Abstract

Numerical simulations show that underwater radiances, irradiances, and reflectances are sensitive to the shape of the scattering phase function at intermediate and large scattering angles, although the exact shape of the phase function in the backscatter directions (for a given backscatter fraction) is not critical if errors of the order of 10% are acceptable. We present an algorithm for generating depth- and wavelength-dependent Fournier-Forand phase functions having any desired backscatter fraction. Modeling of a comprehensive data set of measured inherent optical properties and radiometric variables shows that use of phase functions with the correct backscatter fraction and overall shape is crucial to achieve model-data closure.

© 2002 Optical Society of America

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References

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  4. 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, 7484–7504 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. H. R. Gordon, “Sensitivity of radiative transfer to small-angle scattering in the ocean: quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
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    [CrossRef]
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    [CrossRef]
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  23. D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
    [CrossRef]
  24. M. Lee, M. R. Lewis, “Measurement of the optical volume scattering function in the ocean,” J. Atmos. Oceanic Technol., submitted for publication.
  25. M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
    [CrossRef]
  26. J. R. V. Zaneveld, J. C. Kitchen, C. M. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XI, G. Gilbert, ed., Proc. SPIE1750, 187–200 (1994).
    [CrossRef]
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  28. A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
    [CrossRef]
  29. H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery, a Review; Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol. 4.
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  33. H. R. Gordon, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975).
    [CrossRef] [PubMed]
  34. J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of urface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
    [CrossRef]
  35. H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
    [CrossRef]
  36. R. A. Leathers, T. V. Downes, C. D. Mobley, “Self-shading correction for upwelling sea-surface radiance measurements made with buoyed instruments,” Opt. Exp.8, 561–570 (2001); http://www.opticsexpress.org/oearchive/source/32933.htm .
    [CrossRef]

2001 (4)

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
[CrossRef]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of urface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
[CrossRef]

1999 (1)

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

1997 (2)

1995 (1)

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

1994 (1)

1993 (2)

1992 (1)

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

1990 (1)

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

1988 (1)

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

1985 (1)

G. N. Plass, G. W. Kattawar, T. J. Humphreys, “Influence of the oceanic scattering phase function on the radiance,” J. Geophys. Res. 90(C2), 3347–3351 (1985).
[CrossRef]

1975 (2)

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

H. R. Gordon, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975).
[CrossRef] [PubMed]

1941 (1)

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

Barnard, A.

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
[CrossRef]

Boss, E.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
[CrossRef]

J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of urface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
[CrossRef]

Bricaud, A.

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

D. Stramski, A. Bricaud, A. Morel, “A database of single-particle optical properties,” in Ocean Optics XIV, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmospheric and Space Science and Technology Department, Arlington, Va., 1998).

Carder, K. L.

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

Cleveland, J. S.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Coombes, C. A.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

Dana, D. R.

Ding, K.

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Donaghay, P. L.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Doss, W.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Forand, J. L.

G. 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.

G. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE3761, 62–77 (1999).
[CrossRef]

G. Fournier, Defense Research Establishment Valcartier, Val-Belair, G3J 1X5, Canada (personal communication, 2000).

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

Fry, E. S.

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, 7484–7504 (1993).
[CrossRef] [PubMed]

H. R. Gordon, “Sensitivity of radiative transfer to small-angle scattering in the ocean: quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
[CrossRef] [PubMed]

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

H. R. Gordon, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975).
[CrossRef] [PubMed]

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery, a Review; Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol. 4.
[CrossRef]

H. R. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, ed. (Oxford U. Press, Oxford, UK, 1994), 1–39.

Greenstein, J. L.

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

Gregg, W. W.

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

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.

Harrison, A. W.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

Henyey, L. C.

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

Humphreys, T. J.

G. N. Plass, G. W. Kattawar, T. J. Humphreys, “Influence of the oceanic scattering phase function on the radiance,” J. Geophys. Res. 90(C2), 3347–3351 (1985).
[CrossRef]

Jin, Z.

Jonasz, M.

G. Fournier, M. Jonasz, “Computer-based underwater imaging analysis,” in Airborne and In-water Underwater Imaging, G. Gilbert, ed., Proc. SPIE3761, 62–77 (1999).
[CrossRef]

Kattawar, G. W.

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, 7484–7504 (1993).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, T. J. Humphreys, “Influence of the oceanic scattering phase function on the radiance,” J. Geophys. Res. 90(C2), 3347–3351 (1985).
[CrossRef]

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Kennedy, C. D.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Kitchen, J. C.

J. R. V. Zaneveld, J. C. Kitchen, C. M. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XI, G. Gilbert, ed., Proc. SPIE1750, 187–200 (1994).
[CrossRef]

Lee, M.

M. Lee, M. R. Lewis, “Measurement of the optical volume scattering function in the ocean,” J. Atmos. Oceanic Technol., submitted for publication.

Lewis, M. R.

M. Lee, M. R. Lewis, “Measurement of the optical volume scattering function in the ocean,” J. Atmos. Oceanic Technol., submitted for publication.

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
[CrossRef]

Maffione, R. A.

R. A. Maffione, D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997); see also www.hobilabs.com .

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Maritorena, S.

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

McCluney, W. R.

Mobley, C. D.

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, 7484–7504 (1993).
[CrossRef] [PubMed]

C. D. Mobley, L. K. Sundman, Hydrolight 4.1 Users’ Guide (Sequoia Scientific, Inc., Redmond, Wash., 2000); see also www.sequoiasci.com .

C. D. Mobley, L. K. Sundman, Hydrolight 4.1 Technical Documentation (Sequoia Scientific, Inc., Redmond, Wash., 2000).

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

Moore, C. M.

J. R. V. Zaneveld, J. C. Kitchen, C. M. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XI, G. Gilbert, ed., Proc. SPIE1750, 187–200 (1994).
[CrossRef]

Morel, A.

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

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, 7484–7504 (1993).
[CrossRef] [PubMed]

D. Stramski, A. Bricaud, A. Morel, “A database of single-particle optical properties,” in Ocean Optics XIV, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmospheric and Space Science and Technology Department, Arlington, Va., 1998).

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

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery, a Review; Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol. 4.
[CrossRef]

Mueller, J. L.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Pegau, W. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
[CrossRef]

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Perry, M. J.

M. J. Perry, Darling Marine Center, University of Maine, Walpole, Maine 04573 (personal communication, 2001).

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. SIO 72-78 (Scripps Institution of Oceanography, San Diego, Calif., 1972).

Plass, G. N.

G. N. Plass, G. W. Kattawar, T. J. Humphreys, “Influence of the oceanic scattering phase function on the radiance,” J. Geophys. Res. 90(C2), 3347–3351 (1985).
[CrossRef]

Platt, T.

Pope, R. M.

Reinersman, P.

Roesler, C. S.

C. S. Roesler, Bigelow Laboratory Ocean Sciences, Boothbay Harbor, Maine 04573 (personal communication, 2001).

Sathyendranath, S.

Stamnes, K.

Stavn, R. H.

Stone, R.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

Stramski, D.

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

D. Stramski, A. Bricaud, A. Morel, “A database of single-particle optical properties,” in Ocean Optics XIV, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmospheric and Space Science and Technology Department, Arlington, Va., 1998).

Sullivan, J. M.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Sundman, L. K.

C. D. Mobley, L. K. Sundman, Hydrolight 4.1 Technical Documentation (Sequoia Scientific, Inc., Redmond, Wash., 2000).

C. D. Mobley, L. K. Sundman, Hydrolight 4.1 Users’ Guide (Sequoia Scientific, Inc., Redmond, Wash., 2000); see also www.sequoiasci.com .

Trees, C. C.

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W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
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W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
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M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in Case I and Case II waters,” J. Geophys. Res. 106(C7), 14129–14142 (2001).
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J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of urface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
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M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13201–13220 (1995); see also www.wetlabs.com .
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, C. M. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XI, G. Gilbert, ed., Proc. SPIE1750, 187–200 (1994).
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C. D. Mobley, L. K. Sundman, Hydrolight 4.1 Users’ Guide (Sequoia Scientific, Inc., Redmond, Wash., 2000); see also www.sequoiasci.com .

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Figures (17)

Fig. 1
Fig. 1

Phase functions used in the hydrolight simulations of Section 2. Panel (a) is plotted to emphasize the small scattering angles; panel (b) is plotted to emphasize intermediate and large angles. Each phase function has a backscatter fraction of B = 0.0183. The curve patterns identify the phase functions as defined in Section 2.

Fig. 2
Fig. 2

Contours of the backscatter fraction B p of the FF phase function as determined by Eq. (3). The filled circle on the B p = 0.0183 curve shows the (n, μ) point that gives the best fit to the Petzold phase function of Fig. 1. The filled diamonds along the B p = 0.005 curve show the three (n, μ) pairs used to generate the inset in Fig. 7. The dashed line is Eq. (7).

Fig. 3
Fig. 3

Downwelling plane irradiances for four combinations of high or low scattering and high or low Sun angle. The line pattern identifies the phase function used in the calculations. The phase functions all have B = 0.0183.

Fig. 4
Fig. 4

Upwelling radiances corresponding to the simulations of Fig. 3.

Fig. 5
Fig. 5

Irradiance reflectances corresponding to the simulations of Fig. 3.

Fig. 6
Fig. 6

Remote-sensing reflectances corresponding to the simulations of Fig. 3.

Fig. 7
Fig. 7

FF phase functions as generated by Eq. (1) for different backscatter fractions B p (dashed curves). The corresponding (n, μ) values lie along the dashed line of Fig. 2. The solid curve with B p = 0.0183 is the Petzold average-particle phase function. The pure-water phase function (dotted curve) has B = 0.5. The inset shows the three phase functions corresponding to the three sets of (n, μ) values shown by filled diamonds on the B p = 0.005 contour of Fig. 2.

Fig. 8
Fig. 8

Downwelling plane irradiances for four combinations of high or low scattering and high or low Sun angle. The line pattern identifies the backscatter fraction B of the FF phase function used in the calculations.

Fig. 9
Fig. 9

Upwelling radiances corresponding to the simulations of Fig. 8.

Fig. 10
Fig. 10

In-water remote-sensing reflectances corresponding to the simulations of Fig. 8.

Fig. 11
Fig. 11

Measured IOPs as a function of depth and wavelength, as labeled on the abscissa. (a)–(e) The seven wavelengths are 412, 440, 488, 532, 555, 650, and 676 nm, with wavelength generally increasing from right to left in the plot, as indicated in (a). (f) The wavelengths are 442, 488, 532, 555, and 620 nm, from right to left.

Fig. 12
Fig. 12

Particulate backscatter fraction B p determined from Figs. 11(d) and 11(f). The wavelengths shown are 442, 488, 532, and 555 nm, from right to left. The chlorophyll concentration is also shown to highlight the correlation between B p and Chl. The dashed line at 0.0183 indicates the backscatter fraction of the Petzold phase function.

Fig. 13
Fig. 13

Phase functions used in hydrolight simulations of the LEO-15 data. Solid curve, phase function measured by the VSM at z = 2 m, λ = 530 nm; dotted curve, FF phase function with the same backscatter fraction (0.00415); dashed curve, Petzold phase function with B = 0.0183.

Fig. 14
Fig. 14

Comparison of measured and hydrolight-predicted downwelling plane irradiances at selected wavelengths. Solid curve, measured values; dotted curve, predicted values with the FF phase function; dashed curve, predicted values with the measured phase function; dashed-dotted curve, predicted values with the Petzold phase function.

Fig. 15
Fig. 15

Comparison of measured and hydrolight-predicted upwelling radiances at selected wavelengths. Solid curve, measured values; dotted curve, predicted values with the FF phase function; dashed curve, predicted values with the measured phase function; dashed-dotted curve, predicted values with the Petzold phase function.

Fig. 16
Fig. 16

Comparison of measured and hydrolight-predicted diffuse attenuation for upwelling radiance at 591 nm. Solid curve, measured values; dotted curve, predicted values with the FF phase function; dashed curve, predicted values with the measured phase function; dashed-dotted curve, predicted values with the Petzold phase function.

Fig. 17
Fig. 17

Comparison of measured and hydrolight-predicted remote-sensing reflectance at 0.5-m depth. Solid curve, measured by Hyper-TSRB [as corrected by Eq. (10)]; filled circles, measured values by in-water OCP; dotted curve, predicted values by hydrolight with the FF phase function; dashed curve, predicted values with the measured phase function; dashed-dotted curve, predicted values with the Petzold phase function.

Tables (7)

Tables Icon

Table 1 Rms Percentage Differences in Phase Functions, as Defined by Eq. (6), for Intermediate Scattering Angles 5 ≤ ψ ≤ 90 dega

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Table 2 Rms Percentage Differences in Phase Functions, as in Table 1, for Backscattering Angles 90 ≤ ψ ≤ 180 deg

Tables Icon

Table 3 Rms Percentage Differences in Phase Functions, as in Table 1, for Intermediate and Backscattering Angles 5 ≤ ψ ≤ 180 deg

Tables Icon

Table 4 Data Taken at the LEO-15 Site as Used to Model the In-Water Light Fielda

Tables Icon

Table 5 Rms Percentage Differences in the Three Phase Functions of Fig. 13, as Defined by Eq. (6), for Intermediate Scattering Angles 5 ≤ ψ ≤ 90 dega

Tables Icon

Table 6 Rms Percentage Differences in the Three Phase Functions of Fig. 13, as in Table 5, for Backscattering Angles 90 ≤ ψ ≤ 180 deg

Tables Icon

Table 7 Rms Percentage Differences in the Three Phase Functions of Fig. 13, as in Table 5, for Intermediate and Backscattering Angles 5 ≤ ψ ≤ 180 deg

Equations (13)

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

β˜FFψ= 14π1-δ2δνν1-δ-1-δν +δ1-δν-ν1-δsin-2ψ2 +1-δ180ν16πδ180-1 δ180ν3cos2ψ-1,
ν= 3-μ2, δ=43(n-1)2sin2ψ2.
Bp=1- 1-δ90ν+1-0.51-δ90ν1-δ90δ90ν,
β˜OTHGψ= 14π1-g21+g2-2gcos ψ3/2.
Bp=1-g2g1+g1+g2-1.
β˜TTHGψ =αβ˜OTHGψ, g1 +1-α β˜OTHGψ, g2.
g2=-0.30614+1.0006g1-0.01826g12 +0.03644g13, α= g21+g2g1+g21+g2-g1.
Δβ= 1001ψ2-ψ1ψ1ψ2β˜1ψ-β˜2ψ12β˜1ψ+β˜2ψsin ψ2dψ0.5.
n=1.01+0.1542μ-3,
23δ90 =0.01-0.3084ν2.
Chl=ap676 nm -ap650 nm /0.014 mg m-3.
VSFψ =VSFψ0ψ0ψS,
Lu0.5 mEd0.5 m =LuT0.6 mEdTairEdHairEdH0.5 mLuH0.5 mLuH0.6 m.

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