Abstract

We modify an algorithm for retrieving the absorption (a) and backscattering (b b) coefficient profiles in natural waters by inverting profiles of downwelling and upwelling irradiance so as to include the presence of Raman scattering. For a given wavelength of interest, λ, the light field at the appropriate Raman excitation wavelength λe is first inverted to obtain the Raman source function at λ. Starting from estimates of the inherent optical properties at λ, the contribution to the irradiances at λ from Raman scattering is then estimated and subtracted from the total irradiances to obtain the elastically scattered irradiances. We then inverted the elastically scattered irradiances to find new estimates of a and b b using our original method [Appl. Opt. 37, 3886 (1998)]. The algorithm then operates iteratively: The new estimates are used with the Raman source function to derive a new estimate of the Raman contribution, etc. Sample results are provided that demonstrate the working of the algorithm and show that the absorption and scattering coefficients can be retrieved with accuracies similar to those in the absence of Raman scattering down to depths at which the light field is significantly perturbed by it, e.g., with ∼90% of the upwelling light field originating from Raman scattering.

© 2000 Optical Society of America

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References

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  1. H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
    [CrossRef] [PubMed]
  2. H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
    [CrossRef]
  3. H. R. Gordon, “The sensitivity of radiative transfer to small-angle scattering in the ocean: a quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
    [CrossRef] [PubMed]
  4. S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanog. Soc. Jpn. 40, 397–404 (1984).
    [CrossRef]
  5. R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
    [CrossRef] [PubMed]
  6. B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29, 71–84 (1990).
    [CrossRef] [PubMed]
  7. R. H. Stavn, “Raman scattering effects at the shorter visible wavelengths in clear ocean water,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 94–100 (1990).
    [CrossRef]
  8. G. W. Kattawar, X. Xu, “Filling-in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31, 6491–6500 (1992).
    [CrossRef] [PubMed]
  9. Y. Ge, H. R. Gordon, K. J. Voss, “Simulations of inelastic scattering contributions to the irradiance fields in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
    [PubMed]
  10. K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100C, 13,151–13,161 (1995).
    [CrossRef]
  11. C. Hu, K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
    [CrossRef]
  12. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38, 3166–3174 (1999).
    [CrossRef]
  13. H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
    [CrossRef]
  14. A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
    [CrossRef]
  15. C. H. Chang, L. A. Young, “Sea water temperature measurement from Raman spectra,” (Avco Everett Research Laboratory, Inc., 2385 Revere Beach Parkway, Everett, Mass., 1974).
  16. J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
    [CrossRef]
  17. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, New York, 1994).
  18. 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, 417–427 (1975).
    [CrossRef] [PubMed]
  19. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  20. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
    [CrossRef] [PubMed]
  21. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
  22. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.
  23. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
    [CrossRef]
  24. 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]
  25. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).
  26. D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
    [CrossRef]
  27. M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
    [CrossRef]

1999 (1)

1998 (2)

1997 (5)

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
[CrossRef]

H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
[CrossRef] [PubMed]

C. Hu, K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
[CrossRef]

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

1996 (1)

1995 (1)

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100C, 13,151–13,161 (1995).
[CrossRef]

1993 (3)

1992 (1)

1990 (1)

1988 (1)

1984 (2)

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

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

1981 (1)

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

1977 (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[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, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

Bartlett, J. S.

Boynton, G. C.

Bricaud, A.

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Broenkow, W.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

Brown, O. B.

Chang, C. H.

C. H. Chang, L. A. Young, “Sea water temperature measurement from Raman spectra,” (Avco Everett Research Laboratory, Inc., 2385 Revere Beach Parkway, Everett, Mass., 1974).

Clark, D. K.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).

Fry, E. S.

Ge, Y.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

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

Gentili, B.

Gordon, H. R.

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

H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
[CrossRef]

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
[CrossRef] [PubMed]

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

H. R. Gordon, “The sensitivity of radiative transfer to small-angle scattering in the ocean: a quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
[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, 7484–7504 (1993).
[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, 417–427 (1975).
[CrossRef] [PubMed]

Hu, C.

Ishizaka, J.

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

Jacobs, M. M.

Jin, Z.

Kattawar, G. W.

Kishino, M.

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

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

Labs, D.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Marshall, B. R.

Masayoshi, M.

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

Mobley, C. D.

Morel, A.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
[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, 7484–7504 (1993).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

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

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

Neckel, H.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Okami, N.

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

Pope, R. M.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).

Prieur, L.

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

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

Reinersman, P.

Saitoh, S.

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

Sathyendranath, S.

Senga, Y.

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[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. Oceanog. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).

Trees, C.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).

Vodacek, A.

Voss, K. J.

Waters, K. J.

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100C, 13,151–13,161 (1995).
[CrossRef]

Weidemann, A. D.

Xu, X.

Young, L. A.

C. H. Chang, L. A. Young, “Sea water temperature measurement from Raman spectra,” (Avco Everett Research Laboratory, Inc., 2385 Revere Beach Parkway, Everett, Mass., 1974).

Appl. Opt. (14)

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, 417–427 (1975).
[CrossRef] [PubMed]

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

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

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

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

H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
[CrossRef] [PubMed]

C. Hu, K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
[CrossRef]

H. R. Gordon, G. C. Boynton, “A radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
[CrossRef]

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

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

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

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
[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]

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

J. Geophys. Res. (3)

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100C, 13,151–13,161 (1995).
[CrossRef]

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102D, 17,209–17,217 (1997).
[CrossRef]

M. Kishino, J. Ishizaka, S. Saitoh, Y. Senga, M. Masayoshi, “Verification plan of ocean color and temperature scanner atmospheric correction and phytoplankton pigment by moored optical bouy system,” J. Geophys. Res. 102D, 17,197–17,207 (1997).
[CrossRef]

J. Oceanog. Soc. Jpn. (1)

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

J. Quant. Spectrosc. Radiat. Transfer (1)

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

Limnol. Oceanogr. (2)

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter in the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

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

Sol. Phys. (1)

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Other (5)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, U.K., 1992).

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

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

C. H. Chang, L. A. Young, “Sea water temperature measurement from Raman spectra,” (Avco Everett Research Laboratory, Inc., 2385 Revere Beach Parkway, Everett, Mass., 1974).

R. H. Stavn, “Raman scattering effects at the shorter visible wavelengths in clear ocean water,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 94–100 (1990).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic flow chart of the Raman-scattering addition to the algorithm.

Fig. 2
Fig. 2

Comparison between the measured (solid circles) and reconstructed (continuous curve) AOP profiles at 666 nm when Raman scattering is ignored in the inversion: (a) E d (z); (b) R(z).

Fig. 3
Fig. 3

Percent error in the retrieved IOP profiles at 666 nm when Raman scattering is ignored in the inversion: (a) a(z); (b) b b (z).

Fig. 4
Fig. 4

Percent error in the retrieved IOP profiles at 544 nm when Raman scattering is ignored in the inversion: (a) a(z); (b) b b (z).

Fig. 5
Fig. 5

Percent error in the reconstructed profile of E 2(z) at 544 nm when Raman scattering is ignored in the inversion.

Fig. 6
Fig. 6

Percent error in the retrieved IOP profiles at 666 nm when Raman scattering is included in the algorithm as described in the text: (a) a(z); (b) b b (z).

Fig. 7
Fig. 7

Pigment profile used to provide IOP’s for testing the inversion algorithm in a vertically stratified water body. The pigment concentration is equal to 0.1 mg/m3 for depths greater than 20 m.

Fig. 8
Fig. 8

Retrieved profiles of (a) a(z) and (b) b b (z) at 666 nm for the stratified water body. The filled circles are the true values, the dashed curves are the retrieval ignoring the presence of Raman scattering, the solid curves are the retrieval using the full algorithm (including Raman scattering) and the correct phase function for the water, and the dotted curves are the retrieval using the full algorithm and the incorrect phase function for the water.

Tables (1)

Tables Icon

Table 1 IOP’s for the Algorithm Testa

Equations (10)

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

cos θ dLz, θ, ϕ, λdz=-cz, λLz, θ, ϕ, λ+Ω βz, θθ, ϕϕ, λ×Lz, θ, ϕ, λdΩ+Ω×βrz, θθ, ϕϕ; λeλ×Lz, θ, ϕ, λedΩdλe,
cz, λ=az, λ+bz, λ+ brz; λλdλ,
bz, λ=Ω βz, θθ, ϕϕ, λdΩ, brz; λλ=Ω βrz, θθ, ϕϕ; λλdΩ.
cos θ dL0z, θ, λdz=-cz, λL0z, θ, λ+Ω β0z, θθ, λL0z, θ, λ×sin θdθ+Jrz, θ, λ,
L0z, θ, λ=12π02π Lz, θ, ϕ, λdϕ, β0z, θθ, λ=12π02π βz, θθ, ϕϕ, λdϕ,
Jrz, θ, λ=14π  brz; λeλE0z, λe×1+121-ρλe1+2ρλeE2z, λeE0z, λe×P2cos θdλe,
Elz, λe=2π 0π Plcos θL0z, θ, λesin θdθ,
Jrz, θ, λ=14π bRamanE0z, λe0×1+121-ρλe01+2ρλe0E2z, λe0E0z, λe0×P2cos θ,
bRaman= brz; λeλdλe;
ai+1z=faiz+1-fai-1z,

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