Abstract

This paper is devoted to the derivation of a fast and accurate model of scalar irradiance for stratified Case 2 waters. Five strategies are formulated and employed in the new model, including (1) reallocating the sky radiance, (2) approximating the influence of the air-water interface, (3) constructing a look-up table of average cosine based on the single-scattering albedo and the backscatter fraction, (4) calculating the phase function of surrogate particles in Case 2 waters, and (5) using the average cosine as an index to cope with stratified waters. A comprehensive model-to-model comparison shows that the new model runs more than 1,400 times faster than the commercially-available Hydrolight model, while it limits the percentage error to 2.03% and the maximum error to less than 6.81%. This new model can be used interactively in models of the oceanic system, such as biogeochemical models or the heat budget part of global circulation models.

© 2006 Optical Society of America

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  1. C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, CA, 1994), p. 592.
  2. C.-C. Liu, K. L. Carder, R. L. Miller, and J. E. Ivey, "Fast and accurate model of underwater scalar irradiance," Appl. Opt. 41, 4962-4974 (2002).
  3. A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
  4. H. R. Gordon and A. Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol.  4, p. 114.
  5. J. C. Pernetta and J. D. Milliman, "Land-ocean interactions in the coastal zone implementation plan," IGBP Report 33 (Stockholm, 1995).
  6. S. Sathyendranath, ed., Remote sensing of ocean colour in coastal, and other optically-complex, waters, IOCCG Report (MacNab Print, Dartmouth, Canada, 2000), Vol. 3, p. 140.
  7. A. Albert and C. D. Mobley, "An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters," Opt. Express 11, 2873-2890 (2003).
  8. R. W. Preisendorfer, Hydrologic optics (U. S. Department of Commerce, Seattle, WA, 1976).
  9. R. L. Fante, "Relationship between radiative-transport theory and Maxwell's equations in dielectric media," J. Opt. Soc. Am. 71, 460-468 (1981).
  10. R. M. Measures, Laser remote sensing: fundamentals and applications (Kreiger, Malabar, Florida, 1992), p. 510.
  11. K. Stamnes, "The theory of multiple scattering of radiation in plane parallel atmospheres," Rev. Geophys. 24, 299-310 (1986).
  12. G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system. I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
    [CrossRef]
  13. C.-C. Liu and J. Woods, "Prediction of ocean colour: Monte-Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method," Int. J. Remote Sens. 25, 921-936 (2004).
    [CrossRef]
  14. K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).
  15. R. W. Preisendorfer and C. D. Mobley, "Unpolarized irradiance reflectances and glitter patterns of random capillary waves on lakes and seas, by Monte Carlo simulation," NOAA Technical Memorandum, ERL PMEL-63 (NOAA Pacific Marine Environmental Laboratory, Seattle, WA, 1985).
  16. C. D. Mobley and R. W. Preisendorfer, "A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces," NOAA Technical Memorandum, ERL PMEL-75 (NOAA Pacific Marine Environmental Laboratory, Seattle, WA, 1988).
  17. C. D. Mobley, "A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces," Limnol. Oceanogr. 34, 1473-1483 (1989).
  18. C. D. Mobley, "Hydrolight 3.0 Users' Guide," (SRI International, Menlo Park, CA, 1995).
  19. C.-C. Liu, J. D. Woods, and C. D. Mobley, "Optical model for use in oceanic ecosystem models," Appl. Opt. 38, 4475-4485 (1999).
  20. G. R. Fournier and J. L. Forand, "Analytic phase function for ocean water," presented at the SPIE: Ocean Optics XII, 1994.
  21. N. J. McCormick, "Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient," Limnol. Oceanogr. 40, 1013-1018 (1995).
  22. A. Gershun, "The light field," J. Math. Phys. 18, 51-151 (1939).
  23. V. I. Haltrin, "Chlorophyll-Based Model of Seawater Optical Properties," Appl. Opt. 38, 6826-6832 (1999).
  24. C. D. Mobley, L. K. Sundman, and E. Boss, "Phase function effects on oceanic light fields," Appl. Opt. 41, 1035-1050 (2002).
  25. M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).
  26. L. Prieur and 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).
  27. A. Morel, "Light and marine photosynthesis: a spectral model with geochemical and climatological implications," Prog. Oceanogr. 26, 263-306 (1991).
    [CrossRef]
  28. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, "Phytoplankton pigment concentrations in the Middle Atlantic Bight: Comparison of ship determinations and CZCS estimates," Appl. Opt. 22, 20-36 (1983).
  29. A. Morel, "Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water)," J. Geoph. Res. 93, 10749-10768 (1988).
  30. R. M. Pope and E. S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
  31. R. C. Smith and K. Baker, "Optical properties of the clearest natural waters," Appl. Opt. 20, 177-184 (1981).
  32. R. P. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical properties and remote sensing of inland and coastal waters (CRC Press, 1995), p. 384.

2004 (1)

C.-C. Liu and J. Woods, "Prediction of ocean colour: Monte-Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method," Int. J. Remote Sens. 25, 921-936 (2004).
[CrossRef]

2003 (2)

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

A. Albert and C. D. Mobley, "An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters," Opt. Express 11, 2873-2890 (2003).

2002 (2)

1999 (2)

1997 (1)

1995 (1)

N. J. McCormick, "Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient," Limnol. Oceanogr. 40, 1013-1018 (1995).

1991 (1)

A. Morel, "Light and marine photosynthesis: a spectral model with geochemical and climatological implications," Prog. Oceanogr. 26, 263-306 (1991).
[CrossRef]

1989 (1)

C. D. Mobley, "A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces," Limnol. Oceanogr. 34, 1473-1483 (1989).

1988 (1)

A. Morel, "Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water)," J. Geoph. Res. 93, 10749-10768 (1988).

1986 (1)

K. Stamnes, "The theory of multiple scattering of radiation in plane parallel atmospheres," Rev. Geophys. 24, 299-310 (1986).

1983 (3)

H. R. Gordon and A. Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol.  4, p. 114.

M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, "Phytoplankton pigment concentrations in the Middle Atlantic Bight: Comparison of ship determinations and CZCS estimates," Appl. Opt. 22, 20-36 (1983).

1981 (3)

L. Prieur and 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).

R. C. Smith and K. Baker, "Optical properties of the clearest natural waters," Appl. Opt. 20, 177-184 (1981).

R. L. Fante, "Relationship between radiative-transport theory and Maxwell's equations in dielectric media," J. Opt. Soc. Am. 71, 460-468 (1981).

1977 (1)

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).

1972 (1)

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system. I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
[CrossRef]

1939 (1)

A. Gershun, "The light field," J. Math. Phys. 18, 51-151 (1939).

Albert, A.

Baker, K.

Boss, E.

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Carder, K. L.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

C.-C. Liu, K. L. Carder, R. L. Miller, and J. E. Ivey, "Fast and accurate model of underwater scalar irradiance," Appl. Opt. 41, 4962-4974 (2002).

Chen, R. F.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

Clark, D. K.

Cullen, J. J.

M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).

Davis, C. O.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

English, D. C.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

Evans, R. H.

Fante, R. L.

Fry, E. S.

Gershun, A.

A. Gershun, "The light field," J. Math. Phys. 18, 51-151 (1939).

Gordon, H. R.

H. R. Gordon and A. Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol.  4, p. 114.

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, "Phytoplankton pigment concentrations in the Middle Atlantic Bight: Comparison of ship determinations and CZCS estimates," Appl. Opt. 22, 20-36 (1983).

Haltrin, V. I.

Ivey, J. E.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

C.-C. Liu, K. L. Carder, R. L. Miller, and J. E. Ivey, "Fast and accurate model of underwater scalar irradiance," Appl. Opt. 41, 4962-4974 (2002).

Kattawar, G. W.

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system. I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
[CrossRef]

Lee, Z. P.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

Lewis, M. R.

M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).

Liu, C.-C.

C.-C. Liu and J. Woods, "Prediction of ocean colour: Monte-Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method," Int. J. Remote Sens. 25, 921-936 (2004).
[CrossRef]

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

C.-C. Liu, K. L. Carder, R. L. Miller, and J. E. Ivey, "Fast and accurate model of underwater scalar irradiance," Appl. Opt. 41, 4962-4974 (2002).

C.-C. Liu, J. D. Woods, and C. D. Mobley, "Optical model for use in oceanic ecosystem models," Appl. Opt. 38, 4475-4485 (1999).

McCormick, N. J.

N. J. McCormick, "Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient," Limnol. Oceanogr. 40, 1013-1018 (1995).

Miller, R. L.

Mobley, C. D.

Morel, A.

A. Morel, "Light and marine photosynthesis: a spectral model with geochemical and climatological implications," Prog. Oceanogr. 26, 263-306 (1991).
[CrossRef]

A. Morel, "Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water)," J. Geoph. Res. 93, 10749-10768 (1988).

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).

Morel, A. Y.

H. R. Gordon and A. Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol.  4, p. 114.

Patten, J.

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

Plass, G. N.

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system. I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
[CrossRef]

Platt, T.

M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).

Pope, R. M.

Prieur, L.

L. Prieur and 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).

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).

Sathyendranath, S.

L. Prieur and 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).

Smith, R. C.

Stamnes, K.

K. Stamnes, "The theory of multiple scattering of radiation in plane parallel atmospheres," Rev. Geophys. 24, 299-310 (1986).

Sundman, L. K.

Woods, J.

C.-C. Liu and J. Woods, "Prediction of ocean colour: Monte-Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method," Int. J. Remote Sens. 25, 921-936 (2004).
[CrossRef]

Woods, J. D.

Appl. Opt. (7)

Int. J. Remote Sens. (1)

C.-C. Liu and J. Woods, "Prediction of ocean colour: Monte-Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method," Int. J. Remote Sens. 25, 921-936 (2004).
[CrossRef]

J. Geoph. Res. (2)

M. R. Lewis, J. J. Cullen, and T. Platt, "Phytoplankton and thermal structure in the upper ocean: consequences of nonuniformity in chlorophyll profile," J. Geoph. Res. 88, 2565-2570 (1983).

A. Morel, "Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water)," J. Geoph. Res. 93, 10749-10768 (1988).

J. Math. Phys. (1)

A. Gershun, "The light field," J. Math. Phys. 18, 51-151 (1939).

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system. I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
[CrossRef]

Limnol. Oceanogr. (5)

C. D. Mobley, "A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces," Limnol. Oceanogr. 34, 1473-1483 (1989).

N. J. McCormick, "Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient," Limnol. Oceanogr. 40, 1013-1018 (1995).

L. Prieur and 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).

K. L. Carder, C.-C. Liu, Z. P. Lee, D. C. English, J. Patten, R. F. Chen, J. E. Ivey, and C. O. Davis, "Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos," Limnol. Oceanogr. 48, 355-363 (2003).

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).

New York (1)

H. R. Gordon and A. Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol.  4, p. 114.

Opt. Express (1)

Prog. Oceanogr. (1)

A. Morel, "Light and marine photosynthesis: a spectral model with geochemical and climatological implications," Prog. Oceanogr. 26, 263-306 (1991).
[CrossRef]

Rev. Geophys. (1)

K. Stamnes, "The theory of multiple scattering of radiation in plane parallel atmospheres," Rev. Geophys. 24, 299-310 (1986).

Other (10)

C. D. Mobley, "Hydrolight 3.0 Users' Guide," (SRI International, Menlo Park, CA, 1995).

G. R. Fournier and J. L. Forand, "Analytic phase function for ocean water," presented at the SPIE: Ocean Optics XII, 1994.

J. C. Pernetta and J. D. Milliman, "Land-ocean interactions in the coastal zone implementation plan," IGBP Report 33 (Stockholm, 1995).

S. Sathyendranath, ed., Remote sensing of ocean colour in coastal, and other optically-complex, waters, IOCCG Report (MacNab Print, Dartmouth, Canada, 2000), Vol. 3, p. 140.

C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, CA, 1994), p. 592.

R. W. Preisendorfer, Hydrologic optics (U. S. Department of Commerce, Seattle, WA, 1976).

R. M. Measures, Laser remote sensing: fundamentals and applications (Kreiger, Malabar, Florida, 1992), p. 510.

R. W. Preisendorfer and C. D. Mobley, "Unpolarized irradiance reflectances and glitter patterns of random capillary waves on lakes and seas, by Monte Carlo simulation," NOAA Technical Memorandum, ERL PMEL-63 (NOAA Pacific Marine Environmental Laboratory, Seattle, WA, 1985).

C. D. Mobley and R. W. Preisendorfer, "A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces," NOAA Technical Memorandum, ERL PMEL-75 (NOAA Pacific Marine Environmental Laboratory, Seattle, WA, 1988).

R. P. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical properties and remote sensing of inland and coastal waters (CRC Press, 1995), p. 384.

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