Abstract

For optically deep waters, remote-sensing reflectance (r rs) is traditionally expressed as the ratio of the backscattering coefficient (b b) to the sum of absorption and backscattering coefficients (a + b b) that multiples a model parameter (g, or the so-called f′/Q). Parameter g is further expressed as a function of b b/(a + b b) (or b b/a) to account for its variation that is due to multiple scattering. With such an approach, the same g value will be derived for different a and b b values that provide the same ratio. Because g is partially a measure of the angular distribution of upwelling light, and the angular distribution from molecular scattering is quite different from that of particle scattering; g values are expected to vary with different scattering distributions even if the b b/a ratios are the same. In this study, after numerically demonstrating the effects of molecular and particle scatterings on the values of g, an innovative r rs model is developed. This new model expresses r rs in two separate terms: one governed by the phase function of molecular scattering and one governed by the phase function of particle scattering, with a model parameter introduced for each term. In this way the phase function effects from molecular and particle scatterings are explicitly separated and accounted for. This new model provides an analytical tool to understand and quantify the phase-function effects on r rs, and a platform to calculate r rs spectrum quickly and accurately that is required for remote-sensing applications.

© 2004 Optical Society of America

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2003 (1)

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

2002 (3)

2001 (2)

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

N. K. Hojerslev, “Analytic remote-sensing optical algorithms requiring simple and practical field parameter inputs,” Appl. Opt. 40, 4870–4874 (2001).
[CrossRef]

2000 (2)

1999 (1)

1998 (5)

1997 (3)

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]

S. A. Garver, D. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,” J. Geophys. Res. 102 (C8), 18607–18626 (1997).
[CrossRef]

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

1996 (4)

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing reflectance and its relationship to optical properties of natural waters,” Int. J. Remote Sensing 17, 3135–3155 (1996).
[CrossRef]

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101 (C7), 16631–16648 (1996).
[CrossRef]

D. A. Siegel, A. F. Michaels, “Quantification of non-algal light attenuation in the Sargasso Sea: implications for biogeochemistry and remote sensing,” Deep-Sea Res. Part II 43, 321–345 (1996).
[CrossRef]

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996).
[CrossRef] [PubMed]

1995 (4)

C. S. Roesler, M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100 (C7) 13279–13294 (1995).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res 100, 13135–13142 (1995).
[CrossRef]

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

1994 (2)

1993 (2)

S. B. Hooker, W. E. Esaias, “An overview of the SeaWiFS project,” Eos Trans Am. Geophys. Union 74, 241–246 (1993).
[CrossRef]

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

1991 (3)

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

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

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

1989 (1)

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

1988 (3)

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (1988).
[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, 10909–10924 (1988).
[CrossRef]

1985 (1)

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

1982 (1)

1981 (1)

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Occanogr. 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 (1)

A. Garver, S.

S. A. Garver, D. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,” J. Geophys. Res. 102 (C8), 18607–18626 (1997).
[CrossRef]

Antoine, D.

Arnone, R.

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Austin, R. W.

R. W. Austin, “Inherent spectral radiance signals of the ocean surface,” in Ocean Color Analysis, SIO Ref. 74-10 (Scripps Institution of Oceanography, La Jolla, Calif, 1974).

Baker, K. A.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

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, 10909–10924 (1988).
[CrossRef]

Boss, E.

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. Occanogr. 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, 10909–10924 (1988).
[CrossRef]

Brown, O. B.

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, 10909–10924 (1988).
[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]

Bukata, R. P.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing reflectance and its relationship to optical properties of natural waters,” Int. J. Remote Sensing 17, 3135–3155 (1996).
[CrossRef]

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]

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 1: A semianalytical model,” Appl. Opt. 37, 6329–6338 (1998).
[CrossRef]

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996).
[CrossRef] [PubMed]

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

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Caverhill, C. M.

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

Chapin, A.

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, 10909–10924 (1988).
[CrossRef]

Davis, C.

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Davis, C. O.

E. Hoge, F.

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101 (C7), 16631–16648 (1996).
[CrossRef]

Esaias, W. E.

S. B. Hooker, W. E. Esaias, “An overview of the SeaWiFS project,” Eos Trans Am. Geophys. Union 74, 241–246 (1993).
[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, 10909–10924 (1988).
[CrossRef]

Frouin, R.

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Fry, E. S.

Gentili, B.

Gordon, H. R.

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[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, 10909–10924 (1988).
[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]

H. R. Gordon, R. C. Smith, J. R. V. Zaneveld, “Introduction to ocean optics,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. SPIE208, 14–55 (1979).
[CrossRef]

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.

Harvey, G. R.

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Hawes, S. K.

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

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

Hoge, F. E.

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

Hojerslev, N. K.

Hooker, S.

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Hooker, S. B.

S. B. Hooker, W. E. Esaias, “An overview of the SeaWiFS project,” Eos Trans Am. Geophys. Union 74, 241–246 (1993).
[CrossRef]

Jacobs, M. M.

Jerome, J. H.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing reflectance and its relationship to optical properties of natural waters,” Int. J. Remote Sensing 17, 3135–3155 (1996).
[CrossRef]

Johnson, B.

Kiefer, D. A.

D. Stramski, D. A. Kiefer, “Optical properties of marine bacteria,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 250–268 (1990).
[CrossRef]

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]

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge University, Cambridge, England, 1994).
[CrossRef]

Lee, Z. P.

Lewis, M.

Loisel, H.

A. Morel, H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. 37, 4765–4776 (1998).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in case 1 waters. a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

Longhurst, A.

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

Lyon, P. E.

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101 (C7), 16631–16648 (1996).
[CrossRef]

Maritorena, S.

McLean, S.

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Michaels, A. F.

D. A. Siegel, A. F. Michaels, “Quantification of non-algal light attenuation in the Sargasso Sea: implications for biogeochemistry and remote sensing,” Deep-Sea Res. Part II 43, 321–345 (1996).
[CrossRef]

Miller, J. R.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing reflectance and its relationship to optical properties of natural waters,” Int. J. Remote Sensing 17, 3135–3155 (1996).
[CrossRef]

Mitchell, B. G.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

Mobley, C. D.

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

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

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, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 1: A semianalytical model,” Appl. Opt. 37, 6329–6338 (1998).
[CrossRef]

C. D. Mobley, Hydrolight 3.0 User’s Guide (SRI International, Menlo Park, Calif., 1995).

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, New York, 1994), p. 111.

Monti, M.

Morel, A.

A. Morel, D. Antoine, B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41, 6289–6306 (2002).
[CrossRef] [PubMed]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in case 1 waters. a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

A. Morel, H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. 37, 4765–4776 (1998).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

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 angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (1988).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Occanogr. 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.

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.

Mueller, J. L.

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996).
[CrossRef] [PubMed]

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Ortner, P. B.

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Patch, J. S.

Peacock, T. G.

Perry, M. J.

C. S. Roesler, M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100 (C7) 13279–13294 (1995).
[CrossRef]

Peterson, A. R.

Platt, T.

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

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

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

Pope, R. M.

Preisendorfer, R. W.

R. W. Preisendorfer, Hydrologic Optics, Vol. 1: Introduction (National Technical Information Service, Springfield, Va., 1976).

Prieur, L.

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

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

Robinson, W.

S. Roesler, C.

C. S. Roesler, M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100 (C7) 13279–13294 (1995).
[CrossRef]

Sathyendranath, S.

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

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

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

Siegel, D.

S. A. Garver, D. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,” J. Geophys. Res. 102 (C8), 18607–18626 (1997).
[CrossRef]

Siegel, D. A.

Smith, R. C.

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[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, 10909–10924 (1988).
[CrossRef]

H. R. Gordon, R. C. Smith, J. R. V. Zaneveld, “Introduction to ocean optics,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. SPIE208, 14–55 (1979).
[CrossRef]

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, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 1: A semianalytical model,” Appl. Opt. 37, 6329–6338 (1998).
[CrossRef]

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

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

Stramski, D.

D. Stramski, D. A. Kiefer, “Optical properties of marine bacteria,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 250–268 (1990).
[CrossRef]

Sundman, L. K.

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

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

Voss, K. J.

K. J. Voss, A. Chapin, M. Monti, H. Zhang, “Instrument to measure the bidirectional reflectance distribution function of surfaces,” Appl. Opt. 39, 6197–6206 (2000).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

Wang, M.

Zaneveld, J. R. V.

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res 100, 13135–13142 (1995).
[CrossRef]

J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
[CrossRef] [PubMed]

H. R. Gordon, R. C. Smith, J. R. V. Zaneveld, “Introduction to ocean optics,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. SPIE208, 14–55 (1979).
[CrossRef]

Zhang, H.

Zhang, X. D.

Appl. Opt. (20)

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

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

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

J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
[CrossRef] [PubMed]

A. Morel, D. Antoine, B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41, 6289–6306 (2002).
[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]

S. Maritorena, D. A. Siegel, A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41, 2705–2714 (2002).
[CrossRef] [PubMed]

K. J. Voss, A. Chapin, M. Monti, H. Zhang, “Instrument to measure the bidirectional reflectance distribution function of surfaces,” Appl. Opt. 39, 6197–6206 (2000).
[CrossRef]

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

N. K. Hojerslev, “Analytic remote-sensing optical algorithms requiring simple and practical field parameter inputs,” Appl. Opt. 40, 4870–4874 (2001).
[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]

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

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

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, J. S. Patch, “Hyperspectral remote sensing for shallow waters. 1: A semianalytical model,” Appl. Opt. 37, 6329–6338 (1998).
[CrossRef]

X. D. Zhang, M. Lewis, B. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

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]

A. Morel, H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. 37, 4765–4776 (1998).
[CrossRef]

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

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996).
[CrossRef] [PubMed]

Deep-Sea Res. Part I (1)

S. Sathyendranath, A. Longhurst, C. M. Caverhill, T. Platt, “Regionally and seasonally differentiated primary production in the North Atlantic,” Deep-Sea Res. Part I 42, 1773–1802 (1995).
[CrossRef]

Deep-Sea Res. Part II (1)

D. A. Siegel, A. F. Michaels, “Quantification of non-algal light attenuation in the Sargasso Sea: implications for biogeochemistry and remote sensing,” Deep-Sea Res. Part II 43, 321–345 (1996).
[CrossRef]

Eos Trans Am. Geophys. Union (1)

S. B. Hooker, W. E. Esaias, “An overview of the SeaWiFS project,” Eos Trans Am. Geophys. Union 74, 241–246 (1993).
[CrossRef]

Int. J. Remote Sensing (1)

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing reflectance and its relationship to optical properties of natural waters,” Int. J. Remote Sensing 17, 3135–3155 (1996).
[CrossRef]

J. Geophys. Res (1)

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res 100, 13135–13142 (1995).
[CrossRef]

J. Geophys. Res. (9)

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, 10909–10924 (1988).
[CrossRef]

F. E. Hoge, P. E. Lyon, C. D. Mobley, L. K. Sundman, “Radiative transfer equation inversion: theory and shape factor models for retrieval of oceanic inherent optical properties,” J. Geophys. Res. 108(C12), 3386, doi:3310.1029/2000JC000447 (2003).

K. L. Carder, S. K. Hawes, K. A. Baker, R. C. Smith, R. G. Steward, B. G. Mitchell, “Reflectance model for quantifying chlorophyll a in the presence of productivity degradation products,” J. Geophys. Res. 96, 20599–20611 (1991).
[CrossRef]

S. A. Garver, D. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,” J. Geophys. Res. 102 (C8), 18607–18626 (1997).
[CrossRef]

C. S. Roesler, M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100 (C7) 13279–13294 (1995).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10749–10768 (1988).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101 (C7), 16631–16648 (1996).
[CrossRef]

A. Morel, S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[CrossRef]

Limnol. Occanogr. (1)

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

Limnol. Oceanogr. (5)

K. L. Carder, R. G. Steward, G. R. Harvey, P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

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

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in case 1 waters. a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

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

Science (1)

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

Other (11)

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.

D. Stramski, D. A. Kiefer, “Optical properties of marine bacteria,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 250–268 (1990).
[CrossRef]

H. R. Gordon, R. C. Smith, J. R. V. Zaneveld, “Introduction to ocean optics,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. SPIE208, 14–55 (1979).
[CrossRef]

S. Sathyendranath, ed., “Remote Sensing of Ocean Colour in Coastal, and Other Optically-Complex, Waters,” International Ocean-Colour Coordinating Group (IOCCG) Report No. 3, (IOCCG, Dartmouth, Canada, 2000).

C. D. Mobley, Hydrolight 3.0 User’s Guide (SRI International, Menlo Park, Calif., 1995).

R. W. Austin, “Inherent spectral radiance signals of the ocean surface,” in Ocean Color Analysis, SIO Ref. 74-10 (Scripps Institution of Oceanography, La Jolla, Calif, 1974).

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004, J. L. Mueller, G. S. Fargion, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2002), pp. 171–182.

R. W. Preisendorfer, Hydrologic Optics, Vol. 1: Introduction (National Technical Information Service, Springfield, Va., 1976).

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.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge University, Cambridge, England, 1994).
[CrossRef]

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, New York, 1994), p. 111.

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Figures (6)

Fig. 1
Fig. 1

Variation of g spectra (nadir viewed) for different input parameters. In both (a) and (b) [C] = 1.0 mg/m3, in (a) B p = 0.3 and F varies, in (b) F = 0.2 and B p varies.

Fig. 2
Fig. 2

Nadir-viewed r rs from HydroLight compared with r rs from semianalytical models: (a) r rs is modeled by Eqs. (2) and (3) and (b) r rs is modeled by Eq. (5). In both (a) and (b) [C] = 1.0 mg/m3, F = 0.8, B p varies from 0.1 (circles) and 0.3 (triangles down) to 1.0 (squares).

Fig. 3
Fig. 3

Traditional g [Eq. (2)] from HydroLight-simulated r rs (viewed at nadir). As expected from theory, multiple g values exist for the same b b /(a + b b ) ratios. The solid line represents values from Eq. (3).

Fig. 4
Fig. 4

Calculated g p values (open circles) with g w set as the initial value of 0.1107 sr-1. Most of the g p values are quite predictable with the values of b bp /(a + b b ) (dotted curve), except a few points fall slightly out of the g p versus b bp /(a + b b ) pattern (see text for discussion).

Fig. 5
Fig. 5

g values (of nadir-viewed r rs) from HydroLight compared with g values modeled by a combination of Eqs. (7) and (8).

Fig. 6
Fig. 6

Same as Fig. 5 but g is for r rs viewed at 20° (subsurface) from nadir and 90° from the solar plane.

Tables (2)

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Table 1 Values Used in the HydroLight Simulations

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Table 2 Model Parameters for Sun at 30° and the Average Particle Phase Function

Equations (8)

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rrs=Lu0-Ed0-.
rrs=g bba+bb,
g=g0+g1bba+bb,
bp550=BpC0.62,
rrs=-0.00042+0.112 bba-0.0455bba2.
rrs=gwbbwa+bb+gpbbpa+bb.
g=gwbbwbb+gpbbpbb.
gp=G01-G1exp-G2bbpa+bb,

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