Abstract

A one-parameter model of the inherent optical properties of biologically stable waters is proposed. The model is based on the results of in situ measurements of inherent optical properties that have been conducted at different seas and oceans by a number of researchers. The results of these investigations are processed to force this model to agree satisfactorily with an established regression model that connects the color index with the chlorophyll concentration. The model couples two concentrations of colored dissolved organic matter (concentrations of humic and fulvic acids) and two concentrations of suspended scattering particles (concentrations of terrigenic and biogenic particles) with the chlorophyll concentration. As a result, this model expresses all inherent properties of seawater by a single parameter, the concentration of chlorophyll.

© 1999 Optical Society of America

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  1. Some of the material in this paper has been presented at the Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998 (see Ref. 2).
  2. V. I. Haltrin, “One-parameter model of seawater optical properties,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., November1998).
  3. K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
    [CrossRef]
  4. D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
    [CrossRef]
  5. O. V. Kopelevich, “Small-parametric model of the optical properties of seawater,” in Ocean Optics, I: Physical Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), pp. 208–234 (in Russian).
  6. L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
    [CrossRef]
  7. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water: II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
  8. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  9. A. Morel, “In-water and remote measurement of ocean color,” Boundary-Layer Meteorol. 18, 177–201 (1980).
    [CrossRef]
  10. H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery (Springer-Verlag, Berlin, 1983).
    [CrossRef]
  11. V. A. Timofeyeva, “Optical characteristics of turbid media of the seawater type,” Izv. Atmos. Ocean Phys. 7, 863–865 (1971).
  12. V. I. Haltrin (aka V. I. Khalturin), “Propagation of light in sea depth,” in Optical Remote Sensing of the Sea and the Influence of the Atmosphere, V. A. Urdenko, G. Zimmermann, eds. (German Democratic Republic Academy of Sciences Institute for Space Research, Berlin, 1985), Chap. 2, pp. 20–62 (in Russian).
  13. V. I. Haltrin, “Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth and surface illumination,” Appl. Opt. 37, 3773–3784 (1998).
    [CrossRef]
  14. S. K. Hawes, K. L. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effect on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
    [CrossRef]
  15. V. I. Haltrin, G. W. Kattawar, “Effects of Raman scattering and fluorescence on apparent optical properties of seawater,” (Department of Physics, Texas AM University, College Station, Tex., 1991).
  16. V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. Model,” Appl. Opt. 32, 5356–5367 (1993).
    [CrossRef] [PubMed]
  17. V. I. Haltrin, G. W. Kattawar, A. D. Weidemann, “Modeling of elastic and inelastic scattering effects in oceanic optics,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 597–602 (1997).
    [CrossRef]
  18. If we consider these processes on a macroscopic level.
  19. V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).
  20. In a general case absorption coefficient a is a function of wavelength λ and sea depth z. The angular scattering coefficient β is a function of wavelength λ, sea depth z, and scattering angle ϑ.
  21. V. I. Haltrin, “Theoretical and empirical phase functions for Monte Carlo calculations of light scattering in seawater,” in Proceedings of the Fourth International Conference Remote Sensing for Marine and Coastal Environments, I (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1997), pp. 509–518. [Errata.: in Eq. (45) exponent base e should be replaced by 10. In Fig. 3 the vertical label should be: Logarithm (base 10) of Scattering Phase Function.]
  22. V. A. Timofeyeva, “The diffuse reflection coefficient and its relation to the optical parameters of turbid media,” Izv. Atmos. Ocean Phys. 7, 467–469 (1971).
  23. V. A. Timofeyeva, “Relation between the optical coefficients in turbid media,” Izv. Atmos. Ocean Phys. 8, 654–656 (1972).
  24. V. A. Timofeyeva, “Relation between light field parameters and between scattering phase function characteristics of turbid media, including sea water,” Izv. Atmos. Ocean Phys. 14, 843–848 (1978).
  25. V. A. Timofeyeva, “Determination of light-field parameters in the depth regime from irradiance measurements,” Izv. Atmos. Ocean Phys. 15, 774–776 (1979).
  26. T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters, (Scripps Institute of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).
  27. V. I. Haltrin, “Apparent optical properties of the sea illuminated by Sun and sky: case of the optically deep sea,” Appl. Opt. 37, 8336–8340 (1998).
    [CrossRef]
  28. V. I. Haltrin, “Diffuse reflection coefficient of a stratified sea,” Appl. Opt. 38, 932–936 (1999).
    [CrossRef]
  29. E. Aas, N. K. Hojerslev, B. Lundgren, “Spectral irradiance, radiance and polarization data from the Nordic cruise in the Mediterranean Sea during June–July 1971,” (Institutt for Geofysikk, Universitet i Oslo, September1997).
  30. The explanation of nonlinear dependence on concentration can be found in Ref. 31.
  31. V. I. Haltrin, “Light scattering coefficient of seawater for arbitrary concentrations of hydrosols,” J. Opt. Soc. Am. 16, 1715–1723 (1999).
    [CrossRef]
  32. C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).
  33. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  34. V. I. Haltrin, “An algorithm to restore spectral signatures of all inherent optical properties of seawater using a value of one property at one wavelength,” in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition/21st Canadian Symposium on Remote Sensing, (Environmental Research Institute of Michigan International, Ann Arbor, Mich., 1999), pp. I-680–I-687.
  35. V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

1999

V. I. Haltrin, “Diffuse reflection coefficient of a stratified sea,” Appl. Opt. 38, 932–936 (1999).
[CrossRef]

V. I. Haltrin, “Light scattering coefficient of seawater for arbitrary concentrations of hydrosols,” J. Opt. Soc. Am. 16, 1715–1723 (1999).
[CrossRef]

1998

1997

1993

1989

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

1985

V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).

V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).

1981

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

1980

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

D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
[CrossRef]

1979

V. A. Timofeyeva, “Determination of light-field parameters in the depth regime from irradiance measurements,” Izv. Atmos. Ocean Phys. 15, 774–776 (1979).

1978

V. A. Timofeyeva, “Relation between light field parameters and between scattering phase function characteristics of turbid media, including sea water,” Izv. Atmos. Ocean Phys. 14, 843–848 (1978).

1977

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

1972

V. A. Timofeyeva, “Relation between the optical coefficients in turbid media,” Izv. Atmos. Ocean Phys. 8, 654–656 (1972).

1971

V. A. Timofeyeva, “Optical characteristics of turbid media of the seawater type,” Izv. Atmos. Ocean Phys. 7, 863–865 (1971).

V. A. Timofeyeva, “The diffuse reflection coefficient and its relation to the optical parameters of turbid media,” Izv. Atmos. Ocean Phys. 7, 467–469 (1971).

Aas, E.

E. Aas, N. K. Hojerslev, B. Lundgren, “Spectral irradiance, radiance and polarization data from the Nordic cruise in the Mediterranean Sea during June–July 1971,” (Institutt for Geofysikk, Universitet i Oslo, September1997).

Backer, E. T.

D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
[CrossRef]

Carder, K. L.

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

S. K. Hawes, K. L. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effect on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Clark, D. K.

D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
[CrossRef]

Fry, E. S.

Gordon, H. R.

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery (Springer-Verlag, Berlin, 1983).
[CrossRef]

Haltrin, V. I.

V. I. Haltrin, “Light scattering coefficient of seawater for arbitrary concentrations of hydrosols,” J. Opt. Soc. Am. 16, 1715–1723 (1999).
[CrossRef]

V. I. Haltrin, “Diffuse reflection coefficient of a stratified sea,” Appl. Opt. 38, 932–936 (1999).
[CrossRef]

V. I. Haltrin, “Apparent optical properties of the sea illuminated by Sun and sky: case of the optically deep sea,” Appl. Opt. 37, 8336–8340 (1998).
[CrossRef]

V. I. Haltrin, “Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth and surface illumination,” Appl. Opt. 37, 3773–3784 (1998).
[CrossRef]

V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. Model,” Appl. Opt. 32, 5356–5367 (1993).
[CrossRef] [PubMed]

V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).

V. I. Haltrin, “Theoretical and empirical phase functions for Monte Carlo calculations of light scattering in seawater,” in Proceedings of the Fourth International Conference Remote Sensing for Marine and Coastal Environments, I (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1997), pp. 509–518. [Errata.: in Eq. (45) exponent base e should be replaced by 10. In Fig. 3 the vertical label should be: Logarithm (base 10) of Scattering Phase Function.]

V. I. Haltrin, G. W. Kattawar, A. D. Weidemann, “Modeling of elastic and inelastic scattering effects in oceanic optics,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 597–602 (1997).
[CrossRef]

V. I. Haltrin (aka V. I. Khalturin), “Propagation of light in sea depth,” in Optical Remote Sensing of the Sea and the Influence of the Atmosphere, V. A. Urdenko, G. Zimmermann, eds. (German Democratic Republic Academy of Sciences Institute for Space Research, Berlin, 1985), Chap. 2, pp. 20–62 (in Russian).

V. I. Haltrin, G. W. Kattawar, “Effects of Raman scattering and fluorescence on apparent optical properties of seawater,” (Department of Physics, Texas AM University, College Station, Tex., 1991).

V. I. Haltrin, “One-parameter model of seawater optical properties,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., November1998).

V. I. Haltrin, “An algorithm to restore spectral signatures of all inherent optical properties of seawater using a value of one property at one wavelength,” in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition/21st Canadian Symposium on Remote Sensing, (Environmental Research Institute of Michigan International, Ann Arbor, Mich., 1999), pp. I-680–I-687.

V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

Harvey, G. R.

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

S. K. Hawes, K. L. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effect on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Hawes, S. K.

S. K. Hawes, K. L. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effect on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Hojerslev, N. K.

E. Aas, N. K. Hojerslev, B. Lundgren, “Spectral irradiance, radiance and polarization data from the Nordic cruise in the Mediterranean Sea during June–July 1971,” (Institutt for Geofysikk, Universitet i Oslo, September1997).

Kattawar, G. W.

V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. Model,” Appl. Opt. 32, 5356–5367 (1993).
[CrossRef] [PubMed]

V. I. Haltrin, G. W. Kattawar, A. D. Weidemann, “Modeling of elastic and inelastic scattering effects in oceanic optics,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 597–602 (1997).
[CrossRef]

V. I. Haltrin, G. W. Kattawar, “Effects of Raman scattering and fluorescence on apparent optical properties of seawater,” (Department of Physics, Texas AM University, College Station, Tex., 1991).

Khalturin, V. I.

V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).

V. I. Haltrin (aka V. I. Khalturin), “Propagation of light in sea depth,” in Optical Remote Sensing of the Sea and the Influence of the Atmosphere, V. A. Urdenko, G. Zimmermann, eds. (German Democratic Republic Academy of Sciences Institute for Space Research, Berlin, 1985), Chap. 2, pp. 20–62 (in Russian).

Kopelevich, O. V.

O. V. Kopelevich, “Small-parametric model of the optical properties of seawater,” in Ocean Optics, I: Physical Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), pp. 208–234 (in Russian).

Lundgren, B.

E. Aas, N. K. Hojerslev, B. Lundgren, “Spectral irradiance, radiance and polarization data from the Nordic cruise in the Mediterranean Sea during June–July 1971,” (Institutt for Geofysikk, Universitet i Oslo, September1997).

Mobley, C. D.

C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).

Morel, A.

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

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 (Springer-Verlag, Berlin, 1983).
[CrossRef]

Ortner, P. B.

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters, (Scripps Institute of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).

Pope, R. M.

Prieur, L.

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves 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]

Sathyendranath, S.

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

Shifrin, K. S.

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

Shybanov, E. B.

V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

Stavn, R. H.

V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

Stewart, R. G.

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Strong, A. E.

D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
[CrossRef]

Timofeyeva, V. A.

V. A. Timofeyeva, “Determination of light-field parameters in the depth regime from irradiance measurements,” Izv. Atmos. Ocean Phys. 15, 774–776 (1979).

V. A. Timofeyeva, “Relation between light field parameters and between scattering phase function characteristics of turbid media, including sea water,” Izv. Atmos. Ocean Phys. 14, 843–848 (1978).

V. A. Timofeyeva, “Relation between the optical coefficients in turbid media,” Izv. Atmos. Ocean Phys. 8, 654–656 (1972).

V. A. Timofeyeva, “The diffuse reflection coefficient and its relation to the optical parameters of turbid media,” Izv. Atmos. Ocean Phys. 7, 467–469 (1971).

V. A. Timofeyeva, “Optical characteristics of turbid media of the seawater type,” Izv. Atmos. Ocean Phys. 7, 863–865 (1971).

Weidemann, A. D.

V. I. Haltrin, G. W. Kattawar, A. D. Weidemann, “Modeling of elastic and inelastic scattering effects in oceanic optics,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 597–602 (1997).
[CrossRef]

V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

Appl. Opt.

Boundary-Layer Meteorol.

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

D. K. Clark, E. T. Backer, A. E. Strong, “Upwelled spectral radiance distribution in relation to particular matter in water,” Boundary-Layer Meteorol. 18, 287–298 (1980).
[CrossRef]

Izv. Atmos. Ocean Phys.

V. A. Timofeyeva, “Optical characteristics of turbid media of the seawater type,” Izv. Atmos. Ocean Phys. 7, 863–865 (1971).

V. A. Timofeyeva, “The diffuse reflection coefficient and its relation to the optical parameters of turbid media,” Izv. Atmos. Ocean Phys. 7, 467–469 (1971).

V. A. Timofeyeva, “Relation between the optical coefficients in turbid media,” Izv. Atmos. Ocean Phys. 8, 654–656 (1972).

V. A. Timofeyeva, “Relation between light field parameters and between scattering phase function characteristics of turbid media, including sea water,” Izv. Atmos. Ocean Phys. 14, 843–848 (1978).

V. A. Timofeyeva, “Determination of light-field parameters in the depth regime from irradiance measurements,” Izv. Atmos. Ocean Phys. 15, 774–776 (1979).

V. I. Khalturin (aka V. I. Haltrin), “The self-consistent two-stream approximation in radiative transfer theory for the media with anisotropic scattering,” Izv. Atmos. Ocean Phys. 21, 452–457 (1985).

J. Opt. Soc. Am.

V. I. Haltrin, “Light scattering coefficient of seawater for arbitrary concentrations of hydrosols,” J. Opt. Soc. Am. 16, 1715–1723 (1999).
[CrossRef]

Limnol. Oceanogr.

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

K. L. Carder, R. G. Stewart, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

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

Other

O. V. Kopelevich, “Small-parametric model of the optical properties of seawater,” in Ocean Optics, I: Physical Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), pp. 208–234 (in Russian).

Some of the material in this paper has been presented at the Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998 (see Ref. 2).

V. I. Haltrin, “One-parameter model of seawater optical properties,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., November1998).

V. I. Haltrin (aka V. I. Khalturin), “Propagation of light in sea depth,” in Optical Remote Sensing of the Sea and the Influence of the Atmosphere, V. A. Urdenko, G. Zimmermann, eds. (German Democratic Republic Academy of Sciences Institute for Space Research, Berlin, 1985), Chap. 2, pp. 20–62 (in Russian).

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery (Springer-Verlag, Berlin, 1983).
[CrossRef]

V. I. Haltrin, G. W. Kattawar, A. D. Weidemann, “Modeling of elastic and inelastic scattering effects in oceanic optics,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 597–602 (1997).
[CrossRef]

If we consider these processes on a macroscopic level.

S. K. Hawes, K. L. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effect on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

V. I. Haltrin, G. W. Kattawar, “Effects of Raman scattering and fluorescence on apparent optical properties of seawater,” (Department of Physics, Texas AM University, College Station, Tex., 1991).

C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).

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

V. I. Haltrin, “An algorithm to restore spectral signatures of all inherent optical properties of seawater using a value of one property at one wavelength,” in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition/21st Canadian Symposium on Remote Sensing, (Environmental Research Institute of Michigan International, Ann Arbor, Mich., 1999), pp. I-680–I-687.

V. I. Haltrin, E. B. Shybanov, R. H. Stavn, A. D. Weidemann, “Light scattering coefficient by quartz particles suspended in seawater,” in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS’99, T. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1420–1422.

In a general case absorption coefficient a is a function of wavelength λ and sea depth z. The angular scattering coefficient β is a function of wavelength λ, sea depth z, and scattering angle ϑ.

V. I. Haltrin, “Theoretical and empirical phase functions for Monte Carlo calculations of light scattering in seawater,” in Proceedings of the Fourth International Conference Remote Sensing for Marine and Coastal Environments, I (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1997), pp. 509–518. [Errata.: in Eq. (45) exponent base e should be replaced by 10. In Fig. 3 the vertical label should be: Logarithm (base 10) of Scattering Phase Function.]

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters, (Scripps Institute of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).

E. Aas, N. K. Hojerslev, B. Lundgren, “Spectral irradiance, radiance and polarization data from the Nordic cruise in the Mediterranean Sea during June–July 1971,” (Institutt for Geofysikk, Universitet i Oslo, September1997).

The explanation of nonlinear dependence on concentration can be found in Ref. 31.

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Figures (5)

Fig. 1
Fig. 1

Cases of (a) physical and (b)–(d) nonphysical solutions to Eq. (13). The physical solution should be monotonous, and its derivative should not have infinitely large spikes.

Fig. 2
Fig. 2

Regression between the color index, I c = R(550)/R(440), and the chlorophyll concentration C c computed for different types of illuminations (each symbol represents 324 close values) compared with the regression C c = 1.92I c 1.8 (solid curve).

Fig. 3
Fig. 3

Relationship between the normalized to the beam attenuation coefficient c asymptotic diffuse attenuation coefficient α/c = (1 - ω0)/µ̅ and the single-scattering albedo ω0. The displayed data were computed with the model given by Eqs. (1)–(11) and (14) (14,520 values) and plotted with the experimental data from Ref. 11.

Fig. 4
Fig. 4

Example of restored spectral inherent optical properties.

Fig. 5
Fig. 5

Example of restored seawater scattering phase functions.

Tables (2)

Tables Icon

Table 1 Coefficients of Eqs. (9) for the Two Basic Phase Functions p s and p l

Tables Icon

Table 2 Coefficients of Eqs. (19)–(21)

Equations (24)

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b=0.5 0π βϑsin ϑdϑ;
B=0.5 π/2π pϑsin ϑdϑbB/b;
g=ω0B/1-ω0+ω0BbB/a+bB.
aλ=awλ+ac0λCc/Cc00.602+af0Cf exp-kfλ+ah0Ch exp-khλ,
bλ=bwλ+bs0λCs+bl0λCl,
bBλ=0.5bwλ+Bsbs0λCs+Blbl0λCl,
Bs=0.5 π/2π psϑsin ϑdϑ=0.039,  Bl=0.5 π/2π plϑsin ϑdϑ=6.4×10-4,
bwλ=0.005826m-1400λ4.322.
bs0λ=1.151302 m2/g 400λ1.7,
bl0λ=0.341074 m2/g 400λ0.3.
βHλ, ϑ=bs0λpsϑCs+bl0λplϑCl.
pSϑ=5.61746 expn=15 sn ϑ3n/4,  pLϑ=188.381 expn=15 lnϑ3n/4,
βλ, ϑ=bwλpRϑ+bs0λpsϑCs+bl0λplϑCl,
pRϑ=0.7823+0.6531 cos2 ϑ.
Cr=1.92Ic1.8,  Ic=R550R440,
ΔCc, Cf, Ch, Cs, Cl=|Cc-Cr|Cc-1.92R550R4401.8.
Cf=1.74098Cc exp0.12327Cc/Cc0,  Ch=0.19334Cc exp0.12343Cc/Cc0,  Cs=0.01739g/mgCc exp0.11631Cc/Cc0,  Cl=0.76284g/mgCc exp0.03092Cc/Cc0,
R=R+μsqRs1+μsq,
R=1-μ¯1+μ¯2,  Rs=1-μ¯21+μ¯μs4-μ¯2,  μ¯=aa+3bB+bB4a+9bB1/21/2,  μs=1-cos hs/nw21/2,
Δbλ=bλ-bwλ,
ΔbBλ=bBλ-0.5bwλ,
Cc=Δbσ1+Δbσ2+σ3Δb,  σj=n=03 σjnλ-500500n,  j=1, 2, 3,
bB=0.5bw+Δbγ1+Δbγ2+γ3Δb,  γj=n=03 γjnλ-500500n,  j=1, 2, 3,
b=bw+ΔbBχ1+ΔbBχ2+ΔbBχ3+χ4ΔbB,  χj=n=03 χjnλ-500500n, j=1, 2, 3, 4.

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