Abstract

A theoretical model was developed estimating the scattering by seawater that are due to concentration fluctuation. Combining with the model proposed for density fluctuation (Optics Express, 17, 1671, 2009), we evaluated the overall effect of sea salts on the scattering. The variation of seawater scattering with the salinity is a combination of two factors: decreasing contribution due to density fluctuation and increasing contribution due to concentration fluctuation, with the latter effect dominating. The trend is, however, slightly non-linear and the linear adjustment of scattering with salinity that is frequently used would lead to an underestimate by an average of 2%. The results estimated at S = 38.4‰ agree with the measurements by Morel (Cahiers Oceanographiques, 20, 157, 1968) with an average difference of 1%, well within his experimental error of 2%. The spectral signature also varies with salinity, with the power-law slope increasing from -4.286 to -4.306 for salinity from 0 to 40‰.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Einstein, "Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes," Annalen der Physik 338, 1275-1298 (1910).
    [CrossRef]
  2. X. Zhang and L. Hu, "Estimating scattering of pure water from density fluctuation of the refractive index," Optics Express 17, 1671-1678 (2009).
    [CrossRef] [PubMed]
  3. A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
    [CrossRef]
  4. R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
    [CrossRef]
  5. A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," J. Chimie Physique 10, 1359-1366 (1966).
  6. A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).
  7. A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution," Appl. Opt. 30, 4427-4438 (1991).
    [CrossRef] [PubMed]
  8. A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
    [CrossRef]
  9. M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
    [CrossRef]
  10. E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
    [CrossRef]
  11. C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, 1994).
  12. E. Boss and W. S. Pegau, "Relationship of light scattering at an angle in the backward direction to the backscattering coefficient," Appl. Opt. 40, 5503-5507 (2001).
    [CrossRef]
  13. A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov, and E. S. Nielsen, eds. (Academic Press, New York, 1974), pp. 1-24.
  14. P. Debye, "Light Scattering in Solutions," J. Appl. Phys. 15, 338-342 (1944).
    [CrossRef]
  15. F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
    [CrossRef]
  16. M. Jonasz, and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic Press, New York, 2007).
  17. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  18. X. Quan and E. S. Fry, "Empirical equation for the index of refraction of seawater," Appl. Opt. 34, 3477-3480 (1995).
    [CrossRef] [PubMed]
  19. B. A. Pethica and C. Smart, "Light scattering of electrolyte solutions," Trans. Faraday Soc. 62, 1890-1899 (1966).
    [CrossRef]
  20. F. J. Millero and W. H. Leung, "The thermodynamics of seawater at one atmosphere," Am J Sci 276, 1035-1077 (1976).
    [CrossRef]
  21. UNESCO, "Background papers and supporting data on the International Equation of State of Seawater 1980," UNESCO Technical Papers in Marine Science No. 38 (1981).
  22. P. E. Ciddor, "Refractive index of air: new equations for the visible and near infrared," Appl. Opt. 35, 1566-1573 (1996).
    [CrossRef] [PubMed]
  23. F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
    [CrossRef]
  24. H. C. Brinkman and J. J. Hermans, "The Effect of Non-Homogeneity of Molecular Weight on the Scattering of Light by High Polymer Solutions," J. Chem. Phys. 17, 574-576 (1949).
    [CrossRef]
  25. J. G. Kirkwood and R. J. Goldberg, "Light Scattering Arising from Composition Fluctuations in Multi-Component Systems," J. Chem. Phys. 18, 54-57 (1950).
    [CrossRef]
  26. W. H. Stockmayer, "Light Scattering in Multi-Component Systems," J. Chem. Phys. 18, 58-61 (1950).
    [CrossRef]
  27. G. Oster, "The Scattering of Light and its Application to Chemistry," Chem. Rev. 43, 319-365 (1948).
    [CrossRef] [PubMed]
  28. F. J. Millero, "The Physical Chemistry of Seawater," Annu. Rev. Earth Planet. Sci. 2, 101-150 (1974).
    [CrossRef]
  29. M. R. Wright, An Introduction to Aqueous Electrolyte Solutions (John Wiley & Sons Ltd., West Sussex, 2007).
  30. M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
    [CrossRef]
  31. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).
  32. Y. Shiokawa and S. Suzuki, "Isotropic Rayleigh Light Scattering in Two-component Systems. The Interdependence of the Concentration and the Density Scattering," Bull. Chem. Soc. Japan 48, 171-174 (1975).
    [CrossRef]
  33. D. R. Lide, Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2003).
  34. K. S. Pitzer and G. Mayorga, "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent," J. Phys. Chem. 77, 2300-2308 (1973).
    [CrossRef]
  35. P. D. T. Huibers, "Models for the wavelength dependence of the index of refraction of water," Appl. Opt. 36, 3785-3787 (1997).
    [CrossRef] [PubMed]
  36. I. L. Fabelinskii, Molecular Scattering of Light (Plenum Press, New York, 1968).

2009 (1)

X. Zhang and L. Hu, "Estimating scattering of pure water from density fluctuation of the refractive index," Optics Express 17, 1671-1678 (2009).
[CrossRef] [PubMed]

2008 (1)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

2007 (3)

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

2003 (1)

M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
[CrossRef]

2001 (1)

1997 (1)

1996 (1)

1995 (1)

1992 (1)

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

1991 (1)

1980 (1)

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

1976 (2)

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

F. J. Millero and W. H. Leung, "The thermodynamics of seawater at one atmosphere," Am J Sci 276, 1035-1077 (1976).
[CrossRef]

1975 (1)

Y. Shiokawa and S. Suzuki, "Isotropic Rayleigh Light Scattering in Two-component Systems. The Interdependence of the Concentration and the Density Scattering," Bull. Chem. Soc. Japan 48, 171-174 (1975).
[CrossRef]

1974 (1)

F. J. Millero, "The Physical Chemistry of Seawater," Annu. Rev. Earth Planet. Sci. 2, 101-150 (1974).
[CrossRef]

1973 (1)

K. S. Pitzer and G. Mayorga, "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent," J. Phys. Chem. 77, 2300-2308 (1973).
[CrossRef]

1968 (1)

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

1966 (2)

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," J. Chimie Physique 10, 1359-1366 (1966).

B. A. Pethica and C. Smart, "Light scattering of electrolyte solutions," Trans. Faraday Soc. 62, 1890-1899 (1966).
[CrossRef]

1950 (2)

J. G. Kirkwood and R. J. Goldberg, "Light Scattering Arising from Composition Fluctuations in Multi-Component Systems," J. Chem. Phys. 18, 54-57 (1950).
[CrossRef]

W. H. Stockmayer, "Light Scattering in Multi-Component Systems," J. Chem. Phys. 18, 58-61 (1950).
[CrossRef]

1949 (1)

H. C. Brinkman and J. J. Hermans, "The Effect of Non-Homogeneity of Molecular Weight on the Scattering of Light by High Polymer Solutions," J. Chem. Phys. 17, 574-576 (1949).
[CrossRef]

1948 (1)

G. Oster, "The Scattering of Light and its Application to Chemistry," Chem. Rev. 43, 319-365 (1948).
[CrossRef] [PubMed]

1944 (1)

P. Debye, "Light Scattering in Solutions," J. Appl. Phys. 15, 338-342 (1944).
[CrossRef]

1910 (1)

A. Einstein, "Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes," Annalen der Physik 338, 1275-1298 (1910).
[CrossRef]

Babin, M.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Boss, E.

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

E. Boss and W. S. Pegau, "Relationship of light scattering at an angle in the backward direction to the backscattering coefficient," Appl. Opt. 40, 5503-5507 (2001).
[CrossRef]

Bradshaw, A.

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

Bricaud, A.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Brinkman, H. C.

H. C. Brinkman and J. J. Hermans, "The Effect of Non-Homogeneity of Molecular Weight on the Scattering of Light by High Polymer Solutions," J. Chem. Phys. 17, 574-576 (1949).
[CrossRef]

Chen, C.-T.

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

Ciddor, P. E.

Claustre, H.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Collier, R.

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

Debye, P.

P. Debye, "Light Scattering in Solutions," J. Appl. Phys. 15, 338-342 (1944).
[CrossRef]

Einstein, A.

A. Einstein, "Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes," Annalen der Physik 338, 1275-1298 (1910).
[CrossRef]

Farinato, R. S.

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

Feistel, R.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

Fennel, K.

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

Freeman, S. A.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Fry, E. S.

Gentili, B.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution," Appl. Opt. 30, 4427-4438 (1991).
[CrossRef] [PubMed]

Goldberg, R. J.

J. G. Kirkwood and R. J. Goldberg, "Light Scattering Arising from Composition Fluctuations in Multi-Component Systems," J. Chem. Phys. 18, 54-57 (1950).
[CrossRef]

Hermans, J. J.

H. C. Brinkman and J. J. Hermans, "The Effect of Non-Homogeneity of Molecular Weight on the Scattering of Light by High Polymer Solutions," J. Chem. Phys. 17, 574-576 (1949).
[CrossRef]

Hu, L.

X. Zhang and L. Hu, "Estimating scattering of pure water from density fluctuation of the refractive index," Optics Express 17, 1671-1678 (2009).
[CrossRef] [PubMed]

Hucteau, H.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Huibers, P. D. T.

Huot, Y.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Jonsson, B.

M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
[CrossRef]

Kirkwood, J. G.

J. G. Kirkwood and R. J. Goldberg, "Light Scattering Arising from Composition Fluctuations in Multi-Component Systems," J. Chem. Phys. 18, 54-57 (1950).
[CrossRef]

Larson, G.

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

Leung, W. H.

F. J. Millero and W. H. Leung, "The thermodynamics of seawater at one atmosphere," Am J Sci 276, 1035-1077 (1976).
[CrossRef]

Lund, M.

M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
[CrossRef]

Mayorga, G.

K. S. Pitzer and G. Mayorga, "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent," J. Phys. Chem. 77, 2300-2308 (1973).
[CrossRef]

McDougall, T. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

Megnassan, E.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Millero, F. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

F. J. Millero and W. H. Leung, "The thermodynamics of seawater at one atmosphere," Am J Sci 276, 1035-1077 (1976).
[CrossRef]

F. J. Millero, "The Physical Chemistry of Seawater," Annu. Rev. Earth Planet. Sci. 2, 101-150 (1974).
[CrossRef]

Morel, A.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution," Appl. Opt. 30, 4427-4438 (1991).
[CrossRef] [PubMed]

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," J. Chimie Physique 10, 1359-1366 (1966).

Oster, G.

G. Oster, "The Scattering of Light and its Application to Chemistry," Chem. Rev. 43, 319-365 (1948).
[CrossRef] [PubMed]

Pedersen, T.

M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
[CrossRef]

Pegau, W. S.

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

E. Boss and W. S. Pegau, "Relationship of light scattering at an angle in the backward direction to the backscattering coefficient," Appl. Opt. 40, 5503-5507 (2001).
[CrossRef]

Pethica, B. A.

B. A. Pethica and C. Smart, "Light scattering of electrolyte solutions," Trans. Faraday Soc. 62, 1890-1899 (1966).
[CrossRef]

Pitzer, K. S.

K. S. Pitzer and G. Mayorga, "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent," J. Phys. Chem. 77, 2300-2308 (1973).
[CrossRef]

Proutiere, A.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Quan, X.

Ras, J.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Rowell, R. L.

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

Schleicher, K.

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

Shiokawa, Y.

Y. Shiokawa and S. Suzuki, "Isotropic Rayleigh Light Scattering in Two-component Systems. The Interdependence of the Concentration and the Density Scattering," Bull. Chem. Soc. Japan 48, 171-174 (1975).
[CrossRef]

Smart, C.

B. A. Pethica and C. Smart, "Light scattering of electrolyte solutions," Trans. Faraday Soc. 62, 1890-1899 (1966).
[CrossRef]

Stockmayer, W. H.

W. H. Stockmayer, "Light Scattering in Multi-Component Systems," J. Chem. Phys. 18, 58-61 (1950).
[CrossRef]

Stramski, D.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Suzuki, S.

Y. Shiokawa and S. Suzuki, "Isotropic Rayleigh Light Scattering in Two-component Systems. The Interdependence of the Concentration and the Density Scattering," Bull. Chem. Soc. Japan 48, 171-174 (1975).
[CrossRef]

Tieche, F.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Twardowski, M. S.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Wright, D. G.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

Zhang, X.

X. Zhang and L. Hu, "Estimating scattering of pure water from density fluctuation of the refractive index," Optics Express 17, 1671-1678 (2009).
[CrossRef] [PubMed]

Am J Sci (1)

F. J. Millero and W. H. Leung, "The thermodynamics of seawater at one atmosphere," Am J Sci 276, 1035-1077 (1976).
[CrossRef]

Annalen der Physik (1)

A. Einstein, "Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes," Annalen der Physik 338, 1275-1298 (1910).
[CrossRef]

Annu. Rev. Earth Planet. Sci. (1)

F. J. Millero, "The Physical Chemistry of Seawater," Annu. Rev. Earth Planet. Sci. 2, 101-150 (1974).
[CrossRef]

Appl. Opt. (5)

Biogeosciences (1)

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Bull. Chem. Soc. Japan (1)

Y. Shiokawa and S. Suzuki, "Isotropic Rayleigh Light Scattering in Two-component Systems. The Interdependence of the Concentration and the Density Scattering," Bull. Chem. Soc. Japan 48, 171-174 (1975).
[CrossRef]

Cahiers Oceanographiques (1)

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

Chem. Rev. (1)

G. Oster, "The Scattering of Light and its Application to Chemistry," Chem. Rev. 43, 319-365 (1948).
[CrossRef] [PubMed]

Deep-Sea Res. (1)

F. J. Millero, C.-T. Chen, A. Bradshaw, and K. Schleicher, "A new high pressure equation of state for seawater," Deep-Sea Res. 27A, 255-264 (1980).
[CrossRef]

Deep-Sea Res. I (1)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, "The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale," Deep-Sea Res. I 55, 50-72 (2008).
[CrossRef]

Hydrobiologia (1)

E. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, "Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR," Hydrobiologia 574, 149-159 (2007).
[CrossRef]

J. Appl. Phys. (1)

P. Debye, "Light Scattering in Solutions," J. Appl. Phys. 15, 338-342 (1944).
[CrossRef]

J. Chem. Phys. (4)

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

H. C. Brinkman and J. J. Hermans, "The Effect of Non-Homogeneity of Molecular Weight on the Scattering of Light by High Polymer Solutions," J. Chem. Phys. 17, 574-576 (1949).
[CrossRef]

J. G. Kirkwood and R. J. Goldberg, "Light Scattering Arising from Composition Fluctuations in Multi-Component Systems," J. Chem. Phys. 18, 54-57 (1950).
[CrossRef]

W. H. Stockmayer, "Light Scattering in Multi-Component Systems," J. Chem. Phys. 18, 58-61 (1950).
[CrossRef]

J. Chimie Physique (1)

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," J. Chimie Physique 10, 1359-1366 (1966).

J. Phys. Chem. (2)

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

K. S. Pitzer and G. Mayorga, "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent," J. Phys. Chem. 77, 2300-2308 (1973).
[CrossRef]

Limnol. Oceanogr. (1)

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Marine Chemistry (1)

M. Lund, B. Jonsson, and T. Pedersen, "Activity coefficients in sea water using Monte Carlo simulations," Marine Chemistry 80, 95-101 (2003).
[CrossRef]

Optics Express (1)

X. Zhang and L. Hu, "Estimating scattering of pure water from density fluctuation of the refractive index," Optics Express 17, 1671-1678 (2009).
[CrossRef] [PubMed]

Trans. Faraday Soc. (1)

B. A. Pethica and C. Smart, "Light scattering of electrolyte solutions," Trans. Faraday Soc. 62, 1890-1899 (1966).
[CrossRef]

Other (9)

M. R. Wright, An Introduction to Aqueous Electrolyte Solutions (John Wiley & Sons Ltd., West Sussex, 2007).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).

D. R. Lide, Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2003).

C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, 1994).

A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov, and E. S. Nielsen, eds. (Academic Press, New York, 1974), pp. 1-24.

M. Jonasz, and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic Press, New York, 2007).

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

UNESCO, "Background papers and supporting data on the International Equation of State of Seawater 1980," UNESCO Technical Papers in Marine Science No. 38 (1981).

I. L. Fabelinskii, Molecular Scattering of Light (Plenum Press, New York, 1968).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Scattering by NaCl solution measured by Morel [5] at 546 nm was scaled, following the power-law of a slope of -4.30, to the sodium D line wavelength, 589 nm, at which the thermodynamic parameters for NaCl solution are available. The measured values, shown as % increases relative to the pure water, are compared with theoretical calculations using Eq. (4) and Eq. (5). The theoretical values for pure water were calculated using Eq. (2).

Fig. 2.
Fig. 2.

The difference in βc (90) of seawater estimated using Eq. (4) relative to the estimates using Eq. (9) as a function of salinity.

Fig. 3.
Fig. 3.

Spectral scattering of seawater estimated for S = 38.4‰ and Tc = 20°C are compared with the measurements [5, 6] and the calculations [13] by Morel.

Fig. 4.
Fig. 4.

Scattering of seawater due to density fluctuation (blue line), due to concentration fluctuation (blue dashed line and right Y-axis) and their total are estimated for λ = 546 nm and Tc = 20°C as a function of salinity. The empirical variation estimated using Eq. (3) is shown as red.

Tables (1)

Tables Icon

Table 1. Parameters used in estimating seawater scattering and their formulae for calculation

Equations (26)

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

β ( 90 ) = β d ( 90 ) + β c ( 90 ) ,
β d ( 90 ) = π 2 2 λ 4 ( ρ n 2 ρ ) T 2 k T β T f ( δ )
β ( 90 ) = β pw ( 90 ) ( 1 + 0.3 S 0 S )
β c ( 90 ) = π 2 M ss S 2 λ 4 N A ( n 2 S ) 2 f ( δ ) ρ
β c ( 90 ) = π 2 2 λ 4 N A ( n 2 c ) 2 c V ̅ 0 In a 0 / c f ( δ )
V ¯ 0 = ( V m 0 ) m ss = m 0 ( M 0 m 0 + M ss m ss ρ ) m ss ,
S = M ss m ss M 0 m 0 + M ss m ss
V ¯ 0 = M 0 ρ ( 1 + S ρ ρ S ) ,
β c ( 90 ) = π 2 2 λ 4 N A ( n 2 S ) 2 M 0 ρ S In a 0 / S f ( δ ) .
In a 0 S = M 0 M ss 1 X ss ( 1 S ) 2 M 0 M ss
β c ( 90 ) = π 2 2 λ 4 ΔV Δ ε 2 ¯ f ( δ )
c = m ss Σ f i M i Δ V
dc = d m ss M ss Δ V .
Δ ε 2 ¯ = ( ε c ) 2 Δ c 2 ¯ .
Δ c 2 ¯ = k T ( 2 A / c 2 ) T , V
d A = μ 0 d m 0 + d m ss i f i μ i
Δ V = m 0 V ¯ 0 + m ss i f i V ¯ i
d m 0 = Σ f i V ¯ i V ¯ 0 d m ss .
d A = ( Σ f i μ i Σ f i V ¯ i V ¯ 0 μ 0 ) d m ss .
( A c ) T , V = ( Σ f i μ i Σ f i V ¯ i V ¯ 0 μ 0 ) Δ V M ss
( 2 A c 2 ) T , V = ( Σ f i μ i c Σ f i V ¯ i V ¯ 0 μ 0 c ) Δ V M ss
m 0 d μ 0 + m ss Σ f i d μ i = 0
( 2 A c 2 ) T , V = Δ V V ¯ 0 ( m 0 V ¯ 0 + m ss Σ f i V ¯ i m ss M ss ) ( μ 0 c ) T , V .
( 2 A c 2 ) T , V = Δ V c V 0 ¯ ( μ 0 c ) T , V .
μ = μ 0 + RT In a
( 2 A c 2 ) T , V = R T Δ V c V ¯ 0 ( In a 0 c ) T , V

Metrics