Abstract

A stochastic inverse technique based on a genetic programming (GP) algorithm was developed to invert oceanic constituents from simulated data for case I and case II water applications. The simulations were carried out with the Ordre Successifs Ocean Atmosphere (OSOA) radiative transfer model. They include the effects of oceanic substances such as algal-related chlorophyll, nonchlorophyllous suspended matter, and dissolved organic matter. The synthetic data set also takes into account the directional effects of particles through a variation of their phase function that makes the simulated data realistic. It is shown that GP can be successfully applied to the inverse problem with acceptable stability in the presence of realistic noise in the data. GP is compared with neural network methodology for case I waters; GP exhibits similar retrieval accuracy, which is greater than for traditional techniques such as band ratio algorithms. The application of GP to real satellite data [a Sea-viewing Wide Field-of-view Sensor (SeaWiFS)] was also carried out for case I waters as a validation. Good agreement was obtained when GP results were compared with the SeaWiFS empirical algorithm. For case II waters the accuracy of GP is less than 33%, which remains satisfactory, at the present time, for remote-sensing purposes.

© 2002 Optical Society of America

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2001 (1)

2000 (1)

L. Gross, S. Thiria, R. Frouin, B. G. Mitchell, “Artificial neural networks for modeling the transfer function between marine reflectances and phytoplankton pigment concentration,” J. Geophys. Res. 105, 3483–3495 (2000).
[CrossRef]

1999 (7)

D. Antoine, A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean color (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20, 1875–1916 (1999).
[CrossRef]

D. Buckton, E. O’Mongain, S. Danaher, “The use of neural networks for the estimation of oceanic constituents based on the MERIS instrument,” Int. J. Remote Sens. 20, 1841–1851 (1999).
[CrossRef]

G. F. Moore, J. Aiken, S. Lavender, “The atmospheric correction of water color and the quantitative retrieval of suspended particulate matter in case II waters: application to MERIS,” Int. J. Remote Sens. 20, 1713–1733 (1999).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, “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]

H. Schiller, R. Doerffer, “Neural network for emulation of an inverse model—operational derivation of case II water properties from MERIS data,” Int. J. Remote Sens. 20, 1735–1746 (1999).
[CrossRef]

L. Gross, S. Thiria, R. Frouin, “Applying artificial neural network methodology to ocean color remote sensing,” Ecol. Modelling 120, 237–246 (1999).
[CrossRef]

M. Ye, S. Wang, Y. Lu, T. Hu, Z. Zhu, Y. Xu, “Inversion of particle size distribution from angular light scattering data with genetic algorithms,” Appl. Opt. 38, 2677–2685 (1999).
[CrossRef]

1998 (2)

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll ‘a’ concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

1997 (4)

R. V. Davalos, B. Rubinsky, “An evolutionary-genetic approach to heat transfer analysis,” J. Heat Transfer 118, 528–531 (1997).
[CrossRef]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res. 102, 17,081–17,106 (1997).
[CrossRef]

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

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating measurements,” Appl. Opt. 36, 8710–8723 (1997).
[CrossRef]

1996 (1)

M. R. Jones, M. Q. Brewster, Y. Yamada, “Application of a genetic algorithm to the optical characterization of propellant smoke,” J. Thermophys. Heat Transfer 10, 372–377 (1996).
[CrossRef]

1994 (4)

1993 (1)

1991 (1)

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, 20,599–20,611 (1991).
[CrossRef]

1988 (2)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (Case I waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

1983 (1)

1981 (2)

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

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

1980 (2)

M. Viollier, D. Tanré, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Bound. Layer Meteorol. 18, 247–267 (1980).
[CrossRef]

A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
[CrossRef]

Aiken, J.

G. F. Moore, J. Aiken, S. Lavender, “The atmospheric correction of water color and the quantitative retrieval of suspended particulate matter in case II waters: application to MERIS,” Int. J. Remote Sens. 20, 1713–1733 (1999).
[CrossRef]

J. Aiken, G. F. Moore, D. K. Clark, C. C. Trees, The SeaWiFS CZCS-Type Pigment Algorithm, Vol. 29 of SeaWiFS Tech. Rep. Series, S. B. Hooker, E. R. Firestone, eds., (NASA, Washington, D.C., 1995).

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll ‘a’ concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Antoine, D.

D. Antoine, A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean color (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20, 1875–1916 (1999).
[CrossRef]

Babin, M.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll ‘a’ concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Bagley, J. D.

J. D. Bagley, “The behavior of adaptative system which employ genetic and correlation algorithms,” Diss. Abstr. Int. B28, 5106 B, University of Michigan microfilms 068-7556 (1967).

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, 20,599–20,611 (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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Banzhaf, W.

W. Banzhaf, P. Nordin, R. Keller, F. Francone, Genetic Programming, An Introduction (Morgan Kaufmann, Los Altos, Calif., 1999).

Bersano-Begey, T. F.

J. Daida, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Computer-assisted design classification algorithms: dynamic and static fitness evaluations in a scaffolded genetic programming environment,” in Proceedings of the First Annual Conference on Genetic Programming, J. R. Koza, D. E. Goldberg, D. B. Fogel, R. L. Riolo, eds. (MIT Press, Cambridge, Mass., 1996), pp. 279–284.

J. Daida, J. D. Hommes, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Algorithm discovery using GP paradigm,” in Advances in Genetic Programming 2, P. Angeline, K. Kinnear, eds. (MIT Press, Cambridge, Mass., 1996), Chap. 2, Part IV, pp. 417–442.

Brewster, M. Q.

M. R. Jones, M. Q. Brewster, Y. Yamada, “Application of a genetic algorithm to the optical characterization of propellant smoke,” J. Thermophys. Heat Transfer 10, 372–377 (1996).
[CrossRef]

Bricaud, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll ‘a’ concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

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

Broenkow, W. W.

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Evans, W. W. Broenkow, “Phytoplankton pigment concentration in the middle Atlantic bight, comparison of ship determination and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Buckton, D.

D. Buckton, E. O’Mongain, S. Danaher, “The use of neural networks for the estimation of oceanic constituents based on the MERIS instrument,” Int. J. Remote Sens. 20, 1841–1851 (1999).
[CrossRef]

Carder, K. L.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, “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]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Z. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the 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, 20,599–20,611 (1991).
[CrossRef]

Chami, M.

M. Chami, R. Santer, E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40, 2398–2416 (2001).
[CrossRef]

D. Robilliard, M. Chami, C. Fonlupt, R. Santer, “Using genetic programming to tackle the ocean color problem,” presented at the Ocean Optics XV meeting, Monaco, 16–20 October 2000.

Chen, F. R.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, “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]

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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Evans, W. W. Broenkow, “Phytoplankton pigment concentration in the middle Atlantic bight, comparison of ship determination and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

J. Aiken, G. F. Moore, D. K. Clark, C. C. Trees, The SeaWiFS CZCS-Type Pigment Algorithm, Vol. 29 of SeaWiFS Tech. Rep. Series, S. B. Hooker, E. R. Firestone, eds., (NASA, Washington, D.C., 1995).

Claustre, H.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll ‘a’ concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Daida, J.

J. Daida, J. D. Hommes, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Algorithm discovery using GP paradigm,” in Advances in Genetic Programming 2, P. Angeline, K. Kinnear, eds. (MIT Press, Cambridge, Mass., 1996), Chap. 2, Part IV, pp. 417–442.

J. Daida, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Computer-assisted design classification algorithms: dynamic and static fitness evaluations in a scaffolded genetic programming environment,” in Proceedings of the First Annual Conference on Genetic Programming, J. R. Koza, D. E. Goldberg, D. B. Fogel, R. L. Riolo, eds. (MIT Press, Cambridge, Mass., 1996), pp. 279–284.

Danaher, S.

D. Buckton, E. O’Mongain, S. Danaher, “The use of neural networks for the estimation of oceanic constituents based on the MERIS instrument,” Int. J. Remote Sens. 20, 1841–1851 (1999).
[CrossRef]

Davalos, R. V.

R. V. Davalos, B. Rubinsky, “An evolutionary-genetic approach to heat transfer analysis,” J. Heat Transfer 118, 528–531 (1997).
[CrossRef]

Davis, C. O.

Deschamps, P. Y.

M. Viollier, D. Tanré, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Bound. Layer Meteorol. 18, 247–267 (1980).
[CrossRef]

Dilligeard, E.

Doerffer, R.

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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 semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
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S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, in An Overview of SeaWiFS and Ocean Color, S. B. Hooker, E. R. Firestone, eds., NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992), Vol. 1.

Fischer, J.

R. Doerffer, J. Fischer, “Concentration of chlorophyll, suspended matter, and gelbstoff in case II waters derived from Coastal Zone Color Scanner data with inverse modeling methods,” J. Geophys. Res. 99, 7457–7466 (1994).
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D. Robilliard, M. Chami, C. Fonlupt, R. Santer, “Using genetic programming to tackle the ocean color problem,” presented at the Ocean Optics XV meeting, Monaco, 16–20 October 2000.

C. Fonlupt, D. Robilliard, “Genetic programming with dynamics fitness for a remote sensing application,” in Proceedings of Parallel Problem Solving from Nature (PPSN), M. Schoenauer, ed., Vol. 1917 of Lectures Notes in Computer Science (Springer-Verlag, Berlin, 2001), pp. 191–200.

G. Paris, D. Robilliard, C. Fonlupt, “Applying boosting techniques to genetic programming,” in Proceedings of Artificial Evolution 2001, P. Collet, C. Fonlupt, J. K. Hao, E. Lutton, M. Schoenauer, eds., Vol. 2310 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 2002), pp. 267–280.

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W. Banzhaf, P. Nordin, R. Keller, F. Francone, Genetic Programming, An Introduction (Morgan Kaufmann, Los Altos, Calif., 1999).

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L. Gross, S. Thiria, R. Frouin, B. G. Mitchell, “Artificial neural networks for modeling the transfer function between marine reflectances and phytoplankton pigment concentration,” J. Geophys. Res. 105, 3483–3495 (2000).
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L. Gross, S. Thiria, R. Frouin, “Applying artificial neural network methodology to ocean color remote sensing,” Ecol. Modelling 120, 237–246 (1999).
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Garver, S. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

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H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res. 102, 17,081–17,106 (1997).
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H. R. Gordon, M. Wang, “Retrieval of water leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
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H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Evans, W. W. Broenkow, “Phytoplankton pigment concentration in the middle Atlantic bight, comparison of ship determination and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
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A. Morel, H. R. Gordon, “Report of the working group on water color,” Boundary-Layer Meteorol. 18, 343–355 (1980).
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Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, in An Overview of SeaWiFS and Ocean Color, S. B. Hooker, E. R. Firestone, eds., NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992), Vol. 1.

Gross, L.

L. Gross, S. Thiria, R. Frouin, B. G. Mitchell, “Artificial neural networks for modeling the transfer function between marine reflectances and phytoplankton pigment concentration,” J. Geophys. Res. 105, 3483–3495 (2000).
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L. Gross, S. Thiria, R. Frouin, “Applying artificial neural network methodology to ocean color remote sensing,” Ecol. Modelling 120, 237–246 (1999).
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K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, “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).
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Z. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
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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, 20,599–20,611 (1991).
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H. Krawczyk, A. Neumann, M. Hetscher, “Mathematical and physical background of principal component inversion,” in Proceedings of the 3rd International Workshop on MOS-IRS and Ocean Color (Wissenschaft und Technik-Verlag, Berlin, 1999), pp. 83–92.

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J. Daida, J. D. Hommes, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Algorithm discovery using GP paradigm,” in Advances in Genetic Programming 2, P. Angeline, K. Kinnear, eds. (MIT Press, Cambridge, Mass., 1996), Chap. 2, Part IV, pp. 417–442.

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S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, in An Overview of SeaWiFS and Ocean Color, S. B. Hooker, E. R. Firestone, eds., NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992), Vol. 1.

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Jones, M. R.

M. R. Jones, M. Q. Brewster, Y. Yamada, “Application of a genetic algorithm to the optical characterization of propellant smoke,” J. Thermophys. Heat Transfer 10, 372–377 (1996).
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J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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H. Krawczyk, A. Neumann, M. Hetscher, “Mathematical and physical background of principal component inversion,” in Proceedings of the 3rd International Workshop on MOS-IRS and Ocean Color (Wissenschaft und Technik-Verlag, Berlin, 1999), pp. 83–92.

A. Neumann, M. Hetscher, H. Krawczyk, C. Tschentscher, “Methodological aspects of principal component inversion for case II applications,” in Proceedings of the 2nd International workshop on MOS–IRS and Ocean Color, (Institute of Space Sensor Technology, Berlin, 1998), pp. 163–170.

H. Krawczyk, A. Neumann, T. Walzel, G. Zimmermann, “Investigation of interpretation possibilities of spectral high dimensional measurements by means of principal component analysis—a concept for physical interpretation of those measurements,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, R. A. Schowengerdt, eds., Proc. SPIE1938, 401–411 (1993).

A. Neumann, H. Krawczyk, T. Walzel, “A complex approach to quantitative interpretation of spectral high resolution imagery,” in Proceedings of the Third Thematic Conference on Remote Sensing for Marine and Coastal Environments, by P. Bank, ed. (Environmental Research Institute of Michigan, Ann Arbor, Michigan, 1995), pp. II-641–II-652.

Lavender, S.

G. F. Moore, J. Aiken, S. Lavender, “The atmospheric correction of water color and the quantitative retrieval of suspended particulate matter in case II waters: application to MERIS,” Int. J. Remote Sens. 20, 1713–1733 (1999).
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Lee, Z.

Lee, Z. P.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, “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).
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Lu, Y.

Maritorena, S.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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McClain, C.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, in An Overview of SeaWiFS and Ocean Color, S. B. Hooker, E. R. Firestone, eds., NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992), Vol. 1.

Mitchell, B. G.

L. Gross, S. Thiria, R. Frouin, B. G. Mitchell, “Artificial neural networks for modeling the transfer function between marine reflectances and phytoplankton pigment concentration,” J. Geophys. Res. 105, 3483–3495 (2000).
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J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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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, 20,599–20,611 (1991).
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Moore, G. F.

G. F. Moore, J. Aiken, S. Lavender, “The atmospheric correction of water color and the quantitative retrieval of suspended particulate matter in case II waters: application to MERIS,” Int. J. Remote Sens. 20, 1713–1733 (1999).
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Neumann, A.

H. Krawczyk, A. Neumann, M. Hetscher, “Mathematical and physical background of principal component inversion,” in Proceedings of the 3rd International Workshop on MOS-IRS and Ocean Color (Wissenschaft und Technik-Verlag, Berlin, 1999), pp. 83–92.

A. Neumann, H. Krawczyk, T. Walzel, “A complex approach to quantitative interpretation of spectral high resolution imagery,” in Proceedings of the Third Thematic Conference on Remote Sensing for Marine and Coastal Environments, by P. Bank, ed. (Environmental Research Institute of Michigan, Ann Arbor, Michigan, 1995), pp. II-641–II-652.

H. Krawczyk, A. Neumann, T. Walzel, G. Zimmermann, “Investigation of interpretation possibilities of spectral high dimensional measurements by means of principal component analysis—a concept for physical interpretation of those measurements,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, R. A. Schowengerdt, eds., Proc. SPIE1938, 401–411 (1993).

A. Neumann, M. Hetscher, H. Krawczyk, C. Tschentscher, “Methodological aspects of principal component inversion for case II applications,” in Proceedings of the 2nd International workshop on MOS–IRS and Ocean Color, (Institute of Space Sensor Technology, Berlin, 1998), pp. 163–170.

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W. Banzhaf, P. Nordin, R. Keller, F. Francone, Genetic Programming, An Introduction (Morgan Kaufmann, Los Altos, Calif., 1999).

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J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
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Paris, G.

G. Paris, D. Robilliard, C. Fonlupt, “Applying boosting techniques to genetic programming,” in Proceedings of Artificial Evolution 2001, P. Collet, C. Fonlupt, J. K. Hao, E. Lutton, M. Schoenauer, eds., Vol. 2310 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 2002), pp. 267–280.

Peacock, T. G.

Platt, T.

Pope, R. M.

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. Oceanogr. 26, 43–53 (1981).
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L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
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D. Zhongker, B. Punch, B. Rand, “Lilgp 1.01 user’s manual,” (Michigan State U. East Lansing, Mich.1996).

Robilliard, D.

G. Paris, D. Robilliard, C. Fonlupt, “Applying boosting techniques to genetic programming,” in Proceedings of Artificial Evolution 2001, P. Collet, C. Fonlupt, J. K. Hao, E. Lutton, M. Schoenauer, eds., Vol. 2310 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 2002), pp. 267–280.

C. Fonlupt, D. Robilliard, “Genetic programming with dynamics fitness for a remote sensing application,” in Proceedings of Parallel Problem Solving from Nature (PPSN), M. Schoenauer, ed., Vol. 1917 of Lectures Notes in Computer Science (Springer-Verlag, Berlin, 2001), pp. 191–200.

D. Robilliard, M. Chami, C. Fonlupt, R. Santer, “Using genetic programming to tackle the ocean color problem,” presented at the Ocean Optics XV meeting, Monaco, 16–20 October 2000.

Ross, S. J.

J. Daida, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Computer-assisted design classification algorithms: dynamic and static fitness evaluations in a scaffolded genetic programming environment,” in Proceedings of the First Annual Conference on Genetic Programming, J. R. Koza, D. E. Goldberg, D. B. Fogel, R. L. Riolo, eds. (MIT Press, Cambridge, Mass., 1996), pp. 279–284.

J. Daida, J. D. Hommes, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Algorithm discovery using GP paradigm,” in Advances in Genetic Programming 2, P. Angeline, K. Kinnear, eds. (MIT Press, Cambridge, Mass., 1996), Chap. 2, Part IV, pp. 417–442.

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Santer, R.

M. Chami, R. Santer, E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40, 2398–2416 (2001).
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D. Robilliard, M. Chami, C. Fonlupt, R. Santer, “Using genetic programming to tackle the ocean color problem,” presented at the Ocean Optics XV meeting, Monaco, 16–20 October 2000.

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S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997).
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L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
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H. Schiller, R. Doerffer, “Neural network for emulation of an inverse model—operational derivation of case II water properties from MERIS data,” Int. J. Remote Sens. 20, 1735–1746 (1999).
[CrossRef]

Siegel, D. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean color algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

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, 20,599–20,611 (1991).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Steward, R. G.

Z. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the 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, 20,599–20,611 (1991).
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Thiria, S.

L. Gross, S. Thiria, R. Frouin, B. G. Mitchell, “Artificial neural networks for modeling the transfer function between marine reflectances and phytoplankton pigment concentration,” J. Geophys. Res. 105, 3483–3495 (2000).
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L. Gross, S. Thiria, R. Frouin, “Applying artificial neural network methodology to ocean color remote sensing,” Ecol. Modelling 120, 237–246 (1999).
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J. Aiken, G. F. Moore, D. K. Clark, C. C. Trees, The SeaWiFS CZCS-Type Pigment Algorithm, Vol. 29 of SeaWiFS Tech. Rep. Series, S. B. Hooker, E. R. Firestone, eds., (NASA, Washington, D.C., 1995).

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A. Neumann, M. Hetscher, H. Krawczyk, C. Tschentscher, “Methodological aspects of principal component inversion for case II applications,” in Proceedings of the 2nd International workshop on MOS–IRS and Ocean Color, (Institute of Space Sensor Technology, Berlin, 1998), pp. 163–170.

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J. Daida, J. D. Hommes, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Algorithm discovery using GP paradigm,” in Advances in Genetic Programming 2, P. Angeline, K. Kinnear, eds. (MIT Press, Cambridge, Mass., 1996), Chap. 2, Part IV, pp. 417–442.

J. Daida, T. F. Bersano-Begey, S. J. Ross, J. F. Vesecky, “Computer-assisted design classification algorithms: dynamic and static fitness evaluations in a scaffolded genetic programming environment,” in Proceedings of the First Annual Conference on Genetic Programming, J. R. Koza, D. E. Goldberg, D. B. Fogel, R. L. Riolo, eds. (MIT Press, Cambridge, Mass., 1996), pp. 279–284.

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M. Viollier, D. Tanré, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Bound. Layer Meteorol. 18, 247–267 (1980).
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H. Krawczyk, A. Neumann, T. Walzel, G. Zimmermann, “Investigation of interpretation possibilities of spectral high dimensional measurements by means of principal component analysis—a concept for physical interpretation of those measurements,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, R. A. Schowengerdt, eds., Proc. SPIE1938, 401–411 (1993).

A. Neumann, H. Krawczyk, T. Walzel, “A complex approach to quantitative interpretation of spectral high resolution imagery,” in Proceedings of the Third Thematic Conference on Remote Sensing for Marine and Coastal Environments, by P. Bank, ed. (Environmental Research Institute of Michigan, Ann Arbor, Michigan, 1995), pp. II-641–II-652.

Wang, M.

Wang, S.

Xu, Y.

Yamada, Y.

M. R. Jones, M. Q. Brewster, Y. Yamada, “Application of a genetic algorithm to the optical characterization of propellant smoke,” J. Thermophys. Heat Transfer 10, 372–377 (1996).
[CrossRef]

Ye, M.

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D. Zhongker, B. Punch, B. Rand, “Lilgp 1.01 user’s manual,” (Michigan State U. East Lansing, Mich.1996).

Zhu, Z.

Zimmermann, G.

H. Krawczyk, A. Neumann, T. Walzel, G. Zimmermann, “Investigation of interpretation possibilities of spectral high dimensional measurements by means of principal component analysis—a concept for physical interpretation of those measurements,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, R. A. Schowengerdt, eds., Proc. SPIE1938, 401–411 (1993).

Appl. Opt. (9)

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Evans, W. W. Broenkow, “Phytoplankton pigment concentration in the middle Atlantic bight, comparison of ship determination and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

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

S. Tassan, “Local algorithm using SeaWiFS data for the retrieval of phytoplankton pigments, suspended matter, and yellow substance in coastal waters,” Appl. Opt. 33, 2369–2378 (1994).
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Figures (10)

Fig. 1
Fig. 1

Tree representation of a program for computing the mathematical expression given by Eq. (1): f(x) = 1*(2 + 3).

Fig. 2
Fig. 2

General structure of the GP algorithm. (i) Random creation of an initial populations of programs (open boxes). (ii) Evaluation of the programs by use of the relative RMS error: only highly well-performing programs are selected, and the programs of poor performance are removed; here, the lighter the boxes, the better the programs. (iii) Application of genetic operators (crossover and mutation) in the best selected programs. The best programs are not affected by those operators (the darkest box), unlike for the weakest-performing programs. (iv) A new population of programs is obtained and replaces the old population. A new cycle of reproduction begins. This process is iterated until a stop criterion is reached (see text).

Fig. 3
Fig. 3

Performance of GP in retrieving chlorophyll a concentration in case I waters. The teaching phase of GP uses a Morel data set for (a) clean and (b) noisy subsurface reflectances.

Fig. 4
Fig. 4

Same as Fig. 3, except that the OSOA data set was used to teach GP. Here the normalized water-leaving radiances are inverted.

Fig. 5
Fig. 5

Typical examples of spectra of bidirectional reflectance ρ w = πL w /E d (E d is the downwelling irradiance above water) calculated by the OSOA at nadir for case II waters. Different oceanic conditions are illustrated. See Table 5 for the OSOA input values.

Fig. 6
Fig. 6

Performance of GP in retrieving chlorophyll a concentrations in case II waters. GP is learned for (a) clean and (b) noisy data.

Fig. 7
Fig. 7

Same as Fig. 6 but for retrieval of sediment concentration.

Fig. 8
Fig. 8

Same as Fig. 6 but for retrieval of absorption coefficients of yellow substances.

Fig. 9
Fig. 9

Application of the GP algorithm obtained with synthetic OSOA data (case I waters) for SeaWiFS satellite images acquired on (a) 11 June 1999, (b) 24 July 1999, and (c) 25 July 1999 off the Bay of Biscay (France; (see Table 7 for geographical coordinates of the area).

Fig. 10
Fig. 10

Subsurface reflectance as a function of chlorophyll a concentration for SeaWiFS wavelengths. Reflectance was calculated from Morel’s model and was derived from the Morel data set.

Tables (8)

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Table 1 Evolutionary Parameters for a GP Run for Case I Watersa

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Table 2 Range of Parameters Used in Computation of Water-Leaving Radiance with the OSOA Model as a Training Data Set for Genetic Programming Algorithmsa

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Table 3 Performance of GP in Retrieving Chlorophyll a Concentration in Case I Waters for Noise-Free Morel Dataa

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Table 4 Performance of GP in Retrieving Chlorophyll a Concentration in Case I Waters for Noisy Morel Dataa

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Table 5 Inputs Used in the OSOA Model to Calculate the Examples of Reflectance Spectra Plotted in Fig. 5

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Table 6 Performance of GP in Retrieving All Oceanic Constituents in Case II Waters

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Table 7 Geographic Coordinates of the SeaWiFS Scenes Used for GP Validation

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Table 8 Applications of GP Algorithm to SeaWiFS Images for Retrieval of Chlorophyll a Concentrations: Comparison with Results Obtained with the OC4 Empirical Algorithm

Equations (23)

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

fx=12+3,
gx=1+2, 3.
p logX=log|X|, X0 else p log0=0,
sigmX=1.7159exp1.3333*X-1exp1.3333*X+1.
Relative RMS=1ni=1nCexpectedi-CestimatediCexpectedi21/2,
Rw0-=0.33bb/a,
bb=12bw+0.002+0.0212-14log Cchl550λ×0.30Cchl0.62-bw550,
a=aw+0.06a*Cchl0.651+0.2 exp-0.014λ-440,
aysλ=ays440exp-0.014λ-440.
apλ=ApλCchlEpλ,
bpλ=0.3Cchl0.62550λ.
nr=Kr-v.
RMS=1ni=1nCexpectedi-Cestimatedi21/2.
Rwλ=Mf/Qρwλ,
ΔRwRw=Δρwρw+Δf/Qf/Q,
ΔRwRw=ΔLwLw+Δf/Qf/Q.
Lwλ=Lsatλ-ελ, λrLaλrtdλ,
ΔLwλ=ΔLsatλ+LaλrΔελ, λr+ελ, λrΔLaλrtdλ.
ελ, λr=γλrλα,
Δ1Lwλ=LaλrΔελ, λrtdλ=γλr/λαLaλrlnλr/λΔαtdλ,
Δ2Lwλ=ελ, λrΔLaλrtdλ.
Δ1Lwλ=Δ1Lw443td443443/λα ln865/λtdλln865/443.
ΔLw=ΔLsattd+Δ1Lw+Δ2Lw.

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