Abstract

We present a method to evaluate the combined accuracy of ocean color models and the parameterizations of inherent optical proprieties (IOPs), or model-parametrization setup. The method estimates the ensemble (collective) uncertainty of derived IOPs relative to the radiometric error and is directly applicable to ocean color products without the need for inversion. Validation shows a very good fit between derived and known values for synthetic data, with R2 > 0.95 and mean absolute difference (MADi) <0.25 m−1. Due to the influence of observation errors, these values deteriorate to 0.45 < R2 < 0.5 and 0.65 < MADi < 0.9 for in-situ and ocean color matchup data. The method is also used to estimate the maximum accuracy that could be achieved by a specific model-parametrization setup, which represents the optimum accuracy that should be targeted when deriving IOPs. Application to time series of ocean color global products collected between 1997–2007 shows few areas with increasing annual trends of ensemble uncertainty, up to 8 sr m−1decade−1. This value is translated to an error of 0.04 m−1decade−1 in the sum of derived absorption and backscattering coefficients at the blue wavelength 440 nm. As such, the developed method can be used as a tool for assessing the reliability of model-parametrization setups for specific biophysical conditions and for identifying hot-spots for which the model-parametrization setup should be reconsidered.

© 2011 OSA

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  1. Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
    [CrossRef]
  2. F. Mélin, “Global distribution of the random uncertainty associated with satellite-derived chla,” IEEE Geosci. Remote Sens. Lett. 7, 220–224 (2010).
    [CrossRef]
  3. T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).
    [CrossRef]
  4. P. Wang, E. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt. 44, 4074–4084 (2005).
    [CrossRef] [PubMed]
  5. S. Maritorena and D. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
    [CrossRef]
  6. M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. J. G. Acker and G. Leptoukh, “Online analysis enhances use of NASA earth science data,” Eos, Trans. AGU 88, 14–17 (2005).
    [CrossRef]
  12. 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]
  13. 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]
  14. M. S. Salama and F. Shen, “Stochastic inversion of ocean color data using the cross-entropy method,” Opt. Express 18, 479–499 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. 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.
  18. F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
    [CrossRef]
  19. E. Laws, Mathematical Methods for Oceanographers: An Introduction (John Wiley and Sons, 1997).
  20. C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Res. 30, 79–82 (2005).
    [CrossRef]
  21. M. Salama and Z. Su, “Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors,” Sensors 10, 7561–7575 (2010).
    [CrossRef] [PubMed]
  22. M. S. Salama and Z. Su, “Resolving the subscale spatial variability of apparent and inherent optical properties in ocean color matchup sites,” IEEE Trans. Geosci. Remote Sens. 49, 2612–2622 (2011).
    [CrossRef]
  23. M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
    [CrossRef]
  24. M. S. Salama and F. Shen, “Simultaneous atmospheric correction and quantification of suspended particulate matters from orbital and geostationary earth observation sensors,” Estuarine Coastal Shelf Sci. 86, 499–511 (2010).
    [CrossRef]
  25. E. Aas, “Estimates of radiance reflected towards the zenith at the surface of the sea,” Ocean Sci. 6, 861–876, (2010)
    [CrossRef]

2011 (1)

M. S. Salama and Z. Su, “Resolving the subscale spatial variability of apparent and inherent optical properties in ocean color matchup sites,” IEEE Trans. Geosci. Remote Sens. 49, 2612–2622 (2011).
[CrossRef]

2010 (6)

M. Salama and Z. Su, “Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors,” Sensors 10, 7561–7575 (2010).
[CrossRef] [PubMed]

M. S. Salama and F. Shen, “Stochastic inversion of ocean color data using the cross-entropy method,” Opt. Express 18, 479–499 (2010).
[CrossRef] [PubMed]

F. Mélin, “Global distribution of the random uncertainty associated with satellite-derived chla,” IEEE Geosci. Remote Sens. Lett. 7, 220–224 (2010).
[CrossRef]

Z. Lee, R. Arnone, C. Hu, J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
[CrossRef] [PubMed]

M. S. Salama and F. Shen, “Simultaneous atmospheric correction and quantification of suspended particulate matters from orbital and geostationary earth observation sensors,” Estuarine Coastal Shelf Sci. 86, 499–511 (2010).
[CrossRef]

E. Aas, “Estimates of radiance reflected towards the zenith at the surface of the sea,” Ocean Sci. 6, 861–876, (2010)
[CrossRef]

2009 (3)

M. S. Salama and A. Stein, “Error decomposition and estimation of inherent optical properties,” Appl. Opt. 48, 4926–4962 (2009).
[CrossRef]

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).
[CrossRef]

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

2007 (1)

F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
[CrossRef]

2005 (5)

C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Res. 30, 79–82 (2005).
[CrossRef]

P. Wang, E. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt. 44, 4074–4084 (2005).
[CrossRef] [PubMed]

S. Maritorena and D. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (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 Sens. Environ. 98, 122–140 (2005).
[CrossRef]

J. G. Acker and G. Leptoukh, “Online analysis enhances use of NASA earth science data,” Eos, Trans. AGU 88, 14–17 (2005).
[CrossRef]

2004 (1)

M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
[CrossRef]

2002 (1)

1999 (1)

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]

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, 43–53 (1981).
[CrossRef]

Aas, E.

E. Aas, “Estimates of radiance reflected towards the zenith at the surface of the sea,” Ocean Sci. 6, 861–876, (2010)
[CrossRef]

Acker, J. G.

J. G. Acker and G. Leptoukh, “Online analysis enhances use of NASA earth science data,” Eos, Trans. AGU 88, 14–17 (2005).
[CrossRef]

Arnone, R.

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 Sens. Environ. 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]

Berthon, JF.

F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
[CrossRef]

Boss, E.

Bricaud, A.

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, 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]

Campbell, J. W.

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).
[CrossRef]

Carder, K.

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]

Coppin, P.

M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
[CrossRef]

de Jeu, R.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Dekker, A. G.

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

Dowell, M. D.

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).
[CrossRef]

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]

Gordon, H.

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]

Holleman, I.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Hu, C.

Kopelevich, O.

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.

Laws, E.

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

Lee, Z.

Leptoukh, G.

J. G. Acker and G. Leptoukh, “Online analysis enhances use of NASA earth science data,” Eos, Trans. AGU 88, 14–17 (2005).
[CrossRef]

Levizzani, V.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Lubac, B.

Mannaerts, C. M.

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

Maritorena, S.

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

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

Matsuura, K.

C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Res. 30, 79–82 (2005).
[CrossRef]

Mélin, F.

F. Mélin, “Global distribution of the random uncertainty associated with satellite-derived chla,” IEEE Geosci. Remote Sens. Lett. 7, 220–224 (2010).
[CrossRef]

F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
[CrossRef]

Mobley, C.

Mognard-Campbell, N.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Monbaliu, J.

M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
[CrossRef]

Moore, T. S.

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).
[CrossRef]

Morel, A.

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, 43–53 (1981).
[CrossRef]

Parodi, G.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Patch, J.

Peterson, A.

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,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Rodell, M.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Roebeling, R. A.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Roesler, C.

Rott, H.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Salama, M.

M. Salama and Z. Su, “Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors,” Sensors 10, 7561–7575 (2010).
[CrossRef] [PubMed]

Salama, M. S.

M. S. Salama and Z. Su, “Resolving the subscale spatial variability of apparent and inherent optical properties in ocean color matchup sites,” IEEE Trans. Geosci. Remote Sens. 49, 2612–2622 (2011).
[CrossRef]

M. S. Salama and F. Shen, “Stochastic inversion of ocean color data using the cross-entropy method,” Opt. Express 18, 479–499 (2010).
[CrossRef] [PubMed]

M. S. Salama and F. Shen, “Simultaneous atmospheric correction and quantification of suspended particulate matters from orbital and geostationary earth observation sensors,” Estuarine Coastal Shelf Sci. 86, 499–511 (2010).
[CrossRef]

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

M. S. Salama and A. Stein, “Error decomposition and estimation of inherent optical properties,” Appl. Opt. 48, 4926–4962 (2009).
[CrossRef]

M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
[CrossRef]

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Schulz, J.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Shen, F.

M. S. Salama and F. Shen, “Stochastic inversion of ocean color data using the cross-entropy method,” Opt. Express 18, 479–499 (2010).
[CrossRef] [PubMed]

M. S. Salama and F. Shen, “Simultaneous atmospheric correction and quantification of suspended particulate matters from orbital and geostationary earth observation sensors,” Estuarine Coastal Shelf Sci. 86, 499–511 (2010).
[CrossRef]

Siegel, D.

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

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

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 and Z. Su, “Resolving the subscale spatial variability of apparent and inherent optical properties in ocean color matchup sites,” IEEE Trans. Geosci. Remote Sens. 49, 2612–2622 (2011).
[CrossRef]

M. Salama and Z. Su, “Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors,” Sensors 10, 7561–7575 (2010).
[CrossRef] [PubMed]

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Timmermans, W. J.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Verhoef, W.

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

Wagner, W.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Wang, L.

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
[CrossRef]

Wang, P.

Werdell, J.

Z. Lee, R. Arnone, C. Hu, J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
[CrossRef] [PubMed]

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

Willmott, C. J.

C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Res. 30, 79–82 (2005).
[CrossRef]

Zibordi, G.

F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
[CrossRef]

Appl. Opt. (5)

Climate Res. (1)

C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Res. 30, 79–82 (2005).
[CrossRef]

Eos, Trans. AGU (1)

J. G. Acker and G. Leptoukh, “Online analysis enhances use of NASA earth science data,” Eos, Trans. AGU 88, 14–17 (2005).
[CrossRef]

Estuarine Coastal Shelf Sci. (1)

M. S. Salama and F. Shen, “Simultaneous atmospheric correction and quantification of suspended particulate matters from orbital and geostationary earth observation sensors,” Estuarine Coastal Shelf Sci. 86, 499–511 (2010).
[CrossRef]

Hydrol. Earth Syst. Sci. (1)

M. S. Salama, A. G. Dekker, Z. Su, C. M. Mannaerts, and W. Verhoef, “Deriving inherent optical properties and associated inversion-uncertainties in the dutch lakes,” Hydrol. Earth Syst. Sci. 13, 1113–1121 (2009).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

F. Mélin, “Global distribution of the random uncertainty associated with satellite-derived chla,” IEEE Geosci. Remote Sens. Lett. 7, 220–224 (2010).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

M. S. Salama and Z. Su, “Resolving the subscale spatial variability of apparent and inherent optical properties in ocean color matchup sites,” IEEE Trans. Geosci. Remote Sens. 49, 2612–2622 (2011).
[CrossRef]

Int. J. Remote Sens. (1)

M. S. Salama, J. Monbaliu, and P. Coppin, “Atmospheric correction of advanced very high resolution radiometer imagery,” Int. J. Remote Sens. 25, 1349–1355 (2004).
[CrossRef]

J. Geophys. Res. (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).
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Ocean Sci. (1)

E. Aas, “Estimates of radiance reflected towards the zenith at the surface of the sea,” Ocean Sci. 6, 861–876, (2010)
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Remote Sens. Environ. (4)

J. Werdell and S. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
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F. Mélin, G. Zibordi, and JF. Berthon, “Assessment of satellite ocean color products at a coastal site,” Remote Sens. Environ. 110, 192–215 (2007).
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S. Maritorena and D. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
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Sensors (1)

M. Salama and Z. Su, “Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors,” Sensors 10, 7561–7575 (2010).
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Other (4)

Z. Su, R. A. Roebeling, J. Schulz, I. Holleman, V. Levizzani, W. J. Timmermans, H. Rott, N. Mognard-Campbell, R. de Jeu, W. Wagner, M. Rodell, M. S. Salama, G. Parodi, and L. Wang, “Observation of Hydrological Processes Using Remote Sensing,” in Treatise on Water Science, P. Wilderer, ed. (Academic Press, 2011).
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Z. Lee, “Remote sensing of inherent optical properties: Fundamentals, tests of algorithms, and applications,” Tech. Rep. 5, International Ocean-Colour Coordinating Group (2006).

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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.

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Figures (4)

Fig. 1
Fig. 1

Known versus estimated ensemble-uncertainties at 440 nm expressed in m−1, of derived IOPs from the three data sets of (a) : IOCCG, gray circles ; (b): NOMAD, red triangles and; (c) : SeaWiFS-matchup in blue squares. The values are log transformed.

Fig. 2
Fig. 2

Comparison between known and estimated radiometric uncertainty for different wavelengths: (a) 400 nm, (b) 440 nm, (c) 550 nm, and (d) 670 nm. The values are log transformed.

Fig. 3
Fig. 3

The relationship between the normalized radiometric uncertainty, σ r N , and the sum of known IOPs values, cb k. The values are log transformed.

Fig. 4
Fig. 4

Trends of ensemble uncertainty at 440 nm between the period 1997–2007.

Tables (2)

Tables Icon

Table 1 Goodness-of-Fit Parameters between Known and Derived Ensemble Uncertainties at 440 nm Using the Three Data Sets

Tables Icon

Table 2 Goodness-of-Fit Parameters Between Known and Derived Radiometric Uncertainty as Retrieved from IOCCG Data Set

Equations (12)

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Δ R s w ( λ ) = i = 1 i n w i ( λ ) Δ i o p i ( λ 0 ) + δ ( λ ) ,
Φ ( λ ) = i = 1 i = n w i ( λ ) φ i ( λ ) / i = 1 i = n w i ( λ ) = 1 / i = 1 i = n w i ( λ ) .
Φ ( λ ) = Δ iop ( λ ) Δ R s w ( λ ) ,
σ r 2 ( λ ) = i = 1 i = n w i 2 ( λ ) σ i 2 ( λ 0 ) + δ 2 + ,
i = 1 i = n w i 2 ( λ ) ψ i 2 ( λ ) = 1 ,
Ψ ( λ ) = ( i = 1 i = n w i 2 ( λ ) ψ i 2 ( λ ) / i = 1 i = n w i 2 ( λ ) ) 0.5 = ( i = 1 i = n w i 2 ( λ ) ) 0.5 .
Ψ ( λ ) = σ iop ( λ ) / σ r ( λ ) ,
σ iop ( λ ) = ( Σ w i 2 ( λ ) σ i 2 ( λ 0 ) Σ w i 2 ( λ ) ) 0.5 = σ r ( λ ) ( i = 1 i = n w i 2 ( λ ) ) 0 , 5 .
Ψ N ( λ ) = CV ( λ ) σ r ( λ ) = Ψ ( λ ) c b d ( λ ) ,
σ r N ( λ ) = σ r ( λ ) CV ( λ ) = c b d ( λ ) Ψ ( λ ) .
R s w ( λ ) = t 2 / n 2 i = 1 i = 2 g i u i ( λ ) ,
known _ error 2 ( λ ) = ( Σ w i * 2 ( λ ) Δ i o p i 2 ( λ 0 ) + δ 2 ) / Σ w i * 2 ( λ ) ,

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