Abstract

A simple, surprisingly accurate, method for estimating the influence of Raman scattering on the upwelling light field in natural waters is developed. The method is based on the single (or quasi-single) scattering solution of the radiative transfer equation with the Raman source function. Given the light field at the excitation wavelength, accurate estimates (~1-10%) of the contribution of Raman scattering to the light field at the emission wavelength are obtained. The accuracy is only slightly degraded when typically measured aspects of the light field at the excitation are available.

© 2014 Optical Society of America

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  1. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .
  2. S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
    [CrossRef]
  3. R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27(19), 4002–4011 (1988).
    [CrossRef] [PubMed]
  4. B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29(1), 71–84 (1990).
    [CrossRef] [PubMed]
  5. G. W. Kattawar, X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31(30), 6491–6500 (1992).
    [CrossRef] [PubMed]
  6. V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. model,” Appl. Opt. 32(27), 5356–5367 (1993).
    [CrossRef] [PubMed]
  7. Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32(21), 4028–4036 (1993).
    [PubMed]
  8. R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. 32(33), 6853–6863 (1993).
    [CrossRef] [PubMed]
  9. Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995).
    [CrossRef]
  10. K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995).
    [CrossRef]
  11. J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean color,” 1996, M.S. Thesis, Dalhousie University, Halifax, Nova Scotia.
  12. J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37(15), 3324–3332 (1998).
    [CrossRef] [PubMed]
  13. S. Sathyendranath, T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998).
    [CrossRef] [PubMed]
  14. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999).
    [CrossRef] [PubMed]
  15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).
  16. H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
    [CrossRef] [PubMed]
  17. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  18. H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994).
    [CrossRef] [PubMed]
  19. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12(12), 2803–2804 (1973).
    [CrossRef] [PubMed]
  20. H. R. Gordon, O. B. Brown, 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]
  21. K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34(8), 1614–1622 (1989).
    [CrossRef]
  22. J. Wei, R. Van Dommelen, M. R. Lewis, S. McLean, K. J. Voss, “A new instrument for measuring the high dynamic range radiance distribution in near-surface sea water,” Opt. Express 20(24), 27024–27038 (2012).
    [CrossRef] [PubMed]
  23. D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
    [CrossRef]
  24. M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
    [CrossRef]
  25. T. K. Westberry, E. Boss, Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013).
    [CrossRef] [PubMed]
  26. H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18(8), 1161–1166 (1979).
    [CrossRef] [PubMed]
  27. 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(36), 7484–7504 (1993).
    [CrossRef] [PubMed]

2013

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

T. K. Westberry, E. Boss, Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013).
[CrossRef] [PubMed]

2012

2005

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

1999

1998

1995

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995).
[CrossRef]

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995).
[CrossRef]

1994

1993

1992

1990

1989

K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34(8), 1614–1622 (1989).
[CrossRef]

1988

1984

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
[CrossRef]

1983

1980

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

1979

1975

1973

Antoine, D.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Bartlett, J. S.

Behrenfeld, M. J.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

Boss, E.

T. K. Westberry, E. Boss, Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013).
[CrossRef] [PubMed]

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Buis, J.-P.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Buis, N.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Canini, M.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Clark, D. K.

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Crozel, D.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Evans, R. H.

Fougnie, B.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Ge, Y.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995).
[CrossRef]

Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32(21), 4028–4036 (1993).
[PubMed]

Gentili, B.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[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(36), 7484–7504 (1993).
[CrossRef] [PubMed]

Gordon, H. R.

H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999).
[CrossRef] [PubMed]

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995).
[CrossRef]

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994).
[CrossRef] [PubMed]

Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32(21), 4028–4036 (1993).
[PubMed]

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(36), 7484–7504 (1993).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18(8), 1161–1166 (1979).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, 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]

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

Haltrin, V. I.

Henry, P.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Houyou, A.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Hovis, W. A.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Jacobs, M. M.

Jin, Z.

Kattawar, G. W.

Kishino, M.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
[CrossRef]

Lee, Z.

Lewis, M. R.

Leymarie, E.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Marshall, B. R.

McLean, S.

Meunier, S.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Mobley, C. D.

Morel, A.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[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(36), 7484–7504 (1993).
[CrossRef] [PubMed]

Mueller, J. L.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Okami, N.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
[CrossRef]

Platt, T.

Reinersman, P.

Sathyendranath, S.

Shea, D. M.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

Siegel, D. A.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

Smith, R. C.

Stamnes, K.

Stavn, R. H.

Sugihara, S.

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
[CrossRef]

Van Dommelen, R.

Victori, S.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

Vodacek, A.

Voss, K. J.

Wang, M.

Waters, K. J.

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995).
[CrossRef]

Wei, J.

Weidemann, A. D.

Westberry, T. K.

Xu, X.

Appl. Opt.

R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27(19), 4002–4011 (1988).
[CrossRef] [PubMed]

B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29(1), 71–84 (1990).
[CrossRef] [PubMed]

G. W. Kattawar, X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31(30), 6491–6500 (1992).
[CrossRef] [PubMed]

V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. model,” Appl. Opt. 32(27), 5356–5367 (1993).
[CrossRef] [PubMed]

Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32(21), 4028–4036 (1993).
[PubMed]

R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. 32(33), 6853–6863 (1993).
[CrossRef] [PubMed]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37(15), 3324–3332 (1998).
[CrossRef] [PubMed]

S. Sathyendranath, T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998).
[CrossRef] [PubMed]

H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994).
[CrossRef] [PubMed]

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

H. R. Gordon, O. B. Brown, 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]

T. K. Westberry, E. Boss, Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013).
[CrossRef] [PubMed]

H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18(8), 1161–1166 (1979).
[CrossRef] [PubMed]

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(36), 7484–7504 (1993).
[CrossRef] [PubMed]

Global Biogeochem. Cycles

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[CrossRef]

J. Atmos. Oceanic Technol.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013).
[CrossRef]

J. Geophys. Res.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995).
[CrossRef]

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995).
[CrossRef]

J. Oceanogr. Soc. Jpn

S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984).
[CrossRef]

Limnol. Oceanogr.

K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34(8), 1614–1622 (1989).
[CrossRef]

Opt. Express

Science

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Other

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .

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

J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean color,” 1996, M.S. Thesis, Dalhousie University, Halifax, Nova Scotia.

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Tables (2)

Tables Icon

Table 1 Exact values of the Raman scattering contribution to Lup(0, λ) in mW/cm2µm Sr and Eu(0) at 550 nm for a pure sea water water body, compared with values of Lup(0)(0, λ) and Eu(0, λ) computed using Eqs. (17) and (22), respectively, with u 2 E = µd2 . The values labeled “Approx.” are computed by replacing K0 with Kd, estimating E0 from Ed(0) and Eu(0) and the approximation u 2 E = u 0w 2 .

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Table 2 Exact values of the Raman scattering contribution to Lup(0, λ) in mW/cm2µm Sr and at 450 and 550 nm for a modeled water body with a pigment concentration of 0.3 mg/m3, compared with values of Lup(0)(0, λ) computed using Eq. (16) with u 2 E = µd2 . The solar zenith angle was 60 deg. The values labeled “Approx.” are computed by replacing E0 by its estimate from Ed and Lup (Eq. (18)), and the approximation u 2 E = u 0w 2 . “Model” refers to using Eq. (15) directly with c, or replacing c by a + bb, its quasi-single scattering value.

Equations (22)

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E d (z,λ)= 0 2π dϕ 0 1 uL(z,u,ϕ,λ) du, E u (z,λ)= 0 2π dϕ 0 1 |u|L(z,u,ϕ,λ) du, E 0 (z,λ)= 0 2π dϕ 1 1 L(z,u,ϕ,λ) du,
u dL(z,u,ϕ,λ) dz +c(z,λ)L(z,u,ϕ,λ) = 0 2π dϕ' 1 1 du' β(z,u'u,ϕ'ϕ ,λ)L(z,u',ϕ',λ) + All λ E d λ E 0 2π dϕ' 1 1 du' β I (z,u'u,ϕ'ϕ , λ E λ)L(z,u',ϕ', λ E ),
Q(z,u,ϕ,λ)= All λ E d λ E J(z,u,ϕ, λ E ,λ),
J(z,u,ϕ, λ E ,λ)= 0 2π dϕ' 1 1 du' β I (z,u'u,ϕ'ϕ , λ E λ)L(z,u',ϕ', λ E ).
[ u d dτ +1 ]L= ω 0 4π 0 2π dϕ' 1 1 PLdu' + Q c .
[ u d dτ +1 ] L (0) = Q c [ u d dτ +1 ] L (1) = ω 0 4π 0 2π dϕ' 1 1 P L (0) du' [ u d dτ +1 ] L (2) = ω 0 4π 0 2π dϕ' 1 1 P L (1) du' etc.,
[ u d dτ +1 ] L (n) = f (n) (τ),
L (n) ( τ b )exp( τ b /u) L (n) ( τ a )exp( τ a /u)= 1 u τ a τ b f (n) (τ')exp[ τ'/u ]dτ'.
L (0) (τ,u,ϕ,λ)= exp(τ/u) u τ a τ Q(τ',u,ϕ,λ) c(τ',λ) exp[τ'/u]dτ',
β R (z,u'u,ϕ'ϕ, λ E λ)= b R (z, λ E λ) 4π(1.1833) (1+0.55 cos 2 α),
b R ( λ E λ)Δ λ E =2.61× 10 4 ( 589 λ ) 4.8 ,
Q(z,u=1,ϕ,λ)=0.0673   b R ( λ E λ)Δ λ E 0 2π d ϕ' 1 1 du'(1+0.55u ' 2 )L(z,u',ϕ', λ E ).
u 2 E 0 2π dϕ' 1 1 u ' 2 L(z,u',ϕ', λ E )du' 0 2π dϕ' 1 1 L(z,u',ϕ', λ E )du' ,
Q(z,u=1,ϕ,λ)=0.0637 b R (λ λ E )Δ λ E ( 1+0.55 u ' 2 E ) E 0 (z, λ E ).
E 0d (z, λ E )= 0 2π dϕ 0 1 L(z,u,ϕ, λ E ) du.
L up (0) (τ,λ)=0.0673 b R ( λ E λ)Δ λ E × τ dτ' ( 1+0.55 u 2 E ) exp[(τ'τ)] c(τ',λ) E 0 (τ', λ E ).
L up (0) (z,λ)= 0.0673 b R ( λ E λ)Δ λ E c(λ)+ K 0 ( λ E ) ×( 1+0.55 u 2 E ) E 0 (0, λ E )exp[ K 0 ( λ E )z].
E 0 (0, λ E )= E d (0, λ E )/ μ d + E u (0, λ E )/ μ u ,
L (0) (τ,μ,ϕ,λ)= 0.0673 b R ( λ E λ)Δ λ E μ × 0 2π dϕ' 1 1 du' τ dτ' ( 1+0.55 cos 2 α ) exp[(τ'τ)/μ] c(τ',λ) L(τ',u',ϕ', λ E ),
E u (0) (τ,λ)=0.0673 b R ( λ E λ)Δ λ E 0 2π dϕ 0 1 dμ × 0 2π dϕ' 1 1 du' τ dτ' ( 1+0.55 cos 2 α ) exp[(τ'τ)/μ] c(τ',λ) L(τ',u',ϕ', λ E ).
E u (0) (τ,λ)=0.0673 b R ( λ E λ)Δ λ E 0 1 dμ τ dτ' exp[(τ'τ)/μ] c(τ',λ) ×( 1+0.55[ u 2 E μ 2 +0.5(1 u 2 E )(1 μ 2 ) ] ) E 0 (τ', λ E ).
E u (0) (z,λ)=0.0673 b R ( λ E λ)Δ λ E E 0 (z, λ E )exp[ K 0 ( λ E )z] × 0 1 μdμ ( 1+0.55[ u 2 E μ 2 +0.5(1 u 2 E )(1 μ 2 ) ] ) c(λ)+μ K 0 ( λ E ) .

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