Abstract

Field observations and theoretical studies have found that the volume scattering functions (VSFs) of oceanic particles exhibit minimum variability at angles near 120°. However, its physical interpretation is still unknown. We find this minimum variability angle represents the intersection of two backscattering-normalized VSFs, one representing particles of sizes smaller than the wavelength of light and the other larger than the wavelength of light. This also suggests that the VSFs of oceanic particles at angles between 90° and 180°, which play a critical role in ocean color study, can be modeled by linear mixing of these two end members. We further validate this mixing model using measured VSFs in coastal and oceanic waters around the US and develop a two-component model predicting the backward shapes of the VSFs.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Significance of scattering by oceanic particles at angles around 120 degree

Xiaodong Zhang, Emmanuel Boss, and Deric J. Gray
Opt. Express 22(25) 31329-31336 (2014)

Accurate estimation of the backscattering coefficient by light scattering at two backward angles

Hiroyuki Tan, Tomohiko Oishi, Akihiko Tanaka, and Roland Doerffer
Appl. Opt. 54(25) 7718-7733 (2015)

Angular shape of the oceanic particulate volume scattering function in the backward direction

James M. Sullivan and Michael S. Twardowski
Appl. Opt. 48(35) 6811-6819 (2009)

References

  • View by:
  • |
  • |
  • |

  1. J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13 (1995).
  2. X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17(3), 1671–1678 (2009).
    [Crossref] [PubMed]
  3. X. Zhang and L. Hu, “Scattering by pure seawater at high salinity,” Opt. Express 17(15), 12685–12691 (2009).
    [Crossref] [PubMed]
  4. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17(7), 5698–5710 (2009).
    [Crossref] [PubMed]
  5. D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
    [Crossref]
  6. C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” J. Geophys. Res. 96(D3), 5269–5277 (1991).
    [Crossref]
  7. R. A. Meyer, “Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index,” Appl. Opt. 18(5), 585–588 (1979).
    [Crossref] [PubMed]
  8. T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120 °,” Appl. Opt. 29(31), 4658–4665 (1990).
    [Crossref] [PubMed]
  9. E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40(30), 5503–5507 (2001).
    [Crossref] [PubMed]
  10. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
    [Crossref] [PubMed]
  11. X. Zhang, E. Boss, and D. J. Gray, “Significance of scattering by oceanic particles at angles around 120 degree,” Opt. Express 22(25), 31329–31336 (2014).
    [Crossref] [PubMed]
  12. A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
    [Crossref] [PubMed]
  13. R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36(24), 6057–6067 (1997).
    [Crossref] [PubMed]
  14. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
    [Crossref]
  15. E. J. Davies, D. McKee, D. Bowers, G. W. Graham, and W. A. M. Nimmo-Smith, “Optically significant particle sizes in seawater,” Appl. Opt. 53(6), 1067–1074 (2014).
    [Crossref] [PubMed]
  16. H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, Inc., 1981).
  17. M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353(6342), 342–344 (1991).
    [Crossref]
  18. P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
    [Crossref]
  19. K. A. Stacey, Light-scattering in Physical Chemistry (Butterworths Scientific Publications, 1956), p. 230.
  20. R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
    [Crossref]
  21. M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007), p. 704.
  22. G. R. Fournier, “Backscatter corrected Fournier-Forand phase function for remote sensing and underwater imaging performance evaluation,” in Current Research on Remote Sensing, Laser Probing, and Imagery in Natural Waters, L. M. Levin, G. D. Gilbert, V. I. Haltrin, and C. C. Trees, eds. (SPIE, 2007), pp. 66150N:66151–66157.
  23. G. R. Fournier and G. Neukermans, “An analytical model for light backscattering and scattering coefficients of coccoliths and coccospheres,” in Ocean Optics XXIII, (Victoria, BC, Canada, 2016).
  24. E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18(12), 2223–2249 (1996).
    [Crossref]
  25. X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51(21), 5085–5099 (2012).
    [Crossref] [PubMed]
  26. X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
    [Crossref]
  27. X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
    [Crossref]
  28. X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res.: Oceans 120(10), 6914–6926 (2015).
    [Crossref]
  29. H. Tan, T. Oishi, A. Tanaka, and R. Doerffer, “Accurate estimation of the backscattering coefficient by light scattering at two backward angles,” Appl. Opt. 54(25), 7718–7733 (2015).
    [Crossref] [PubMed]
  30. H. M. Nussenzveig, “Does the glory have a simple explanation?” Opt. Lett. 27(16), 1379–1381 (2002).
    [Crossref] [PubMed]
  31. W. Arnott and P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. 5(4), 496–506 (1988).
    [Crossref]
  32. O. V. Kopelevich, “Low-parametric model of seawater optical properties,” in Ocean Optics I: Physical Ocean Optics, A. S. Monin, ed. (Nauka Pub., 1983), pp. 208–234.
  33. V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Appl. Opt. 38(33), 6826–6832 (1999).
    [Crossref] [PubMed]
  34. J. Ronald and V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21(22), 4146–4150 (1982).
    [Crossref] [PubMed]
  35. S. Q. Duntley, R. W. Austin, W. H. Wilson, C. F. Edgerton, and S. E. Moran, “Ocean Color Analysis,” SIO Ref. 74–10, Scripps Institution of Oceanography (1974).
  36. H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975).
    [Crossref] [PubMed]
  37. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
    [Crossref]
  38. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
    [Crossref] [PubMed]
  39. Z. P. Lee, K. Du, K. J. Voss, G. Zibordi, B. Lubac, R. Arnone, and A. Weidemann, “An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance,” Appl. Opt. 50(19), 3155–3167 (2011).
    [Crossref] [PubMed]
  40. Z. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002).
    [Crossref] [PubMed]

2015 (2)

2014 (3)

2013 (1)

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

2009 (5)

2004 (1)

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

2002 (2)

2001 (1)

1999 (1)

1998 (1)

P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
[Crossref]

1997 (1)

1996 (2)

1995 (1)

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

1991 (2)

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” J. Geophys. Res. 96(D3), 5269–5277 (1991).
[Crossref]

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353(6342), 342–344 (1991).
[Crossref]

1990 (1)

1988 (1)

W. Arnott and P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. 5(4), 496–506 (1988).
[Crossref]

1982 (1)

1979 (1)

1977 (1)

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

1976 (1)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[Crossref]

1975 (1)

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18(12), 2223–2249 (1996).
[Crossref]

Arnone, R.

Arnone, R. A.

Arnott, W.

W. Arnott and P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. 5(4), 496–506 (1988).
[Crossref]

Behrenfeld, M. J.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Bi, L.

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

Bohren, C. F.

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” J. Geophys. Res. 96(D3), 5269–5277 (1991).
[Crossref]

Boss, E.

Bowers, D.

Brown, O. B.

Carder, K. L.

Chin, W.-C.

P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
[Crossref]

Cowles, T. J.

Dall’Olmo, G.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Dana, D. R.

Davies, E. J.

Doerffer, R.

Du, K.

Falster, A. U.

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[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(2), 593–595 (1976).
[Crossref]

Gentili, B.

Goldberg, E. D.

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353(6342), 342–344 (1991).
[Crossref]

Gordon, H. R.

Gould, R. W.

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Graham, G. W.

Gray, D.

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Gray, D. J.

X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res.: Oceans 120(10), 6914–6926 (2015).
[Crossref]

X. Zhang, E. Boss, and D. J. Gray, “Significance of scattering by oceanic particles at angles around 120 degree,” Opt. Express 22(25), 31329–31336 (2014).
[Crossref] [PubMed]

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51(21), 5085–5099 (2012).
[Crossref] [PubMed]

Haltrin, V. I.

He, M.-X.

Hu, L.

Huot, Y.

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51(21), 5085–5099 (2012).
[Crossref] [PubMed]

Jacobs, M. M.

Karp-Boss, L.

Lee, Z.

Lee, Z. P.

Lubac, B.

Maffione, R. A.

Marston, P. L.

W. Arnott and P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. 5(4), 496–506 (1988).
[Crossref]

McKee, D.

Meyer, R. A.

Morel, A.

Nimmo-Smith, W. A. M.

Nussenzveig, H. M.

Oishi, T.

Orellana, M. V.

P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
[Crossref]

Pegau, W. S.

Prieur, L.

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

Rhea, W. J.

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

Ronald, J.

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(2), 593–595 (1976).
[Crossref]

Singham, S. B.

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” J. Geophys. Res. 96(D3), 5269–5277 (1991).
[Crossref]

Slade, W. H.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Stavn, R. H.

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Stramski, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

Sullivan, J. M.

Tan, H.

Tanaka, A.

Twardowski, M. S.

Verdugo, P.

P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
[Crossref]

Voss, K. J.

Weidemann, A.

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

Z. P. Lee, K. Du, K. J. Voss, G. Zibordi, B. Lubac, R. Arnone, and A. Weidemann, “An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance,” Appl. Opt. 50(19), 3155–3167 (2011).
[Crossref] [PubMed]

Wells, M. L.

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353(6342), 342–344 (1991).
[Crossref]

Westberry, T. K.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Whitmire, A. L.

You, Y.

Zaneveld, J. R. V.

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

Zaneveld, V.

Zhang, X.

X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res.: Oceans 120(10), 6914–6926 (2015).
[Crossref]

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

X. Zhang, E. Boss, and D. J. Gray, “Significance of scattering by oceanic particles at angles around 120 degree,” Opt. Express 22(25), 31329–31336 (2014).
[Crossref] [PubMed]

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51(21), 5085–5099 (2012).
[Crossref] [PubMed]

X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17(3), 1671–1678 (2009).
[Crossref] [PubMed]

X. Zhang and L. Hu, “Scattering by pure seawater at high salinity,” Opt. Express 17(15), 12685–12691 (2009).
[Crossref] [PubMed]

X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17(7), 5698–5710 (2009).
[Crossref] [PubMed]

Zibordi, G.

Appl. Opt. (14)

R. A. Meyer, “Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index,” Appl. Opt. 18(5), 585–588 (1979).
[Crossref] [PubMed]

T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120 °,” Appl. Opt. 29(31), 4658–4665 (1990).
[Crossref] [PubMed]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40(30), 5503–5507 (2001).
[Crossref] [PubMed]

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
[Crossref] [PubMed]

R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36(24), 6057–6067 (1997).
[Crossref] [PubMed]

E. J. Davies, D. McKee, D. Bowers, G. W. Graham, and W. A. M. Nimmo-Smith, “Optically significant particle sizes in seawater,” Appl. Opt. 53(6), 1067–1074 (2014).
[Crossref] [PubMed]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51(21), 5085–5099 (2012).
[Crossref] [PubMed]

H. Tan, T. Oishi, A. Tanaka, and R. Doerffer, “Accurate estimation of the backscattering coefficient by light scattering at two backward angles,” Appl. Opt. 54(25), 7718–7733 (2015).
[Crossref] [PubMed]

V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Appl. Opt. 38(33), 6826–6832 (1999).
[Crossref] [PubMed]

J. Ronald and V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21(22), 4146–4150 (1982).
[Crossref] [PubMed]

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975).
[Crossref] [PubMed]

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
[Crossref] [PubMed]

Z. P. Lee, K. Du, K. J. Voss, G. Zibordi, B. Lubac, R. Arnone, and A. Weidemann, “An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance,” Appl. Opt. 50(19), 3155–3167 (2011).
[Crossref] [PubMed]

Z. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002).
[Crossref] [PubMed]

Biogeosciences (2)

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10(9), 6029–6043 (2013).
[Crossref]

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Estuar. Coast. Shelf Sci. (1)

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould., “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuar. Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

J. Chem. Phys. (1)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[Crossref]

J. Geophys. Res. (2)

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

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” J. Geophys. Res. 96(D3), 5269–5277 (1991).
[Crossref]

J. Geophys. Res.: Oceans (1)

X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res.: Oceans 120(10), 6914–6926 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

W. Arnott and P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. 5(4), 496–506 (1988).
[Crossref]

J. Plankton Res. (1)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18(12), 2223–2249 (1996).
[Crossref]

Limnol. Oceanogr. (1)

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

Nature (2)

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353(6342), 342–344 (1991).
[Crossref]

P. Verdugo, W.-C. Chin, and M. V. Orellana, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391(6667), 568–572 (1998).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Prog. Oceanogr. (1)

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

Other (7)

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007), p. 704.

G. R. Fournier, “Backscatter corrected Fournier-Forand phase function for remote sensing and underwater imaging performance evaluation,” in Current Research on Remote Sensing, Laser Probing, and Imagery in Natural Waters, L. M. Levin, G. D. Gilbert, V. I. Haltrin, and C. C. Trees, eds. (SPIE, 2007), pp. 66150N:66151–66157.

G. R. Fournier and G. Neukermans, “An analytical model for light backscattering and scattering coefficients of coccoliths and coccospheres,” in Ocean Optics XXIII, (Victoria, BC, Canada, 2016).

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, Inc., 1981).

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

S. Q. Duntley, R. W. Austin, W. H. Wilson, C. F. Edgerton, and S. E. Moran, “Ocean Color Analysis,” SIO Ref. 74–10, Scripps Institution of Oceanography (1974).

K. A. Stacey, Light-scattering in Physical Chemistry (Butterworths Scientific Publications, 1956), p. 230.

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

α(θ) computed between 90 and 180° for very small (PS) particles with different depolarization ratio (δ) and for very large (PL) particles with different refractive indexes (m).

Fig. 2
Fig. 2

Fitting Eq. (7) with αS and αL shown in Fig. 1 to measured α(θ). (a) the sum of derived coefficients f, which has a mean value = 1.011 ± 0.009 with 8 end members (EM) and 1.006 ± 0.014 with 2 end members; (b) percentage root mean square differences between measured and fitted α(θ) with 8 and 2 end members, respectively; (c) the total numbers of αS and αL that have non-zero coefficients; (d) the distribution of end members that have non-zero coefficients. For the x-axis in (d), the first three values (0.01, 0.03 and 0.05) are for δ needed to compute αS(θ) using Eq. (4) and the rest of the values (1.02, 1.06, 1.10, 1.14 and 1.18) are for m needed to compute αL(θ) using Eqs. (5) and (6).

Fig. 3
Fig. 3

Examples, one from each site (a: Chesapeake Bay, b: Mobile Bay, c: Monterey Bay, d: SABOR Cruise, North Atlantic Ocean), of fitting Eq. (7) with αS (δ = 0.01) and αL (m = 1.02) as the two end members. Gray lines: α(θ) estimated from measured VSFs; dotted lines: reproduced α(θ) from linear mixing of the two end members.

Fig. 4
Fig. 4

(a) α(θ) estimated for hypothetical particle populations with PS (δ = 0.01) and PL (m = 1.02) as two end members. The legend shows the fractional bb contribution by PS. (b) α(θ) measured in coastal waters of Chesapeake Bay in 2009, Mobile Bay in 2009, and Monterey Bay in 2010, and during the 2014 SABOR cruise in North Atlantic Ocean. The data were smoothed to remove high frequency variability. (c) variation of estimated fS or bbS/bb as a function of total particle backscattering coefficients.

Equations (11)

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

b b =2π π/2 π β(θ)sinθdθ .
α(θ) 1 χ(θ) = 2πβ(θ) b b = β(θ) π/2 π β(θ)sinθdθ .
β(θ)1+ 1δ 1+δ cos 2 θ,
α S (θ)= 3 2 1+δ+(1δ) cos 2 θ 2+δ .
β(θ) | r | 2 + | r | 2 + | r | 2 (1 | r | 2 ) 2 + | r | 2 (1 | r | 2 ) 2 ,
b b b b + b b b b = 3 m 4 16m + 3 12 m 2 1+2 (2 m 2 1) 3/2 6 ( m 2 1) 2 b b =[ (3ln16)+ 37 40 ( m1 m+1 ) ] b b .
α(θ)= i=1 n f Si α Si (θ) + j=1 m f Lj α Lj (θ) ,
i=1 n f Si + j=1 m f Lj =1,
α(θ)= f S α S (θ)+ f L α L (θ),
α(θ)= b bS b b α S (θ)+ b bL b b α L (θ).
f S =0.45(±0.05) (log b b ) 2 +1.90(±0.21)log b b +2.29(±0.21).

Metrics