Abstract

For analytical or semianalytical retrieval of shallow-water bathymetry and/or optical properties of the water column from remote sensing, the contribution to the remotely sensed signal from the water column has to be separated from that of the bottom. The mathematical separation involves three diffuse attenuation coefficients: one for the downwelling irradiance (K d), one for the upwelling radiance of the water column (K u C), and one for the upwelling radiance from bottom reflection (K u B). Because of the differences in photon origination and path lengths, these three coefficients in general are not equal, although their equality has been assumed in many previous studies. By use of the Hydrolight radiative-transfer numerical model with a particle phase function typical of coastal waters, the remote-sensing reflectance above (R rs) and below (r rs) the surface is calculated for various combinations of optical properties, bottom albedos, bottom depths, and solar zenith angles. A semianalytical (SA) model for r rs of shallow waters is then developed, in which the diffuse attenuation coefficients are explicitly expressed as functions of in-water absorption (a) and backscattering (b b). For remote-sensing inversion, parameters connecting R rs and r rs are also derived. It is found that r rs values determined by the SA model agree well with the exact values computed by Hydrolight (∼3% error), even for Hydrolight r rs values calculated with different particle phase functions. The Hydrolight calculations included b b/a values as high as 1.5 to simulate high-turbidity situations that are occasionally found in coastal regions.

© 1998 Optical Society of America

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  1. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  2. D. R. Lyzenga, “Passive remote-sensing techniques for mapping water depth and bottom features,” Appl. Opt. 17, 379–883 (1978).
    [CrossRef] [PubMed]
  3. W. D. Philpot, “Bathymetric mapping with passive multispectral imagery,” Appl. Opt. 28, 1569–1578 (1989).
    [CrossRef] [PubMed]
  4. N. T. O’Neill, J. R. Miller, “On calibration of passive optical bathymetry through depth soundings analysis and treatment of errors resulting from the spatial variation of environmental parameters,” Int. J. Remote Sensing 10, 1481–1501 (1989).
    [CrossRef]
  5. Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
    [CrossRef] [PubMed]
  6. S. Maritorena, A. Morel, B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39, 1689–1703 (1994).
    [CrossRef]
  7. J. M. Paredes, R. E. Spero, “Water depth mapping from passive remote sensing data under a generalized ratio assumption,” Appl. Opt. 22, 1134–1135 (1983).
    [CrossRef] [PubMed]
  8. D. Spitzer, R. W. J. Dirks, “Bottom influence on the reflectance of the sea,” Int. J. Remote Sensing 8, 279–290 (1987).
    [CrossRef]
  9. R. W. Preisendorfer, Hydrologic Optics, Vol. 1: Introduction, NTIS PB-259 793/8ST (National Technical Information Service, Springfield, Va., 1976).
  10. J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467 (1991).
    [CrossRef]
  11. 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]
  12. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, New York, 1994).
  13. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
    [CrossRef]
  14. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  15. H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
    [CrossRef]
  16. C. D. Mobley, Hydrolight 3.0 Users’ Guide, Final Report (SRI International, Menlo Park, Calif., 1995).
  17. T. Tyrrell, P. M. Holligan, C. D. Mobley are preparing the following paper for publication: “Optical impacts of oceanic coccolithophore blooms.”
  18. J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer are preparing the following paper for publication: “The effect of Raman scattering on the underwater light field.”
  19. C. D. Mobley, D. Stramski.“Effects of microbial particles on oceanic optics: methodology for radiative transfer modeling and example simulations,” Limnol. Oceanogr. 42, 550–560 (1997).
    [CrossRef]
  20. W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
    [CrossRef]
  21. R. Pope, E. Fry, “Absorption spectrum (380-700 nm) of pure waters: II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
  22. Z. P. Lee, “Visible-infrared remote-sensing model and applications for ocean waters,” Ph.D. dissertation (Department of Marine Science, University of South Florida, St. Petersburg, Fla., 1994).
  23. L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
    [CrossRef]
  24. A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
    [CrossRef]
  25. A. Morel, “Optical properties of pure water and pure sea waters,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.
  26. H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: a Review (Springer-Verlag, New York, 1983), p. 44.
  27. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
    [CrossRef]
  28. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angles as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
    [CrossRef] [PubMed]
  29. J. H. Jerome, R. P. Bukata, J. E. Burton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988).
    [CrossRef] [PubMed]
  30. H. R. Gordon, G. C. Boynton, “Radiance—irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
    [CrossRef] [PubMed]
  31. S. Sathyendranath, T. Platt, “Analytical model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
    [CrossRef] [PubMed]
  32. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  33. W. D. Philpot, “Radiative transfer in stratified waters: a single-scattering approximation for irradiance,” Appl. Opt. 26, 4123–4132 (1987).
    [CrossRef] [PubMed]
  34. H. R. Gordon, O. B. Brown, “Influence of bottom depth and albedo on the diffuse reflectance of a flat homogeneous ocean,” Appl. Opt. 13, 2153–2159 (1974).
    [CrossRef] [PubMed]
  35. D. R. Lyzenga, “Reflectance of a flat ocean in the limit of zero water depth,” Appl. Opt. 16, 282–283 (1977).
    [CrossRef] [PubMed]

1997 (4)

1994 (2)

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

S. Maritorena, A. Morel, B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39, 1689–1703 (1994).
[CrossRef]

1993 (2)

1991 (2)

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]

1989 (4)

H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

W. D. Philpot, “Bathymetric mapping with passive multispectral imagery,” Appl. Opt. 28, 1569–1578 (1989).
[CrossRef] [PubMed]

N. T. O’Neill, J. R. Miller, “On calibration of passive optical bathymetry through depth soundings analysis and treatment of errors resulting from the spatial variation of environmental parameters,” Int. J. Remote Sensing 10, 1481–1501 (1989).
[CrossRef]

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

1988 (2)

J. H. Jerome, R. P. Bukata, J. E. Burton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

1987 (2)

D. Spitzer, R. W. J. Dirks, “Bottom influence on the reflectance of the sea,” Int. J. Remote Sensing 8, 279–290 (1987).
[CrossRef]

W. D. Philpot, “Radiative transfer in stratified waters: a single-scattering approximation for irradiance,” Appl. Opt. 26, 4123–4132 (1987).
[CrossRef] [PubMed]

1983 (1)

1981 (2)

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

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

1978 (1)

1977 (2)

D. R. Lyzenga, “Reflectance of a flat ocean in the limit of zero water depth,” Appl. Opt. 16, 282–283 (1977).
[CrossRef] [PubMed]

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

1975 (1)

1974 (1)

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Boynton, G. C.

Bricaud, A.

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

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Brown, O. B.

Bukata, R. P.

Burton, J. E.

Carder, K. L.

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

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

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Davis, C. O.

Dirks, R. W. J.

D. Spitzer, R. W. J. Dirks, “Bottom influence on the reflectance of the sea,” Int. J. Remote Sensing 8, 279–290 (1987).
[CrossRef]

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Fry, E.

Gentili, B.

Gordon, H. R.

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

H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “Influence of bottom depth and albedo on the diffuse reflectance of a flat homogeneous ocean,” Appl. Opt. 13, 2153–2159 (1974).
[CrossRef] [PubMed]

H. R. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: a Review (Springer-Verlag, New York, 1983), p. 44.

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]

Hawes, S. K.

Jacobs, M. M.

Jerome, J. H.

Jin, Z.

Kattawar, G. W.

Kirk, J. T. O.

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467 (1991).
[CrossRef]

Lee, Z. P.

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

Z. P. Lee, “Visible-infrared remote-sensing model and applications for ocean waters,” Ph.D. dissertation (Department of Marine Science, University of South Florida, St. Petersburg, Fla., 1994).

Lyzenga, D. R.

Maritorena, S.

S. Maritorena, A. Morel, B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39, 1689–1703 (1994).
[CrossRef]

Miller, J. R.

N. T. O’Neill, J. R. Miller, “On calibration of passive optical bathymetry through depth soundings analysis and treatment of errors resulting from the spatial variation of environmental parameters,” Int. J. Remote Sensing 10, 1481–1501 (1989).
[CrossRef]

Mobley, C. D.

C. D. Mobley, D. Stramski.“Effects of microbial particles on oceanic optics: methodology for radiative transfer modeling and example simulations,” Limnol. Oceanogr. 42, 550–560 (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]

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

C. D. Mobley, Hydrolight 3.0 Users’ Guide, Final Report (SRI International, Menlo Park, Calif., 1995).

Morel, A.

S. Maritorena, A. Morel, B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39, 1689–1703 (1994).
[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]

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

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angles as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of 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 waters,” 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 (Springer-Verlag, New York, 1983), p. 44.

O’Neill, N. T.

N. T. O’Neill, J. R. Miller, “On calibration of passive optical bathymetry through depth soundings analysis and treatment of errors resulting from the spatial variation of environmental parameters,” Int. J. Remote Sensing 10, 1481–1501 (1989).
[CrossRef]

Paredes, J. M.

Peacock, T. G.

Philpot, W. D.

Platt, T.

Pope, R.

Preisendorfer, R. W.

R. W. Preisendorfer, Hydrologic Optics, Vol. 1: Introduction, NTIS PB-259 793/8ST (National Technical Information Service, Springfield, Va., 1976).

Prieur, L.

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of 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.

Sathyendranath, S.

S. Sathyendranath, T. Platt, “Analytical model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
[CrossRef] [PubMed]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Spero, R. E.

Spitzer, D.

D. Spitzer, R. W. J. Dirks, “Bottom influence on the reflectance of the sea,” Int. J. Remote Sensing 8, 279–290 (1987).
[CrossRef]

Stamnes, K.

Stavn, R. H.

Steward, R. G.

Stramski., D.

C. D. Mobley, D. Stramski.“Effects of microbial particles on oceanic optics: methodology for radiative transfer modeling and example simulations,” Limnol. Oceanogr. 42, 550–560 (1997).
[CrossRef]

Appl. Opt. (15)

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

D. R. Lyzenga, “Passive remote-sensing techniques for mapping water depth and bottom features,” Appl. Opt. 17, 379–883 (1978).
[CrossRef] [PubMed]

W. D. Philpot, “Bathymetric mapping with passive multispectral imagery,” Appl. Opt. 28, 1569–1578 (1989).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

J. M. Paredes, R. E. Spero, “Water depth mapping from passive remote sensing data under a generalized ratio assumption,” Appl. Opt. 22, 1134–1135 (1983).
[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. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

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

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angles as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

J. H. Jerome, R. P. Bukata, J. E. Burton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988).
[CrossRef] [PubMed]

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

S. Sathyendranath, T. Platt, “Analytical model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
[CrossRef] [PubMed]

W. D. Philpot, “Radiative transfer in stratified waters: a single-scattering approximation for irradiance,” Appl. Opt. 26, 4123–4132 (1987).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “Influence of bottom depth and albedo on the diffuse reflectance of a flat homogeneous ocean,” Appl. Opt. 13, 2153–2159 (1974).
[CrossRef] [PubMed]

D. R. Lyzenga, “Reflectance of a flat ocean in the limit of zero water depth,” Appl. Opt. 16, 282–283 (1977).
[CrossRef] [PubMed]

Int. J. Remote Sensing (2)

D. Spitzer, R. W. J. Dirks, “Bottom influence on the reflectance of the sea,” Int. J. Remote Sensing 8, 279–290 (1987).
[CrossRef]

N. T. O’Neill, J. R. Miller, “On calibration of passive optical bathymetry through depth soundings analysis and treatment of errors resulting from the spatial variation of environmental parameters,” Int. J. Remote Sensing 10, 1481–1501 (1989).
[CrossRef]

J. Geophys. Res. (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Limnol. Oceanogr. (9)

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467 (1991).
[CrossRef]

H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

S. Maritorena, A. Morel, B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39, 1689–1703 (1994).
[CrossRef]

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

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

C. D. Mobley, D. Stramski.“Effects of microbial particles on oceanic optics: methodology for radiative transfer modeling and example simulations,” Limnol. Oceanogr. 42, 550–560 (1997).
[CrossRef]

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

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

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

Other (8)

A. Morel, “Optical properties of pure water and pure sea waters,” 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 (Springer-Verlag, New York, 1983), p. 44.

Z. P. Lee, “Visible-infrared remote-sensing model and applications for ocean waters,” Ph.D. dissertation (Department of Marine Science, University of South Florida, St. Petersburg, Fla., 1994).

R. W. Preisendorfer, Hydrologic Optics, Vol. 1: Introduction, NTIS PB-259 793/8ST (National Technical Information Service, Springfield, Va., 1976).

C. D. Mobley, Hydrolight 3.0 Users’ Guide, Final Report (SRI International, Menlo Park, Calif., 1995).

T. Tyrrell, P. M. Holligan, C. D. Mobley are preparing the following paper for publication: “Optical impacts of oceanic coccolithophore blooms.”

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer are preparing the following paper for publication: “The effect of Raman scattering on the underwater light field.”

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

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Figures (13)

Fig. 1
Fig. 1

Examples of simulated pigment absorption coefficients as computed by Eqs. (12) and (13) for three different chlorophyll a concentrations; curves are normalized to 1.0 at 440 nm to show the curvature dependence on [chl-a].

Fig. 2
Fig. 2

Particle phase functions used in the Hydrolight calculations. The solid curve represents the calculations used in the parameter determination; the dashed curve represents the calculations used in the test.

Fig. 3
Fig. 3

Dependence of deep water r rs on b b /(a + b b ), as simulated by Hydrolight. The simulations include various environmental conditions as shown in Table 1.

Fig. 4
Fig. 4

Dependence of deep water r rs on b b /a.

Fig. 5
Fig. 5

Comparison of deep water r rs values as computed by Hydrolight and by the SA model. Values for the different solar zenith angles are identified.

Fig. 6
Fig. 6

Examples of r rs spectra as computed by Hydrolight (filled symbols) and by the SA model (open symbols).

Fig. 7
Fig. 7

Comparison of r rs dp values as determined by three different expressions.

Fig. 8
Fig. 8

Comparison of shallow water r rs values as computed by Hydrolight and by the SA model for different solar zenith angles.

Fig. 9
Fig. 9

Dependence of distribution functions on b b /(a + b b ).

Fig. 10
Fig. 10

Ratios of r rs at two wavelengths as a function of bottom depth and reflectance.

Fig. 11
Fig. 11

Comparison of deep water r rs values computed by Hydrolight with the Kopelevich phase function of Fig. 2 with r rs values given by the SA model, which is based on the coastal particle phase function of Fig. 2.

Fig. 12
Fig. 12

Comparison of shallow water r rs values computed by Hydrolight with the Kopelevich phase function of Fig. 2 with r rs values given by the SA model, which is based on the coastal particle phase function of Fig. 2.

Fig. 13
Fig. 13

Comparison of R rs values computed by Hydrolight and by approximation (25).

Tables (2)

Tables Icon

Table 1 Environmental Input used in the Hydrolight Simulations

Tables Icon

Table 2 Parameters for the Empirical aϕ(λ) Simulation by Eq. (12)a

Equations (29)

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S US S US dp 1 - exp - 2 KH + S US B   exp - 2 KH .
r rs r rs dp 1 - A 0 exp - K d + K u C H + A 1 ρ × exp - K d + K u B H ,
α a + b b ,
K = D α .
K d = D d α ,   K u C = D u C α ,   K u B = D u B α ,
r rs r rs dp 1 - A 0 exp - D d + D u C α H + A 1 ρ   exp - D d + D u B α H .
u b b / a + b b ,
r rs dp gu ,
g g 0 + g 1 u g 2 .
D d 1 / cos θ w ,
D u = D 0 1 + D 1 u 0.5
r rs = g 0 + g 1 u g 2 u 1 - A 0 exp - 1 cos θ w + D 0 1 + D 1 u 0.5 α H + A 1 ρ   exp - 1 cos θ w + D 0 1 + D 1 u 0.5 α H .
a ϕ λ = a 0 λ + a 1 λ ln a ϕ 440 a ϕ ( 440 ) .
a ϕ 440 = 0.06 chl-a 0.65 .
a g λ = a g 440 exp - 0.014 λ - 440 ,
b p λ = B chl-a 0.62 550 / λ .
δ = mean ln r rs s r rs H ,
r rs dp 0.070 + 0.155 u 0.752 u .
r rs dp 0.0949 + 0.0794 u u .
r rs dp 0.0922 b b / a ,
r rs dp 0.0922 1 - u   u .
A 0 1.03 ,   A 1 0.31 , D u C 1.2 1 + 2.0 u 0.5 ,
D u B 1.1 1 + 4.9 u 0.5 .
r rs 0.070 + 0.155 u 0.752 u 1 - 1.03   exp - 1 cos θ w + 1.2 1 + 2.0 u 0.5 α H + 0.31 ρ   exp - 1 cos θ w + 1.1 × 1 + 4.9 u 0.5 α H .
R rs = L w E d + = t - t + n 2 R Q 1 - γ R ,
r rs = L u - E d - = R Q ,
ζ = t - t + n 2
R rs = ζ r rs 1 - Γ r rs ,
R rs 0.518 r rs 1 - 1.562 r rs .

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