Abstract

Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties. In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data. The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process. The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets. Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R 2 and root mean square of error (RMSE) are mentioned hereafter. Accurate values of total absorption coefficient are derived with R 2 > 0.91 and RMSE, of log transformed data, less than 0.55. Reliable values of the total backscattering coefficient are also obtained with R 2 > 0.7 (after removing outliers) and RMSE < 0.37. The developed algorithm has the ability to derive reliable results from noisy data with R 2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients.

The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species. It gives consistently accurate results and is therefore worth considering for ocean color global products.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Zaneveld, "New developments of the theory of radiative transfer in the ocean," in "Optical Aspects of Oceanography," N. Jerlov, ed. (Academic Press, London, 1973), pp. 121-134.
  2. S. Duntley, "Light in the sea," J. Opt. Soc. Am. 53, 214-233 (1963).
    [CrossRef]
  3. H. Gordon, O. Brown, and M. Jacobs, "Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean," Appl. Opt. 14, 417-427 (1975).
    [CrossRef] [PubMed]
  4. A. Morel and L. Prieur, "Analysis of variation in ocean color," Limnology and Oceanography 22, 709-722 (1977).
    [CrossRef]
  5. R. Walker, Marine Light Field Statistics, Wiley serie on pure and Appl. Opt. (John Wiley & Sons, INC., NW, 1994).
  6. J. Kirk, The relationship between the inherent and apparent optical properties of surface waters and its dependence on the shape of the volume scattering function, (Oxford University Press, 1994), p. 283.
  7. H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
    [CrossRef]
  8. S. Garver and D. Siegel, "Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation I. Time series from the sargasso sea," J. Geophys. Res. 102, 18607-18625 (1997).
    [CrossRef]
  9. F. E. Hoge and P. E. Lyon, "Satellite retrieval of inherent optical properties by linear matrix inversion of ocean radiance models: An analysis of model and radiance measurement errors," J. Geophys. Res. 101, 16631-16648 (1996).
    [CrossRef]
  10. Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters. 1. A semianalytical model," Appl. Opt. 37, 6329-6338 (1998).
    [CrossRef]
  11. S. Maritorena, D. Siegel, and A. Peterson, "Optimization of a semianalytical ocean color model for global-scale applications," Appl. Opt. 41, 2705-2714 (2002).
    [CrossRef] [PubMed]
  12. Z. Lee, K. Carder, and R. Arnone, "Deriving inherent optical properties from water color: A multiband quasianalytical algorithm for optically deep waters," Appl. Opt. 41, 5755-5772 (2002).
    [CrossRef] [PubMed]
  13. H. Gordon, "Inverse methods in hydrologic optics," Oceanologia 44, 9-58 (2002).
  14. Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
    [CrossRef]
  15. A. Albert and P. Gege, "Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties," Appl. Opt. 45, 2331-2343 (2006).
    [CrossRef] [PubMed]
  16. M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
    [CrossRef]
  17. H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
    [CrossRef]
  18. M. Chami and D. Robilliard, "Inversion of oceanic constituents in case i and ii waters with genetic programming algorithms," Appl. Opt. 41, 6260-6275 (2002).
    [CrossRef] [PubMed]
  19. P. Kempeneers, S. Sterckx, W. Debruyn, S. De Backer, P. Scheunders, Y. Park, and K. Ruddick, "Retrieval of oceanic constituents from ocean color using simulated annealing," in "Geoscience and Remote Sensing Symposium," Vol. 8 of IGARSS (IEEE International, 2005), vol. 8 of IGARSS, pp. 5651-5654.
  20. W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
    [CrossRef]
  21. R. Souto, H. Campos Velho, S. Stephany, and M. Kampel, "Chlorophyll concentration profiles from in situ radiances by ant colony optimization," in "4th AIP International Conference and the 1st Congress of the IPIA," Vol. 124 of Journal of Physics (2008), pp. 1-12.
  22. M.S. Salama and A. Stein, "Error decomposition and estimation of inherent optical properties," Appl. Opt. 48, 4947-4962 (2009).
    [CrossRef] [PubMed]
  23. G. Dueck and T. Scheur, "Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing," Journal of Computational Physics 90, 161-175 (1990).
    [CrossRef]
  24. W. Gong, Y. Ho, and W. Zhai, "Stochastic comparison algorithm for discrete optimization with estimation," in "Proceedings of the 31st IEEE Conference," Vol. 1 of Decision and Controle (1992), pp. 795-800.
  25. F. Glover, "Tabu search: A tutorial," Interfaces 20, 74-94 (1990).
    [CrossRef]
  26. R. Rubinstein, "The cross-entropy method for combinatorial and continuous optimization," Methodology and Computing in Applied Probability 2, 127-190 (1999).
    [CrossRef]
  27. R. Rubinstein and D. Kroese, The Cross-Entropy Method: A unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning, Information Science and Statistics (Springer, New York, 2004).
    [PubMed]
  28. Z. Lee, "Remote sensing of inherent optical properties: Fundamentals, tests of algorithms, and applications," Tech. Rep. 5, International Ocean-Colour Coordinating Group (2006).
  29. R. Pope and E. Fry, "Absorption spectrum (380-700nm) of pure water: II, Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
    [CrossRef]
  30. C. Mobley, Light and water radiative transfer in natural waters (Academic Press, 1994).
  31. A. Bricaud, A. Morel, and L. Prieur, "Absorption by dissolved organic-matter of the sea (yellow substance) in the UV and visible domains," Limnology and Oceanography 26, 43-53 (1981).
    [CrossRef]
  32. O. Kopelevich, "Small-parameter model of optical properties of sea waters," in "Ocean Optics," Vol. 1 Physical Ocean Optics, A. Monin, ed. (Nauka, 1983), pp. 208-234.
  33. T. Petzold, "Volume scattering functions for selected ocean waters," in "Light in the Sea," Vol. 12, J. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsburg, Pa. USA, 1977), pp. 150-174.
  34. V. Singh, Entropy-based parameter estimation in Hydrology, Vol. 30 of Water Science and Technology Library (Kluwer Academic Publishers, Dordrecht, 1998).
  35. C. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423, 623-656 (1948).
  36. S. Kullback and R. Leibler, "On information and sufficiency," The Annals of Mathematical Statistics 22, 79-86 (1951).
    [CrossRef]
  37. D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
    [CrossRef]
  38. R. Rubinstein and D. Kroese, Simulation and the Monte Carlo Method, Wiley Series in Probability and Statistics (2008), 2nd Ed.
  39. R. Srinivasan, Importance sampling: Applications in communications and detection (Springer-Verlag, Berlin, 2002).
  40. T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
    [CrossRef]
  41. W. Gregg, and K. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnology and Oceanography 35, 1657-1675 (1990).
    [CrossRef]
  42. J. Werdell and S. Bailey, "An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation," Remote Sensing of Environment 98, 122-140 (2005).
    [CrossRef]
  43. S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  44. E. Laws, Mathematical Methods for Oceanographers: An introduction (John Wiley and Sons, New York, 1997).
  45. R. Doerffer, "Analysis of the signal/noise and the water leaving radiance finnish lakes," Tech. Rep., Brockmann Consult (2008).
  46. H. Neckel and D. Labs, "Improved data of solar spectral irradiance from 0.33 to 1.25 mm," Solar Physics 74, 231-249 (1981).
    [CrossRef]
  47. D. Doxaran, M. Babin, and E. Leymarie, "Near-infrared light scattering by particles in coastal waters," Opt. Express 15, 12834-12849 (2007).
    [CrossRef] [PubMed]
  48. J. Werdell, B. Franz, S. Bailey, L. Harding, and G. Feldman, "Approach for the long-term spatial and temporal evaluation of ocean color satellite data products in a coastal environment," in "Proceedings of SPIE, the International Society for Optical Engineering," Vol. 6680 of Coastal ocean remote sensing, (2007), pp. 66800G.1-66800G.12.
  49. A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters II. Bidirectional aspects," Appl. Opt. 32, 6864-6879 (1993).
    [CrossRef] [PubMed]
  50. A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters.3. Implication of bidirectionality for the remote sensing problem," Appl. Opt. 35, 4850-4862 (1996).
    [CrossRef] [PubMed]
  51. A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
    [CrossRef]
  52. A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
    [CrossRef]
  53. K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
    [CrossRef]
  54. A. Whitmire, E. Boss, T. Cowls, and W. Pegau, "Spectral variability of particulate backscattering ratio," Opt. Express 15, 7019-7031 (2007).
    [CrossRef] [PubMed]
  55. D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
    [CrossRef]
  56. M. Sydor, R. Gould, R. Arnone, V. Haltrin, and W. Goode, "Uniqueness in remote sensing of the inherent optical properties of ocean water," Appl. Opt. 43, 2156-2162 (2004).
    [CrossRef] [PubMed]

2009 (3)

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

M.S. Salama and A. Stein, "Error decomposition and estimation of inherent optical properties," Appl. Opt. 48, 4947-4962 (2009).
[CrossRef] [PubMed]

2007 (2)

2006 (2)

D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
[CrossRef]

A. Albert and P. Gege, "Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties," Appl. Opt. 45, 2331-2343 (2006).
[CrossRef] [PubMed]

2005 (2)

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

J. Werdell and S. Bailey, "An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation," Remote Sensing of Environment 98, 122-140 (2005).
[CrossRef]

2004 (2)

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

M. Sydor, R. Gould, R. Arnone, V. Haltrin, and W. Goode, "Uniqueness in remote sensing of the inherent optical properties of ocean water," Appl. Opt. 43, 2156-2162 (2004).
[CrossRef] [PubMed]

2003 (1)

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

2002 (4)

1999 (3)

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
[CrossRef]

R. Rubinstein, "The cross-entropy method for combinatorial and continuous optimization," Methodology and Computing in Applied Probability 2, 127-190 (1999).
[CrossRef]

1998 (2)

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters. 1. A semianalytical model," Appl. Opt. 37, 6329-6338 (1998).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

1997 (2)

R. Pope and E. Fry, "Absorption spectrum (380-700nm) of pure water: II, Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
[CrossRef]

S. Garver and D. Siegel, "Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation I. Time series from the sargasso sea," J. Geophys. Res. 102, 18607-18625 (1997).
[CrossRef]

1996 (2)

F. E. Hoge and P. E. Lyon, "Satellite retrieval of inherent optical properties by linear matrix inversion of ocean radiance models: An analysis of model and radiance measurement errors," J. Geophys. Res. 101, 16631-16648 (1996).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters.3. Implication of bidirectionality for the remote sensing problem," Appl. Opt. 35, 4850-4862 (1996).
[CrossRef] [PubMed]

1995 (1)

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
[CrossRef]

1993 (1)

1990 (3)

G. Dueck and T. Scheur, "Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing," Journal of Computational Physics 90, 161-175 (1990).
[CrossRef]

F. Glover, "Tabu search: A tutorial," Interfaces 20, 74-94 (1990).
[CrossRef]

W. Gregg, and K. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnology and Oceanography 35, 1657-1675 (1990).
[CrossRef]

1988 (1)

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1981 (2)

H. Neckel and D. Labs, "Improved data of solar spectral irradiance from 0.33 to 1.25 mm," Solar Physics 74, 231-249 (1981).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, "Absorption by dissolved organic-matter of the sea (yellow substance) in the UV and visible domains," Limnology and Oceanography 26, 43-53 (1981).
[CrossRef]

1977 (1)

A. Morel and L. Prieur, "Analysis of variation in ocean color," Limnology and Oceanography 22, 709-722 (1977).
[CrossRef]

1975 (1)

1963 (1)

1951 (1)

S. Kullback and R. Leibler, "On information and sufficiency," The Annals of Mathematical Statistics 22, 79-86 (1951).
[CrossRef]

1948 (1)

C. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423, 623-656 (1948).

Albert, A.

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

Arnone, R.

Babin, M.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

D. Doxaran, M. Babin, and E. Leymarie, "Near-infrared light scattering by particles in coastal waters," Opt. Express 15, 12834-12849 (2007).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
[CrossRef]

Bailey, S.

J. Werdell and S. Bailey, "An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation," Remote Sensing of Environment 98, 122-140 (2005).
[CrossRef]

Baker, K.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Boss, E.

Bricaud, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (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," Limnology and Oceanography 26, 43-53 (1981).
[CrossRef]

Brown, J.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Brown, O.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

H. Gordon, O. Brown, and M. Jacobs, "Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean," Appl. Opt. 14, 417-427 (1975).
[CrossRef] [PubMed]

Carder, K.

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

Z. Lee, K. Carder, and R. Arnone, "Deriving inherent optical properties from water color: A multiband quasianalytical algorithm for optically deep waters," Appl. Opt. 41, 5755-5772 (2002).
[CrossRef] [PubMed]

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
[CrossRef]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters. 1. A semianalytical model," Appl. Opt. 37, 6329-6338 (1998).
[CrossRef]

W. Gregg, and K. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnology and Oceanography 35, 1657-1675 (1990).
[CrossRef]

Chami, M.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

M. Chami and D. Robilliard, "Inversion of oceanic constituents in case i and ii waters with genetic programming algorithms," Appl. Opt. 41, 6260-6275 (2002).
[CrossRef] [PubMed]

Chen, C.

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

Chen, F.

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Clark, D.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Claustre, H.

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
[CrossRef]

Cowls, T.

De Boer, T.

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

Dekker, A.

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

Doxaran, D.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

D. Doxaran, M. Babin, and E. Leymarie, "Near-infrared light scattering by particles in coastal waters," Opt. Express 15, 12834-12849 (2007).
[CrossRef] [PubMed]

Dueck, G.

G. Dueck and T. Scheur, "Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing," Journal of Computational Physics 90, 161-175 (1990).
[CrossRef]

Duntley, S.

Evans, R.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Fry, E.

Garver, S.

S. Garver and D. Siegel, "Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation I. Time series from the sargasso sea," J. Geophys. Res. 102, 18607-18625 (1997).
[CrossRef]

Gege, P.

Gelatt, C.

S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Gentili, B.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters.3. Implication of bidirectionality for the remote sensing problem," Appl. Opt. 35, 4850-4862 (1996).
[CrossRef] [PubMed]

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

Glover, F.

F. Glover, "Tabu search: A tutorial," Interfaces 20, 74-94 (1990).
[CrossRef]

Goode, W.

Gordon, H.

H. Gordon, "Inverse methods in hydrologic optics," Oceanologia 44, 9-58 (2002).

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

H. Gordon, O. Brown, and M. Jacobs, "Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean," Appl. Opt. 14, 417-427 (1975).
[CrossRef] [PubMed]

Gould, R.

Gregg, W.

W. Gregg, and K. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnology and Oceanography 35, 1657-1675 (1990).
[CrossRef]

Haltrin, V.

Hawes, S.

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Hoge, F. E.

F. E. Hoge and P. E. Lyon, "Satellite retrieval of inherent optical properties by linear matrix inversion of ocean radiance models: An analysis of model and radiance measurement errors," J. Geophys. Res. 101, 16631-16648 (1996).
[CrossRef]

Jacobs, M.

Kamykowski, D.

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Kroese, D.

D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
[CrossRef]

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

Kullback, S.

S. Kullback and R. Leibler, "On information and sufficiency," The Annals of Mathematical Statistics 22, 79-86 (1951).
[CrossRef]

Labs, D.

H. Neckel and D. Labs, "Improved data of solar spectral irradiance from 0.33 to 1.25 mm," Solar Physics 74, 231-249 (1981).
[CrossRef]

Lee, Z.

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

Z. Lee, K. Carder, and R. Arnone, "Deriving inherent optical properties from water color: A multiband quasianalytical algorithm for optically deep waters," Appl. Opt. 41, 5755-5772 (2002).
[CrossRef] [PubMed]

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
[CrossRef]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters. 1. A semianalytical model," Appl. Opt. 37, 6329-6338 (1998).
[CrossRef]

Leibler, R.

S. Kullback and R. Leibler, "On information and sufficiency," The Annals of Mathematical Statistics 22, 79-86 (1951).
[CrossRef]

Leymarie, E.

Lyon, P. E.

F. E. Hoge and P. E. Lyon, "Satellite retrieval of inherent optical properties by linear matrix inversion of ocean radiance models: An analysis of model and radiance measurement errors," J. Geophys. Res. 101, 16631-16648 (1996).
[CrossRef]

Mannaerts, C.

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

Mannor, S.

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

Maritorena, S.

McKee, D.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

Miller, R.

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

Mobley, C.

Morel, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters.3. Implication of bidirectionality for the remote sensing problem," Appl. Opt. 35, 4850-4862 (1996).
[CrossRef] [PubMed]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
[CrossRef]

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

A. Bricaud, A. Morel, and L. Prieur, "Absorption by dissolved organic-matter of the sea (yellow substance) in the UV and visible domains," Limnology and Oceanography 26, 43-53 (1981).
[CrossRef]

A. Morel and L. Prieur, "Analysis of variation in ocean color," Limnology and Oceanography 22, 709-722 (1977).
[CrossRef]

Musavi, M.

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

Neckel, H.

H. Neckel and D. Labs, "Improved data of solar spectral irradiance from 0.33 to 1.25 mm," Solar Physics 74, 231-249 (1981).
[CrossRef]

Patch, J.

Pegau, W.

Peterson, A.

Pope, R.

Porotsky, S.

D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
[CrossRef]

Prieur, L.

A. Bricaud, A. Morel, and L. Prieur, "Absorption by dissolved organic-matter of the sea (yellow substance) in the UV and visible domains," Limnology and Oceanography 26, 43-53 (1981).
[CrossRef]

A. Morel and L. Prieur, "Analysis of variation in ocean color," Limnology and Oceanography 22, 709-722 (1977).
[CrossRef]

Ressom, H.

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

Robilliard, D.

Rubinstein, R.

D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
[CrossRef]

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

R. Rubinstein, "The cross-entropy method for combinatorial and continuous optimization," Methodology and Computing in Applied Probability 2, 127-190 (1999).
[CrossRef]

Ruddick, K.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

Salama, M. S.

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

Salama, M.S.

Scheur, T.

G. Dueck and T. Scheur, "Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing," Journal of Computational Physics 90, 161-175 (1990).
[CrossRef]

Shannon, C.

C. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423, 623-656 (1948).

Shi, P.

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

Siegel, D.

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

S. Garver and D. Siegel, "Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation I. Time series from the sargasso sea," J. Geophys. Res. 102, 18607-18625 (1997).
[CrossRef]

Slade, W.

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

Smith, R.

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Stein, A.

Steward, R.

Su, Z.

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

Sydor, M.

Tailliez, D.

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

Vecchi, M.

S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Verhoef, W.

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

Werdell, J.

J. Werdell and S. Bailey, "An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation," Remote Sensing of Environment 98, 122-140 (2005).
[CrossRef]

Whitmire, A.

Zhan, H.

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

Annals of Operations Research (1)

T. De Boer, D. Kroese, S. Mannor, and R. Rubinstein, "A tutorial on the cross-entropy method," Annals of Operations Research 134, 19-67 (2005).
[CrossRef]

Appl. Opt. (12)

H. Gordon, O. Brown, and M. Jacobs, "Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean," Appl. Opt. 14, 417-427 (1975).
[CrossRef] [PubMed]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters. 1. A semianalytical model," Appl. Opt. 37, 6329-6338 (1998).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters.3. Implication of bidirectionality for the remote sensing problem," Appl. Opt. 35, 4850-4862 (1996).
[CrossRef] [PubMed]

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

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
[CrossRef]

R. Pope and E. Fry, "Absorption spectrum (380-700nm) of pure water: II, Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
[CrossRef]

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

Z. Lee, K. Carder, and R. Arnone, "Deriving inherent optical properties from water color: A multiband quasianalytical algorithm for optically deep waters," Appl. Opt. 41, 5755-5772 (2002).
[CrossRef] [PubMed]

M. Chami and D. Robilliard, "Inversion of oceanic constituents in case i and ii waters with genetic programming algorithms," Appl. Opt. 41, 6260-6275 (2002).
[CrossRef] [PubMed]

M. Sydor, R. Gould, R. Arnone, V. Haltrin, and W. Goode, "Uniqueness in remote sensing of the inherent optical properties of ocean water," Appl. Opt. 43, 2156-2162 (2004).
[CrossRef] [PubMed]

A. Albert and P. Gege, "Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties," Appl. Opt. 45, 2331-2343 (2006).
[CrossRef] [PubMed]

M.S. Salama and A. Stein, "Error decomposition and estimation of inherent optical properties," Appl. Opt. 48, 4947-4962 (2009).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

C. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423, 623-656 (1948).

Hydrology and Earth System Sciences (1)

M. S. Salama, A. Dekker, Z. Su, C. Mannaerts, and W. Verhoef, "Deriving inherent optical properties and associated inversion-uncertainties in the Dutch lakes," Hydrology and Earth System Sciences 13, 1113-1121 (2009).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

H. Zhan, Z. Lee, P. Shi, C. Chen, and K. Carder, "Retrieval of water optical properties for optically deep waters using genetic algorithms," IEEE Trans. Geosci. Remote Sens. 41, 1123-1128 (2003).
[CrossRef]

W. Slade, H. Ressom, M. Musavi, and R. Miller, "Inversion of ocean color observations using particle swarm optimization," IEEE Trans. Geosci. Remote Sens. 42, 1915-1923 (2004).
[CrossRef]

Interfaces (1)

F. Glover, "Tabu search: A tutorial," Interfaces 20, 74-94 (1990).
[CrossRef]

J. Geophys. Res. (6)

A. Bricaud, M. Babin, A. Morel, and H. Claustre, "Variability in the chlorophyll-specific absorption coefficients of naturnal phytoplankton: Analysis and parameterization," J. Geophys. Res. 100, 13,321-13,332 (1995).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and 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 (1998).
[CrossRef]

K. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, "Semianalytical moderate-resolution imaging spectrometer algorithms for chlorophyll-a and absorption with bio-optical domains based on nitrate-depletion temperature," J. Geophys. Res. 104, 5403-5421. (1999).
[CrossRef]

H. Gordon, O. Brown, R. Evans, J. Brown, R. Smith, K. Baker, and D. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

S. Garver and D. Siegel, "Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation I. Time series from the sargasso sea," J. Geophys. Res. 102, 18607-18625 (1997).
[CrossRef]

F. E. Hoge and P. E. Lyon, "Satellite retrieval of inherent optical properties by linear matrix inversion of ocean radiance models: An analysis of model and radiance measurement errors," J. Geophys. Res. 101, 16631-16648 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

Journal of Computational Physics (1)

G. Dueck and T. Scheur, "Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing," Journal of Computational Physics 90, 161-175 (1990).
[CrossRef]

Limnology and Oceanography (4)

W. Gregg, and K. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnology and Oceanography 35, 1657-1675 (1990).
[CrossRef]

D. Doxaran, K. Ruddick, D. McKee, B. Gentili, D. Tailliez, M. Chami, and M. Babin, "Spectral variations of light scattering by marine particles in coastal waters, from visible to near infrared," Limnology and Oceanography 54, 1257-1271 (2009).
[CrossRef]

A. Morel and L. Prieur, "Analysis of variation in ocean color," Limnology and Oceanography 22, 709-722 (1977).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, "Absorption by dissolved organic-matter of the sea (yellow substance) in the UV and visible domains," Limnology and Oceanography 26, 43-53 (1981).
[CrossRef]

Methodology and Computing in Applied Probability (2)

R. Rubinstein, "The cross-entropy method for combinatorial and continuous optimization," Methodology and Computing in Applied Probability 2, 127-190 (1999).
[CrossRef]

D. Kroese, S. Porotsky, and R. Rubinstein, "The cross-entropy method for continuous multi-extremal optimization," Methodology and Computing in Applied Probability 8, 383-407 (2006).
[CrossRef]

Oceanologia (1)

H. Gordon, "Inverse methods in hydrologic optics," Oceanologia 44, 9-58 (2002).

Opt. Express (2)

Remote Sensing of Environment (1)

J. Werdell and S. Bailey, "An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation," Remote Sensing of Environment 98, 122-140 (2005).
[CrossRef]

Science (1)

S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Solar Physics (1)

H. Neckel and D. Labs, "Improved data of solar spectral irradiance from 0.33 to 1.25 mm," Solar Physics 74, 231-249 (1981).
[CrossRef]

The Annals of Mathematical Statistics (1)

S. Kullback and R. Leibler, "On information and sufficiency," The Annals of Mathematical Statistics 22, 79-86 (1951).
[CrossRef]

Other (17)

R. Souto, H. Campos Velho, S. Stephany, and M. Kampel, "Chlorophyll concentration profiles from in situ radiances by ant colony optimization," in "4th AIP International Conference and the 1st Congress of the IPIA," Vol. 124 of Journal of Physics (2008), pp. 1-12.

C. Mobley, Light and water radiative transfer in natural waters (Academic Press, 1994).

O. Kopelevich, "Small-parameter model of optical properties of sea waters," in "Ocean Optics," Vol. 1 Physical Ocean Optics, A. Monin, ed. (Nauka, 1983), pp. 208-234.

T. Petzold, "Volume scattering functions for selected ocean waters," in "Light in the Sea," Vol. 12, J. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsburg, Pa. USA, 1977), pp. 150-174.

V. Singh, Entropy-based parameter estimation in Hydrology, Vol. 30 of Water Science and Technology Library (Kluwer Academic Publishers, Dordrecht, 1998).

P. Kempeneers, S. Sterckx, W. Debruyn, S. De Backer, P. Scheunders, Y. Park, and K. Ruddick, "Retrieval of oceanic constituents from ocean color using simulated annealing," in "Geoscience and Remote Sensing Symposium," Vol. 8 of IGARSS (IEEE International, 2005), vol. 8 of IGARSS, pp. 5651-5654.

R. Walker, Marine Light Field Statistics, Wiley serie on pure and Appl. Opt. (John Wiley & Sons, INC., NW, 1994).

J. Kirk, The relationship between the inherent and apparent optical properties of surface waters and its dependence on the shape of the volume scattering function, (Oxford University Press, 1994), p. 283.

J. Zaneveld, "New developments of the theory of radiative transfer in the ocean," in "Optical Aspects of Oceanography," N. Jerlov, ed. (Academic Press, London, 1973), pp. 121-134.

E. Laws, Mathematical Methods for Oceanographers: An introduction (John Wiley and Sons, New York, 1997).

R. Doerffer, "Analysis of the signal/noise and the water leaving radiance finnish lakes," Tech. Rep., Brockmann Consult (2008).

R. Rubinstein and D. Kroese, Simulation and the Monte Carlo Method, Wiley Series in Probability and Statistics (2008), 2nd Ed.

R. Srinivasan, Importance sampling: Applications in communications and detection (Springer-Verlag, Berlin, 2002).

W. Gong, Y. Ho, and W. Zhai, "Stochastic comparison algorithm for discrete optimization with estimation," in "Proceedings of the 31st IEEE Conference," Vol. 1 of Decision and Controle (1992), pp. 795-800.

R. Rubinstein and D. Kroese, The Cross-Entropy Method: A unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning, Information Science and Statistics (Springer, New York, 2004).
[PubMed]

Z. Lee, "Remote sensing of inherent optical properties: Fundamentals, tests of algorithms, and applications," Tech. Rep. 5, International Ocean-Colour Coordinating Group (2006).

J. Werdell, B. Franz, S. Bailey, L. Harding, and G. Feldman, "Approach for the long-term spatial and temporal evaluation of ocean color satellite data products in a coastal environment," in "Proceedings of SPIE, the International Society for Optical Engineering," Vol. 6680 of Coastal ocean remote sensing, (2007), pp. 66800G.1-66800G.12.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

IOCCG: Derived versus known values of IOPs of the IOCCG data set. (a): absorption of Chla at 440 nm; (b): absorption ofdg at 440 nm; (c): the backscattering of SPM at 550 nm; and (d): the total absorption at 440 nm.

Fig. 2.
Fig. 2.

NOMAD: Derived versus measured values of IOPs of the NOMAD data set. (a): absorption of Chla at 440 nm; (b): absorption ofdg at 440 nm; (c): the backscattering of SPM at 550 nm; and (d): the total absorption at 440 nm.

Fig. 3.
Fig. 3.

SeaWiFS match-up: Derived SeaWiFS IOPs versus measured IOPs of the NOMAD data set. (a): absorption of Chla at 440 nm;(b): absorption of dg at 440 nm; (c): the backscattering of SPM at 550 nm; and (d): the total absorption at 440 nm.

Fig. 4.
Fig. 4.

Examples of inversion from noisy-IOCCG data set. Six spectra of the noisy-IOCCG spectra are shown: (a) 1st; (b) 100th; and to (f) the last spectrum number 500. The black lines are spectra derived from the noisy spectra (dark gray lines) using the proposed stochastic inversion. Original noise-free spectra are shown in light gray lines. Maximum noise level is kept to ±70% of the original values.

Fig. 5.
Fig. 5.

RMSE between derived and known values of normalized Chla absorptioncoefficient,ā chla (λ) of(a): NOMAD data set and (b): SeaWiFS match-up data set.

Tables (7)

Tables Icon

Table 1. IOCCG: RMSE and regression (type II) goodness-of-fit parameters between derived and known values of IOCCG data set. n is the number of data points.

Tables Icon

Table 2. Noise level: Introduced noise level, per wavelength, averaged over the spectra of IOCCG data set. MERIS-NER and IOCCG standard deviation (std)were used to generate the noise from a normal distribution. MERIS-NER is shown as a percentage of the average original spectra. Only few wavelengths are shown.

Tables Icon

Table 3. Noisy IOCCG: RMSE and regression (type II)goodness-of-fit parameters between known values and derived IOPs from noisy IOCCG spectra.n is the number of data points.

Tables Icon

Table 4. NOMAD: RMSE and regression (type II) goodness-of-fit parameters between measured and derived IOPs IOPs values using the NOMAD data set.n is the number of data points.

Tables Icon

Table 5. SeaWiFS match-up: RMSE and regression (type II)goodness-of-fit parameters between measured and derived IOPs values using SeaWiFS match-up data set. n is the number of data points.

Tables Icon

Table 6. Number of iteration: Statistical parameters for number of iterations per spectrum averaged over each data set. Average and standard deviation values were rounded up to the closest integer.

Tables Icon

Table 7. Total processing time: Statistical parameters for total processing time (in seconds) per spectrum averaged over each data set.

Equations (25)

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

R s w ( λ ) = t n w 2 i = 1 2 g i ( b b ( λ ) b b ( λ ) + a ( λ ) ) i
a ( λ ) = a w ( λ ) + a chl a ( λ ) + a dg ( λ )
b b ( λ ) = b b , w ( λ ) + b b , spm ( λ )
a chl a ( λ ) = ( a 0 ( λ ) + a 1 ( λ ) ln a chl a ( 440 ) ) a chl a ( 440 )
a dg ( λ ) = a dg ( 440 ) exp [ s ( λ 440 ) ]
b b , spm ( λ ) = b b , spm ( 550 ) ( 550 λ ) y
iop = [ a chl a ( 440 ) , a dg ( 440 ) , b b , spm ( 550 ) , y , s ]
𝓗 ( g ) = 𝔼 ln g ( iop ) 1 N g ( iop ) · ln g ( iop )
𝓗 ( g , f ) = 1 N g ( iop ) · ln f ( iop )
𝓓 ( g , f ) = 1 N g ( iop ) ln g ( iop ) f ( iop )
𝓓 ( g , f ) = 𝓗 ( g , f ) 𝓗 ( g )
ϕ ( iop ) = i = 1 m [ R s w ( i ) R s w m ( i ) ] 2
ε min = min ϕ ( iop )
= ( ϕ ( iop ) ε )
= 𝔼 f I { ϕ ( iop ) ε } = i = 1 N I { ϕ ( iop i ) ε } f ( iop i , iop * )
= 𝔼 g I { ϕ ( iop ) ε } f ( iop , iop * ) g ( iop )
g * ( iop ) = I { ϕ ( iop ) ε } f ( iop , iop * )
iop = arg max iop * = 𝔼 f I { ϕ ( iop ) ε } ln f ( iop , iop * )
iop * = i = 1 N I { ϕ ( iop i ) ε } iop i i = 1 N I { ϕ ( iop i ) ε }
bias = 𝔼 ( log iop known log iop derived )
RMSE = [ ( n 2 ) 1 i n ( log iop known log iop derived ) 2 ] 0.5
a chl a ( 440 ) = 0.072 r 1 1.62
a dg ( 440 ) = a chl a ( 440 )
b b , spm ( 550 ) = 30 a w ( 640 ) R s w ( 640 )
y = 3.44 [ 1 3.17 exp ( 2.01 r 2 ) ]

Metrics