Abstract

The link between the spectral shape of the beam attenuation spectrum and the shape of the particle size distribution (PSD) of oceanic particles is revisited to evaluate the extent to which one can be predicted from the other. Assuming a hyperbolic (power-law) PSD, N(D) ∝ D , past studies have found for an infinite distribution of nonabsorbing spheres with a constant index of refraction that the attenuation spectrum is hyperbolic and that the attenuation spectral slope γ is related to the PSD slope ξ by ξ = γ + 3. Here we add a correction to this model because of the finite size of the biggest particle in the population. This inversion model is given by ξ = γ + 3 - 0.5 exp(-6γ). In most oceanic observations ξ > 3, and the deviation between these two models is negligible. To test the robustness of this inversion, we perturbed its assumptions by allowing for populations of particles that are nonspherical, or absorbing, or with an index of refraction that changes with wavelength. We found the model to provide a good fit for the range of parameters most often encountered in the ocean. In addition, we found that the particulate attenuation spectrum, c p(λ), is well described by a hyperbolic relation to the wavelength c p ∝ λ throughout the range of the investigated parameters, even when the inversion model does not apply. This implies that knowledge of the particulate attenuation at two visible wavelengths could provide, to a high degree of accuracy, the particulate attenuation at other wavelengths in the visible spectrum.

© 2001 Optical Society of America

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  1. 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]
  2. C. M. Boyd, G. W. Johnson, “Precision of size determination of resistive electronic particle counters,” J. Plankton Res. 17, 41–58 (1995).
    [CrossRef]
  3. W. D. Gardner, “Incomplete extraction of rapidly settling particles from water samples,” Limnol. Oceanogr. 22, 764–768 (1977).
    [CrossRef]
  4. I. N. McCave, “Particulate size spectra, behavior, and origin of nephloid layers over the Nova Scotian continental rise,” J. Geophys. Res. 88, 7647–7666 (1983).
    [CrossRef]
  5. C. Moore, E. J. Bruce, W. S. Pegau, A. D. Weidemann, “WET Labs ac-9: field calibration protocol, deployment techniques, data processing and design improvements,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 725–730 (1997).
  6. G. V. Middleton, J. B. Southard, “Mechanics of sediment movement,” SEPM Short Course 3 (Society for Sedimentary Geology, Tulsa, Okla., 1984).
  7. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  8. K. S. Shifrin, G. Tonna, “Inverse problem related to light scattering in the atmosphere and ocean,” in Advances in Geophysics, R. Dmowska, B. Saltzman, eds. (Academic, San Diego, Calif., 1993), Vol. 34.
    [CrossRef]
  9. F. Volz, “Die Optik und Meterologie der atmospharischen Trubung,” Ber. Dtsch. Wetterdienstes 2, 3–47 (1954).
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  11. P. Diehl, H. Haardt, “Measurement of the spectral attenuation to support biological research in a ‘plankton tube’ experiment,” Oceanologica Acta 3, 89–96 (1980).
  12. E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
    [CrossRef]
  13. K. J. Voss, “A spectral model of the beam attenuation coefficient in the ocean and coastal areas,” Limnol. Oceanogr. 37, 501–509 (1992).
    [CrossRef]
  14. A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys. Res. 103, 24955–24968 (1998).
    [CrossRef]
  15. G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
    [CrossRef]
  16. H. Bader, “The hyperbolic distribution of particle sizes,” J. Geophys. Res. 75, 2822–2830 (1970).
    [CrossRef]
  17. D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  18. K. J. Voss, R. W. Austin, “Beam-attenuation measurement error due to small-angle scattering,” J. Atmos. Ocean. Technol. 10, 113–121 (1992).
    [CrossRef]
  19. M. Jonasz, “Particle size distributions in the Baltic,” Tellus Ser. B 35, 346–358 (1983).
    [CrossRef]
  20. D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. 40, 1459–1473 (1993).
    [CrossRef]
  21. I. N. McCave, “Size spectra and aggregation of suspended particles in the deep ocean,” Deep-Sea Res. 31, 329–352 (1984).
    [CrossRef]
  22. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  23. D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
    [CrossRef]
  24. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  25. W. H. Press, S. A. Teukolsky, W. T. Vattering, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).
  26. G. R. Fournier, T. N. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
    [CrossRef] [PubMed]
  27. B. T. N. Evans, G. R. Fournier, “Analytic approximation to randomly oriented spheroid extinction,” Appl. Opt. 33, 5796–5804 (1994).
    [CrossRef] [PubMed]
  28. P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J Appl. Phys. 50, 4550–4566 (1979).
    [CrossRef]
  29. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).
  30. H. Barth, K. Grisard, K. Holtsch, R. Reuter, U. Stute, “Polychromatic transmissometer for in situ measurements of suspended particles and gelbstoff in water,” Appl. Opt. 36, 7919–7928 (1997).
    [CrossRef]
  31. E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
    [CrossRef]
  32. D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplanktonic cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
    [CrossRef] [PubMed]
  33. M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Ocenaogr. 32, 1059–1065 (1987).
    [CrossRef]
  34. E. Aas, “Influence of shape and structure on light scattering by marine particles,” (University of Oslo, Oslo, 1984).
  35. J. T. O. Kirk, “A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters,” New Phytol. 77, 341–358 (1976).
    [CrossRef]
  36. P. Hill, Department of Oceanography, Dalhousie University, 1355 Oxford Street, Halifax, Nova Scotia B3H 4J1, Canada (personal communication, 2000).
  37. 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]
  38. R. Iturriaga, D. A. Siegel, “Microphotometric characterization of phytoplankton and detrital absorption properties in the Sargasso Sea,” Limnol. Oceanogr. 34, 1706–1726 (1989).
    [CrossRef]
  39. Y. C. Agrawal, H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 99–114 (2000).
    [CrossRef]
  40. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

2001 (1)

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

2000 (1)

Y. C. Agrawal, H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 99–114 (2000).
[CrossRef]

1998 (1)

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys. Res. 103, 24955–24968 (1998).
[CrossRef]

1997 (3)

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

H. Barth, K. Grisard, K. Holtsch, R. Reuter, U. Stute, “Polychromatic transmissometer for in situ measurements of suspended particles and gelbstoff in water,” Appl. Opt. 36, 7919–7928 (1997).
[CrossRef]

1996 (1)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
[CrossRef]

1995 (1)

C. M. Boyd, G. W. Johnson, “Precision of size determination of resistive electronic particle counters,” J. Plankton Res. 17, 41–58 (1995).
[CrossRef]

1994 (1)

1993 (1)

D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. 40, 1459–1473 (1993).
[CrossRef]

1992 (2)

K. J. Voss, R. W. Austin, “Beam-attenuation measurement error due to small-angle scattering,” J. Atmos. Ocean. Technol. 10, 113–121 (1992).
[CrossRef]

K. J. Voss, “A spectral model of the beam attenuation coefficient in the ocean and coastal areas,” Limnol. Oceanogr. 37, 501–509 (1992).
[CrossRef]

1991 (2)

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

G. R. Fournier, T. N. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
[CrossRef] [PubMed]

1989 (1)

R. Iturriaga, D. A. Siegel, “Microphotometric characterization of phytoplankton and detrital absorption properties in the Sargasso Sea,” Limnol. Oceanogr. 34, 1706–1726 (1989).
[CrossRef]

1988 (1)

1987 (1)

M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Ocenaogr. 32, 1059–1065 (1987).
[CrossRef]

1984 (1)

I. N. McCave, “Size spectra and aggregation of suspended particles in the deep ocean,” Deep-Sea Res. 31, 329–352 (1984).
[CrossRef]

1983 (2)

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

I. N. McCave, “Particulate size spectra, behavior, and origin of nephloid layers over the Nova Scotian continental rise,” J. Geophys. Res. 88, 7647–7666 (1983).
[CrossRef]

1982 (1)

1980 (1)

P. Diehl, H. Haardt, “Measurement of the spectral attenuation to support biological research in a ‘plankton tube’ experiment,” Oceanologica Acta 3, 89–96 (1980).

1979 (1)

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

1977 (1)

W. D. Gardner, “Incomplete extraction of rapidly settling particles from water samples,” Limnol. Oceanogr. 22, 764–768 (1977).
[CrossRef]

1976 (1)

J. T. O. Kirk, “A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters,” New Phytol. 77, 341–358 (1976).
[CrossRef]

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]

1970 (1)

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

1954 (1)

F. Volz, “Die Optik und Meterologie der atmospharischen Trubung,” Ber. Dtsch. Wetterdienstes 2, 3–47 (1954).

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
[CrossRef]

E. Aas, “Influence of shape and structure on light scattering by marine particles,” (University of Oslo, Oslo, 1984).

Agrawal, Y. C.

Y. C. Agrawal, H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 99–114 (2000).
[CrossRef]

Alldredge, A. L.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

Austin, R. W.

K. J. Voss, R. W. Austin, “Beam-attenuation measurement error due to small-angle scattering,” J. Atmos. Ocean. Technol. 10, 113–121 (1992).
[CrossRef]

Bader, H.

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

Barnard, A. H.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys. Res. 103, 24955–24968 (1998).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

Barth, H.

Bohren, C. F.

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

Boss, E.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

Boyd, C. M.

C. M. Boyd, G. W. Johnson, “Precision of size determination of resistive electronic particle counters,” J. Plankton Res. 17, 41–58 (1995).
[CrossRef]

Bricaud, A.

Bruce, E. J.

C. Moore, E. J. Bruce, W. S. Pegau, A. D. Weidemann, “WET Labs ac-9: field calibration protocol, deployment techniques, data processing and design improvements,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 725–730 (1997).

Chang, G. C.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

Costello, D. K.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

Dam, H. G.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

Dickey, T. D.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

Diehl, P.

P. Diehl, H. Haardt, “Measurement of the spectral attenuation to support biological research in a ‘plankton tube’ experiment,” Oceanologica Acta 3, 89–96 (1980).

Evans, B. T. N.

Evans, T. N.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vattering, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Fournier, G. R.

Gardner, W. D.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

W. D. Gardner, “Incomplete extraction of rapidly settling particles from water samples,” Limnol. Oceanogr. 22, 764–768 (1977).
[CrossRef]

Grisard, K.

Haardt, H.

P. Diehl, H. Haardt, “Measurement of the spectral attenuation to support biological research in a ‘plankton tube’ experiment,” Oceanologica Acta 3, 89–96 (1980).

Hill, P.

P. Hill, Department of Oceanography, Dalhousie University, 1355 Oxford Street, Halifax, Nova Scotia B3H 4J1, Canada (personal communication, 2000).

Holtsch, K.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

Huffman, D. R.

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

Iturriaga, R.

R. Iturriaga, D. A. Siegel, “Microphotometric characterization of phytoplankton and detrital absorption properties in the Sargasso Sea,” Limnol. Oceanogr. 34, 1706–1726 (1989).
[CrossRef]

Jackson, G. A.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

Johnson, G. W.

C. M. Boyd, G. W. Johnson, “Precision of size determination of resistive electronic particle counters,” J. Plankton Res. 17, 41–58 (1995).
[CrossRef]

Jonasz, M.

M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Ocenaogr. 32, 1059–1065 (1987).
[CrossRef]

M. Jonasz, “Particle size distributions in the Baltic,” Tellus Ser. B 35, 346–358 (1983).
[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, “A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters,” New Phytol. 77, 341–358 (1976).
[CrossRef]

Kitchen, J. C.

Logan, B. E.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

Maffione, R. E.

G. A. Jackson, R. E. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, H. G. Dam, “Particle size spectra between 1µm and 1cm at Monterey Bay determined using multiple instruments,” Deep-Sea Res. 44, 1739–1768 (1997).
[CrossRef]

McCave, I. N.

I. N. McCave, “Size spectra and aggregation of suspended particles in the deep ocean,” Deep-Sea Res. 31, 329–352 (1984).
[CrossRef]

I. N. McCave, “Particulate size spectra, behavior, and origin of nephloid layers over the Nova Scotian continental rise,” J. Geophys. Res. 88, 7647–7666 (1983).
[CrossRef]

Middleton, G. V.

G. V. Middleton, J. B. Southard, “Mechanics of sediment movement,” SEPM Short Course 3 (Society for Sedimentary Geology, Tulsa, Okla., 1984).

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

Mobley, C. D.

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

Moore, C.

C. Moore, E. J. Bruce, W. S. Pegau, A. D. Weidemann, “WET Labs ac-9: field calibration protocol, deployment techniques, data processing and design improvements,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 725–730 (1997).

Morel, A.

D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplanktonic cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
[CrossRef] [PubMed]

A. Morel, “Diffusion de la lumiere par les eaux de mer. Resultat experimentaux et approch theorique,” in Agard Lecture Series 61 on Optics of the Sea (Advisory Group for Aerospace Research and Development; NATO, London, 1973), pp. 3.1.1–76.

Pak, H.

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]

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.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, T. D. Dickey, “The spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. 106, 9509–9516 (2001).
[CrossRef]

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys. Res. 103, 24955–24968 (1998).
[CrossRef]

C. Moore, E. J. Bruce, W. S. Pegau, A. D. Weidemann, “WET Labs ac-9: field calibration protocol, deployment techniques, data processing and design improvements,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 725–730 (1997).

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

Pottsmith, H. C.

Y. C. Agrawal, H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 99–114 (2000).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vattering, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

Reuter, R.

Risovic, D.

D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. 40, 1459–1473 (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]

Shifrin, K. S.

K. S. Shifrin, G. Tonna, “Inverse problem related to light scattering in the atmosphere and ocean,” in Advances in Geophysics, R. Dmowska, B. Saltzman, eds. (Academic, San Diego, Calif., 1993), Vol. 34.
[CrossRef]

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

Siegel, D. A.

R. Iturriaga, D. A. Siegel, “Microphotometric characterization of phytoplankton and detrital absorption properties in the Sargasso Sea,” Limnol. Oceanogr. 34, 1706–1726 (1989).
[CrossRef]

Southard, J. B.

G. V. Middleton, J. B. Southard, “Mechanics of sediment movement,” SEPM Short Course 3 (Society for Sedimentary Geology, Tulsa, Okla., 1984).

Stramski, D.

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M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. (to be published).

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Figures (6)

Fig. 1
Fig. 1

(a). Particulate beam attenuation slope, γ, as function of beam attenuation at 660 nm obtained with a Slow Decent Rate Optical Profiler in situ and (b) PSD slope, ξ, as function of beam attenuation at 660 nm measured on water obtained from fitting of Coulter counter data on samples obtained by a Rosette platform. The measurements span two sampling periods (fall 1996, denoted by × and +, and spring 1997, denoted by ○) and are described and discussed in Boss et al. 12 The correlation of both attenuation slope and PSD slope with beam attenuation (and therefore with each other) is the primary motivation of the present study.

Fig. 2
Fig. 2

PSD slope, ξ, as function of the attenuation spectrum (γ) of nonabsorbing particle populations. The modeled populations have slopes 5 ≥ ξ ≥ 2.5, indices of refraction n = 1.02, 1.05, 1.09, 1.15, and 1.2, and a size range 300 ≥ D ≥ 0.01 µm. The dashed and the dotted curves represent the ξ - γ relationships of Eqs. (4) and (6), respectively. Maximum deviation of the attenuation spectrum from a hyperbolic model [Eq. (3)] is 0.35% (mean rms 0.0003%).

Fig. 3
Fig. 3

Effect of changing the population size limits. Difference between input and modeled [Eq. (6)] PSD slope (ξ) as a function of the size of the smallest particles (D min, upper two panels) and largest particles (D max, lower two panels) for populations with different ξ. Left-hand panels are for nonabsorbing particles with index of refraction n = 1.02, and right-hand panels are for n = 1.2. Negative values indicate that the model [Eq. (5)] overestimates the population’s PSD slope. Maximum deviation of the attenuation spectrum from a hyperbolic model [Eq. (3)] with varying D max was 2.1% (mean rms 0.01%) and when varying D min was 0.23% (mean rms 0.007%).

Fig. 4
Fig. 4

Effect of spectrally varying refractive index. PSD slope, ξ, as function of the attenuation spectrum (γ) of calcite and opal particle populations with different size distribution slopes (ξ) with a constant size range 300 ≥ D ≥ 0.01µm. The spectrally variable index of refraction was computed from Eq. (7) with the parameters in the text. The dashed and the dotted curves are the proposed ξ–γ relationships based on Eq. (4) and Eq. (6), respectively. Maximum deviation of the attenuation spectrum from a hyperbolic model [Eq. (3)] for calcite was 0.3% (rms 0.006%) and for opal was 0.06% (rms 0.0004%).

Fig. 5
Fig. 5

Effect of absorption. Difference between input and modeled [Eq. (6)] PSD slope (ξ) as a function of the magnitude of the imaginary part of the index of refraction for populations with different ξ. Left-hand panel is for absorbing particles with index of refraction n = 1.02, and right-hand panel is for n = 1.2. Negative values indicate that the model [Eq. (6)] overestimates the population’s PSD slope. Maximum deviation of the attenuation spectrum from a hyperbolic model [Eq. (3)] was 0.26% (rms 0.003%).

Fig. 6
Fig. 6

Volume-specific attenuation coefficient as function of diameter. (a) Changes due to wavelength change (λ = 420, 500, 580, 660 m) for a constant index of refraction, n = 1.05, are displayed in the top panel. (b) Effects due to variation in the real part of the index of refraction (n = 1.02, 1.05, 1.1, 1.15, 1.2), where n′ = 0 and λ = 550 nm. (c) The effect of absorption (n′ = 0, 0.002, 0.005, 0.01) for n = 1.05 and λ = 550 nm.

Equations (8)

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0ND=N0D/D0-ξ  D>Dmax  D<DminDmax>D>Dmin,
D¯DminDmin DN(D)dDDminDmax N(D)dD =1 - ξ2 - ξ×Dmax2-ξ - Dmin2-ξDmax1-ξ - Dmin1-ξDminDmax1 - ξ2 - ξDmin.
cpλ=Aλ-γ.
ξ=γ+3.
cp=DminDmax CextDNDdD,
ξ=γ+3-0.5 exp-6γ.
nλ=P+Q/λ2,
n=1cpij cextDj, niNDj, nini.

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