Abstract

The effective cell size is expected to be one of the principal causes of variability in the inherent optical properties (IOPs) of a phytoplankton population. However, establishing simple size descriptors is complicated by the typically complex particle size distributions of natural phytoplankton assemblages. This study compares the use of measured and equivalent particle size distributions on the modeled IOPs of a wide range of natural phytoplankton assemblages. It demonstrates that several equivalent size distributions, using simple parameterizations of complex size distributions based on the effective radius or diameter, are capable of modeling phytoplankton IOPs with sufficient accuracy for further use in marine bio-optical models. The results offered here are expected to be of use in bio-optical studies of phytoplankton dynamics e.g. harmful algal bloom oriented inverse reflectance models.

© 2007 Optical Society of America

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  1. Z.V. Finkel and A.J. Irwin, “Modelling size-dependent photosynthesis: light absorption and the allometric rule,”. J. Theor. Biol. 204, 361–369 (2000)
    [CrossRef] [PubMed]
  2. A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep-Sea Res. 28, 1375–1393 (1981).
    [CrossRef]
  3. D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
    [CrossRef]
  4. J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
    [CrossRef] [PubMed]
  5. E. Boss, M.S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
    [CrossRef]
  6. A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
    [CrossRef] [PubMed]
  7. D. Risovic, “Two component model of sea particle size distribution,” Deep-Sea Res. 40, 1459–1473 (1993).
    [CrossRef]
  8. M. Jonasz and G. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
    [CrossRef]
  9. E.C. Junge, Air chemistry and radioactivity (Academic Press1963), pp.382.
  10. R.W. Sheldon, A. Prakash, and W.H. Sutcliffe, Jr., “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
    [CrossRef]
  11. S. Bernard, T.A. Probyn, and R.G. Barlow, “Measured and modelled optical properties of particulate matter in the southern Benguela,” S. Afr. J. Sci. 97, 410–420 (2001).
  12. Y.X. Hu and K. Stamnes, “An accurate Parameterization of Cloud Radiative Properties Suitable for Climate Modeling,” J. Climate. 6, 728–742 (1993).
    [CrossRef]
  13. M.D. Alexandrov and A.A. Lacis, “A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function,” Appl. Math. Comput. 116, 153–165 (2000)
    [CrossRef]
  14. R. McGraw, S. Nemesure, and S. E. Schwartz, “Properties and evolution of aerosols with size distributions having identical moments,” J. Aerosol. Sci. 29, 761–772 (1998).
    [CrossRef]
  15. J.E. Hansen and L.D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  16. C.S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr. 7, 207–217 (1962).
    [CrossRef]
  17. C.S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
    [CrossRef]
  18. M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).
  19. D. Stramski and J. Piskozub, “Estimation of scattering error in spectrophotometric measurements of light absorption by aquatic particles from 3-D radiative transfer equations,” Appl. Opt.,  42, 3634–46 (2003).
    [CrossRef] [PubMed]
  20. D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
    [CrossRef]
  21. R.G. Barlow, D. G. Cummings, and S. W. Gibb, “Improved resolution of mono- and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC,” Mar. Ecol. Prog. Ser. 161, 303–307 (1997).
    [CrossRef]
  22. A. Morel and A. Bricaud, “Inherent properties of algal cells including picoplankton: theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci.,  214, 521–559 (1986).
  23. H.C. Van de Hulst,. Light Scattering by Small Particles (Wiley1957), pp. 470.
  24. C.F. Bohren and D.R. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, 1983), pp. 530.
  25. A. Bricaud, A.L. Bedhomme, and A. Morel, “Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation,” J. Plankton Res. 10, 851–873 (1988).
    [CrossRef]
  26. A.L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [CrossRef]
  27. O.B. Toon and T.P. Ackerman, “Algorithms for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657–3660 (1981).
    [CrossRef] [PubMed]
  28. A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res.,  93, 10,749-10,768 (1988).
    [CrossRef]
  29. A.M. Ciotti, M. R. Lewis, and J.J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
    [CrossRef]
  30. M.I. Mishchenko and A.A. Lacis, “Morphology-dependent resonances of nearly spherical particles in random orientation,” Appl. Opt. 42, 5551–5556 (2003).
    [CrossRef] [PubMed]

2003 (2)

2002 (1)

A.M. Ciotti, M. R. Lewis, and J.J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

2001 (4)

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

E. Boss, M.S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

S. Bernard, T.A. Probyn, and R.G. Barlow, “Measured and modelled optical properties of particulate matter in the southern Benguela,” S. Afr. J. Sci. 97, 410–420 (2001).

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

2000 (2)

Z.V. Finkel and A.J. Irwin, “Modelling size-dependent photosynthesis: light absorption and the allometric rule,”. J. Theor. Biol. 204, 361–369 (2000)
[CrossRef] [PubMed]

M.D. Alexandrov and A.A. Lacis, “A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function,” Appl. Math. Comput. 116, 153–165 (2000)
[CrossRef]

1998 (2)

R. McGraw, S. Nemesure, and S. E. Schwartz, “Properties and evolution of aerosols with size distributions having identical moments,” J. Aerosol. Sci. 29, 761–772 (1998).
[CrossRef]

C.S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
[CrossRef]

1997 (1)

R.G. Barlow, D. G. Cummings, and S. W. Gibb, “Improved resolution of mono- and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC,” Mar. Ecol. Prog. Ser. 161, 303–307 (1997).
[CrossRef]

1996 (1)

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

1994 (1)

D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
[CrossRef]

1993 (2)

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

Y.X. Hu and K. Stamnes, “An accurate Parameterization of Cloud Radiative Properties Suitable for Climate Modeling,” J. Climate. 6, 728–742 (1993).
[CrossRef]

1988 (2)

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res.,  93, 10,749-10,768 (1988).
[CrossRef]

A. Bricaud, A.L. Bedhomme, and A. Morel, “Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation,” J. Plankton Res. 10, 851–873 (1988).
[CrossRef]

1986 (2)

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

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

1985 (1)

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

1981 (2)

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep-Sea Res. 28, 1375–1393 (1981).
[CrossRef]

O.B. Toon and T.P. Ackerman, “Algorithms for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657–3660 (1981).
[CrossRef] [PubMed]

1974 (1)

J.E. Hansen and L.D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1972 (1)

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

1963 (1)

E.C. Junge, Air chemistry and radioactivity (Academic Press1963), pp.382.

1962 (1)

C.S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr. 7, 207–217 (1962).
[CrossRef]

1951 (1)

A.L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Ackerman, T.P.

Aden, A.L.

A.L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Alexandrov, M.D.

M.D. Alexandrov and A.A. Lacis, “A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function,” Appl. Math. Comput. 116, 153–165 (2000)
[CrossRef]

Allen, J.T.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Barlow, R.G.

S. Bernard, T.A. Probyn, and R.G. Barlow, “Measured and modelled optical properties of particulate matter in the southern Benguela,” S. Afr. J. Sci. 97, 410–420 (2001).

R.G. Barlow, D. G. Cummings, and S. W. Gibb, “Improved resolution of mono- and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC,” Mar. Ecol. Prog. Ser. 161, 303–307 (1997).
[CrossRef]

Bedhomme, A.L.

A. Bricaud, A.L. Bedhomme, and A. Morel, “Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation,” J. Plankton Res. 10, 851–873 (1988).
[CrossRef]

Berges, J.A.

D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
[CrossRef]

Bernard, S.

S. Bernard, T.A. Probyn, and R.G. Barlow, “Measured and modelled optical properties of particulate matter in the southern Benguela,” S. Afr. J. Sci. 97, 410–420 (2001).

Blanco, J.M.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Bohren, C.F.

C.F. Bohren and D.R. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, 1983), pp. 530.

Boss, E.

Bricaud, A.

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

A. Bricaud, A.L. Bedhomme, and A. Morel, “Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation,” J. Plankton Res. 10, 851–873 (1988).
[CrossRef]

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

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

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep-Sea Res. 28, 1375–1393 (1981).
[CrossRef]

Ciotti, A.M.

A.M. Ciotti, M. R. Lewis, and J.J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

Cullen, J.J.

A.M. Ciotti, M. R. Lewis, and J.J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

Cummings, D. G.

R.G. Barlow, D. G. Cummings, and S. W. Gibb, “Improved resolution of mono- and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC,” Mar. Ecol. Prog. Ser. 161, 303–307 (1997).
[CrossRef]

Echevarria, F.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Finkel, Z.V.

Z.V. Finkel and A.J. Irwin, “Modelling size-dependent photosynthesis: light absorption and the allometric rule,”. J. Theor. Biol. 204, 361–369 (2000)
[CrossRef] [PubMed]

Fournier, G.

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

Gibb, S. W.

R.G. Barlow, D. G. Cummings, and S. W. Gibb, “Improved resolution of mono- and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC,” Mar. Ecol. Prog. Ser. 161, 303–307 (1997).
[CrossRef]

Gomis, D.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Hansen, J.E.

J.E. Hansen and L.D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Harrison, P.J.

D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
[CrossRef]

Herring, S.

Hu, Y.X.

Y.X. Hu and K. Stamnes, “An accurate Parameterization of Cloud Radiative Properties Suitable for Climate Modeling,” J. Climate. 6, 728–742 (1993).
[CrossRef]

Huffman, D.R.

C.F. Bohren and D.R. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, 1983), pp. 530.

Hulst, H.C. Van de

H.C. Van de Hulst,. Light Scattering by Small Particles (Wiley1957), pp. 470.

Ichimura, S.

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

Irwin, A.J.

Z.V. Finkel and A.J. Irwin, “Modelling size-dependent photosynthesis: light absorption and the allometric rule,”. J. Theor. Biol. 204, 361–369 (2000)
[CrossRef] [PubMed]

Jimenez-Gomez, F.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Jonasz, M.

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

Junge, E.C.

E.C. Junge, Air chemistry and radioactivity (Academic Press1963), pp.382.

Kerker, M.

A.L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Kishino, M.

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

Lacis, A.A.

M.I. Mishchenko and A.A. Lacis, “Morphology-dependent resonances of nearly spherical particles in random orientation,” Appl. Opt. 42, 5551–5556 (2003).
[CrossRef] [PubMed]

M.D. Alexandrov and A.A. Lacis, “A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function,” Appl. Math. Comput. 116, 153–165 (2000)
[CrossRef]

Lewis, M. R.

A.M. Ciotti, M. R. Lewis, and J.J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

McGraw, R.

R. McGraw, S. Nemesure, and S. E. Schwartz, “Properties and evolution of aerosols with size distributions having identical moments,” J. Aerosol. Sci. 29, 761–772 (1998).
[CrossRef]

Mishchenko, M.I.

Montagnes, D.J.S.

D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
[CrossRef]

Morel, A.

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res.,  93, 10,749-10,768 (1988).
[CrossRef]

A. Bricaud, A.L. Bedhomme, and A. Morel, “Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation,” J. Plankton Res. 10, 851–873 (1988).
[CrossRef]

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

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

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep-Sea Res. 28, 1375–1393 (1981).
[CrossRef]

Nemesure, S.

R. McGraw, S. Nemesure, and S. E. Schwartz, “Properties and evolution of aerosols with size distributions having identical moments,” J. Aerosol. Sci. 29, 761–772 (1998).
[CrossRef]

Okami, N.

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

Piskozub, J.

Prakash, A.

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

Probyn, T.A.

S. Bernard, T.A. Probyn, and R.G. Barlow, “Measured and modelled optical properties of particulate matter in the southern Benguela,” S. Afr. J. Sci. 97, 410–420 (2001).

Reul, A.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Risovic, D.

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

Rodriguez, J.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Rodriguez, V.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Roesler, C.S.

C.S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
[CrossRef]

Ruiz, J.

J. Rodriguez, J. Tintore, J.T. Allen, J.M. Blanco, D. Gomis, A. Reul, J. Ruiz, V. Rodriguez, F. Echevarria, and F. Jimenez-Gomez, “Mesoscale vertical motion and the size structure of phytoplankton in the ocean,” Nature 410, 360–363 (2001).
[CrossRef] [PubMed]

Schwartz, S. E.

R. McGraw, S. Nemesure, and S. E. Schwartz, “Properties and evolution of aerosols with size distributions having identical moments,” J. Aerosol. Sci. 29, 761–772 (1998).
[CrossRef]

Sheldon, R.W.

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

Stamnes, K.

Y.X. Hu and K. Stamnes, “An accurate Parameterization of Cloud Radiative Properties Suitable for Climate Modeling,” J. Climate. 6, 728–742 (1993).
[CrossRef]

Stramski, D.

Sutcliffe, Jr., W.H.

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

Takahashi, M.

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

Taylor, F.J.R.

D.J.S. Montagnes, J.A. Berges, P.J. Harrison, and F.J.R. Taylor, “Estimating carbon, nitrogen, protein, and chlorophyll a from cell volume in marine phytoplankton,” Limnol. Oceanogr. 39,1044–1060 (1994).
[CrossRef]

Tintore, J.

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Figures (4)

Fig. 1.
Fig. 1.

Optical and size related data for all samples analysed. (a) Chl a-specific phytoplankton absorption, (b) Chl a-specific algal size distributions by volume, (c) imaginary part of the phytoplankton refractive index, (d) real part of the phytoplankton refractive index. Coloured lines are used simply to discriminate between samples.

Fig. 2.
Fig. 2.

Mean spectral RMS errors and standard deviations of the best performing inverse Gaussian equivalent distribution. (a) attenuation coefficient, (b) scattering coefficient, (c) absorption coefficient, (d) backscattering coefficient (e) package effect parameter. High magnitude morphology-dependent resonance effects [30] can cause extremely high mean errors in phase function simulations, and such errors are therefore not calculated for the phase function. Fig. 2(f) shows a comparison between computed phase functions from the full, inverse Gaussian and Junge distributions at 530 nm for the same example assemblage as Fig.3.

Fig. 3.
Fig. 3.

Equivalent size distributions and their IOPs for an example assemblage, composed of mixed dinoflagellate and diatom species. Chlorophyll specific data shown are (a) measured and equivalent phytoplankton size distributions, (b) phytoplankton beam attenuation coefficient cϕ *, (c) phytoplankton absorption coefficient aϕ *, (d) package effect parameter Qa *, (e) phytoplankton scattering coefficient bϕ *, (f) phytoplankton backscattering coefficient b *. Close matches for the calculated optical properties of the equivalent inverse-Gaussian and Standard distributions can be observed, as can the difference in the shapes of the equivalent size distributions relative to the highly multimodal measured distribution.

Fig. 4.
Fig. 4.

Scaling parameters ASF for the (a) inverse Gaussian and (b) Standard distributions, calculated as surface area equivalent to the thirty-four measured algal Chl a specific size distributions. The results suggest that ASF can be confidently expressed as a function of Deff for a wide variety of algal assemblages for the above distributions.

Tables (2)

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Table 1. General description of sampled assemblages.

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Table 2. Maximal RMS errors (SD) between IOPs for measured and equivalent distributions.

Equations (13)

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< r k > = 0 r k F ( r ) d ( r )
a ϕ ( λ ) = π Q ̅ a ( λ ) 0 F ( r ) r 2 d ( r )
Q a ( λ ) = 1 + 2 e ρ ' ρ ' + 2 e ρ ' 1 ρ ' 2
< SA > = 0.5 50 πr 2 F ( r ) d ( r )
F ( r ) = ASF r 7 2 r eff 5 2 2 πv eff ( 1 + 3 v eff + 3 v eff 2 ) exp [ 1 2 v eff ( 2 - r eff r r r eff ) ]
F ( r ) = ASEr [ ( 1 3 v eff ) / v eff ] exp [ r / ( r eff v eff ) ]
F ( r ) = ASF exp [ ( ln ( r ) ln ( r g ) ) 2 2 σ g 2 ]
F ( r ) = ASEr ξ
Q a * = 3 2 Q a a cm 2 r
RMS error ( λ ) = [ mean ( a equiv ( λ ) a meas ( λ ) a meas ( λ ) ) ] 2
SD of RMS error ( λ ) = [ SD ( a equiv ( λ ) a meas ( λ ) a meas ( λ ) ) ] 2
F ( r ) = 2 × 10 9 ( 2 r eff ) 3.0264 [ r 7 2 r eff 5 2 7.9232 ] exp [ 0.7939 ( 2 r eff r r r eff ) ]
F ( r ) = 1 × 10 9 ( 2 r eff ) 2.6443 r ( 1.4127 ) exp [ r / 0.63 r eff ]

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