Abstract

Mie theory is used to model the backscattering ratio (the ratio of the backscattering coefficient to the total scattering coefficient) of marine particles with the assumption that they follow a Junge–type size distribution. Results show that the backscattering ratio is very sensitive to the presence of submicrometer particles and depends strongly on the shape of the size distribution. However, it is not affected significantly by absorption and does not vary with wavelength over the visible range. The implications for modeling of backscattering and ocean color in terms of phytoplankton pigment concentration are discussed.

© 1994 Optical Society of America

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    [CrossRef] [PubMed]
  2. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  3. A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacteria and algal cells,” J. Mar. Res. 49, 177–202 (1991).
    [CrossRef]
  4. D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  5. H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particles,” Limnol. Oceanogr. 17, 826–832 (1972).
    [CrossRef]
  6. O. B. Brown, H. R. Gordon, “Two component Mie scattering models of Sargasso Sea particles,” Appl. Opt. 12, 2461–2465 (1973).
    [CrossRef] [PubMed]
  7. O. B. Brown, H. R. Gordon, “Size-refractive index distribution of clear coastal water particulates from light scattering,” Appl. Opt. 13, 2874–2881 (1974).
    [CrossRef] [PubMed]
  8. A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lect. Ser. 63, 3.1.1–3.1.76 (1973).
  9. I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
    [CrossRef]
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    [CrossRef]
  11. R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Monogr. Int. Union Geod. Geophys. Paris 10, 11–30 (1961).
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    [CrossRef]
  13. A. Morel, “Optical modeling in the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (1988).
    [CrossRef]
  14. 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, 10909–10924 (1988).
    [CrossRef]
  15. A. Morel, “In-water and remote measurements of ocean color,” Boundary Layer Meterol. 18, 177–201 (1980).
    [CrossRef]
  16. A. Morel, A. Bricaud, “Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 313–327.
    [CrossRef]
  17. A. Morel, A. Bricaud, “Inherent optical properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).
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    [CrossRef]
  21. T. Platt, M. Lewis, R. Geider, “Thermodynamics of the pelagic ecosystem: elelementary closure conditions for biological production in the open ocean,” in Flows of Energy and Materialin Marine Ecosystems, M. J. R. Fasham, ed. (Plenum, New York, 1984), pp. 49–84.
    [CrossRef]
  22. J. Rodriguez, M. Mullin, “Relation between biomass and body weight of plankton in a steady-state oceanic ecosystem,” Limnol. Oceanogr. 31, 361–370 (1986).
    [CrossRef]
  23. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  24. T. Platt, K. Denman, “Organization in the pelagic ecosystem,” Helgol. Wiss. Meeresunters. 30, 575–581 (1977).
    [CrossRef]
  25. D. A. Kiefer, J. Berwald, “A random encounter model for the microbial planktonic community,” Limnol. Oceanogr. 37, 457–467 (1992).
    [CrossRef]
  26. M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
    [CrossRef]
  27. W. G. Sprules, M. Munawar, “Plankton size spectra in relation to ecosystem productivity, size, and perturbation,” Can. J. Fish. Aquat. Sci. 43, 1789–1794 (1986).
    [CrossRef]
  28. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  29. A. H. Morris, “NSWC library of mathematics subroutines,” Rep. NSWC TR 90–21 (Naval Surface Warfare Center, Dahlgren, Va., 1990).
  30. 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]
  31. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, 72–79 (Scripps Institution of Oceanogrpahy, La Jolla, Calif., 1972).
  32. G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).
  33. M. L. Wells, E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
    [CrossRef]
  34. S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  35. A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 1: Cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction,” Appl. Opt. 25, 1235–1244 (1985).
    [CrossRef]
  36. J. C. Kitchen, J. R. V. Zaneveld, H. Pak, “Effect of particle size distribution and chlorophyll content on beam attenuation spectra,” Appl. Opt. 21, 3913–3918 (1982).
    [CrossRef] [PubMed]
  37. J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
    [CrossRef]
  38. Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
    [CrossRef]

1992 (5)

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

D. A. Kiefer, J. Berwald, “A random encounter model for the microbial planktonic community,” Limnol. Oceanogr. 37, 457–467 (1992).
[CrossRef]

M. L. Wells, E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
[CrossRef]

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

1991 (2)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacteria and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

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

1990 (1)

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

1989 (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]

1988 (3)

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

A. Morel, “Optical modeling in the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (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, 10909–10924 (1988).
[CrossRef]

1986 (3)

A. Morel, A. Bricaud, “Inherent optical properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

W. G. Sprules, M. Munawar, “Plankton size spectra in relation to ecosystem productivity, size, and perturbation,” Can. J. Fish. Aquat. Sci. 43, 1789–1794 (1986).
[CrossRef]

J. Rodriguez, M. Mullin, “Relation between biomass and body weight of plankton in a steady-state oceanic ecosystem,” Limnol. Oceanogr. 31, 361–370 (1986).
[CrossRef]

1985 (1)

1983 (1)

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
[CrossRef]

1982 (1)

1980 (2)

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

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

1977 (2)

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

T. Platt, K. Denman, “Organization in the pelagic ecosystem,” Helgol. Wiss. Meeresunters. 30, 575–581 (1977).
[CrossRef]

1975 (1)

1974 (1)

1973 (2)

A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lect. Ser. 63, 3.1.1–3.1.76 (1973).

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

1972 (2)

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

R. W. Sheldon, A. Prakash, W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

1970 (1)

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

1968 (1)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

1961 (1)

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Monogr. Int. Union Geod. Geophys. Paris 10, 11–30 (1961).

Ahn, Y.-H.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacteria and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

Asano, S.

Bader, H.

H. Bader, “The hyperbolic distribution of particles sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
[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, 10909–10924 (1988).
[CrossRef]

Bautista, B.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Berwald, J.

D. A. Kiefer, J. Berwald, “A random encounter model for the microbial planktonic community,” Limnol. Oceanogr. 37, 457–467 (1992).
[CrossRef]

Bird, D. F.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bricaud, A.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

A. Morel, A. Bricaud, “Inherent optical properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

A. Morel, A. Bricaud, “Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 313–327.
[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 semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

Brown, O. B.

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, 10909–10924 (1988).
[CrossRef]

Denman, K.

T. Platt, K. Denman, “Organization in the pelagic ecosystem,” Helgol. Wiss. Meeresunters. 30, 575–581 (1977).
[CrossRef]

Dickie, P.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

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, 10909–10924 (1988).
[CrossRef]

Geider, R.

T. Platt, M. Lewis, R. Geider, “Thermodynamics of the pelagic ecosystem: elelementary closure conditions for biological production in the open ocean,” in Flows of Energy and Materialin Marine Ecosystems, M. J. R. Fasham, ed. (Plenum, New York, 1984), pp. 49–84.
[CrossRef]

Goldberg, E. D.

M. L. Wells, E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

Gordon, H. R.

Hara, S.

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jacobs, M. M.

Jonasz, M.

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
[CrossRef]

Kiefer, D. A.

D. A. Kiefer, J. Berwald, “A random encounter model for the microbial planktonic community,” Limnol. Oceanogr. 37, 457–467 (1992).
[CrossRef]

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

Kitchen, J. C.

J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
[CrossRef]

J. C. Kitchen, J. R. V. Zaneveld, H. Pak, “Effect of particle size distribution and chlorophyll content on beam attenuation spectra,” Appl. Opt. 21, 3913–3918 (1982).
[CrossRef] [PubMed]

Kogure, K.

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

Koike, I.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

Kopkay, P.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Kullenberg, G.

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

Lewis, M.

T. Platt, M. Lewis, R. Geider, “Thermodynamics of the pelagic ecosystem: elelementary closure conditions for biological production in the open ocean,” in Flows of Energy and Materialin Marine Ecosystems, M. J. R. Fasham, ed. (Plenum, New York, 1984), pp. 49–84.
[CrossRef]

Li, W. K. W.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Longhurst, A. R.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Morel, A.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacteria and algal cells,” J. Mar. Res. 49, 177–202 (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]

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

A. Morel, A. Bricaud, “Inherent optical properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

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

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

A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lect. Ser. 63, 3.1.1–3.1.76 (1973).

A. Morel, A. Bricaud, “Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 313–327.
[CrossRef]

Morris, A. H.

A. H. Morris, “NSWC library of mathematics subroutines,” Rep. NSWC TR 90–21 (Naval Surface Warfare Center, Dahlgren, Va., 1990).

Mugnai, A.

Mullin, M.

J. Rodriguez, M. Mullin, “Relation between biomass and body weight of plankton in a steady-state oceanic ecosystem,” Limnol. Oceanogr. 31, 361–370 (1986).
[CrossRef]

Munawar, M.

W. G. Sprules, M. Munawar, “Plankton size spectra in relation to ecosystem productivity, size, and perturbation,” Can. J. Fish. Aquat. Sci. 43, 1789–1794 (1986).
[CrossRef]

Pak, H.

Partonsky, F.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, 72–79 (Scripps Institution of Oceanogrpahy, La Jolla, Calif., 1972).

Platt, T.

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

T. Platt, K. Denman, “Organization in the pelagic ecosystem,” Helgol. Wiss. Meeresunters. 30, 575–581 (1977).
[CrossRef]

T. Platt, M. Lewis, R. Geider, “Thermodynamics of the pelagic ecosystem: elelementary closure conditions for biological production in the open ocean,” in Flows of Energy and Materialin Marine Ecosystems, M. J. R. Fasham, ed. (Plenum, New York, 1984), pp. 49–84.
[CrossRef]

Prakash, A.

R. W. Sheldon, A. Prakash, W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Monogr. Int. Union Geod. Geophys. Paris 10, 11–30 (1961).

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]

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

Rodriguez, J.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

J. Rodriguez, M. Mullin, “Relation between biomass and body weight of plankton in a steady-state oceanic ecosystem,” Limnol. Oceanogr. 31, 361–370 (1986).
[CrossRef]

Ruiz, J.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Sathyendranath, S.

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 surfaces of the ocean: a model for application and in the interior in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
[CrossRef]

Sato, M.

Sheldon, R. W.

R. W. Sheldon, A. Prakash, W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

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 semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
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Sprules, W. G.

W. G. Sprules, M. Munawar, “Plankton size spectra in relation to ecosystem productivity, size, and perturbation,” Can. J. Fish. Aquat. Sci. 43, 1789–1794 (1986).
[CrossRef]

Stramski, D.

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

R. W. Sheldon, A. Prakash, W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

Terauchi, T.

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wells, M.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
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Wells, M. L.

M. L. Wells, E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
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Wiscombe, W. J.

Zaneveld, J. R. V.

J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
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J. C. Kitchen, J. R. V. Zaneveld, H. Pak, “Effect of particle size distribution and chlorophyll content on beam attenuation spectra,” Appl. Opt. 21, 3913–3918 (1982).
[CrossRef] [PubMed]

Appl. Opt. (6)

Boundary Layer Meterol. (1)

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

Can. Bull. Fish. Aquat. Sci. (1)

A. Morel, A. Bricaud, “Inherent optical properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

Can. J. Fish. Aquat. Sci. (1)

W. G. Sprules, M. Munawar, “Plankton size spectra in relation to ecosystem productivity, size, and perturbation,” Can. J. Fish. Aquat. Sci. 43, 1789–1794 (1986).
[CrossRef]

Deep-Sea Res. (3)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kopkay, F. Partonsky, B. Bautista, J. Ruiz, M. Wells, D. F. Bird, “Submicron particles in northwest Atlantic shelf water,” Deep-Sea Res. 39, 1–7, (1992).
[CrossRef]

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

Helgol. Wiss. Meeresunters. (1)

T. Platt, K. Denman, “Organization in the pelagic ecosystem,” Helgol. Wiss. Meeresunters. 30, 575–581 (1977).
[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).
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J. Geophys. Res. (4)

H. Bader, “The hyperbolic distribution of particles sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
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S. Sathyendranath, T. Platt, “The spectral irradiance field at the surfaces of the ocean: a model for application and in the interior in oceanography and remote sensing,” J. Geophys. Res. 93, 9270–9280 (1988).
[CrossRef]

A. Morel, “Optical modeling in the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (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, 10909–10924 (1988).
[CrossRef]

J. Mar. Res. (1)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacteria and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

Limnol. Oceanogr. (6)

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

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

R. W. Sheldon, A. Prakash, W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

J. Rodriguez, M. Mullin, “Relation between biomass and body weight of plankton in a steady-state oceanic ecosystem,” Limnol. Oceanogr. 31, 361–370 (1986).
[CrossRef]

D. A. Kiefer, J. Berwald, “A random encounter model for the microbial planktonic community,” Limnol. Oceanogr. 37, 457–467 (1992).
[CrossRef]

J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
[CrossRef]

Mar. Chem. (1)

M. L. Wells, E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

Monogr. Int. Union Geod. Geophys. Paris (1)

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Monogr. Int. Union Geod. Geophys. Paris 10, 11–30 (1961).

Nature (London) (1)

I. Koike, S. Hara, T. Terauchi, K. Kogure, “Role of submicrometer particles in the ocean,” Nature (London) 345, 242–244(1990).
[CrossRef]

Optics of the Sea (1)

A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lect. Ser. 63, 3.1.1–3.1.76 (1973).

Prog. Oceanogr. (1)

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

Tellus (1)

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
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Other (7)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. H. Morris, “NSWC library of mathematics subroutines,” Rep. NSWC TR 90–21 (Naval Surface Warfare Center, Dahlgren, Va., 1990).

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

T. Platt, M. Lewis, R. Geider, “Thermodynamics of the pelagic ecosystem: elelementary closure conditions for biological production in the open ocean,” in Flows of Energy and Materialin Marine Ecosystems, M. J. R. Fasham, ed. (Plenum, New York, 1984), pp. 49–84.
[CrossRef]

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, 72–79 (Scripps Institution of Oceanogrpahy, La Jolla, Calif., 1972).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

A. Morel, A. Bricaud, “Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 313–327.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Effect of the lower limit in the particle-size distribution Dmin on the particle backscattering ratio b ˜ bp for m = 1.05–0.001i and Dmax = 200 μm. The results are given for three wavelengths (λ) in the visible range. (b) Effect of the maximum particle diameter of the size distribution Dmax, on the particle-backscattering ratio.

Fig. 2
Fig. 2

Effect of the real part of the refractive index n on the backscattering ratio b ˜ bp.

Fig. 3
Fig. 3

Effect of the imaginary part of the refractive index n′ on the backscattering ratio b ˜ bp.

Fig. 4
Fig. 4

The backscattering ratio b ˜ bp as a function of wavelength for particles with a Junge–type size distribution and a diameter range 0.01 ≤ D ≤ 200 μm.

Fig. 5
Fig. 5

Effect of the exponent ξ in the Junge–type size distribution on the backscattering ratio b ˜ bp for different values of the refractive index m.

Fig. 6
Fig. 6

(a) The backscattering ratio of nonchlorophyllous particles b ˜ bx as a function of phytoplankton pigment concentration (chlorophyll a + phaeopigments). The b ˜ bx values were derived when a model of reflectance was fitted to observed reflectance spectra.30 (b) The backscattering ratio of total particles b ˜ bp for the same data set [obtained from Eq. (13) in the text] as a function of pigment concentration. The stations plotted represent case 1 waters and correspond to the cruises of Antiprod, Discoverer, and Cineca V (Ref. 30). Stations 16, 35, 47, and 72 of the Cineca V cruise were excluded because they seem to be in case 2 waters.

Equations (14)

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b b = b bw + b bp ,
b bp = b ˜ bp × b p ,
b ˜ bp = 0 Q b b ( m , x ) x 2 f ( x ) d x 0 Q b ( m , x ) x 2 f ( x ) d x ,
x = π D n w λ ,
m = n - i n ,
f ( D ) = K D - ξ ,
K = ( ξ - 1 ) ( D min 1 - ξ - D max 1 - ξ ) ,
lim x 0 f ( x ) = lim D 0 f ( D ) = .
lim x f ( x ) = lim D f ( D ) = 0 ,
R ( λ ) = 0.33 b b ( λ ) a ( λ )
b b = b bw + b ˜ bc b c + b ˜ bx b x ,
b c [ 550 ] = 0.12 C 0.62 ,
b ˜ bp = b bc χ + b ˜ bx ( 1 - χ ) ,
b ˜ bp = 0.78 - 0.42 log 10 C .

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