Abstract

Volume scattering functions (VSFs) and other optical seawater parameters were measured during a cruise in the Southern Baltic. Phase functions (PFs) calculated from VSFs were compared with Fournier-Forand phase functions parameterized with backscattering ratios. Due to significant divergences between experimental and modeled data a new method of Fournier-Forand phase function parameterization is proposed.

© 2007 Optical Society of America

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References

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  1. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, Scripps Institute of Oceanography, U. California, San Diego (1972).
  2. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif.,1994).
  3. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [Crossref]
  4. V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in IGARSS ’99: Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York,1999), pp. 1423–1425.
  5. G. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
    [Crossref]
  6. M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
    [Crossref]
  7. E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.
  8. G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE 3761, 62–77 (1999).
    [Crossref]
  9. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase Function Effects on Oceanic Light Fields,” Appl. Opt. 41, 1035–1050 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=ao-41-6-1035.
    [Crossref] [PubMed]
  10. M. Chami, D. McKee, E. Leymarie, and G. Khomenko, “Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflectance,” Appl. Opt. 45, 9210–9220 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-36-9210.
    [Crossref] [PubMed]
  11. D. McKee and A. Cunningham, “Evidence for wavelength dependence of the scattering phase function and its implication for modeling radiance transfer in shelf seas,” Appl. Opt. 44, 126–135 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ao-44-1-126
    [PubMed]
  12. A. H. Hakim and N. J. McCormick, “Ocean Optics Estimation for Absorption, Backscattering, and Phase Function Parameters,” Appl. Opt. 42, 931–938 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=ao-42-6-931
    [Crossref] [PubMed]

2007 (1)

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

2006 (1)

2005 (1)

2003 (2)

A. H. Hakim and N. J. McCormick, “Ocean Optics Estimation for Absorption, Backscattering, and Phase Function Parameters,” Appl. Opt. 42, 931–938 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=ao-42-6-931
[Crossref] [PubMed]

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[Crossref]

2002 (1)

1999 (2)

V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in IGARSS ’99: Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York,1999), pp. 1423–1425.

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE 3761, 62–77 (1999).
[Crossref]

1994 (1)

G. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
[Crossref]

1941 (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Boss, E.

Chami, M.

Cunningham, A.

Forand, J. L.

G. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Fournier, G.

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE 3761, 62–77 (1999).
[Crossref]

G. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Freda, W.

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

Greenstein, J. L.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hakim, A. H.

Haltrin, V. I.

V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in IGARSS ’99: Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York,1999), pp. 1423–1425.

Hapter, R.

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

Henyey, L. C.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Jonasz, M.

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE 3761, 62–77 (1999).
[Crossref]

Khomenko, G.

Król, T.

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

Lee, M. E.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[Crossref]

Lewis, M. R.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[Crossref]

Leymarie, E.

Martynov, O. V.

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

McCormick, N. J.

McKee, D.

Mobley, C. D.

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, Scripps Institute of Oceanography, U. California, San Diego (1972).

Shybanov, E. B.

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

Sundman, L. K.

Appl. Opt. (4)

Astrophys. J. (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

J. Atmos. Ocean. Technol. (1)

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[Crossref]

Proc. SPIE (2)

G. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
[Crossref]

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE 3761, 62–77 (1999).
[Crossref]

Other (4)

E. B. Shybanov, O. V. Martynov, T. Król, W. Freda, and R. Hapter, “Scattering functions of Southern Baltic sea waters”, in Physicochemical Problems of Natural Waters Ecology, T. Król ed., (Gdynia Maritime University Publishing,2007),  Vol. 5, pp. 90–95.

V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in IGARSS ’99: Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York,1999), pp. 1423–1425.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78, Scripps Institute of Oceanography, U. California, San Diego (1972).

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif.,1994).

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Figures (2)

Fig. 1.
Fig. 1.

Contours of the backscatter fraction Bp determined by Eq. (2). Black points denote parameters of the FF phase functions obtained from the best fit of the FF shape to measured VSF at wavelength 443nm. Red dashed line is Mobley’s way to obtain parameters n and μ when Bp is given. The red circle shows parameters n and μ for the best fit to Petzold phase function.

Fig. 2.
Fig. 2.

Factors (n - 1)/(μ - 3) plotted with absorption coefficients a for wavelengths: a) 443nm, b) 490 nm, c) 555nm, d) 620nm.

Tables (1)

Tables Icon

Tab. 1. Average differences D (in %) between measured PF and calculated FF for three algorithms.

Equations (7)

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β ( θ ) = 1 4 π ( 1 δ ) 2 δ ν ( [ ν ( 1 δ ) ( 1 δ ν ) ] + 4 u 2 [ δ ( 1 δ ν ) ν ( 1 δ ) ] ) ,
ν = 3 μ 2 , δ = u 2 3 ( n 1 ) 2 , u = 2 sin ( θ 2 ) .
μ = 2 log ( 2 B p ( δ 90 1 ) + 1 ) log δ 90 + 3
D = θ [ PF ( θ ) FF ( θ ) ] 2 sin θ θ PF ( θ ) 2 sin θ
n ( 443 nm ) = ( 1.34 . a 0.36 ) ( μ 3 ) + 1
n ( 490 nm ) = ( 2.01 . a 0.23 ) ( μ 3 ) + 1
n ( 555 nm ) = ( 3.57 . a 0.15 ) ( μ 3 ) + 1

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