Abstract

We present a method to quantify the uncertainties in the in-water constituent absorption and backscattering coefficients obtained from an inversion of remotely sensed reflectance (rrs). We first find a set of positive inversion solutions within a given uncertainty range around the values of the inverted rrs. The uncertainties of the solutions are then computed based on the statistics of these solutions. We demonstrate the uncertainty calculation algorithm using a specific semianalytic inversion model applied to both a field and a simulated data set. When the associated uncertainties are taken into account, the inverted parameters are generally within the uncertainties of the measured (or simulated) parameters, highlighting the success of the inversion and the method to obtain uncertainties. The specific inversion we use, however, fails to retrieve two spectral parameters within a usable range. The method presented is general and can be applied to all existing semianalytical inversion algorithms.

© 2005 Optical Society of America

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    [CrossRef]
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  39. E. Boss, M. S. Twardowski, S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
    [CrossRef]
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    [CrossRef]
  41. E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
    [CrossRef]
  42. M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).
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    [CrossRef] [PubMed]

2005 (2)

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

S. Maritorena, D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
[CrossRef]

2004 (3)

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

2003 (2)

C. Roesler, E. Boss, “A novel ocean color inversion model: retrieval of beam attenuation and particle size distribution,” Geophys. Res. Let. 30, (2003).
[CrossRef]

G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
[CrossRef] [PubMed]

2002 (6)

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

Z. P. Lee, K. L. Carder, R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002).
[CrossRef] [PubMed]

M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).

A. M. Ciotti, M. R. Lewis, J. J. Cullen, “Assessment of the relationship between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[CrossRef]

2001 (3)

1999 (2)

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, 5403–5421 (1999).
[CrossRef]

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

1998 (1)

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys, Res. 103, 24955–24968 (1998).
[CrossRef]

1997 (4)

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

A. H. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation. 1. Time series from the Sargasso Sea,” J. Geophys, Res. 102, 18607–18625 (1997).
[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]

W. S. Pegau, D. Gray, J. RonaldV. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36, 6035–6046 (1997).
[CrossRef] [PubMed]

1996 (2)

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]

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, 16631–16648 (1996).
[CrossRef]

1995 (1)

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

1989 (1)

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1501–1523 (1989).
[CrossRef]

1988 (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys, Res. 93, 10909–10924 (1988).
[CrossRef]

1986 (1)

1978 (1)

A. Morel, “Available, usable and stored radiant energy in relation to marine photosynthesis,” Deep-Sea Res. 25, 673–688 (1978).
[CrossRef]

1977 (1)

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

1975 (2)

Arnone, R. A.

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]

Baratange, F.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

Barnard, A. H.

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys, Res. 103, 24955–24968 (1998).
[CrossRef]

Behrenfeld, M. J.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

Bergmann, T.

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Boss, E.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

C. Roesler, E. Boss, “A novel ocean color inversion model: retrieval of beam attenuation and particle size distribution,” Geophys. Res. Let. 30, (2003).
[CrossRef]

G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
[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]

E. Boss, W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

E. Boss, M. S. Twardowski, S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

Bricaud, A.

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.

Carder, K. L.

Z. P. Lee, K. L. Carder, R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002).
[CrossRef] [PubMed]

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, 5403–5421 (1999).
[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]

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1501–1523 (1989).
[CrossRef]

Chang, G. C.

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, 5403–5421 (1999).
[CrossRef]

Ciotti, A. M.

A. M. Ciotti, M. R. Lewis, J. J. Cullen, “Assessment of the relationship between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys, Res. 93, 10909–10924 (1988).
[CrossRef]

Cullen, J. J.

A. M. Ciotti, M. R. Lewis, J. J. Cullen, “Assessment of the relationship between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

Davis, C. O.

Davis, R. F.

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

Dickey, T. D.

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]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992), pp. 655–675.

Fry, E. S.

Garver, A. H.

A. H. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation. 1. Time series from the Sargasso Sea,” J. Geophys, Res. 102, 18607–18625 (1997).
[CrossRef]

Gordon, H. R.

Grassl, H.

D. Pozdnyakov, H. Grassl, “Colour of Inland and Coastal Waters,” (Springer, Chichester, 2003).

Gray, D.

Hansell, D. A.

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[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, 5403–5421 (1999).
[CrossRef]

Herring, S.

Hoge, F. E.

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, 16631–16648 (1996).
[CrossRef]

Jacobs, M. M.

Kahru, M.

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

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, 5403–5421 (1999).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, U.K., 1994).
[CrossRef]

Korotaev, G.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

Lee, M.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

Lee, Z. P.

Lewis, M.

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

Lewis, M. R.

A. M. Ciotti, M. R. Lewis, J. J. Cullen, “Assessment of the relationship between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

Lorenzi-Kayser, M.

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[CrossRef]

Lyon, P. E.

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, 16631–16648 (1996).
[CrossRef]

Maritorena, S.

S. Maritorena, D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
[CrossRef]

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[CrossRef]

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]

Mitchell, B. G.

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

Mobley, C. D.

G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
[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]

C. D. Mobley, “Notes on converting TSRB data to remote-sensing reflectance,” Sequoia Scientific, Inc., Bellevue, Wash. (personal communication, 2000).

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

Moore, C. C.

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

Morel, A.

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

A. Morel, “Available, usable and stored radiant energy in relation to marine photosynthesis,” Deep-Sea Res. 25, 673–688 (1978).
[CrossRef]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Ocean. 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.

Mueller, J. L.

Napp, J. M.

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

Peacock, T. G.

Pegau, E. W. S.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

Pegau, W. S.

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, 13279–13294 (1995).
[CrossRef]

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1501–1523 (1989).
[CrossRef]

Peterson, A. R.

Pope, R. M.

Pozdnyakov, D.

D. Pozdnyakov, H. Grassl, “Colour of Inland and Coastal Waters,” (Springer, Chichester, 2003).

Preisendorfer, R. W.

R. W. Preisendorfer, Hydrologic Optics, (U. S. Department of Commerce, U.S. GPO, Washington, D.C., 1976).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992), pp. 655–675.

Prieur, L.

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

Reynolds, R. A.

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

Roesler, C.

C. Roesler, E. Boss, “A novel ocean color inversion model: retrieval of beam attenuation and particle size distribution,” Geophys. Res. Let. 30, (2003).
[CrossRef]

Roesler, C. S.

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

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1501–1523 (1989).
[CrossRef]

RonaldV. Zaneveld, J.

Shea, D. M.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

Shybanov, E.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

Siegel, D. A.

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

S. Maritorena, D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
[CrossRef]

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]

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[CrossRef]

A. H. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation. 1. Time series from the Sargasso Sea,” J. Geophys, Res. 102, 18607–18625 (1997).
[CrossRef]

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys, Res. 93, 10909–10924 (1988).
[CrossRef]

Stramski, D.

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

Sundman, L. K.

Sydor, M.

M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992), pp. 655–675.

Thralowa, A. M.

M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).

Twardowski, M. S.

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

E. Boss, M. S. Twardowski, S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992), pp. 655–675.

Voss, K. J.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Wolz, B. D.

M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).

Zaneveld, J. R. V.

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys, Res. 103, 24955–24968 (1998).
[CrossRef]

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

Appl. Opt. (13)

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, O. B. Brown, “The diffuse reflectance of the ocean: some effects of vertical structure,” Appl. Opt. 14, 2892–2895 (1975).
[CrossRef] [PubMed]

W. S. Pegau, D. Gray, J. RonaldV. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36, 6035–6046 (1997).
[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]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

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]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

E. Boss, M. S. Twardowski, S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

E. Boss, W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

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

Z. P. Lee, K. L. Carder, R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002).
[CrossRef] [PubMed]

G. C. Chang, T. D. Dickey, C. D. Mobley, E. Boss, W. S. Pegau, “Toward closure of upwelling radiance in coastal waters,” Appl. Opt. 42, 1574–1582 (2003).
[CrossRef] [PubMed]

Deep-Sea Res. (1)

A. Morel, “Available, usable and stored radiant energy in relation to marine photosynthesis,” Deep-Sea Res. 25, 673–688 (1978).
[CrossRef]

Geophys. Res. Let. (1)

C. Roesler, E. Boss, “A novel ocean color inversion model: retrieval of beam attenuation and particle size distribution,” Geophys. Res. Let. 30, (2003).
[CrossRef]

Global Biogeochem. Cycles (1)

M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space”Global Biogeochem. Cycles 19, GB1006, doi: (2005).
[CrossRef]

J. Coast. Res. (1)

M. Sydor, B. D. Wolz, A. M. Thralowa, “Spectral analysis of bulk reflectance from coastal waters: deconvolution of diffuse spectra due to scattering and absorption by coastal water,” J. Coast. Res. 18, 352–361 (2002).

J. Geophys, Res. (4)

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]

A. H. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation. 1. Time series from the Sargasso Sea,” J. Geophys, Res. 102, 18607–18625 (1997).
[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, 5403–5421 (1999).
[CrossRef]

A. H. Barnard, W. S. Pegau, J. R. V. Zaneveld, “Global relationships of the inherent optical properties of the oceans,” J. Geophys, Res. 103, 24955–24968 (1998).
[CrossRef]

J. Geophys. Res. (4)

D. A. Siegel, S. Maritorena, D. A. Hansell, M. Lorenzi-Kayser, “Global distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res. 107, (2002).
[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, 16631–16648 (1996).
[CrossRef]

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

E. Boss, E. W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “The particulate backscattering ratio at LEO 15 and its use to study particles composition and distribution,” J. Geophys. Res. 109, (2004).
[CrossRef]

J. Geophys.Res. (1)

R. F. Davis, C. C. Moore, J. R. V. Zaneveld, J. M. Napp, “Reducing the effects of fouling on chlorophyll estimates derived from long-term deployments of optical instruments,” J. Geophys.Res. 102, 5851–5855 (1997).
[CrossRef]

Limnol. Ocean. (1)

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

Limnol. Oceanogr. (2)

A. M. Ciotti, M. R. Lewis, J. J. Cullen, “Assessment of the relationship between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef]

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1501–1523 (1989).
[CrossRef]

Oceanography (1)

E. Boss, D. Stramski, T. Bergmann, W. S. Pegau, M. Lewis, “Why should we measure the optical backscattering coefficient?” Oceanography 17, 44–49 (2004).
[CrossRef]

Prog. Oceanogr. (1)

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Remote Sens. Environ. (1)

S. Maritorena, D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
[CrossRef]

Science (1)

D. Stramski, R. A. Reynolds, M. Kahru, B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285, 239–242 (1999).
[CrossRef] [PubMed]

Other (11)

Z. P. Lee, http://www.ioccg.org/groups/lee_data.pdf (2004).

Z. P. Lee, http://www.ioccg.org/groups/lee.html (2004).

Z. P. Lee, http://www.ioccg.org/groups/OCAG_data.html (2204).

R. W. Preisendorfer, Hydrologic Optics, (U. S. Department of Commerce, U.S. GPO, Washington, D.C., 1976).

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

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992), pp. 655–675.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, U.K., 1994).
[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.

J. L. Mueller, G. S. Fargion, C. R. McClain, eds., Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 4, in Vol. IV: Inherent Optical Properties: Instruments, Characterizations, Field Measurements and Data Analysis Protocols, TM-2003-211621/Rev4-Vol.IV (NASA, 2003), http://www.wetlabs.com/appnotes/Vol%201V%20v4%20final.pdf .

C. D. Mobley, “Notes on converting TSRB data to remote-sensing reflectance,” Sequoia Scientific, Inc., Bellevue, Wash. (personal communication, 2000).

D. Pozdnyakov, H. Grassl, “Colour of Inland and Coastal Waters,” (Springer, Chichester, 2003).

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Figures (7)

Fig. 1
Fig. 1

Comparison of a measured rrs (7/23/2001, bold curve) with the median values of all the inversion solutions (526) for which the reconstructed rrs is within 10% of the measured rrs at all wavelengths (thin line) and the 5th and 95th percentiles of those solutions (dotted curves).

Fig. 2
Fig. 2

Schematic flow chart of the inversion scheme and determination of the uncertainty in the inverted parameters.

Fig. 3
Fig. 3

Histograms of (a) the inverted total absorption coefficient (ap+CDOM = aph + aCDOM+NAP) at 440 nm, (b) the particulate backscattering coefficient (bbp) at 555 nm, (c) the phytoplankton absorption coefficient (aph) at 440 nm, (d) the CDOM and NAP absorption coefficient (aCDOM+NAP) at 440 nm for the rrs presented in Fig. 1.

Fig. 4
Fig. 4

Comparison of the inverted values of (a) ap+CDOM(440), (b) bbp(550), (c) aph(440), (d) aCDOM+NAP(440) relative to the input values (x axis) for the simulated data set. Dots denote the median inverted values, whereas the lines denote the 90% confidence interval.

Fig. 5
Fig. 5

Comparison (a) between the directly calculated and the inverted spectral slope of CDOM+NAP(S), (b) of the spectral slope of particle backscattering, (c) between the size parameter (Sf) for phytoplankton and the ratio of aph at 440 to 680 nm of the input phytoplankton spectrum. Dots denote the median inverted values, whereas the lines denote the 90% confidence interval in the inverted parameters (based on the statistics of all acceptable solutions).

Fig. 6
Fig. 6

Comparison for the in situ data set between (a) the inverted ap+CDOM(440) versus ac–9 measured, ap+CDOM(440), (b) the inverted bbp(555) versus HS6-measured bbp(555), (c) the inverted aph(676) versus aph(676) derived from ac-9 measurements, (d) the inverted aCDOM+NAP(440) versus ac-9-measured aCDOM(440). Dots denote the median values, whereas the vertical lines denote the 90% confidence interval in the inverted parameters. Horizontal lines denote the distance between maximum and minimum values of the in situ measured parameters (when larger than the size of the dot).

Fig. 7
Fig. 7

(a) Comparison between the inverted spectral slope of CDOM and NAP and the calculated spectral slop of CDOM measured with the ac-9. (b) Comparison between the inverted spectral slope of particulate backscattering and the calculated spectral slope of particulate backscattering (Y) based on measurements with the HS-6. (c) Comparison between the phytoplankton size factor Sf and the slope of the particulate beam attenuation for the in situ data. Uncertainties in measured spectral slopes were less than 0.002 for S, 0.1 for Y, and 0.1 for the slope of cp. Dots denote the median values, whereas the lines denote the 90% confidence interval.

Tables (3)

Tables Icon

Table 1 Comparison between the Inverted and the Input IOP Values of the Simulated Data Set

Tables Icon

Table 2 Comparison between the Inverted and the Input IOP Values of the In Situ Data Set

Equations (14)

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R r s = L w ( λ , 0 + ) E d ( λ , 0 + ) = C ( λ ) L w ( λ , 0.66 m ) E d ( λ , 0 + ) , C ( λ ) = t n 2 exp [ 0.66 k L ( λ ) ] ,
r r s = R r s 0.52 + 1.7 * R r s .
r r s ( λ ) = L u ( λ , 0 ) E d ( λ , 0 ) 0.0949 b b ( λ ) a ( λ ) + b b ( λ ) + 0.0794 ( b b ( λ ) a ( λ ) + b b ( λ ) ) 2 ,
a ( λ ) = a sw ( λ ) + a ph ( λ ) + a CDOM + NAP ( λ ) ,
a ph ( λ ) = a ph ( λ 0 ) [ S f a pico ( λ ) + ( 1 S f ) a micro ( λ ) ] ,
a CDOM + NAP ( λ ) = a CDOM + NAP ( λ 0 ) exp [ S ( λ λ 0 ) ] ,
b b ( λ ) = b b sw ( λ ) + b b p ( λ ) ,
b b p ( λ ) = b b p ( λ 0 ) ( λ / λ 0 ) Y ,
X b b a + b b a + b b ( 1 1 X ) = 0 ,
a ph ( λ i ) + a CDOM + NAP ( λ i ) + b b p ( λ i ) υ ( λ i ) = [ a sw ( λ i ) + b bsw ( λ i ) υ ( λ i ) ] .
a ph ( λ i ) + a CDOM + NAP ( λ i ) + b b p ( λ i ) υ ( λ i ) = h ( λ i ) .
a ph ( λ 0 ) [ S f a pico ( λ i ) + ( 1 S f ) a micro ( λ i ) ] + a CDOM + NAP ( λ 0 ) exp [ S ( λ i λ 0 ) ] + υ ( λ i ) b b p ( λ 0 ) ( λ i / λ 0 ) Y = h ( λ i ) .
ε = 1 N [ i = 1 N ( input fit input ) 2 ] 1 / 2 .
a ph ( 676 ) = a p + CDOM ( 676 ) 0.6 a p + CDOM ( 650 ) .

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