Abstract

Even though it is well known that both the magnitude and detailed angular shape of scattering (phase function, PF), particularly in the backward angles, affect the color of the ocean, the current remote-sensing reflectance (Rrs) models typically account for the effect of its magnitude only through the backscattering coefficient (bb). Using 116 volume scattering function (VSF) measurements previously collected in three coastal waters around the U.S. and in the water of the North Atlantic Ocean, we re-examined the effect of particle PF on Rrs in four scenarios. In each scenario, the magnitude of particle backscattering (i.e., bbp) is known, but the knowledge on the angular shape of particle backscattering is assumed to increase from knowing nothing about the shape of particle PFs to partially knowing the particle backscattering ratio (Bp), the exact backscattering shape as defined by β˜p(γ90°) (particle VSF normalized by the particle total scattering coefficient), and the exact backscattering shape as defined by the χp factor (particle VSF normalized by the particle backscattering coefficient). At sun zenith angle=30°, the nadir-viewed Rrs would vary up to 65%, 35%, 20%, and 10%, respectively, as the constraints on the shape of particle backscattering become increasingly stringent from scenarios 1 to 4. In all four scenarios, the Rrs variations increase with both viewing and sun angles and are most prominent in the direction opposite the sun. Our results show a greater impact of the measured particle PFs on Rrs than previously found, mainly because our VSF data show a much greater variability in Bp, β˜p(γ90°), and χp than previously known. Among the uncertainties in Rrs due to the particle PFs, about 97% can be explained by χp, 90% by β˜p(γ90°), and 27% by Bp. The results indicate that the uncertainty in ocean color remote sensing can be significantly constrained by accounting for χp of the VSFs.

© 2017 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
    [Crossref]
  2. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. II Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [Crossref]
  3. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
    [Crossref]
  4. 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, 417–427 (1975).
    [Crossref]
  5. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [Crossref]
  6. Z. Lee, K. L. Carder, and K. Du, “Effects of molecular and particle scatterings on the model parameter for remote-sensing reflectance,” Appl. Opt. 43, 4957–4964 (2004).
    [Crossref]
  7. A. Morel and H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. 37, 4765–4776 (1998).
    [Crossref]
  8. J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
    [Crossref]
  9. 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. Oceans 100, 13135–13142 (1995).
    [Crossref]
  10. W. Freda and J. Piskozub, “Revisiting the role of oceanic phase function in remote sensing reflectance,” Oceanologia 54, 29–38 (2012).
    [Crossref]
  11. Z. 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, 3155–3167 (2011).
    [Crossref]
  12. B. Bulgarelli, G. Zibordi, and J.-F. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
    [Crossref]
  13. G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, and W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
    [Crossref]
  14. I. Lefering, F. Bengil, C. Trees, R. Röttgers, D. Bowers, A. Nimmo-Smith, J. Schwarz, and D. McKee, “Optical closure in marine waters from in situ inherent optical property measurements,” Opt. Express 24, 14036–14052 (2016).
    [Crossref]
  15. J. Pitarch, G. Volpe, S. Colella, R. Santoleri, and V. Brando, “Absorption correction and phase function shape effects on the closure of apparent optical properties,” Appl. Opt. 55, 8618–8636 (2016).
    [Crossref]
  16. A. Tonizzo, M. Twardowski, S. McLean, K. Voss, M. Lewis, and C. Trees, “Closure and uncertainty assessment for ocean color reflectance using measured volume scattering functions and reflective tube absorption coefficients with novel correction for scattering,” Appl. Opt. 56, 130–146 (2017).
    [Crossref]
  17. M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
    [Crossref]
  18. E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
    [Crossref]
  19. M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
    [Crossref]
  20. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
    [Crossref]
  21. X. Zhang, E. Boss, and D. J. Gray, “Significance of scattering by oceanic particles at angles around 120 degree,” Opt. Express 22, 31329–31336 (2014).
    [Crossref]
  22. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009).
    [Crossref]
  23. A. Morel, “Light scattering in seawater: experimental results and theoretical approach,” in Optics of the Sea (Interface and In-water Transmission and Imaging) (AGARD, 1973).
  24. H. R. Gordon, “Sensitivity of radiative transfer to small-angle scattering in the ocean: quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
    [Crossref]
  25. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
    [Crossref]
  26. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
    [Crossref]
  27. G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
    [Crossref]
  28. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).
  29. 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).
    [Crossref]
  30. 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, 5085–5099 (2012).
    [Crossref]
  31. 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, 6029–6043 (2013).
    [Crossref]
  32. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  33. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
    [Crossref]
  34. V. I. Mankovsky and V. I. Haltrin, “Light scattering phase functions measured in waters of Mediterranean Sea,” in MTS/IEEE OCEANS (2002), Vol. 2364, pp. 2368–2373.
  35. V. I. Mankovsky and V. I. Haltrin, “Phase functions of light scattering measured in waters of world ocean and lake Baykal,” in IEEE International Geoscience and Remote Sensing Symposium (2002), Vol. 3576, pp. 3570–3572.
  36. X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res. Oceans 120, 6914–6926 (2015).
    [Crossref]
  37. C. D. Mobley, “Hydrolight 5.2,” Technical Documentation (Sequoia Scientific, 2013).
  38. IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications,” in Reports of the International Ocean-Colour Coordinating Group, Z.-P. Lee, ed. (IOCCG, 2006), Vol. 5.
  39. G. N. Plass, G. W. Kattawar, and T. J. Humphreys, “Influence of the oceanic scattering phase function on the radiance,” J. Geophys. Res. Oceans 90, 3347–3351 (1985).
    [Crossref]
  40. N. G. Jerlov, Marine Optics, Elsevier Oceanography Series (Elsevier, 1976), Vol. 14, p. 231.
  41. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
    [Crossref]
  42. C. D. Mobley, E. Boss, and C. Roesler, “Ocean optics web book: the quasi-single-scattering approximation,” http://www.oceanopticsbook.info/view/radiative_transfer_theory/level_2/the_quasisinglescattering_approximation , retrieved June 20, 2017, 2011.
  43. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
    [Crossref]
  44. G. F. Beardsley and J. R. V. Zaneveld, “Theoretical dependence of the near-asymptotic apparent optical properties on the inherent optical properties of sea water*,” J. Opt. Soc. Am. 59, 373–377 (1969).
    [Crossref]
  45. X. Zhang, G. R. Fournier, and D. J. Gray, “Interpretation of scattering by oceanic particles around 120 degrees and its implication in ocean color studies,” Opt. Express 25, A191–A199 (2017).
    [Crossref]
  46. R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
    [Crossref]
  47. 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, 15073–15093 (2010).
    [Crossref]

2017 (2)

2016 (2)

2015 (1)

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

2014 (1)

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, 6029–6043 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (1)

2009 (2)

2006 (3)

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

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).
[Crossref]

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

2004 (2)

Z. Lee, K. L. Carder, and K. Du, “Effects of molecular and particle scatterings on the model parameter for remote-sensing reflectance,” Appl. Opt. 43, 4957–4964 (2004).
[Crossref]

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

2003 (2)

2002 (1)

2001 (1)

1999 (1)

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

1998 (1)

1996 (1)

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. Oceans 100, 13135–13142 (1995).
[Crossref]

1994 (1)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

1993 (3)

1989 (1)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[Crossref]

1988 (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

1985 (1)

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

1982 (1)

1977 (1)

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

1975 (1)

1973 (1)

1969 (1)

Ahmad, Z.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Arnone, R.

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

Balch, W. M.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

Beardsley, G. F.

Bengil, F.

Berthon, J.-F.

Bi, L.

Boss, E.

Bowers, D.

Brando, V.

Brown, C. W.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

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, 417–427 (1975).
[Crossref]

Bulgarelli, B.

Carder, K. L.

Chami, M.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

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).
[Crossref]

Chang, G. C.

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

Colella, S.

Cowles, T. J.

Dickey, T. D.

Du, K.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Fournier, G. R.

X. Zhang, G. R. Fournier, and D. J. Gray, “Interpretation of scattering by oceanic particles around 120 degrees and its implication in ocean color studies,” Opt. Express 25, A191–A199 (2017).
[Crossref]

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Freda, W.

W. Freda and J. Piskozub, “Revisiting the role of oceanic phase function in remote sensing reflectance,” Oceanologia 54, 29–38 (2012).
[Crossref]

Gallegos, C. L.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Gentili, B.

Gordon, H. R.

Gray, D. J.

Guillard, R. R. L.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

Haltrin, V. I.

V. I. Mankovsky and V. I. Haltrin, “Light scattering phase functions measured in waters of Mediterranean Sea,” in MTS/IEEE OCEANS (2002), Vol. 2364, pp. 2368–2373.

V. I. Mankovsky and V. I. Haltrin, “Phase functions of light scattering measured in waters of world ocean and lake Baykal,” in IEEE International Geoscience and Remote Sensing Symposium (2002), Vol. 3576, pp. 3570–3572.

Harding, L. W.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

He, M.-X.

Herman, J. R.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Hu, L.

Humphreys, T. J.

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

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, 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, 5085–5099 (2012).
[Crossref]

Jacobs, M. M.

Jerlov, N. G.

N. G. Jerlov, Marine Optics, Elsevier Oceanography Series (Elsevier, 1976), Vol. 14, p. 231.

Jin, Z.

Jonasz, M.

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Karp-Boss, L.

Kattawar, G. W.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[Crossref]

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

Khomenko, G.

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).
[Crossref]

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

Korotaev, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

Lee, Z.

Lefering, I.

Lewis, M.

Leymarie, E.

Loisel, H.

Lubac, B.

Mankovsky, V. I.

V. I. Mankovsky and V. I. Haltrin, “Phase functions of light scattering measured in waters of world ocean and lake Baykal,” in IEEE International Geoscience and Remote Sensing Symposium (2002), Vol. 3576, pp. 3570–3572.

V. I. Mankovsky and V. I. Haltrin, “Light scattering phase functions measured in waters of Mediterranean Sea,” in MTS/IEEE OCEANS (2002), Vol. 2364, pp. 2368–2373.

Marken, E.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

McKee, D.

McLean, S.

Mobley, C. D.

Morel, A.

Neale, P. J.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Nimmo-Smith, A.

Pegau, W. S.

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).

Piskozub, J.

W. Freda and J. Piskozub, “Revisiting the role of oceanic phase function in remote sensing reflectance,” Oceanologia 54, 29–38 (2012).
[Crossref]

Pitarch, J.

Plass, G. N.

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

Prieur, L.

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

Reinersman, P.

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, 6029–6043 (2013).
[Crossref]

Röttgers, R.

Santoleri, R.

Schwarz, J.

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

Stamnes, J. J.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

Stamnes, K.

Stavn, R. H.

Subramaniam, A.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Sullivan, J. M.

Sundman, L. K.

Tonizzo, A.

Trees, C.

Twardowski, M.

Twardowski, M. S.

Tzortziou, M.

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

Vaillancourt, R. D.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

Volpe, G.

Voss, K.

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, 6029–6043 (2013).
[Crossref]

Z. 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, 3155–3167 (2011).
[Crossref]

Whitmire, A. L.

You, Y.

Zaneveld, J. R. V.

Zhang, X.

Zibordi, G.

Appl. Opt. (19)

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. II Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[Crossref]

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

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, 417–427 (1975).
[Crossref]

Z. Lee, K. L. Carder, and K. Du, “Effects of molecular and particle scatterings on the model parameter for remote-sensing reflectance,” Appl. Opt. 43, 4957–4964 (2004).
[Crossref]

A. Morel and H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. 37, 4765–4776 (1998).
[Crossref]

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

Z. 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, 3155–3167 (2011).
[Crossref]

B. Bulgarelli, G. Zibordi, and J.-F. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[Crossref]

G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, and W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
[Crossref]

J. Pitarch, G. Volpe, S. Colella, R. Santoleri, and V. Brando, “Absorption correction and phase function shape effects on the closure of apparent optical properties,” Appl. Opt. 55, 8618–8636 (2016).
[Crossref]

A. Tonizzo, M. Twardowski, S. McLean, K. Voss, M. Lewis, and C. Trees, “Closure and uncertainty assessment for ocean color reflectance using measured volume scattering functions and reflective tube absorption coefficients with novel correction for scattering,” Appl. Opt. 56, 130–146 (2017).
[Crossref]

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

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

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

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[Crossref]

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).
[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, 5085–5099 (2012).
[Crossref]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[Crossref]

H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
[Crossref]

Biogeosciences (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, 6029–6043 (2013).
[Crossref]

Estuarine Coastal Shelf Sci. (1)

M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramaniam, L. W. Harding, and Z. Ahmad, “Bio-optics of the Chesapeake Bay from measurements and radiative transfer closure,” Estuarine Coastal Shelf Sci. 68, 348–362 (2006).
[Crossref]

J. Geophys. Res. Atmos. (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93, 10909–10924 (1988).
[Crossref]

J. Geophys. Res. Oceans (4)

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

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. Oceans 111, C05013 (2006).
[Crossref]

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. Oceans 100, 13135–13142 (1995).
[Crossref]

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

J. Opt. Soc. Am. (1)

J. Plankton Res. (1)

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[Crossref]

Limnol. Oceanogr. (2)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[Crossref]

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

Oceanologia (1)

W. Freda and J. Piskozub, “Revisiting the role of oceanic phase function in remote sensing reflectance,” Oceanologia 54, 29–38 (2012).
[Crossref]

Opt. Express (5)

Proc. SPIE (2)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Other (9)

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).

A. Morel, “Light scattering in seawater: experimental results and theoretical approach,” in Optics of the Sea (Interface and In-water Transmission and Imaging) (AGARD, 1973).

C. D. Mobley, “Hydrolight 5.2,” Technical Documentation (Sequoia Scientific, 2013).

IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications,” in Reports of the International Ocean-Colour Coordinating Group, Z.-P. Lee, ed. (IOCCG, 2006), Vol. 5.

V. I. Mankovsky and V. I. Haltrin, “Light scattering phase functions measured in waters of Mediterranean Sea,” in MTS/IEEE OCEANS (2002), Vol. 2364, pp. 2368–2373.

V. I. Mankovsky and V. I. Haltrin, “Phase functions of light scattering measured in waters of world ocean and lake Baykal,” in IEEE International Geoscience and Remote Sensing Symposium (2002), Vol. 3576, pp. 3570–3572.

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

N. G. Jerlov, Marine Optics, Elsevier Oceanography Series (Elsevier, 1976), Vol. 14, p. 231.

C. D. Mobley, E. Boss, and C. Roesler, “Ocean optics web book: the quasi-single-scattering approximation,” http://www.oceanopticsbook.info/view/radiative_transfer_theory/level_2/the_quasisinglescattering_approximation , retrieved June 20, 2017, 2011.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Comparison of particle PFs derived from: our measurements (gray lines); samples of historical Petzold’s measurements in clear water of the Tongue of the Ocean (black dotted line), in California offshore coastal water (black dashed line), and in very turbid water of San Diego harbor (black dotted-dashed line) [32]; the average particle PF of Petzold’s measurements in San Diego harbor [33] (black solid line); the analytical Fournier–Forand (FF) formula having a B p = 1.83 % [25] (blue dashed line); and a series of particle PFs generated by linear mixing of B p = 1 % FF PF and the average Petzold PF, as used in Lee et al. [11] (green solid lines). The red line is one of the measured particle PFs referred to in Fig. 5. To highlight the variations, the x axes are in logarithmic scale for angles < 30 ° and in linear scales for larger angles. (b) Corresponding χ p factors. (c) Histogram of B p calculated from measured particle PFs.

Fig. 2.
Fig. 2.

R rs ( θ s = 30 ° , θ v = 0 ° ) simulated with measured particle phase functions (color coded by the measurement locations) are shown as a function of b b / ( a + b b ) .

Fig. 3.
Fig. 3.

Percentage difference between R rs ( θ s = 30 ° , θ v = 0 ° ) simulated with two different particle phase functions. The whiskers boxes, showing the minimum, lower quartile, median, upper quartile, and maximum values, summarize the differences at the selected b b / ( a + b b ) values. (a) Simulations performed with same b b p values. (b) Simulations performed with same b b p values and phase functions having the same B p values. The dotted line at 10% represents the maximum difference found in Ref. [25], the dashed line at 20% represents the maximum difference found in Ref. [29], and the dotted-dashed line at 40% represents the maximum difference found in Ref. [16]. (c) Simulations performed with same b b p values and very similar β ˜ p ( γ 90 ° ) (logarithmic value within 1%). (d) Simulations performed with same b b p values and very similar χ p factor (within 1%).

Fig. 4.
Fig. 4.

Distribution of the maximum value of d R rs . In the polar plots, ao-56-24-6881-i001 indicates θ s , radial direction represents θ v , and polar direction represents ϕ . Column (a) results with same b b p ; column (b) results with same b b p and B p ; column (c) results with same b b p and similar β ˜ p ( γ 90 ° ) (logarithmic value within 1%); column (d) results with same b b p and similar χ p factor (within 1%).

Fig. 5.
Fig. 5.

Comparison between R rs simulated with one of the measured phase functions (red line in Fig. 1) by HydroLight and R rs estimated using the Lee’s et al. [11] model at all viewing geometries ( θ s = 0 75 ° , θ v = 0 70 ° , and ϕ = 0 180 ° ).

Equations (13)

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R rs ( λ , θ s , θ v , φ ) = L w ( λ , θ s , θ v , φ ) E d ( λ , θ s ) ,
R rs = f Q b b a + b b .
b b = 2 π π / 2 π β ( γ ) sin γ d γ ,
β ˜ ( γ ) = β ( γ ) b ,
B = b b b = 2 π π / 2 π β ˜ ( γ ) sin γ d γ ,
χ ( γ 90 ° ) = b b 2 π β ( γ ) = B 2 π β ˜ ( γ ) .
β p ( γ ) = A γ m ,
b p = 2 π 2 m β p ( γ 1 ) γ 1 2 + 2 π 0.1 π β p ( γ ) sin γ d γ .
d R rs ( a , b b , θ s , θ v , φ ) = | R rs ( i , a , b b , θ s , θ v , φ ) R rs ( j , a , b b , θ s , θ v , φ ) | 1 2 [ R rs ( i , a , b b , θ s , θ v , φ ) + R rs ( j , a , b b , θ s , θ v , φ ) ] × 100 % ,
R rs ( θ , ϕ , θ s ) = 1 cos θ v + cos θ s β ( γ s ) a + b b ,
R rs ( θ , ϕ , θ s ) = 1 2 π χ ( γ s ) 1 cos θ v + cos θ s b b a + b b .
R rs ( θ , ϕ , θ s ) = β ˜ ( γ s ) B 1 cos θ v + cos θ s b b a + b b .
{ σ s 2 = 0.65 2 σ s 2 σ B p 2 = 0.35 2 σ s 2 σ > 90 2 = 0.20 2 σ s 2 σ χ 2 = 0.10 2 .