Abstract

A spectral model of scalar irradiance with depth is applied to calculations of photosynthetically available radiation for a vertically homogeneous water column. The model runs more than 14,000 times faster than the full Hydrolight code, while it limits the percentage error to 2.20% and the maximum error to less than 4.78%. The distribution of incident sky radiance and the effects of a wind-roughened surface are integrated into this model. It can be applied to case 1 waters as well as to case 2 waters that happen to be gelbstoff rich, and the volume-scattering phase function can be generated dynamically based on the backscatter fraction. This new model is both fast and accurate and is, therefore, suitable for use interactively in models of the oceanic system, such as biogeochemical models or the heat budget part of global circulation models. It can also be applied by use of remote-sensing data to improve light-field calculations as a function of depth, which is needed for the estimation of global ocean carbon production and the ocean heat budget.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  34. P. W. Francisco, N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
    [CrossRef]
  35. J. P. Doyle, G. Zibordi, “Correction of oceanographic tower-shading effects on in-water radiance and irradiance measurements,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).
  36. A. Y. Morel, H. H. Loisel, B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).
  37. Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
    [CrossRef]
  38. K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
    [CrossRef]
  39. J. L. Mueller, R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
    [CrossRef]
  40. T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
    [CrossRef]
  41. V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Appl. Opt. 38, 6826–6832 (1999).
    [CrossRef]
  42. Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
    [CrossRef]

2002 (1)

1999 (4)

1998 (1)

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

1997 (1)

1995 (2)

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995).
[CrossRef]

N. J. McCormick, “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr. 40, 1013–1018 (1995).
[CrossRef]

1994 (2)

P. W. Francisco, N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
[CrossRef]

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

1993 (3)

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]

J. L. Sarmiento, “Atmospheric CO2 stalled,” Nature 365, 697–698 (1993).
[CrossRef]

T. R. Anderson, “A spectrally averaged model of light penetration and photosynthesis,” Limnol. Oceanogr. 38, 1403–1419 (1993).
[CrossRef]

1992 (2)

N. J. McCormick, “Asymptotic optical attenuation,” Limnol. Oceanogr. 37, 1570–1578 (1992).
[CrossRef]

T. T. Bannister, “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr. 37, 773–780 (1992).
[CrossRef]

1991 (1)

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

1990 (2)

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990).
[CrossRef]

M. J. R. Fasham, H. W. Ducklow, S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
[CrossRef]

1989 (2)

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

J. L. Mueller, R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
[CrossRef]

1988 (3)

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[CrossRef]

A. Morel, “Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res. 93(C9), 10749–10768 (1988).
[CrossRef]

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

1983 (1)

1981 (3)

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]

J. J. Simpson, T. D. Dickey, “Alternative parameterizations of downward irradiance and their dynamical significance,” J. Phys. Oceanogr. 11, 876–882 (1981).
[CrossRef]

R. C. Smith, K. Baker, “Optical properties of the clearest natural waters,” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

1980 (1)

F. Kasten, G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24, 177–189 (1980).
[CrossRef]

1954 (1)

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

Anderson, T. R.

T. R. Anderson, “A spectrally averaged model of light penetration and photosynthesis,” Limnol. Oceanogr. 38, 1403–1419 (1993).
[CrossRef]

Antoine, D.

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

Baker, K.

Bannister, T. T.

T. T. Bannister, “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr. 37, 773–780 (1992).
[CrossRef]

Barnes, R. A.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Berwald, J.

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995).
[CrossRef]

Boss, E.

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Carder, K. L.

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990).
[CrossRef]

Caverhill, C. M.

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[CrossRef]

Chen, F. R.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

Clark, D. K.

Coombes, C. A.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

Cox, C.

Czeplak, G.

F. Kasten, G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24, 177–189 (1980).
[CrossRef]

Darzi, M.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Davis, C. O.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

Dickey, T. D.

J. J. Simpson, T. D. Dickey, “Alternative parameterizations of downward irradiance and their dynamical significance,” J. Phys. Oceanogr. 11, 876–882 (1981).
[CrossRef]

Doyle, J. P.

J. P. Doyle, G. Zibordi, “Correction of oceanographic tower-shading effects on in-water radiance and irradiance measurements,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

Ducklow, H. W.

M. J. R. Fasham, H. W. Ducklow, S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
[CrossRef]

Early, E. A.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Evans, R. H.

Fasham, M. J. R.

M. J. R. Fasham, H. W. Ducklow, S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
[CrossRef]

Forand, J. L.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Fournier, G. R.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Francisco, P. W.

P. W. Francisco, N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
[CrossRef]

Fry, E. S.

Gentili, B.

Gentili, B. B.

A. Y. Morel, H. H. Loisel, B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

Gordon, H. R.

Gregg, W. W.

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990).
[CrossRef]

Haltrin, V. I.

Harrison, A. W.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

Hawes, S. K.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), p. 231.

N. G. Jerlov, Optical Oceanography, Elsevier Oceanography Series (Elsevier, Amsterdam, 1968), p. 194.

Jin, Z.

Johnson, B. C.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Kamykowski, D.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

Kasten, F.

F. Kasten, G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24, 177–189 (1980).
[CrossRef]

Kattawar, G. W.

Kiefer, D. A.

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, 2nd ed. (Cambridge University, Cambridge, England, 1994), p. 509.

Kumar, L.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Lange, R. E.

J. L. Mueller, R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
[CrossRef]

Lee, Z. P.

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

Lewis, M. R.

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[CrossRef]

Liu, C.-C.

Loisel, H. H.

A. Y. Morel, H. H. Loisel, B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

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).
[CrossRef]

P. W. Francisco, N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
[CrossRef]

N. J. McCormick, “Asymptotic optical attenuation,” Limnol. Oceanogr. 37, 1570–1578 (1992).
[CrossRef]

McKelvie, S. M.

M. J. R. Fasham, H. W. Ducklow, S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
[CrossRef]

Mellor, G. L.

G. L. Mellor, Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model (Princeton University, Princeton, N.J., 1998).

Mobley, C. D.

Morel, A.

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (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, “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. Geophys. Res. 93(C9), 10749–10768 (1988).
[CrossRef]

Morel, A. Y.

H. R. Gordon, 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.

A. Y. Morel, H. H. Loisel, B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

Mueller, J. L.

J. L. Mueller, R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
[CrossRef]

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Munk, W.

Patch, J. S.

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
[CrossRef]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

Peacock, T. G.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

Platt, T.

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[CrossRef]

Pope, R. M.

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]

Reinersman, P.

Sarmiento, J. L.

J. L. Sarmiento, “Atmospheric CO2 stalled,” Nature 365, 697–698 (1993).
[CrossRef]

Sathyendranath, S.

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[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]

Simpson, J. J.

J. J. Simpson, T. D. Dickey, “Alternative parameterizations of downward irradiance and their dynamical significance,” J. Phys. Oceanogr. 11, 876–882 (1981).
[CrossRef]

Smith, R. C.

Stamnes, K.

Stavn, R. H.

Steward, R. G.

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
[CrossRef]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

Stramski, D.

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995).
[CrossRef]

Sundman, L. K.

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

C. D. Mobley, L. K. Sundman, Hydrolight 4.2 Users Guide (Sequoia Scientific, Inc., Redmond, Wash., 2001).

Trees, C. C.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Woods, J. D.

Yeh, E.-N.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

Zaneveld, J. R. V.

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

Zibordi, G.

J. P. Doyle, G. Zibordi, “Correction of oceanographic tower-shading effects on in-water radiance and irradiance measurements,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

Appl. Opt. (8)

Deep-Sea Res. (1)

T. Platt, S. Sathyendranath, C. M. Caverhill, M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
[CrossRef]

J. Geophys. Res. (3)

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[CrossRef]

A. Morel, “Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res. 93(C9), 10749–10768 (1988).
[CrossRef]

J. Mar. Res. (1)

M. J. R. Fasham, H. W. Ducklow, S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
[CrossRef]

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (2)

A. Morel, D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
[CrossRef]

J. J. Simpson, T. D. Dickey, “Alternative parameterizations of downward irradiance and their dynamical significance,” J. Phys. Oceanogr. 11, 876–882 (1981).
[CrossRef]

Limnol. Oceanogr. (10)

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990).
[CrossRef]

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

T. R. Anderson, “A spectrally averaged model of light penetration and photosynthesis,” Limnol. Oceanogr. 38, 1403–1419 (1993).
[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]

J. L. Mueller, R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
[CrossRef]

J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995).
[CrossRef]

T. T. Bannister, “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr. 37, 773–780 (1992).
[CrossRef]

N. J. McCormick, “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr. 40, 1013–1018 (1995).
[CrossRef]

N. J. McCormick, “Asymptotic optical attenuation,” Limnol. Oceanogr. 37, 1570–1578 (1992).
[CrossRef]

P. W. Francisco, N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
[CrossRef]

Nature (1)

J. L. Sarmiento, “Atmospheric CO2 stalled,” Nature 365, 697–698 (1993).
[CrossRef]

Prog. Oceanogr. (1)

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

Sol. Energy (2)

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[CrossRef]

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
[CrossRef]

Other (11)

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, 2nd ed. (Cambridge University, Cambridge, England, 1994), p. 509.

H. R. Gordon, 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.

E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.

N. G. Jerlov, Optical Oceanography, Elsevier Oceanography Series (Elsevier, Amsterdam, 1968), p. 194.

G. L. Mellor, Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model (Princeton University, Princeton, N.J., 1998).

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), p. 231.

C. D. Mobley, L. K. Sundman, Hydrolight 4.2 Users Guide (Sequoia Scientific, Inc., Redmond, Wash., 2001).

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994), p. 592.

J. P. Doyle, G. Zibordi, “Correction of oceanographic tower-shading effects on in-water radiance and irradiance measurements,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

A. Y. Morel, H. H. Loisel, B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).

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Figures (5)

Fig. 1
Fig. 1

Illustration of possible errors by use of a constant K d to calculate the underwater light field without considering the actual constituents of water content, the depth-dependent property of K d , and the incident solar angle θ s . Various values of K d based on the classification of water types by Jerlov7 and Morel10 were employed to calculate the downwelling planar irradiance E d . In contrast, the measured IOPs at 440 nm, as listed in Table 1, were used in the Hydrolight model. Note that two different solar angles 0° and 60°, were both used in the Hydrolight simulation to illustrate the variation of the underwater light field within one day: (a) FSLE4, (b) Friday Harbor, (c) CoBOP 98.

Fig. 2
Fig. 2

Illustration of the default equal-angle partition used in the Hydrolight 4.2 version, which has a total number of 217 quads in the upper sphere (24 quads in the ϕ direction times nine quads in the θ direction plus one polar quad). We can still obtain the same integrated result of E 0(z) by reallocating all the light sources with the same value of θ (e.g., quads represented by a cross) to the plane of the Sun toward the Sun’s direction (ϕ = 0°, e.g., the quad represented by a filled triangle). There are a total of ten quads (triangles) in the ϕ = 0° direction, denoted as quad i , where i = 1, … , 10.

Fig. 3
Fig. 3

Examination of the assumption that CW is a weak function of the water content. The Y axis gives the values of CW by taking Chl into consideration, whereas the X axis shows the corresponding values of CW for clear water. A very high correlation (r = 0.999365) was obtained and the deviation was not more than 2.6%. This verifies that the result of CW obtained from the case of clear water can be applied to other types of water.

Fig. 4
Fig. 4

Validation for gelbstoff-rich case 2 waters. The arbitrary composition of the concentration of chlorophyll and CDOM were selected as those 32 cases listed in Tables 5 and 6. Both Hydrolight (filled circles) and our model (solid curves) were used to simulate the profiles of μ̅(ζ). The corresponding profiles of μ̅′(ζ) from the ω0-based LUT w (dotted curves) were also plotted for comparison: (a) λ = 670 nm and (b) λ = 440 nm.

Fig. 5
Fig. 5

Comparison of accuracy and speed in simulating E 0,PAR(z) (W m-2) between our model and Hydrolight. A very high correlation (r = 0.999969) as well as a large CSR of 14518 was obtained. The percentage error ε% is 2.20% and the maximum relative error εmax is not more than 4.78%.

Tables (6)

Tables Icon

Table 1 Measured IOPs at Three Sites with Different Types of Water

Tables Icon

Table 2 Example of Implementing Eqs. (3) and (5) to Calculate E 0(z, 560)a

Tables Icon

Table 3 Part of the Chlorophyll-Based LUTc

Tables Icon

Table 4 Part of the Albedo-Based LUTw

Tables Icon

Table 5 Arbitrary Composition of the Concentration of Chlorophyll and Extra CDOM at λ = 670 nma

Tables Icon

Table 6 Same as Table 5 with λ = 440 nm

Equations (19)

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

E0z=Ξ LzdΩ=ϕ=02πθ=0π Lzsin θdθdϕ.
Ed0+=i=110 Ēd0+; quadi.
E0z=i=110 Ē0z; quadiĒd0+; quadi,
CWVwindVwind; quadiĒ00-; Vwind; quadiĒ00-; Vwind; quadi.
E0z; Vwind=i=110 Ē0z; quadiĒd0+; quadi×CWVwindVwind; quadi,
az; λ=awλ+0.06ac*λChl0.65+F0.06ac*440Chl0.65×exp-0.014λ-440,
bλ=bwλ+0.30550λChl0.62,
β˜ψ; λbwλbλ β˜wψ+bpλbλ β˜pψ; λ.
μ¯zEzE0z.
KNETz=azμ¯z,
KNETz-d ln Ezdz=-d lnEdz-Euzdz,
1μ¯ζ=B0+B1 exp-Pζ+B2 exp-Qζ,
ω0=ba+b=bw+bϕaw+aϕ+ag+bw+bϕ.
Ω0=bw+bϕaw+aϕ+bw+bϕ.
Δζ=Mζ-Mζ.
δζ=Δζ2ω0Ω0+aw+aϕaw+aϕ+ag.
μ¯ζ=μ¯ζ-Δζ2ω0Ω0+aw+aϕaw+aϕ+ag.
ε%=10RMSElog10-1,
RMSElog10=n=1Nlog10E0,PARmodel-log10E0,PARHydrolight2N1/2.

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