Abstract

This study addresses the regression of in-water radiometric profile data with the objective of investigating solutions to minimize uncertainties of derived products like subsurface radiance and irradiance (Lu0 and Ed0) and diffuse attenuation coefficients. Analyses are conducted using radiometric profiles generated through Monte Carlo simulations and field measurements. A nonlinear NL approach is presented as an alternative to the standard linear method LN. Results indicate that the LN method, relying on log-transformed data, tends to underestimate regression results with respect to NL operating on non-transformed data. The log-transformation is thus identified as the source of biases in data products. Observed differences between LN and NL regression results for Lu0 are of the order of 1–2%, that is well below the target uncertainty for data products from in situ measurements (i.e., 5%). For Ed0, instead, differences can easily exceed 5% as a result of more pronounced light focusing and defocusing effects due to wave perturbations. This work also remarks the importance of applying the multi-cast measurement scheme as a mean to increase the precision of data products.

© 2013 OSA

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  1. W. B. Philip and C. D. Scott, “Modelling regional responses by marine pelagic ecosystems to global climate change,” Geophys. Res. Lett.29, 1806 (2002).
  2. J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
    [CrossRef]
  3. M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
    [CrossRef] [PubMed]
  4. B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
    [CrossRef]
  5. T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
    [CrossRef]
  6. G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
    [CrossRef]
  7. T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
    [CrossRef]
  8. D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
    [CrossRef]
  9. S. Sathyendranath, “Remote sensing of ocean colour in coastal, and other optically-complex waters,” International Ocean-Colour Coordinating Group, IOCCG Report NUMBER 3 (2000).
  10. S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.
  11. G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing(Springer, 2010), chap. 18, pp. 307–334.
  12. P. J. Werdell and S. W. 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]
  13. G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
    [CrossRef]
  14. J. R. Zaneveld, E. Boss, and P. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express9, 260–266 (2001).
    [CrossRef] [PubMed]
  15. J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
    [CrossRef]
  16. G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
    [CrossRef]
  17. Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
    [CrossRef]
  18. M. Hieronymi and A. Macke, “On the influence of wind and waves on underwater irradiance fluctuations,” Ocean Sci.8, 455–471 (2012).
    [CrossRef]
  19. M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
    [CrossRef]
  20. J. L. Muller and R. W. Austin, Ocean Optics Protocols SeaWiFS for Validation, Revision 1(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 25 of SeaWiFS Technical Report SERIES, chap. 6, pp. 48–59.
  21. D. A. Siegel, Results of the SeaWiFS Data Analysis Round-Robin, July 1994 (DARR-94)(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 26 of SeaWiFS Technical Report SERIES, chap. 3, pp. 44–48.
  22. J. J. Beauchamp and J. S. Olson, “Corrections for bias in regression estimates after logarithmic transformation,” Ecology54, 1403–1407 (1973).
    [CrossRef]
  23. D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
    [CrossRef]
  24. T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.
  25. D. Schattschneider, “Proof without words: The arithmetic mean-geometric mean inequality,” Math. Mag.59, 11 (1986).
    [CrossRef]
  26. G. A. F. Seber and C. J. Wild, Nonlinear regression, Wiley series in probability and statistics (J. Wiley & Sons, 2003).
  27. P. E. Gill, W. Murray, and M. H. Wright, The Levenberg-Marquardt Method(Academic Press, 1981), chap. 4.7.3, pp. 136–137.
  28. Y. Yuan, “A Review of Trust Region Algorithms for Optimization,” in “ICIAM 99,” (Oxford University, 2000), pp. 271–282.
  29. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in “Ocean Optics XII,” (1994), no. 2558 in SPIE, pp. 194–201.
  30. G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” P. Soc. Photo-opt. Ins.3761, 62–70 (1999).
  31. T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” (2011), vol. 4, pp. 2186–2195. Proceedings of the International Conference on Computational Science, ICCS2011.
  32. T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.
  33. T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A statistical approach to performance tuning of Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012).
  34. J. Escher and T. Schlurmann, “On the recovery of the free surface from the pressure within periodic traveling water waves,” J. Nonlinear Math. Phys.15, 50–57 (2008).
    [CrossRef]
  35. N. L. Jones and S. G. Monismith, “Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge,” Limnol. Oceanogr.: Methods5, 317–327 (2007).
    [CrossRef]
  36. C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
    [CrossRef]

2013 (3)

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
[CrossRef]

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
[CrossRef]

2012 (3)

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

M. Hieronymi and A. Macke, “On the influence of wind and waves on underwater irradiance fluctuations,” Ocean Sci.8, 455–471 (2012).
[CrossRef]

M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
[CrossRef]

2011 (2)

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.

2010 (2)

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

2008 (1)

J. Escher and T. Schlurmann, “On the recovery of the free surface from the pressure within periodic traveling water waves,” J. Nonlinear Math. Phys.15, 50–57 (2008).
[CrossRef]

2007 (2)

N. L. Jones and S. G. Monismith, “Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge,” Limnol. Oceanogr.: Methods5, 317–327 (2007).
[CrossRef]

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

2006 (1)

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

2005 (2)

P. J. Werdell and S. W. 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]

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

2004 (2)

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
[CrossRef]

2001 (2)

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
[CrossRef]

J. R. Zaneveld, E. Boss, and P. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express9, 260–266 (2001).
[CrossRef] [PubMed]

1999 (1)

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” P. Soc. Photo-opt. Ins.3761, 62–70 (1999).

1994 (1)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in “Ocean Optics XII,” (1994), no. 2558 in SPIE, pp. 194–201.

1986 (1)

D. Schattschneider, “Proof without words: The arithmetic mean-geometric mean inequality,” Math. Mag.59, 11 (1986).
[CrossRef]

1973 (1)

J. J. Beauchamp and J. S. Olson, “Corrections for bias in regression estimates after logarithmic transformation,” Ecology54, 1403–1407 (1973).
[CrossRef]

1806 (1)

W. B. Philip and C. D. Scott, “Modelling regional responses by marine pelagic ecosystems to global climate change,” Geophys. Res. Lett.29, 1806 (2002).

Austin, R. W.

J. L. Muller and R. W. Austin, Ocean Optics Protocols SeaWiFS for Validation, Revision 1(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 25 of SeaWiFS Technical Report SERIES, chap. 6, pp. 48–59.

Bailey, S. W.

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

P. J. Werdell and S. W. 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]

Barber, R.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Barnard, A.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
[CrossRef]

Beauchamp, J. J.

J. J. Beauchamp and J. S. Olson, “Corrections for bias in regression estimates after logarithmic transformation,” Ecology54, 1403–1407 (1973).
[CrossRef]

Behrenfeld, M. J.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Berthon, J.-F.

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
[CrossRef]

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

Bopp, L.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Boss, E.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
[CrossRef]

J. R. Zaneveld, E. Boss, and P. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express9, 260–266 (2001).
[CrossRef] [PubMed]

Boss, E. S.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Canuti, E.

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

Cunha, J.

T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.

Cunha, J. C.

T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A statistical approach to performance tuning of Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012).

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” (2011), vol. 4, pp. 2186–2195. Proceedings of the International Conference on Computational Science, ICCS2011.

D’Alimonte, D.

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A statistical approach to performance tuning of Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012).

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” (2011), vol. 4, pp. 2186–2195. Proceedings of the International Conference on Computational Science, ICCS2011.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.

DAlimonte, D.

T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.

Darecki, M.

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

Doney, S. C.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Escher, J.

J. Escher and T. Schlurmann, “On the recovery of the free surface from the pressure within periodic traveling water waves,” J. Nonlinear Math. Phys.15, 50–57 (2008).
[CrossRef]

Falkowski, P. G.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Feldman, G. C.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in “Ocean Optics XII,” (1994), no. 2558 in SPIE, pp. 194–201.

Fournier, G. R.

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” P. Soc. Photo-opt. Ins.3761, 62–70 (1999).

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in “Ocean Optics XII,” (1994), no. 2558 in SPIE, pp. 194–201.

Franz, B. A.

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, The Levenberg-Marquardt Method(Academic Press, 1981), chap. 4.7.3, pp. 136–137.

Hieronymi, M.

M. Hieronymi and A. Macke, “On the influence of wind and waves on underwater irradiance fluctuations,” Ocean Sci.8, 455–471 (2012).
[CrossRef]

M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
[CrossRef]

Hirst, A. C.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Hooker, S.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

Huang, M.

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Hwang, P.

Jonasz, M.

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” P. Soc. Photo-opt. Ins.3761, 62–70 (1999).

Jones, N. L.

N. L. Jones and S. G. Monismith, “Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge,” Limnol. Oceanogr.: Methods5, 317–327 (2007).
[CrossRef]

Kajiyama, T.

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A statistical approach to performance tuning of Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012).

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” (2011), vol. 4, pp. 2186–2195. Proceedings of the International Conference on Computational Science, ICCS2011.

T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.

Kattawar, G. W.

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

Kleypas, J.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Letelier, R. M.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Li, H.

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Lin, Y.

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Macke, A.

M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
[CrossRef]

M. Hieronymi and A. Macke, “On the influence of wind and waves on underwater irradiance fluctuations,” Ocean Sci.8, 455–471 (2012).
[CrossRef]

Maritorena, S.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

Matear, R.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

McClain, C. R.

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Mclean, S.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

Mélin, F.

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

Mikolajewicz, U.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Milligan, A. J.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Monfray, P.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Monismith, S. G.

N. L. Jones and S. G. Monismith, “Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge,” Limnol. Oceanogr.: Methods5, 317–327 (2007).
[CrossRef]

Muller, J. L.

J. L. Muller and R. W. Austin, Ocean Optics Protocols SeaWiFS for Validation, Revision 1(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 25 of SeaWiFS Technical Report SERIES, chap. 6, pp. 48–59.

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, The Levenberg-Marquardt Method(Academic Press, 1981), chap. 4.7.3, pp. 136–137.

Olson, J. S.

J. J. Beauchamp and J. S. Olson, “Corrections for bias in regression estimates after logarithmic transformation,” Ecology54, 1403–1407 (1973).
[CrossRef]

ÓMalley, R. T.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Philip, W. B.

W. B. Philip and C. D. Scott, “Modelling regional responses by marine pelagic ecosystems to global climate change,” Geophys. Res. Lett.29, 1806 (2002).

Sarmiento, J. L.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Sathyendranath, S.

S. Sathyendranath, “Remote sensing of ocean colour in coastal, and other optically-complex waters,” International Ocean-Colour Coordinating Group, IOCCG Report NUMBER 3 (2000).

Schattschneider, D.

D. Schattschneider, “Proof without words: The arithmetic mean-geometric mean inequality,” Math. Mag.59, 11 (1986).
[CrossRef]

Schlurmann, T.

J. Escher and T. Schlurmann, “On the recovery of the free surface from the pressure within periodic traveling water waves,” J. Nonlinear Math. Phys.15, 50–57 (2008).
[CrossRef]

Scott, C. D.

W. B. Philip and C. D. Scott, “Modelling regional responses by marine pelagic ecosystems to global climate change,” Geophys. Res. Lett.29, 1806 (2002).

Seber, G. A. F.

G. A. F. Seber and C. J. Wild, Nonlinear regression, Wiley series in probability and statistics (J. Wiley & Sons, 2003).

Siegel, D. A.

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

D. A. Siegel, Results of the SeaWiFS Data Analysis Round-Robin, July 1994 (DARR-94)(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 26 of SeaWiFS Technical Report SERIES, chap. 3, pp. 44–48.

Sildam, J.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

Slater, R.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Soldatov, V.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Spall, S. A.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Stouffer, R.

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

Stramski, D.

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

Tsai, C.

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Voss, K.

G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing(Springer, 2010), chap. 18, pp. 307–334.

Werdell, P. J.

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

P. J. Werdell and S. W. 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]

Wild, C. J.

G. A. F. Seber and C. J. Wild, Nonlinear regression, Wiley series in probability and statistics (J. Wiley & Sons, 2003).

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, The Levenberg-Marquardt Method(Academic Press, 1981), chap. 4.7.3, pp. 136–137.

You, Y.

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

Young, F.

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Yuan, Y.

Y. Yuan, “A Review of Trust Region Algorithms for Optimization,” in “ICIAM 99,” (Oxford University, 2000), pp. 271–282.

Zaneveld, J. R.

Zaneveld, J. R. V.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
[CrossRef]

Zibordi, G.

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
[CrossRef]

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing(Springer, 2010), chap. 18, pp. 307–334.

T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.

Zielinski, O.

M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
[CrossRef]

Appl. Optics (4)

Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Optics49, 1041–1053 (2010).
[CrossRef]

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics40, 1442–1449 (2001).
[CrossRef]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics49, 4936–4950 (2010).
[CrossRef]

B. A. Franz, S. W. Bailey, P. J. Werdell, and C. R. McClain, “Sensor-independent approach to the vicarious calibration of satellite ocean color radiometry,” Appl. Optics46, 5068–5082 (2007).
[CrossRef]

Concurrency Computat.: Pract. Exper (1)

T. Kajiyama, D. DAlimonte, and J. C. Cunha, “A high-performance computing framework for large-scale ocean color Monte Carlo simulations,” Concurrency Computat.: Pract. Exper pp. 1–22 (2011). Submitted for publications.

Ecology (1)

J. J. Beauchamp and J. S. Olson, “Corrections for bias in regression estimates after logarithmic transformation,” Ecology54, 1403–1407 (1973).
[CrossRef]

Geophys. Res. Lett. (1)

W. B. Philip and C. D. Scott, “Modelling regional responses by marine pelagic ecosystems to global climate change,” Geophys. Res. Lett.29, 1806 (2002).

Global Biogeochem. Cycles (1)

J. L. Sarmiento, R. Slater, R. Barber, L. Bopp, S. C. Doney, A. C. Hirst, J. Kleypas, R. Matear, U. Mikolajewicz, P. Monfray, V. Soldatov, S. A. Spall, and R. Stouffer, “Response of ocean ecosystems to climate warming,” Global Biogeochem. Cycles18, 23 (2004).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (2)

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Regional algorithms for European seas: a case study based on MERIS data,” IEEE Geosci. Remote Sens. Lett.10, 283–287 (2013).
[CrossRef]

T. Kajiyama, D. D’Alimonte, and G. Zibordi, “Match-up analysis of MERIS radiometric data in the Northern Adriatic Sea,” IEEE Geosci. Remote Sens. Lett. (2013). Accepted for publication.
[CrossRef]

J. Nonlinear Math. Phys. (1)

J. Escher and T. Schlurmann, “On the recovery of the free surface from the pressure within periodic traveling water waves,” J. Nonlinear Math. Phys.15, 50–57 (2008).
[CrossRef]

J. of Atm. and Ocean. Tech. (1)

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. of Atm. and Ocean. Tech.21, 1059–1073 (2004).
[CrossRef]

Limnol. Oceanogr.: Methods (1)

N. L. Jones and S. G. Monismith, “Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge,” Limnol. Oceanogr.: Methods5, 317–327 (2007).
[CrossRef]

Math. Mag. (1)

D. Schattschneider, “Proof without words: The arithmetic mean-geometric mean inequality,” Math. Mag.59, 11 (1986).
[CrossRef]

Nature (1)

M. J. Behrenfeld, R. T. ÓMalley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature444, 752–755 (2006).
[CrossRef] [PubMed]

Ocean Eng. (1)

C. Tsai, M. Huang, F. Young, Y. Lin, and H. Li, “On the recovery of surface wave by pressure transfer function,” Ocean Eng.32, 1247–1259 (2005).
[CrossRef]

Ocean Sci. (2)

M. Hieronymi and A. Macke, “On the influence of wind and waves on underwater irradiance fluctuations,” Ocean Sci.8, 455–471 (2012).
[CrossRef]

M. Hieronymi, A. Macke, and O. Zielinski, “Modeling of wave-induced irradiance variability in the upper ocean mixed layer,” Ocean Sci.8, 103–120 (2012).
[CrossRef]

Ocean Sci. Discuss. (1)

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss.10, 219–259 (2013).
[CrossRef]

Opt. Express (1)

P. Soc. Photo-opt. Ins. (1)

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” P. Soc. Photo-opt. Ins.3761, 62–70 (1999).

Remote Sens. Environ. (3)

P. J. Werdell and S. W. 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]

G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: the BiOMaP radiometric dataset,” Remote Sens. Environ.115, 2104–2115 (2011).
[CrossRef]

D. D’Alimonte, G. Zibordi, J.-F. Berthon, E. Canuti, and T. Kajiyama, “Performance and applicability of bio-optical algorithms in different European seas,” Remote Sens. Environ.124, 402–412 (2012).
[CrossRef]

Other (12)

S. Sathyendranath, “Remote sensing of ocean colour in coastal, and other optically-complex waters,” International Ocean-Colour Coordinating Group, IOCCG Report NUMBER 3 (2000).

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, Results of the Second SeaWiFS Data AnalysisRound Robin, (DARR-00)(NASAGSFC, Greenbelt, MD, USA, 2001), vol. 15 of SeaWiFS Technical Report SERIES, chap. 1, pp. 4–45.

G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing(Springer, 2010), chap. 18, pp. 307–334.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” (2011), vol. 4, pp. 2186–2195. Proceedings of the International Conference on Computational Science, ICCS2011.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A statistical approach to performance tuning of Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012).

G. A. F. Seber and C. J. Wild, Nonlinear regression, Wiley series in probability and statistics (J. Wiley & Sons, 2003).

P. E. Gill, W. Murray, and M. H. Wright, The Levenberg-Marquardt Method(Academic Press, 1981), chap. 4.7.3, pp. 136–137.

Y. Yuan, “A Review of Trust Region Algorithms for Optimization,” in “ICIAM 99,” (Oxford University, 2000), pp. 271–282.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in “Ocean Optics XII,” (1994), no. 2558 in SPIE, pp. 194–201.

J. L. Muller and R. W. Austin, Ocean Optics Protocols SeaWiFS for Validation, Revision 1(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 25 of SeaWiFS Technical Report SERIES, chap. 6, pp. 48–59.

D. A. Siegel, Results of the SeaWiFS Data Analysis Round-Robin, July 1994 (DARR-94)(NASA GSFC, Greenbelt, MD, USA, 1995), vol. 26 of SeaWiFS Technical Report SERIES, chap. 3, pp. 44–48.

T. Kajiyama, D. D’Alimonte, J. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the Geo-info project,” in “Parallel Processing and Applied Mathematics,”, vol. 6068 of Lecture Notes in Computer Science,R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068 of Lecture Notes in Computer Science, pp. 370–379.

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Figures (15)

Fig. 1
Fig. 1

Schematics of MOX simulation domain and photon tracing (the depicted path can be referred equally to a photon starting from the sun or from the sky). The radiometric sensor of a virtual free-fall profiler is represented by the “collecting bins” located at the nodes of the 2D grid. Simulations presented in this study were performed with resolution and collecting bin size of 1 cm, over a domain 50 m deep and 10 m width.

Fig. 2
Fig. 2

MOX simulations illustrating Ed radiometric fields and optical profiles in the case of a single harmonic component at the sea-surface (l = 5 m and h = 0.5 m). Results for sun-zenith angles θs = 30° and θs = 60° are in the top and bottom row panels, respectively.

Fig. 3
Fig. 3

As in Fig 2, but with two harmonic components at the sea-surface (l1 = 5 m, h1 = 0.5 m and l2 = 0.5 m, h2 = 0.05 m).

Fig. 4
Fig. 4

As in Fig 2, but for Lu.

Fig. 5
Fig. 5

As in Fig 4, but with two harmonics at the sea-surface.

Fig. 6
Fig. 6

Frequency distribution of δEd0 and δKEd values derived from MOX simulations in the case of a single wave component at the sea-surface. The comparison between NL and LN results is based on the following data partitioning: 1) one hundred single-casts, each made by single virtual profile; 2) one hundred multi-casts, each formed by five individual profiles randomly sampled from the single-casts pool; and 3) one all-cast, containing all 100 single-casts.

Fig. 7
Fig. 7

As in Fig 6, but for Lu.

Fig. 8
Fig. 8

In-situ optical profiles.

Fig. 9
Fig. 9

Continued from Fig 8.

Fig. 10
Fig. 10

Ed case study based on the r30c0d6a0d50 MOX simulation. The same data are presented on linear and log scale in the left and right column panels, respectively. Regression results for the [0.25, 5], [0.25, 15] and [5, 15] m layer are from the top to the bottom row panels.

Fig. 11
Fig. 11

As in Fig. 10, but considering Lu data from the r60c1d0a0d20 MOX simulation.

Fig. 12
Fig. 12

Average photon traveling direction. Results for θs =30° and θs =60° in Panel 12(a) and 12(b), respectively (c = 1.0 and a = 0.20 m−1 in both cases). Details for spots labeled in the right panel are displayed in Fig. 13.

Fig. 13
Fig. 13

Examples of probability density (adimensional) of photon direction at position selected in Fig. 12. Both x and z are in units of m. The nadir is at θ =180°.

Fig. 14
Fig. 14

Ed0 variability as a function of the number of samples per unit depth. Top panels report results for θs = 30° and 60° on the left and right, respectively. Bottom panels show results for a sea-surface with one and two harmonics on the left and right, respectively.

Fig. 15
Fig. 15

As in Fig 14, but for Lu.

Tables (4)

Tables Icon

Table 1 MOX simulation parameters. Inputs in brackets indicate sets of values applied in different simulations. The coefficients of the Fournier-Forand volume scattering function [29, 30] are: slope of the Junge distribution m =3.5835 and refraction index n =1.34.

Tables Icon

Table 2 MOX case-names with corresponding simulation parameters. Taking the r30c0d6a0d50 case-name as an example: 1) the first letter corresponds to the sea-surface model ( r for a single harmonic component and q for two harmonic components); 2) the following two-digit number indicates the sun elevation (i.e., 30 means θs = 30°); and 3) seawater attenuation and absorption coefficients are at the end (i.e., c0d6 indicates c = 0.6 m−1 and a0d50 indicates a = 0.50 m−1).

Tables Icon

Table 3 LN vs. NL regression results expressed by the mean difference μ (Eq. 8) in the case of simulated data. Standard deviation values (σ, Eq. 9) are within brackets.

Tables Icon

Table 4 LN vs. NL regression results expressed by the mean difference μ (Eq. 8). Analysis based on in situ radiometric profiles.

Equations (17)

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( z ) = 0 e z 0 z K ( z ) d z ,
( z ) = 0 e K z
log ( ( z ) ) = log ( 0 ) K z .
SSE LN ( 0 , K ) = i = 1 N { log [ ( z i ) ] [ log ( 0 ) K z i ] } 2 .
SSE LN α = 0 and SSE LN K = 0 ,
SSE NL ( 0 , K ) = i = 1 N [ ( z i ) 0 e K z i ] 2 ,
δ , j = 100 j LN j NL j NL ,
μ = 1 M j = 1 M δ , j , and
σ = 1 M j = 1 M { δ , j μ } 2 .
MSE = 1 N j i = 1 N j [ ( z i ) 0 e K z i ] 2 ,
p dir ( θ | z ) = p dir ( θ | x , z ) p ( x | z ) d x
δ ^ j X ( N d ) = 100 [ 0 X ( N d ) ] j ^ 0 NL ^ 0 NL ,
μ ^ X ( N d ) = 1 N cast j = 1 N cast δ ^ j X ( N d ) , and
σ ^ X ( N d ) = 1 N cast j = 1 N cast { δ ^ j X ( N d ) μ ^ j X ( N d ) } 2 ,
S = i = 1 N w i ( y i y ^ i ) 2
w i = 1 ε ^ 2 ( z i ) + ε 2 ( z i ) .
y ^ ( 0 ) = y i e γ 1 z i ¯ / e γ 1 z i ¯ ,

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