Abstract

We revisit the problem of computing the backscattering coefficient based on the measurement of scattering at one angle in the back direction. Our approach uses theory and new observations of the volume scattering function (VSF) to evaluate the choice of angle used to estimate b b. We add to previous studies by explicitly treating the molecular backscattering of water (b bw) and its contribution to the VSF shape and to b b. We find that there are two reasons for the tight correlation between observed scattering near 120° and the backscattering coefficient reported by Oishi [Appl. Opt. 29, 4658, (1990)], namely, that (1) the shape of the VSF of particles (normalized to the backscattering) does not vary much near that angle for particle assemblages of differing optical properties and size, and (2) the ratio of the VSF to the backscattering is not sensitive to the contribution by water near this angle. We provide a method to correct for the water contribution to backscattering when single-angle measurements are used in the back direction (for angles spanning from near 90° to 160°) that should provide improved estimates of the backscattering coefficient.

© 2001 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
    [CrossRef]
  2. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
    [CrossRef]
  3. T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°,” Appl. Opt. 29, 4658–4665 (1990).
    [CrossRef] [PubMed]
  4. R. A. Maffione, D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
    [CrossRef] [PubMed]
  5. A. Morel, 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]
  6. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6878 (1993).
    [CrossRef] [PubMed]
  7. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Neilsen, eds. (Academic, New York, 1974), pp. 1–24.
  8. T. J. Petzold, “Volume scattering functions for selected ocean waters,” Rep. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  9. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7505 (1993).
    [CrossRef] [PubMed]
  10. G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
    [CrossRef]
  11. G. P. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-Water Underwater Imaging, G. D. Gilbert, ed., Proc. SPIE3761, 62–70 (1999).
    [CrossRef]
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  13. A. Morel, A. Bricaud, “Light attenuation and scattering by planktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
    [CrossRef]
  14. D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  15. C. D. Mobley, Sequoia Scientific, Inc., 15317 NE 90th St., Redmond, Wash. 98052 (personal communication, 2001).
  16. V. I. Haltrin, M. E. Lee, O. V. Martynov, “Polar nephlometer for sea truth measurements,” in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1996), pp. 444–450.
  17. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

2001

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

1997

1993

1991

1990

1988

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

1986

Baker, K. C.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Boss, E.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Bricaud, A.

Brown, J. W.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Clark, D. C.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Dana, D. R.

Evans, R. E.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Forand, J. L.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Fournier, G. P.

G. P. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-Water Underwater Imaging, G. D. Gilbert, ed., Proc. SPIE3761, 62–70 (1999).
[CrossRef]

Fournier, G. R.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Gentili, B.

Gordon, H. R.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7505 (1993).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Haltrin, V. I.

V. I. Haltrin, M. E. Lee, O. V. Martynov, “Polar nephlometer for sea truth measurements,” in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1996), pp. 444–450.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jin, Z.

Jonasz, M.

G. P. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-Water Underwater Imaging, G. D. Gilbert, ed., Proc. SPIE3761, 62–70 (1999).
[CrossRef]

Kattawar, G. W.

Kiefer, D. A.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Lee, M. E.

V. I. Haltrin, M. E. Lee, O. V. Martynov, “Polar nephlometer for sea truth measurements,” in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1996), pp. 444–450.

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Maffione, R. A.

Martynov, O. V.

V. I. Haltrin, M. E. Lee, O. V. Martynov, “Polar nephlometer for sea truth measurements,” in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1996), pp. 444–450.

Mobley, C. D.

Morel, A.

Oishi, T.

Pegau, W. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Rep. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Reinersman, P.

Smith, R. C.

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Stamnes, K.

Stavn, R. H.

Stramski, D.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Twardowski, M. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Zaneveld, J. R. V.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Appl. Opt.

J. Geophys. Res.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for retrieving oceanic particle composition and size distribution from measurements of the backscattering ratio and spectral attenuation,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

J. Geophys. Res. D

H. R. Gordon, O. B. Brown, R. E. Evans, J. W. Brown, R. C. Smith, K. C. Baker, D. C. Clark, “A semianalytic model of ocean color,” J. Geophys. Res. D 96, 10909–10924 (1988).
[CrossRef]

Prog. Oceanogr.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Other

C. D. Mobley, Sequoia Scientific, Inc., 15317 NE 90th St., Redmond, Wash. 98052 (personal communication, 2001).

V. I. Haltrin, M. E. Lee, O. V. Martynov, “Polar nephlometer for sea truth measurements,” in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1996), pp. 444–450.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Neilsen, eds. (Academic, New York, 1974), pp. 1–24.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Rep. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

G. P. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-Water Underwater Imaging, G. D. Gilbert, ed., Proc. SPIE3761, 62–70 (1999).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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Figures (5)

Fig. 1
Fig. 1

VSF normalized by the backscattering coefficient [β(θ)/b b ] for cases in which water contributes 0% (gray curve) to 100% (bold black curve) of the backscattering coefficient in increments of 10%. For this illustrative example, we chose the average particulate Petzold VSF.8,9

Fig. 2
Fig. 2

χ(θ) = b b /[2π β(θ)] for cases in which water contributes 0% (gray curve) to 100% (bold black curve) of the backscattering coefficient in increments of 10%. For this illustrative example, we chose the average particulate Petzold VSF.9 Note that, for these curves, all the curves intersect near 118°.

Fig. 3
Fig. 3

χ based on Oishi (bold gray curve) and χ w (δ = 0.07, 0.09, 0.11, thin gray curves). (a) χ p based on the Fournier and Forand (FF)10 and the Fournier and Jonasz11 approximations for n = 1.05–1.17 and Junge slope 3.3–4.5 (black curves denoted by FF). (b) χ p based on Mie calculations (bold solid black curve, dashed black curve; 10th and 90th percentiles, thin black curves).

Fig. 4
Fig. 4

χ based on 44 VSF measurements by use of the VSM instrument (bold solid black curve, dashed black curve; 10th and 90th percentiles, thin black curves). χ based on Oishi (bold gray curve) and χ w (δ = 0.07, 0.09, 0.11) (thin gray curves).

Fig. 5
Fig. 5

χ p based on 41 VSM measurements in turbid waters (black curves) and based on 150 Mie theory calculations (gray curves). The thin curves denote the 10th and 90th percentiles in each angle. The dashed black curve denotes χ p based on the average Petzold particulate phase function.8,9

Tables (1)

Tables Icon

Table 1 χ p Based on 41 VSF Measurementsa

Equations (10)

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

βθ=βwθ+βpθ.
bb=bbw+bbp,
bb=2π π/2π βθsin θdθ.
βwθ=Aλ, S*1+cos2 θ1-δ/1+δ,
Aλ, S=1.38λ/500 nm-4.32×1+0.3S/37 psu×10-4 m-1 sr-1,
2πβwθχwθ=bbw, 2πβpθχpθ=bbp.
2πβθχθ=bb.
χθ=χwθβwθ/βθ+χpθβpθ/βθ=χwθy+χpθ1-y,
χwθ=1+131-δ1+δ1+1-δ1+δcos2 θ.
bb=χpθβθ-βwθ+bbw.

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