, “A simple spectral solar model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (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]

Claustre, H.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

Cox, C.

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

Esaias, W. E.

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

Feldman, G. C.

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Gentili, B.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
[CrossRef] [PubMed]

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, 13143–13151 (1995).
[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, 7884–7504 (1993).
[CrossRef]

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]

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, 7884–7504 (1993).
[CrossRef]

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (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]

O. B. Brown, H. R. Gordon, “Two component Mie scattering models of Sargasso Sea particles,” Appl. Opt. 12, 2461–2465 (1973).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

Gregg, W. W.

W. W. Gregg, K. L. Carder, “A simple spectral solar model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Haltrin, V. I.

V. I. Haltrin, G. Kattawar, “Light fields with Raman scattering and fluorescence in sea water,” Tech. Rep. (Department of Physics, Texas A & M University, College Station, Texas, 1991).

Hojerslev, N. K.

E. Aas, N. K. Hojerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

Hooker, S. B.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Jin, Z.

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, 7884–7504 (1993).
[CrossRef]

Kattawar, G.

V. I. Haltrin, G. Kattawar, “Light fields with Raman scattering and fluorescence in sea water,” Tech. Rep. (Department of Physics, Texas A & M University, College Station, Texas, 1991).

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, 7884–7504 (1993).
[CrossRef]

Kiefer, D. A.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Kirk, J. T. O.

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]

Kopelevich, O. V.

O. V. Kopelevich, “Small parameter model of optical properties of seawater,” in Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), Vol. 1, Chap. 8 (in Russian).

Labs, D.

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

Leblanc, K.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

Loisel, H.

H. Loisel, A. Morel, “Non-isotropy of the upward radiance field in typical coastal (Case 2) waters,” Int. J. Remote Sens. 22, 275–295 (2001).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Maritorena, S.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

McClain, C. R.

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Mobley, C. D.

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, 7884–7504 (1993).
[CrossRef]

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

Morel, A.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

H. Loisel, A. Morel, “Non-isotropy of the upward radiance field in typical coastal (Case 2) waters,” Int. J. Remote Sens. 22, 275–295 (2001).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
[CrossRef] [PubMed]

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, 13143–13151 (1995).
[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, 7884–7504 (1993).
[CrossRef]

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]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case 1 waters),” J. Geophys. Res. 93, 10749–10768 (1988).
[CrossRef]

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

Munk, W.

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

Neckel, H.

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

Oubelkheir, K.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

Pak, H.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

Pegau, W. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Rep. 510, Ref. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Platt, T.

Preisendorfer, R. W.

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea,” in The Sea, M. N. Hill, ed. (Wiley-Interscience, New York, 1962), Vol. 1, pp. 397–448.

Queginer, B.

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

Reinersman, P.

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, 7884–7504 (1993).
[CrossRef]

Roach, D. M.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

Sathyendranath, S.

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

Stamnes, K.

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, 7884–7504 (1993).
[CrossRef]

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, 7884–7504 (1993).
[CrossRef]

Stramski, D.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Twardowski, M. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Tyler, J. E.

J. E. Tyler, “Radiance distribution as a function of depth in a underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–412 (1960).

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea,” in The Sea, M. N. Hill, ed. (Wiley-Interscience, New York, 1962), Vol. 1, pp. 397–448.

Ulloa, O.

Vodacek, A.

Voss, K. J.

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[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, 13143–13151 (1995).
[CrossRef]

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

Zaneveld, J. R. V.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

Zaneveld, R. V.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Zibordi, G.

G. Zibordi, J.-F. Berthon, “Relationship between the Q-factor and seawater optical properties in a coastal region,” Limnol. Oceanogr. 46, 1130–1140 (2001).
[CrossRef]

Appl. Opt. (8)

Bull. Scripps Inst. Oceanogr. (1)

J. E. Tyler, “Radiance distribution as a function of depth in a underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–412 (1960).

Geophys. Res. Lett. (1)

H. Claustre, A. Morel, S. B. Hooker, D. Antoine, K. Oubelkheir, A. Bricaud, K. Leblanc, B. Queginer, S. Maritorena, “Is desert dust making oligotrophic waters greener?” Geophys. Res. Lett. 29, 10.1029/2001GL014056 (2002).
[CrossRef]

Int. J. Remote Sens. (1)

H. Loisel, A. Morel, “Non-isotropy of the upward radiance field in typical coastal (Case 2) waters,” Int. J. Remote Sens. 22, 275–295 (2001).
[CrossRef]

J. Geophys. Res. (7)

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case 1 waters),” J. Geophys. Res. 93, 10749–10768 (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, 13143–13151 (1995).
[CrossRef]

E. Aas, N. K. Hojerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

J. Mar. Res. (1)

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

J. Plankton Res. (1)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2248 (1996).
[CrossRef]

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

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Limnol. Oceanogr. (6)

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

W. W. Gregg, K. L. Carder, “A simple spectral solar model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

G. Zibordi, J.-F. Berthon, “Relationship between the Q-factor and seawater optical properties in a coastal region,” Limnol. Oceanogr. 46, 1130–1140 (2001).
[CrossRef]

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[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]

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

Opt. Eng. (1)

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

Prog. Oceanogr. (1)

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Sol. Phys. (1)

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

Other (10)

J. L. Mueller, G. S. Fargion, eds., “Ocean optics protocols for satellite ocean color sensor validation, revision 3,” (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea,” in The Sea, M. N. Hill, ed. (Wiley-Interscience, New York, 1962), Vol. 1, pp. 397–448.

SeaWiFS (Orbital Sciences Corp., NASA) is an ocean color sensor, operating since September 1997. See also S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “An overview of SeaWiFS and ocean color,” NASA Tech. Memo. 1045661, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

The PROSOPE cruise (4 September–4 October 1999), on board the research vessel Thalassa, started in Agadir, Morocco, and ended in Toulon, France.

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

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Rep. 510, Ref. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

O. V. Kopelevich, “Small parameter model of optical properties of seawater,” in Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), Vol. 1, Chap. 8 (in Russian).

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

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

V. I. Haltrin, G. Kattawar, “Light fields with Raman scattering and fluorescence in sea water,” Tech. Rep. (Department of Physics, Texas A & M University, College Station, Texas, 1991).

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Figures (20)

Fig. 1
Fig. 1

Spectral irradiance reflectance below the surface in oceanic waters with two differing Chls, as indicated. Solid curves, field determinations; dashed curves, modeled values (Morel and Maritorena11); and dotted curves, modeled values when the backscattering efficiency is given the constant value 1.9% (derived from Petzold phase function) instead of that derived from Eq. (1). (a) 9 September 1999, Atlantic Ocean, Moroccan upwelling area (10.02 °W, 31.01 °N); (b) 18–22 November 1994, Pacific Ocean (150 °W, 5 °S). Note that the chlorophyll fluorescence peak, around 683 nm, clearly seen in the measured reflectances, is not modeled.

Fig. 2
Fig. 2

Backscattering probability of marine particles as a function of the Chl. Curve 1, from Eq. (1), and the superimposed circles derived from the phase functions shown in Fig. 3(a), by appropriate integration; curve 2, from the Kopelevich–Haltrin–Kattawar model [namely, from Eqs. (3.43) and (3.45), and Table 3.14 of Mobley21]; curve 3, also from the Russian model by integration of the particle phase functions [Eq. (3.38) and Table 3.13 of Mobley21]; curve 4, from Gordon et al.12; curve 5, from Twardowski et al.15; and curve 6, from Ulloa et al.14

Fig. 3
Fig. 3

(a) Phase functions for the populations of small and large particles (see text); in between, phase functions for their mixtures varying along with the Chl, according to Eqs. (3)–(5). The particle phase function derived21 from Petzold’s measurements7 is also displayed. (b) Global phase functions at λ = 550 nm [Eq. (6)] merging molecular and particle scattering for various Chls, as indicated.

Fig. 4
Fig. 4

Ratio ℜ0/ℜ(θ, w) is plotted as a function of θ, for four wind speeds; θ c ′ is the critical angle. The θ′ scale in relation to the θ scale is also shown; the remote-sensing (RS) domain assumes that the maximal viewing angle (θ v ) is 47°, corresponding to θ ≅ 54° (θ′ ≅ 37°), for a satellite at an altitude of approximately 705 km, operating without tilt (solid vertical line). With a tilt of 20° [Sea-viewing Wide Field-of-view Sensor (SeaWiFS)], values as high as θ ≅ 76° and θ′ ≅ 46° occur for the edges of the full swath (dashed line).

Fig. 5
Fig. 5

Concomitant spectral variations of ϖ [or ñ, Eq. (15)] and η b [Eq. (16)] for various Chls; reference wavelengths dealt with in the present study are indicated.

Fig. 6
Fig. 6

(a) Comparison of the new f values, when the Raman emission is not included, with the previous ones (MG-96); the Chl is limited to 3 mg m-3. (b) New f values, computed with or without Raman inelastic scattering (the Chl is as high as 10 mg m-3).

Fig. 7
Fig. 7

(a) Spectral values of the factor f 0 for various Chls, as indicated. (b) Evolution of the f factor with the solar zenith angle, for six Chl values and four selected wavelengths, as indicated.

Fig. 8
Fig. 8

(a) Comparison of the new values of the bidirectional function Q, when the Raman emission is not included, with the previous ones (MG-96); the Chl is limited to 3 mg m-3. (b) New Q values, computed with and without Raman inelastic scattering (the Chl is as high as 10 mg m-3). The departures (lowering of the Q values) resulting from the Raman influence when the Chl is low enough are identified.

Fig. 9
Fig. 9

(a) Spectral values of the Q 0 function computed with and without the Raman emission for six Chl values, as indicated. (b) Evolution of the Q n function with increasing Chls for various wavelengths and solar zenith angles, as indicated. (c) Q n as a function of the solar zenith angle for various wavelengths and Chls [same data as in (b)]; the open symbols correspond to Eq. (17).

Fig. 10
Fig. 10

Polar representation in the solar principal plane of the upward radiance field, normalized by the upward irradiance [i.e., the ratio L u /E u = Q -1, Eq. (10)] for three Chl values (rows) and two wavelengths (columns). This polar diagram represents the normalized radiances as vectors, the length of which corresponds to magnitude, ending at the center. The solar zenith angle is 45° in air (31.8° in water), and the ñ and η b values for each case are indicated, as well as the critical angle (48°).

Fig. 11
Fig. 11

Spectral values of the f 0/Q 0 ratio for the six Chls, as indicated.

Fig. 12
Fig. 12

Selected examples of the f/ Q ratio as a function of θ′ (restricted to ±50°) within the principal plane (ϕ = 0 or π) and within the perpendicular half-plane (ϕ = π/2). This figure is to be compared with Fig. 6 of MG-96 (a similar figure for other Chls is also provided in Ref. 34).

Fig. 13
Fig. 13

Evolution of the f 0/f ratio with the Chl and for solar angles as indicated by the shaded areas (the values for θ s = 60°, which overlap those for 45° and 75°, are not displayed); the symbols are for the various wavelengths.

Fig. 14
Fig. 14

Variations in the Q/ Q 0 ratio. The horizontal scale is based on the Q 0 (Chl, λ) values, which allow the various Chl domains to be discriminated (shaded or white vertical bands). Each band contains six vertical lines corresponding to the six wavelengths (not indicated); each vertical line corresponds to an accumulation of dots displaying the Q/ Q 0 values, for all θ s , ϕ, and θ′ values.

Fig. 15
Fig. 15

Variations in the (ℜ0/ℜ)(f 0/Q 0)(f/ Q)-1 quantity [the corrective term appearing in Eq. (13)], plotted as a function of the Chl. (a) The vertical bars are made of the dots corresponding to all ϕ and λ values and to the θ′ values less than 37° (cf. Fig. 4); The six vertical bars in each grouping correspond to the six solar angles (θ s = 0°, 15°, 30°, 45°, 60°, and 75°), whatever λ. (b) As in (a) except for the grouping that now corresponds to the discrete wavelengths (412.5, 442.5, 490, 510, 560, 620, 660 nm), whatever θ s . The (ℜ0/ℜ) values used for this figure are those computed for a wind speed of 4 m s-1. With increasing speed, all the vertical bars migrate slightly upward; especially the upper values (which always correspond to large θ′) are significantly enhanced. The corresponding lower and upper ends of the bars for W = 16 m s-1 are shown as open circles.

Fig. 16
Fig. 16

Upward radiance field L u (θ′) (arbitrary units) at a depth of 5 m and λ = 465 nm for various Sun zenith angles θ s . The symbols are reproduced from Fig. 4 of Ref. 36 and represent data obtained in the Mediterranean Sea (south of Sardinia, 2 July 1971). The curves have been computed for the same θ s and with Chl = 0.1 mg m-3. The vertical log scale (arbitrary units) allows the two kinds of result to be put in approximate coincidence by translation, without changing the respective positions of either the theoretical curves or the experimental data.

Fig. 17
Fig. 17

SeaWiFS normalized water-leaving radiances at λ = 443 nm, (a) before and (b) after bidirectional corrections (see text). The circle represents the average value derived from field reflectance measurements (at 22 °E, 34 °N) carried out during the same period. The Chl in this zone is below 0.1 mg m-3. The diamonds show the extreme pixels considered near the swath edge, before and after correction.

Fig. 18
Fig. 18

Selected examples of the computed f factor plotted as a function of (1 - cos θ s ) and the corresponding linear fit valid within the interval 0 < θ s < 60° [Eq. (B1) and Table 1].

Fig. 19
Fig. 19

Selected examples of computed Q n values plotted as a function of (1 - cos θ s ) and corresponding linear fits valid within the interval 0 < θ s < 60° [Eq. (B2) and Table 2].

Fig. 20
Fig. 20

Selected examples of computed f/ Q n values plotted as a function of (1 - cos θ s ) and corresponding linear fit (Table 3).

Tables (3)

Tables Icon

Table 1 f 0 Parameter and the Associated Slope of Its Relationship to the Cosine of the Sun Zenith Angle

Tables Icon

Table 2 Q 0 Parameter and the Associated Slope of Its Relationship to the Cosine of the Sun Zenith Angle

Tables Icon

Table 3 f 0 /Q 0 Ratio and the Associated Slope of Its Relationship to the Cosine of the Sun Zenith Angle

Equations (24)

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

bbp/bp=b˜bp=0.002+0.010.5-0.25 log10Chl.
Nx=Kx-j,
β˜pψ, Chl=αsChlβ˜p,sψ+αlChlβ˜p,lψ,
αs+αl=1,
αsChl=0.8550.5-0.25 log10Chl.
β˜p+wψ, Chl=bpChlβ˜pψ, Chl+bwβ˜wψ/bpChl+bw,
bw550=1.93×10-4m-1, β˜wψ=3/4π3+p1+p cos2ψ,
bp550, Chl=0.416Chl0.766
bwλ=bw550λ/550-4.3.
Lw0+, θs, τa, W, θ, ϕ, λ, IOP=Ed0+, θs, τa, λ×θ, Wfθs, τa, W, IOPQθs, τa, W, θ, ϕ, IOPbba.
Q=Eu0-/Lu0-, θ, ϕ,
R=Eu0-/Ed0-=fbb/a.
LwλN=Lw0+, θ, ϕ, λ/Ed0+, λF0λ,
LwNex=LwN0θ, Wf0τa, W, IOPQ0τa, W, IOP×fθs, τa, W, IOPQθs, θ, ϕ, τa, W, IOP-1,
bpλ, Chl/bp550, Chl=λ/550v,
v=1/2log10Chl-0.3,
v=0,
ñ=1-ϖ-1,
ηb=bbw/bbw+bbp,
Qn=5.20±0.24-1.82±0.035cos θs.
fθs, λ, Chl=f00, λ, Chl+Sfλ, Chl1-cos θs.
Qnθs, λ, Chl=Q00, λ, Chl+SQnλ, Chl1-cos θs,
LwNex=LwNf0Chl, λQ0Chl, λfθs, Chl, λQnθs, Chl, λ-1,
f/Qnθs, λ, Chl=f0/Q00, λ, Chl+Sf/Qλ, Chl1-cos θs.

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