Abstract

Spectral optimization algorithm (SOA) is a well-accepted scheme for the retrieval of water constituents from the measurement of ocean color radiometry. It defines an error function between the input and output remote sensing reflectance spectrum, with the latter modeled with a few variables that represent the optically active properties, while the variables are solved numerically by minimizing the error function. In this paper, with data from numerical simulations and field measurements as input, we evaluate four computational methods for minimization (optimization) for their efficiency and accuracy on solutions, and illustrate impact of bio-optical models on the retrievals. The four optimization routines are the Levenberg-Marquardt (LM), the Generalized Reduced Gradient (GRG), the Downhill Simplex Method (Amoeba), and the Simulated Annealing-Downhill Simplex (i.e. SA + Amoeba, hereafter abbreviated as SAA). The Garver-Siegel-Maritorena SOA model is used as a base to test these computational methods. It is observed that 1) LM is the fastest method, but SAA has the largest number of valid retrievals; 2) the quality of final solutions are strongly influenced by the forms of spectral models (or eigen functions); and 3) dynamically-varying eigen functions are necessary to obtain smaller errors for both reflectance spectrum and retrievals. Results of this study provide helpful guidance for the selection of a computational method and spectral models if an SOA scheme is to be used to process ocean color images.

© 2013 OSA

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2012 (2)

C. M. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: a novel approach based on three-band reflectance difference,” J. Geophys. Res., Oceans117(C1), C01011 (2012).
[CrossRef]

V. E. Brando, A. G. Dekker, Y. J. Park, and T. Schroeder, “Adaptive semianalytical inversion of ocean color radiometry in optically complex waters,” Appl. Opt.51(15), 2808–2833 (2012).
[CrossRef] [PubMed]

2009 (2)

A. Morel, “Are the empirical relationships describing the bio-optical properties of case 1 waters consistent and internally compatible?” J. Geophys. Res.114(C1), C01016 (2009).
[CrossRef]

C. R. McClain, “A decade of satellite ocean color observations,” Annu. Rev. Mar. Sci.1(1), 19–42 (2009).
[CrossRef] [PubMed]

2008 (1)

J. Werdell, Global bio-optical algorithms for ocean color satelliteapplications: Inherent Optical Properties Algorithm Workshop at Ocean Optics XIX,” Eos Trans. AGU90, 4 (2008).

2007 (1)

R. Doerffer and H. Schiller, “The MERIS case 2 water algorithm,” Int. J. Remote Sens.28(3-4), 517–535 (2007).
[CrossRef]

2006 (1)

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

2005 (4)

S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ.94(4), 429–440 (2005).
[CrossRef]

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

P. J. Werdell and S. W. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ.98(1), 122–140 (2005).
[CrossRef]

P. Wang, E. S. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt.44(19), 4074–4085 (2005).
[CrossRef] [PubMed]

2004 (1)

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

2003 (1)

V. E. Brando and A. G. Dekker, “Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality,” IEEE Trans. Geosci. Rem. Sens.41(6), 1378–1387 (2003).
[CrossRef]

2002 (4)

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt.41(27), 5755–5772 (2002).
[CrossRef] [PubMed]

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt.41(15), 2705–2714 (2002).
[CrossRef] [PubMed]

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.47(2), 404–417 (2002).
[CrossRef]

1999 (1)

1998 (2)

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. a semianalytical model,” Appl. Opt.37(27), 6329–6338 (1998).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

F. E. Hoge and 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., Oceans101(C7), 16631–16648 (1996).
[CrossRef]

1995 (2)

C. S. Roesler and M. J. Perry, “In-situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res., Oceans100(C7), 13279–13294 (1995).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

1994 (1)

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case-ii waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res., Oceans99(C4), 7457–7466 (1994).
[CrossRef]

1989 (1)

S. Sathyendranath, L. Prieur, and A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sens.10(8), 1373–1394 (1989).
[CrossRef]

1988 (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science220(4598), 671–680 (1983).
[CrossRef] [PubMed]

1981 (1)

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr.26(1), 43–53 (1981).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math.11(2), 431–441 (1963).
[CrossRef]

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math.2, 164–168 (1944).

Arnone, R. A.

Babin, M.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

Bailey, S. W.

P. J. Werdell and S. W. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ.98(1), 122–140 (2005).
[CrossRef]

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Behrenfeld, M. J.

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

Boss, E.

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

Boss, E. S.

Brando, V. E.

V. E. Brando, A. G. Dekker, Y. J. Park, and T. Schroeder, “Adaptive semianalytical inversion of ocean color radiometry in optically complex waters,” Appl. Opt.51(15), 2808–2833 (2012).
[CrossRef] [PubMed]

V. E. Brando and A. G. Dekker, “Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality,” IEEE Trans. Geosci. Rem. Sens.41(6), 1378–1387 (2003).
[CrossRef]

Bricaud, A.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr.26(1), 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, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 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, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Carder, K. L.

Ciotti, A. M.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.47(2), 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, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Claustre, H.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

Cullen, J. J.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.47(2), 404–417 (2002).
[CrossRef]

Dekker, A. G.

V. E. Brando, A. G. Dekker, Y. J. Park, and T. Schroeder, “Adaptive semianalytical inversion of ocean color radiometry in optically complex waters,” Appl. Opt.51(15), 2808–2833 (2012).
[CrossRef] [PubMed]

V. E. Brando and A. G. Dekker, “Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality,” IEEE Trans. Geosci. Rem. Sens.41(6), 1378–1387 (2003).
[CrossRef]

Devred, E.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

Doerffer, R.

R. Doerffer and H. Schiller, “The MERIS case 2 water algorithm,” Int. J. Remote Sens.28(3-4), 517–535 (2007).
[CrossRef]

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case-ii waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res., Oceans99(C4), 7457–7466 (1994).
[CrossRef]

Donaghay, P. L.

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Fischer, J.

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case-ii waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res., Oceans99(C4), 7457–7466 (1994).
[CrossRef]

Franz, B.

C. M. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: a novel approach based on three-band reflectance difference,” J. Geophys. Res., Oceans117(C1), C01011 (2012).
[CrossRef]

Garver, S. A.

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Gordon, H. R.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Gray, D.

Hansell, D. A.

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

Hoge, F. E.

F. E. Hoge and 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., Oceans101(C7), 16631–16648 (1996).
[CrossRef]

Hu, C. M.

C. M. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: a novel approach based on three-band reflectance difference,” J. Geophys. Res., Oceans117(C1), C01011 (2012).
[CrossRef]

Kahru, M.

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Lee, Z.

C. M. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: a novel approach based on three-band reflectance difference,” J. Geophys. Res., Oceans117(C1), C01011 (2012).
[CrossRef]

Lee, Z. P.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math.2, 164–168 (1944).

Lewis, M. R.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.47(2), 404–417 (2002).
[CrossRef]

Lorenzi-Kayser, M.

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

Lyon, P. E.

F. E. Hoge and 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., Oceans101(C7), 16631–16648 (1996).
[CrossRef]

Maass, H.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

Maritorena, S.

S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ.94(4), 429–440 (2005).
[CrossRef]

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt.41(15), 2705–2714 (2002).
[CrossRef] [PubMed]

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math.11(2), 431–441 (1963).
[CrossRef]

McClain, C.

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

McClain, C. R.

C. R. McClain, “A decade of satellite ocean color observations,” Annu. Rev. Mar. Sci.1(1), 19–42 (2009).
[CrossRef] [PubMed]

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Mitchell, B. G.

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Mobley, C. D.

Morel, A.

A. Morel, “Are the empirical relationships describing the bio-optical properties of case 1 waters consistent and internally compatible?” J. Geophys. Res.114(C1), C01016 (2009).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

S. Sathyendranath, L. Prieur, and A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sens.10(8), 1373–1394 (1989).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr.26(1), 43–53 (1981).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Nelson, N. B.

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

O'Reilly, J. E.

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Park, Y. J.

Patch, J. S.

Pegau, W. S.

Perry, M. J.

C. S. Roesler and M. J. Perry, “In-situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res., Oceans100(C7), 13279–13294 (1995).
[CrossRef]

Peterson, A. R.

Platt, T.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

Prieur, L.

S. Sathyendranath, L. Prieur, and A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sens.10(8), 1373–1394 (1989).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr.26(1), 43–53 (1981).
[CrossRef]

Roesler, C.

Roesler, C. S.

C. S. Roesler and M. J. Perry, “In-situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res., Oceans100(C7), 13279–13294 (1995).
[CrossRef]

Sathyendranath, S.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

S. Sathyendranath, L. Prieur, and A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sens.10(8), 1373–1394 (1989).
[CrossRef]

Schiller, H.

R. Doerffer and H. Schiller, “The MERIS case 2 water algorithm,” Int. J. Remote Sens.28(3-4), 517–535 (2007).
[CrossRef]

Schroeder, T.

Shea, D. M.

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

Siegel, D. A.

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ.94(4), 429–440 (2005).
[CrossRef]

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt.41(15), 2705–2714 (2002).
[CrossRef] [PubMed]

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

Steward, R. G.

Stuart, V.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

Sullivan, J. M.

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

Twardowski, M. S.

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

Ulloa, O.

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Wang, P.

Werdell, J.

J. Werdell, Global bio-optical algorithms for ocean color satelliteapplications: Inherent Optical Properties Algorithm Workshop at Ocean Optics XIX,” Eos Trans. AGU90, 4 (2008).

Werdell, P. J.

P. J. Werdell and S. W. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ.98(1), 122–140 (2005).
[CrossRef]

Zaneveld, J. R. V.

Annu. Rev. Mar. Sci. (1)

C. R. McClain, “A decade of satellite ocean color observations,” Annu. Rev. Mar. Sci.1(1), 19–42 (2009).
[CrossRef] [PubMed]

Appl. Opt. (7)

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt.41(27), 5755–5772 (2002).
[CrossRef] [PubMed]

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt.41(15), 2705–2714 (2002).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. deriving bottom depths and water properties by optimization,” Appl. Opt.38(18), 3831–3843 (1999).
[CrossRef] [PubMed]

V. E. Brando, A. G. Dekker, Y. J. Park, and T. Schroeder, “Adaptive semianalytical inversion of ocean color radiometry in optically complex waters,” Appl. Opt.51(15), 2808–2833 (2012).
[CrossRef] [PubMed]

W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt.36(24), 6035–6046 (1997).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. a semianalytical model,” Appl. Opt.37(27), 6329–6338 (1998).
[CrossRef] [PubMed]

P. Wang, E. S. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt.44(19), 4074–4085 (2005).
[CrossRef] [PubMed]

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Eos Trans. AGU (1)

J. Werdell, Global bio-optical algorithms for ocean color satelliteapplications: Inherent Optical Properties Algorithm Workshop at Ocean Optics XIX,” Eos Trans. AGU90, 4 (2008).

Global Biogeochem. Cycles (1)

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19(1), 1006 (2005).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens. (1)

V. E. Brando and A. G. Dekker, “Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality,” IEEE Trans. Geosci. Rem. Sens.41(6), 1378–1387 (2003).
[CrossRef]

Int. J. Remote Sens. (2)

R. Doerffer and H. Schiller, “The MERIS case 2 water algorithm,” Int. J. Remote Sens.28(3-4), 517–535 (2007).
[CrossRef]

S. Sathyendranath, L. Prieur, and A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sens.10(8), 1373–1394 (1989).
[CrossRef]

J. Geophys. Res. (2)

D. A. Siegel, S. Maritorena, N. B. Nelson, D. A. Hansell, and M. Lorenzi-Kayser, “Global ocean distribution and dynamics of colored dissolved and detrital organic materials,” J. Geophys. Res.107(C12), 3228 (2002).
[CrossRef]

A. Morel, “Are the empirical relationships describing the bio-optical properties of case 1 waters consistent and internally compatible?” J. Geophys. Res.114(C1), C01016 (2009).
[CrossRef]

J. Geophys. Res., Atmospheres (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res., Atmospheres93(D9), 10909–10924 (1988).
[CrossRef]

J. Geophys. Res., Oceans (7)

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption-coefficients of natural phytoplankton - analysis and parameterization,” J. Geophys. Res., Oceans100(C7), 13321–13332 (1995).
[CrossRef]

F. E. Hoge and 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., Oceans101(C7), 16631–16648 (1996).
[CrossRef]

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case-ii waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res., Oceans99(C4), 7457–7466 (1994).
[CrossRef]

C. M. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: a novel approach based on three-band reflectance difference,” J. Geophys. Res., Oceans117(C1), C01011 (2012).
[CrossRef]

J. E. O'Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res., Oceans103(C11), 24937–24953 (1998).
[CrossRef]

E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: theory and applications,” J. Geophys. Res., Oceans111(C3), C03011 (2006).
[CrossRef]

C. S. Roesler and M. J. Perry, “In-situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res., Oceans100(C7), 13279–13294 (1995).
[CrossRef]

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math.11(2), 431–441 (1963).
[CrossRef]

Limnol. Oceanogr. (2)

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.47(2), 404–417 (2002).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr.26(1), 43–53 (1981).
[CrossRef]

Mar. Chem. (1)

M. S. Twardowski, E. Boss, J. M. Sullivan, and P. L. Donaghay, “Modeling the spectral shape of absorption by chromophoric dissolved organic matter,” Mar. Chem.89(1-4), 69–88 (2004).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math.2, 164–168 (1944).

Remote Sens. Environ. (2)

S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ.94(4), 429–440 (2005).
[CrossRef]

P. J. Werdell and S. W. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ.98(1), 122–140 (2005).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Other (9)

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

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: the art of scientific computing, 2nd ed. (Cambridge University Press, 1992).

IOCCG, Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications, Z.-P. Lee, ed., Reports of the International Ocean Colour Coordinating Group, No. 5, (IOCCG, Dartmouth, Canada, 2006).

Z. P. Lee, Visible-Infrared Remote-Sensing Model and Applications for Ocean Waters (University of South Florida, 1994).

R. P. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing Of Inland and Coastal Waters (CRC Press, 1995).

IOCCG, Atmospheric Correction for Remotely-Sensed Ocean-Colour Products, M. Wang, ed., Reports of the International Ocean-Colour Coordinating Group, No.10, (IOCCG, Dartmouth, Canada, 2010).

J. Abadie and J. Carpentier, “Generalization of the wolfe reduced gradient method to the case of nonlinear constraints,” in Optimization, R. Fletcher, ed. (Academic Press, 1969).

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

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

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Figures (7)

Fig. 1
Fig. 1

Distribution of δ R rs obtained with the IOCCG simulated Rrs using GSM; (a) δ R rs of each input (with X axis representing the sample number and lower for clearer waters and higher number for more turbid waters); (b) frequency distribution of δ R rs .

Fig. 2
Fig. 2

Distribution of δ IOP obtained with the IOCCG simulated Rrs using GSM; the left column shows values for each input and the right column shows frequency distribution; (a) δ a ph ; (b) δ a dg ; (c) δ b bp

Fig. 3
Fig. 3

Scatter plot of derived IOPs versus known values using the IOCCG simulated data set; (left) 410 nm; (right) 440 nm; (a) aph; (b) adg; (c) bbp.

Fig. 4
Fig. 4

Scatter plot of derived IOPs versus known values for the NOMAD data set; (left) 412 nm; (right) 443 nm; (a) aph; (b) adg; (c) bbp.

Fig. 5
Fig. 5

Distribution of δ R rs and δ IOP derived from the IOCCG simulated Rrs using GSM and modified models, computed by applying MGRG; the left column shows values for each input and the right column shows frequency distribution; (a) δ R rs ; (b) δ a ph ; (c) δ a dg ; (d) δ b bp .

Fig. 6
Fig. 6

Scatter plot of derived 440nm IOPs versus known values for the IOCCG simulated data set; GSM and three modified models were used, computed by applying MGRG; (a) aph, (b) adg, (c) bbp.

Fig. 7
Fig. 7

Scatter plot of derived IOPs versus known values for the NOMAD data set; GSM and three modified models were used, computed by applying MGRG; while measured Rrs at six SeaWiFS bands were used as model input, output IOPs at five bands (without 670 nm) were put together and compared with measured data; (a) aph; (b) adg; (c) bbp

Tables (2)

Tables Icon

Table 1 Results of Different Optimization Schemes for the IOCCG Simulated Data set (n = 500)

Tables Icon

Table 2 Compare Derived IOPs with Known IOPs of the First Five Bands (Except 667 nm) of the IOCCG Data set

Equations (14)

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

R rs (λ)=Fun(a(λ), b b (λ))
R rs = 0.52 r rs 11.7 r rs
r rs =( 0.0949+0.0794 b b a+ b b ) b b a+ b b
δ R rs = Λ λ 1 λ 2 ( R ˜ rs (λ) R rs (λ) ) 2 Λ λ 1 λ 2 R rs (λ)
a(λ)= a w (λ)+ a ph (λ)+ a dg (λ)
b b (λ)= b bw (λ)+ b bp (λ)
a ph (λ)= X 1 a ˜ ph (λ)
a dg (λ)= X 2 a ˜ dg (λ)
b bp (λ)= X 3 b ˜ bp (λ)
a ˜ dg (λ)= e S(λ λ 0 )
b ˜ bp (λ)= ( λ 0 λ ) Y
a ˜ ph (λ)= a ph * (λ)
a ˜ ph (λ)= a 0 (λ)+ a 1 (λ)ln( X 1 ) here X 1 = a ph ( λ 0 )
Y=2(11.2 e 0.9 R rs (440)/ R rs (550) )

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