Abstract

Mie theory is used to study the influence of the particle-size distribution (PSD) on the backscattering ratio for case 1 and 2 waters. Several in situ measured PSDs from coastal water and the open ocean, representing typical case 2 and 1 waters, were used in this investigation. Calculation of the backscattering ratio requires integration of the PSD over a much broader size range than is usually measured. Consequently extrapolation from fitted data is necessary. To that purpose the measured data are fitted with hyperbolic (Junge) and the two-component model of the PSD. It is shown that the result of extrapolation, hence the backscattering ratio, critically depends on the chosen PSD model. For a particular PSD model the role of submicrometer particles and the applied integration limits on the backscattering ratio is discussed. The use of the hyperbolic PSD model largely overestimates the number of small (submicrometer) particles that significantly contribute to backscattering and consequently leads to an erroneously high backscattering ratio. The two-component model proves to be an adequate PSD model for use in backscattering/scattering calculations providing satisfactory results complying with experimental data. The results are relevant for the inversion of remotely sensed data and the prediction of optical properties and the concentration of phytoplankton pigments, suspended sediment, and yellow substance.

© 2002 Optical Society of America

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2001 (1)

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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

2000 (2)

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

Z. Lee, K. L. Carder, “Band-ratio or spectral-curvature algorithms for satellite remote sensing?” Appl. Opt. 39, 4377–4380(2000).
[CrossRef]

1999 (2)

1998 (2)

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

1997 (1)

1996 (2)

M. Jonasz, G. Fournier, “Approximation of the size distribution of marine particles by a sum of lognormal functions,” Limnol. Oceanogr. 41, 744–754 (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 (2)

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13,135–13,142(1995)
[CrossRef]

D. Risović, M. Martinis, “A comparative analysis of sea-particle-size distribution models,” Fiz. B 4 (2), 111–120 (1995).

1994 (2)

1993 (1)

D. Risović, “Two component model of the sea particle size distribution,” Deep-Sea Res. Part I Oceanogr. Res. Papers 40, 1459–1473 (1993).
[CrossRef]

1991 (2)

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

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

1990 (1)

J. C. Kitchen, J. R. Zaneveld, “On the noncorrelation of the vertical structure of light scattering and chlorophyll a in case I waters,” J. Geophys. Res. 95, 20,237–20,246 (1990).
[CrossRef]

1988 (1)

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

1986 (4)

M. Jonasz, H. Prandtke, “Comparison of measured and computed light scattering in the Baltic,” Tellus Ser. B 38, 144–157 (1986).
[CrossRef]

R. W. Spinrad, J. F. Brown, “Relative real refractive index of marine microorganisms: a technique for flow cytometric estimation,” Appl. Opt. 25, 1930–1934 (1986).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

H. R. Gordon, “Ocean color remote sensing: influence of the particle phase function and the solar zenith angle,” Eos (Trans. Am. Geophys. Union) 14, 1055–1061(1986).

1983 (1)

M. Jonasz, “Particle size distributions in the Baltic,” Tellus Ser B 35, 345–358 (1983).
[CrossRef]

1982 (1)

1981 (2)

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

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

1980 (1)

R. Reuter, “Characterization of marine particle suspensions by light scattering I (1980). Numerical predictions from Mie theory,” Oceanologica Acta 3, 317–332 (1980).

1977 (2)

J. E. Harris, “Characterization of suspended matter in the Gulf of Mexico—II Particle size analysis of suspended matter from deep water,” Deep-Sea Res. 24, 1055–1061 (1977).
[CrossRef]

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

1975 (1)

1974 (1)

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction of particles suspended in the ocean,” J. Geophys. Res. 77, 2677–2680 (1974).
[CrossRef]

1972 (1)

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

1971 (2)

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Mie scattering by suspended clay particles,” J. Geophys. Res. 76, 5065–5069 (1971).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Particle size distribution in the Eastern equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

1970 (1)

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

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Arnone, R. A.

Babin, M.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Bader, H.

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

Baker, K. S.

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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

A. H. Barnard, J. R. V. Zaneveld, W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117(1999).
[CrossRef]

Beardsley, G. F.

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Particle size distribution in the Eastern equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Mie scattering by suspended clay particles,” J. Geophys. Res. 76, 5065–5069 (1971).
[CrossRef]

Bohren, C. F.

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

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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

Bricaud, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

Brown, J. F.

Brown, O. B.

Carder, K. L.

Z. Lee, K. L. Carder, “Band-ratio or spectral-curvature algorithms for satellite remote sensing?” Appl. Opt. 39, 4377–4380(2000).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Claustre, H.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Fournier, G.

M. Jonasz, G. Fournier, “Approximation of the size distribution of marine particles by a sum of lognormal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

Garver, S. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Gentili, B.

Gordon, H. R.

H. R. Gordon, “Ocean color remote sensing: influence of the particle phase function and the solar zenith angle,” Eos (Trans. Am. Geophys. Union) 14, 1055–1061(1986).

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationship between the inherent and apparent optical properties of flat homogenous 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: a review,” in Lecture Notes on Coastal and Estuarine Studies, M. Bowman, ed. (Springer-Verlag, Berlin, 1983).

Gould, R. W.

Harris, J. E.

J. E. Harris, “Characterization of suspended matter in the Gulf of Mexico—II Particle size analysis of suspended matter from deep water,” Deep-Sea Res. 24, 1055–1061 (1977).
[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, G. Fournier, “Approximation of the size distribution of marine particles by a sum of lognormal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

M. Jonasz, H. Prandtke, “Comparison of measured and computed light scattering in the Baltic,” Tellus Ser. B 38, 144–157 (1986).
[CrossRef]

M. Jonasz, “Particle size distributions in the Baltic,” Tellus Ser B 35, 345–358 (1983).
[CrossRef]

Junge, C. E.

C. E. Junge, Air Chemistry and Radioactivity (Academic, New York, 1963), p.382

Kiefer, D. A.

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. Zaneveld, “On the noncorrelation of the vertical structure of light scattering and chlorophyll a in case I waters,” J. Geophys. Res. 95, 20,237–20,246 (1990).
[CrossRef]

Lee, Z.

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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

Mahru, M.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Maritorena, S.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Martinis, M.

D. Risović, M. Martinis, “A comparative analysis of sea-particle-size distribution models,” Fiz. B 4 (2), 111–120 (1995).

Martinolich, P. M.

McClain, C.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Mitchell, B. G.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Morel, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (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, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

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

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery: a review,” in Lecture Notes on Coastal and Estuarine Studies, M. Bowman, ed. (Springer-Verlag, Berlin, 1983).

O’Reilly, J. E.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Pak, H.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction of particles suspended in the ocean,” J. Geophys. Res. 77, 2677–2680 (1974).
[CrossRef]

Pak, H. J.

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Particle size distribution in the Eastern equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Mie scattering by suspended clay particles,” J. Geophys. Res. 76, 5065–5069 (1971).
[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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

A. H. Barnard, J. R. V. Zaneveld, W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117(1999).
[CrossRef]

Pennock, J. R.

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Petzold, T. J.

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

Platt, T.

Prakash, A.

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

Prandtke, H.

M. Jonasz, H. Prandtke, “Comparison of measured and computed light scattering in the Baltic,” Tellus Ser. B 38, 144–157 (1986).
[CrossRef]

Prieur, L.

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

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

Reuter, R.

R. Reuter, “Characterization of marine particle suspensions by light scattering I (1980). Numerical predictions from Mie theory,” Oceanologica Acta 3, 317–332 (1980).

Risovic, D.

D. Risović, M. Martinis, “A comparative analysis of sea-particle-size distribution models,” Fiz. B 4 (2), 111–120 (1995).

D. Risović, “Two component model of the sea particle size distribution,” Deep-Sea Res. Part I Oceanogr. Res. Papers 40, 1459–1473 (1993).
[CrossRef]

Roach, D. M.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction of particles suspended in the ocean,” J. Geophys. Res. 77, 2677–2680 (1974).
[CrossRef]

Sathyendranath, S.

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

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

Sheldon, R. W.

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

R. W. Sheldon, Government of Canada Fisheries Oceans Northwest Atlantic Fisheries Centre St. John’s, Newfoundland, A1C5x1 (personal communication, 1990).

Siegel, D. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

Smith, R. C.

Spinrad, R. W.

Stramski, D.

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

Stumpf, R. P.

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Sutclife, W. H.

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

Sydor, M.

Tassan, S.

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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

Ulloa, O.

Zaneveld, J. R.

J. C. Kitchen, J. R. Zaneveld, “On the noncorrelation of the vertical structure of light scattering and chlorophyll a in case I waters,” J. Geophys. Res. 95, 20,237–20,246 (1990).
[CrossRef]

Zaneveld, J. R. V.

A. H. Barnard, J. R. V. Zaneveld, W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117(1999).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13,135–13,142(1995)
[CrossRef]

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

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction of particles suspended in the ocean,” J. Geophys. Res. 77, 2677–2680 (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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Particle size distribution in the Eastern equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Mie scattering by suspended clay particles,” J. Geophys. Res. 76, 5065–5069 (1971).
[CrossRef]

Appl. Opt. (12)

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationship between the inherent and apparent optical properties of flat homogenous ocean,” Appl. Opt. 14, 417–427(1975).
[CrossRef] [PubMed]

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

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

R. W. Spinrad, J. F. Brown, “Relative real refractive index of marine microorganisms: a technique for flow cytometric estimation,” Appl. Opt. 25, 1930–1934 (1986).
[CrossRef] [PubMed]

S. Tassan “Local algorithms using SeaWiFS data for the retrieval of phytoplankton, pigments, suspended sediment, and yellow substance in coastal waters,” Appl. Opt. 33, 2369–2378(1994).
[CrossRef] [PubMed]

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

M. Sydor, R. A. Arnone, “Effect of suspended particulate and dissolved organic matter on remote sensing of coastal and riverine waters,” Appl. Opt. 36, 6905–6912 (1997).
[CrossRef]

A. H. Barnard, J. R. V. Zaneveld, W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117(1999).
[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]

R. W. Gould, R. A. Arnone, P. M. Martinolich, “Spectral dependence of the scattering coefficient in case 1 and case 2 waters,” Appl. Opt. 38, 2377–2383(1999).
[CrossRef]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

Z. Lee, K. L. Carder, “Band-ratio or spectral-curvature algorithms for satellite remote sensing?” Appl. Opt. 39, 4377–4380(2000).
[CrossRef]

Deep-Sea Res. (1)

J. E. Harris, “Characterization of suspended matter in the Gulf of Mexico—II Particle size analysis of suspended matter from deep water,” Deep-Sea Res. 24, 1055–1061 (1977).
[CrossRef]

Deep-Sea Res. Part I Oceanogr. Res. Papers (1)

D. Risović, “Two component model of the sea particle size distribution,” Deep-Sea Res. Part I Oceanogr. Res. Papers 40, 1459–1473 (1993).
[CrossRef]

Eos (Trans. Am. Geophys. Union) (1)

H. R. Gordon, “Ocean color remote sensing: influence of the particle phase function and the solar zenith angle,” Eos (Trans. Am. Geophys. Union) 14, 1055–1061(1986).

Eos Trans. Am. Geophys. Union (1)

J. B. Macdonald, M. S. Twardowski, W. S. Pegau, A. H. Barnard, E. Boss, R. V. Zaneveld, “Characterization of spectral backscattering in the Gulf of California,” Eos Trans. Am. Geophys. Union 80 (49), Ocean Sci. Meet. Suppl. OS22E-12 (2000).

Fiz. B (1)

D. Risović, M. Martinis, “A comparative analysis of sea-particle-size distribution models,” Fiz. B 4 (2), 111–120 (1995).

J. Geophys. Res. (10)

J. C. Kitchen, J. R. Zaneveld, “On the noncorrelation of the vertical structure of light scattering and chlorophyll a in case I waters,” J. Geophys. Res. 95, 20,237–20,246 (1990).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Mie scattering by suspended clay particles,” J. Geophys. Res. 76, 5065–5069 (1971).
[CrossRef]

H. J. Pak, R. V. Zaneveld, G. F. Beardsley, “Particle size distribution in the Eastern equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13,135–13,142(1995)
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Mahru, C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953(1998).
[CrossRef]

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

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The determination of the index of refraction of particles suspended in the ocean,” J. Geophys. Res. 77, 2677–2680 (1974).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll-a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[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 II waters,” J. Geophys. Res. 106, (C7), 14,129–14,142 (2001).
[CrossRef]

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

Limnol. Oceanogr. (4)

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

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

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

M. Jonasz, G. Fournier, “Approximation of the size distribution of marine particles by a sum of lognormal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

Oceanologica Acta (1)

R. Reuter, “Characterization of marine particle suspensions by light scattering I (1980). Numerical predictions from Mie theory,” Oceanologica Acta 3, 317–332 (1980).

Prog. Oceanogr. (1)

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

Remote Sens. Environ. (1)

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Tellus Ser B (1)

M. Jonasz, “Particle size distributions in the Baltic,” Tellus Ser B 35, 345–358 (1983).
[CrossRef]

Tellus Ser. B (1)

M. Jonasz, H. Prandtke, “Comparison of measured and computed light scattering in the Baltic,” Tellus Ser. B 38, 144–157 (1986).
[CrossRef]

Other (7)

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

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery: a review,” in Lecture Notes on Coastal and Estuarine Studies, M. Bowman, ed. (Springer-Verlag, Berlin, 1983).

C. E. Junge, Air Chemistry and Radioactivity (Academic, New York, 1963), p.382

W. Spinrad, ed., Ocean Optics (Wiley, New York, 1994).

R. W. Sheldon, Government of Canada Fisheries Oceans Northwest Atlantic Fisheries Centre St. John’s, Newfoundland, A1C5x1 (personal communication, 1990).

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

R/V Barnes cruise (August1998), http://ocean.washington.edu/data .

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Figures (13)

Fig. 1
Fig. 1

Schematic representation of Junge and the 2C PSD models.

Fig. 2
Fig. 2

Measured particle-size distributions in symbols, case 2 water and, curves, corresponding fits and extrapolations with hyperbolic and 2C PSD models. Surface particle-size distribution from the bay at Villefranche SE France: a, Sample #15. Parameters of the corresponding fitted (integral) distributions are as defined: exponent k = 3.09 for the hyperbolic model (R 2 = 0.766), γ A = 0.108, γ B = 0.196, C A :C B = 5.045 × 1015 for the 2C model (R 2 = 0.960). b, Sample #13. Parameters of the corresponding distributions are as follows: exponent k = 3.0 for the hyperbolic model (R 2 = 0.746), γ A = 0.093, γ B = 0.202, and C A :C B = 5.834 × 1015 for the 2C model (R 2 = 0.931).

Fig. 3
Fig. 3

Measured particle-size distributions in symbols, case 1 water and, curves, corresponding fits and extrapolations with hyperbolic and 2C PSD models. Surface particle-size distributions from North Atlantic (25°54′N:62̊45′W) and North Pacific (4̊43′N:149̊58′W): a, North Atlantic sample #2. Parameters of the corresponding fitted (integral) distributions are as follows: exponent k = 2.92 for the hyperbolic model (R 2 = 0.495), γ A = 0.094, γ B = 0.198, and C A :C B = 4.58 × 1015 for the 2C model (R 2 = 0.995). b, North Pacific sample #4. Parameters of the corresponding distributions are as follows: exponent k = 2.97 for the hyperbolic model (R 2 = 0.927), γ A = 0.087, γ B = 0.187, and C A :C B = 1.39 × 1016 for the 2C model (R 2 = 0.947).

Fig. 4
Fig. 4

Dependence of backscattering ratio B on the upper limit of integration for the hyperbolic and 2C model of PSDs corresponding to case 2 and 1 water samples depicted in Figs. 2a and 3a, respectively: λ = 532 nm, n = 1.05. Symbols, calculated values; curves, corresponding fit with the B-spline function.

Fig. 5
Fig. 5

Dependence of backscattering ratio B on the lower limit of integration for the hyperbolic and 2C model of the PSD corresponding to the case 2 water sample depicted in Fig. 2a (#15): λ = 532 nm, n = 1.05. Symbols, calculated values; curves, corresponding fit with a B-spline function.

Fig. 6
Fig. 6

Contribution of particles smaller than the given size (r <) to the backscattering coefficient b b calculated from the hyperbolic (Junge) and the 2C model corresponding to the case 2 water PSD (sample #15 from Fig 2a): λ = 532 nm, m = 1.05 + 0i. Symbols, calculated values; curves, corresponding fit with a B-spline function.

Fig. 7
Fig. 7

Influence of the index of refraction (of the components) on the backscattering ratio in the 2C model (abscissa, the real part of the small component’s index of refraction; parameter, the large B component’s index of refraction) and comparison with the Junge model. Calculated values at λ = 532 nm for the parameters corresponding symbols, to #15 PSD and curves, to the B-spline fit.

Fig. 8
Fig. 8

Influence of the γ parameters on the backscattering ratio in the 2C model. B versus γ A (the parameter is γ B ). Symbols, calculated values and, curves, the corresponding fit with the B-spline for C A :C B = 2 × 1016, λ = 532 nm, and real indices of refraction, n A = n B = 1.05.

Fig. 9
Fig. 9

Spectral dependence of the backscattering ratio B for the representative case 2 water samples calculated from the Junge and the 2C model. Symbols, calculated values and, curves, corresponding fit with the B-spline function.

Fig. 10
Fig. 10

Symbols, Measured particle-size distribution from the Washington East Sound at a depth of 2 m; curves, corresponding fit with the Junge and the 2C model. Junge distribution: k = 2.11, R 2 = 0.685; 2C model: γ A = 0.130, γ B = 0.159, C A :C B = 2.132 × 1016, R 2 = 0.987. Inset: extrapolations to the submicrometer particle-size range from the hyperbolic fit (k = 2.11), segmented hyperbolic fit (small segment, k = 6.06), and the 2C model.

Fig. 11
Fig. 11

Spectral dependence of the measured (Hydroscat-6 and AC-9, East Sound, 2 m) and b, calculated scattering coefficient; b b , backscattering coefficient; B, backscattering ratio. a, Comparison of measured values with results from the 2C model for n A = 1.085 and n B = 1.03. b, Comparison of measured values with results from the Junge model for n = 1.05. Measured values are represented by larger, symbols while the calculated values are represented by small solid symbols and lines corresponding to the B-spline fit. The measured and calculated scattering parameters correspond to the PSD shown in Fig. 10.

Fig. 12
Fig. 12

Dependence of the backscattering ratio B on the lower limit of integration for the hyperbolic and the 2C model of the PSD corresponding to the case 1 water sample depicted in Fig. 3a:  λ = 532 nm, m = 1.05 + Oi. Symbols, calculated values; (curves, corresponding fit with the B-spline function).

Fig. 13
Fig. 13

Spectral dependence of the backscattering ratio B for representative case 1 water samples calculated from the Junge and the 2C model. Symbols, calculated values; curves, corresponding fit with the B-spline function.

Equations (17)

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

bb=bbw+bbp,
Qs=Cs/πr2,
Qbs=Cbs/πr2,
Qs= 2α2n=12n+1|ans|2+|bns|2,
Qbs= 1α2n=12n+1-1nan-bn2,
α=2πmwrλ0,
bbp=Bbp,
B=0 Qbsm, αα2Nαdα0 Qsm, αα2Nαdα,
Nα=Ntotfα,
0 fαdα=1.
Cbb r=100 · rminr QbsNrr2drrminrmax QbsNrr2dr.
dNr=Cr-kdr,
rminrmaxdNr.
dNr=dNAr+dNBr=CAFArdr+CBFBrdr,FAr=r2 exp-52rγA,FBr=r2 exp-17rγB,
rminrmaxdNr,
rmindNr
limr0Nr=,

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