Abstract

This work investigates the effects of integration time on in-water downward irradiance Ed, upward irradiance Eu and upwelling radiance Lu profile data acquired with free-fall hyperspectral systems. Analyzed quantities are the subsurface value and the diffuse attenuation coefficient derived by applying linear and non-linear regression schemes. Case studies include oligotrophic waters (Case-1), as well as waters dominated by Colored Dissolved Organic Matter (CDOM) and Non-Algal Particles (NAP). Assuming a 24-bit digitization, measurements resulting from the accumulation of photons over integration times varying between 8 and 2048ms are evaluated at depths corresponding to: 1) the beginning of each integration interval (Fst); 2) the end of each integration interval (Lst); 3) the averages of Fst and Lst values (Avg); and finally 4) the values weighted accounting for the diffuse attenuation coefficient of water (Wgt). Statistical figures show that the effects of integration time can bias results well above 5% as a function of the depth definition. Results indicate the validity of the Wgt depth definition and the fair applicability of the Avg one. Instead, both the Fst and Lst depths should not be adopted since they may introduce pronounced biases in Eu and Lu regression products for highly absorbing waters. Finally, the study reconfirms the relevance of combining multiple radiometric casts into a single profile to increase precision of regression products.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Regression of in-water radiometric profile data

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Monte Carlo code for high spatial resolution ocean color simulations

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Appl. Opt. 49(26) 4936-4950 (2010)

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2017 (1)

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A high-performance computing framework for Monte Carlo ocean color simulations,” Concurrency Computat.: Pract. Exper. 29, e3860 (2017).
[Crossref]

2016 (2)

2015 (1)

2014 (2)

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. 11, 19–23 (2014).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[Crossref]

2013 (3)

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss. 9, 521–533 (2013).
[Crossref]

M. Hieronymi, “Monte Carlo code for the study of the dynamic light field at the wavy atmosphere-ocean interface,” J. Eur. Opt. Soc. Rapid. Publ. 8, 13039 (2013).
[Crossref]

D. D’Alimonte, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27707–27733 (2013).
[Crossref]

2012 (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]

2011 (1)

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]

2010 (3)

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. Optics 49, 1041–1053 (2010).
[Crossref]

M. Hieronymi and A. Macke, “Spatio-temporal underwater light field fluctuations in the open ocean,” J. Eur. Opt. Soc. Rapid. Publ. 5, 10019s (2010).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 4936–4950 (2010).
[Crossref]

2009 (1)

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[Crossref]

2008 (2)

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

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.: Methods 5, 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. Optics 46, 5068–5082 (2007).
[Crossref]

2005 (2)

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]

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]

2004 (1)

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

2002 (1)

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

2001 (1)

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics 40, 1442–1449 (2001).
[Crossref]

1999 (1)

G. R. Fournier and M. Jonasz, “Computer-based Underwater Imaging Analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

1997 (1)

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[Crossref]

1994 (1)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 4483, 194–201 (1994).
[Crossref]

1986 (1)

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

1984 (1)

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic biooptical profiling system,” Appl. Optics 23, 2791–2797 (1984).
[Crossref]

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1957 (1)

Antoine, D.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

Austin, R. W.

J. L. Mueller and R. W. Austin, “Ocean Optics Protocols SeaWiFS for Validation, Revision 1,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 1995) vol. 25, 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. Optics 46, 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]

Bardey, P.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

Barnard, A.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics 40, 1442–1449 (2001).
[Crossref]

Barnes, R. A.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

Bécu, G.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

Berthon, J.-F.

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[Crossref]

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss. 9, 521–533 (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]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. 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 Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, pp. 4–45.

Blumthaler, M.

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).

Booth, C. R.

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic biooptical profiling system,” Appl. Optics 23, 2791–2797 (1984).
[Crossref]

Boss, E.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics 40, 1442–1449 (2001).
[Crossref]

Brown, W.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

Bulgarelli, B.

B. Bulgarelli and D. D’Alimonte, “Simulation of in situ visible radiometric measurements,” in Optical Radiometry for Oceans Climate Measurements, G. Zibordi, C. Donlon, and A. Parr, eds. (Elsevier, 2014), Chap. 3.

Buras, R.

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[Crossref]

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. 9, 521–533 (2013).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover Publications, 1960).

Chapron, B.

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[Crossref]

Clark, D. K.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

Cunha, J. C.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A high-performance computing framework for Monte Carlo ocean color simulations,” Concurrency Computat.: Pract. Exper. 29, e3860 (2017).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 4936–4950 (2010).
[Crossref]

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” in Procedia Computer Science, M. Sato, S. Matsuoka, P. M. Sloot, G. D. van Albada, and J. Dongarra, eds. (Elsevier, 2011), vol. 4, pp. 2186–2195.
[Crossref]

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

D’Alimonte, D.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A high-performance computing framework for Monte Carlo ocean color simulations,” Concurrency Computat.: Pract. Exper. 29, e3860 (2017).
[Crossref]

D. D’Alimonte and T. Kajiyama, “Effects of light polarization and waves slope statistics on the sea-surface reflectance,” Opt. Express 24, 7922–7942 (2016).
[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. 11, 19–23 (2014).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[Crossref]

D. D’Alimonte, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27707–27733 (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]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 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. Atmos. Ocean. Tech. 21, 1059–1073 (2004).
[Crossref]

D. D’Alimonte and G. Zibordi, “The JRC Data Processing System,” in “SeaWiFS Technical Report SERIES”(NASA GSFC, 2001), vol. 15, pp. 52–56.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, “Results of the Second SeaWiFS Data Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, pp. 4–45.

B. Bulgarelli and D. D’Alimonte, “Simulation of in situ visible radiometric measurements,” in Optical Radiometry for Oceans Climate Measurements, G. Zibordi, C. Donlon, and A. Parr, eds. (Elsevier, 2014), Chap. 3.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” in Procedia Computer Science, M. Sato, S. Matsuoka, P. M. Sloot, G. D. van Albada, and J. Dongarra, eds. (Elsevier, 2011), vol. 4, pp. 2186–2195.
[Crossref]

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

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. Optics 49, 1041–1053 (2010).
[Crossref]

DeGroot, M. H.

M. H. DeGroot and M. J. Schervish, Probability and Statistics (Addison Wesley, 2012).

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D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

Elfouhaily, T.

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[Crossref]

Emde, C.

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[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]

Feinholz, M.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 4483, 194–201 (1994).
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Fournier, G. R.

G. R. Fournier and M. Jonasz, “Computer-based Underwater Imaging Analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 4483, 194–201 (1994).
[Crossref]

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. Optics 46, 5068–5082 (2007).
[Crossref]

Guevel, P.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

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J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
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Hieronymi, M.

M. Hieronymi, “Polarized reflectance and transmittance distribution functions of the ocean surface,” Opt. Express 24, A1045–A1068 (2016).
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M. Hieronymi, “Monte Carlo code for the study of the dynamic light field at the wavy atmosphere-ocean interface,” J. Eur. Opt. Soc. Rapid. Publ. 8, 13039 (2013).
[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]

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 and A. Macke, “Spatio-temporal underwater light field fluctuations in the open ocean,” J. Eur. Opt. Soc. Rapid. Publ. 5, 10019s (2010).
[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 Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, 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).
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C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).

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N. G. Jerlov, Marine Optics (Elsevier, 1976).

Johnson, C.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

Jonasz, M.

G. R. Fournier and M. Jonasz, “Computer-based Underwater Imaging Analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

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.: Methods 5, 317–327 (2007).
[Crossref]

Kajiyama, T.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A high-performance computing framework for Monte Carlo ocean color simulations,” Concurrency Computat.: Pract. Exper. 29, e3860 (2017).
[Crossref]

D. D’Alimonte and T. Kajiyama, “Effects of light polarization and waves slope statistics on the sea-surface reflectance,” Opt. Express 24, 7922–7942 (2016).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[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. 11, 19–23 (2014).
[Crossref]

D. D’Alimonte, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27707–27733 (2013).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 4936–4950 (2010).
[Crossref]

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

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Performance prediction of ocean color Monte Carlo simulations using multi-layer perceptron neural networks,” in Procedia Computer Science, M. Sato, S. Matsuoka, P. M. Sloot, G. D. van Albada, and J. Dongarra, eds. (Elsevier, 2011), vol. 4, pp. 2186–2195.
[Crossref]

Katsaros, K.

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[Crossref]

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. Optics 49, 1041–1053 (2010).
[Crossref]

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]

Louis, F.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[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]

M. Hieronymi and A. Macke, “Spatio-temporal underwater light field fluctuations in the open ocean,” J. Eur. Opt. Soc. Rapid. Publ. 5, 10019s (2010).
[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 Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, pp. 4–45.

Mayer, B.

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[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. Optics 46, 5068–5082 (2007).
[Crossref]

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 Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, 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. 9, 521–533 (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]

Mobley, C. D.

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.: Methods 5, 317–327 (2007).
[Crossref]

Mueller, J. L.

J. L. Mueller and R. W. Austin, “Ocean Optics Protocols SeaWiFS for Validation, Revision 1,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 1995) vol. 25, pp. 48–59.

Penndorf, R.

Schattschneider, D.

D. Schattschneider, “Proof without words: The arithmetic mean-geometric mean inequality,” Math. Mag. 59, 11 (1986).
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Schervish, M. J.

M. H. DeGroot and M. J. Schervish, Probability and Statistics (Addison Wesley, 2012).

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, A. J.

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

Seber, G. A. F.

G. A. F. Seber and C. J. Wild, Nonlinear Regression (J. Wiley & Sons, 2003).

Shybanov, E. B.

Siegel, D. A.

D. A. Siegel, “Results of the SeaWiFS Data Analysis Round-Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 1995), vol. 26, 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 Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, pp. 4–45.

Smith, R. C.

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic biooptical profiling system,” Appl. Optics 23, 2791–2797 (1984).
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V. V. Sobolev, Light Scattering in Planetary Atmospheres(Pergamon, 1975).

Star, J. L.

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic biooptical profiling system,” Appl. Optics 23, 2791–2797 (1984).
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Steven, Y. S. K.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[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. Optics 49, 1041–1053 (2010).
[Crossref]

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[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]

Van De Hulst, H. C.

H. C. Van De Hulst, Light Scattering by Small Particles (Dover Publications, 1957).

Vandemark, D.

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[Crossref]

Voss, K.

G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing (Springer, 2010), Chap. 18.

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. Optics 46, 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 (J. Wiley & Sons, 2003).

Yarbrough, M.

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

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. Optics 49, 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]

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Y. Yuan, “A Review of Trust Region Algorithms for Optimization,” in “Proceedings of the Fourth International Congress on Industrial and Applied Mathematics”, J. M. Ball and J. C. R. Hunt, eds. (Oxford University Press, 2000), pp. 271–282.

Zaneveld, J. R. V.

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics 40, 1442–1449 (2001).
[Crossref]

Zibordi, G.

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[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. 11, 19–23 (2014).
[Crossref]

G. Zibordi, F. Mélin, J.-F. Berthon, and E. Canuti, “Assessment of MERIS ocean color data products for European seas,” Ocean Sci. Discuss. 9, 521–533 (2013).
[Crossref]

D. D’Alimonte, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27707–27733 (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]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 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. Atmos. Ocean. Tech. 21, 1059–1073 (2004).
[Crossref]

G. Zibordi and K. Voss, Field Radiometry and Ocean Colour Remote Sensing (Springer, 2010), Chap. 18.

D. D’Alimonte and G. Zibordi, “The JRC Data Processing System,” in “SeaWiFS Technical Report SERIES”(NASA GSFC, 2001), vol. 15, pp. 52–56.

S. Hooker, G. Zibordi, J.-F. Berthon, D. D’Alimonte, S. Maritorena, S. Mclean, and J. Sildam, “Results of the Second SeaWiFS Data Analysis Round Robin,” in “SeaWiFS Technical Report SERIES” (NASA GSFC, 2001), vol. 15, pp. 4–45.

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

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. Opt. (1)

Appl. Optics (5)

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. Optics 46, 5068–5082 (2007).
[Crossref]

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic biooptical profiling system,” Appl. Optics 23, 2791–2797 (1984).
[Crossref]

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J. C. Cunha, “Monte Carlo code for high spatial resolution ocean color simulations,” Appl. Optics 49, 4936–4950 (2010).
[Crossref]

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. Optics 49, 1041–1053 (2010).
[Crossref]

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Optics 40, 1442–1449 (2001).
[Crossref]

Atmos. Chem. Phys. Discuss. (1)

C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aerosols on polarized sky radiance: model development, validation, and applications,” Atmos. Chem. Phys. Discuss. 9, 17753–17791 (2009).
[Crossref]

Concurrency Computat.: Pract. Exper. (1)

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “A high-performance computing framework for Monte Carlo ocean color simulations,” Concurrency Computat.: Pract. Exper. 29, e3860 (2017).
[Crossref]

IEEE Geosci. Remote Sens. Lett. (1)

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. 11, 19–23 (2014).
[Crossref]

J. Atmos. 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. Atmos. Ocean. Tech. 21, 1059–1073 (2004).
[Crossref]

J. Atmos. Oceanic Tech. (1)

D. Antoine, P. Guevel, J.-F. Desté, G. Bécu, F. Louis, A. J. Scott, and P. Bardey, “The “BOUSSOLE” buoy—a new transparent-to-swell taut mooring dedicated to marine optics: Design, tests, and performance at sea,” J. Atmos. Oceanic Tech. 25, 968–989 (2008).
[Crossref]

J. Eur. Opt. Soc. Rapid. Publ. (2)

M. Hieronymi, “Monte Carlo code for the study of the dynamic light field at the wavy atmosphere-ocean interface,” J. Eur. Opt. Soc. Rapid. Publ. 8, 13039 (2013).
[Crossref]

M. Hieronymi and A. Macke, “Spatio-temporal underwater light field fluctuations in the open ocean,” J. Eur. Opt. Soc. Rapid. Publ. 5, 10019s (2010).
[Crossref]

J. Geophys. Res. Oc. (1)

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 10215781–15796 (1997).
[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. Opt. Soc. Am. (1)

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.: Methods 5, 317–327 (2007).
[Crossref]

Math. Mag. (1)

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

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. 9, 521–533 (2013).
[Crossref]

Opt. Express (3)

Proc. SPIE (3)

D. K. Clark, M. Feinholz, M. Yarbrough, C. Johnson, Y. S. K. Steven, W. Brown, and R. A. Barnes, “Overview of the radiometric calibration of MOBY,” Proc. SPIE 4483, 64–76 (2002).
[Crossref]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 4483, 194–201 (1994).
[Crossref]

G. R. Fournier and M. Jonasz, “Computer-based Underwater Imaging Analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Remote Sens. Environ. (3)

D. D’Alimonte, G. Zibordi, T. Kajiyama, and J.-F. Berthon, “Comparison between MERIS and regional high-level products in European seas,” Remote Sens. Environ. 140, 378–395 (2014).
[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]

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Figures (17)

Fig. 1
Fig. 1 Panel (a) shows an example of the distribution of the diffuse sky-radiance (i.e., without the solar disk) for θsun = 30° and in units of W m−2 nm−1. The probability density function (PDF) and the cumulative distribution function (CDF) of incoming photon direction θ in the solar plane are presented in Panels (b) and (c), respectively.
Fig. 2
Fig. 2 Schematics of photon tracing. The radiometric sensor of the virtual profiler is represented by the “ray collecting bins” located at the nodes of the simulation grid.
Fig. 3
Fig. 3 Example of an Ed radiometric field simulated for highly absorbing marine waters (CDOM-dominated), vwnd =4ms−1 and θsun =30°.
Fig. 4
Fig. 4 Example of diagonal virtual trajectory below a fixed sea surface applied to compute the optical profile (see text for details).
Fig. 5
Fig. 5 (a) Example of iso-depth lines accounting for the pressure gauge correction due to surface waves generated with vwnd = 8ms−1. (b) Standard deviation of the difference between subsequent iso-depth lines.
Fig. 6
Fig. 6 Schematic of the process determining the integration times applied for measuring Ed, Eu and Lu values. The radiometric boundaries are specified in Table 6.
Fig. 7
Fig. 7 Schematics of the weighted (Wgt) measurement depth determined as a function of the diffuse attenuation coefficient.
Fig. 8
Fig. 8 Number of radiometric measurements per unit depth (i.e., density of data) for overcast illumination and still sea surface. The deployment speed of the optical system is vprf = 0.2ms−1. The Case-1, CDOM-dominated and NAP-dominated water cases are ordered from top to bottom. Results for Ed, Eu and Lu are reported from the left to the right column panels. The integration time as a function of depth is displayed in each panel inset.
Fig. 9
Fig. 9 Statistical figures from the comparison of regression products determined with Eq. (15) for a still sea and overcast sky.
Fig. 10
Fig. 10 As in Fig. 8, but considering a clear sky (θsun = 30°) and a wavy sea-surface (vwnd =4ms−1).
Fig. 11
Fig. 11 As in Fig. 9, but in the presence of a clear sky (θsun =30°) and a wind-driven sea surface (vwnd =4ms−1).
Fig. 12
Fig. 12 As in Fig. 11, but for a signal 10 times lower than that applied for the determination of the integration time.
Fig. 13
Fig. 13 Number of simulated data per unit depth obtained during clear sky with latency time of 250ms and 1 dark-signal recording after every 5 successive measurements. Ed and Lu results are presented in the top and bottom row panels, respectively. Experimental and simulated values (referring to vprf =0.2ms−1, vwnd =4ms−1, θsun =30°, a=0.15m−1 and b=0.05m−1) are displayed in the left and right column, respectively.
Fig. 14
Fig. 14 As in Fig. 11, but considering 16-bit ADC and accounting for both the latency time of 250ms and dark-signal recording.
Fig. 15
Fig. 15 Virtual optical profiles for Case-1, NAP and CDOM-dominated waters, considering 16-bit ADC, latency time of 250ms and dark-signal recording, and assuming a clear sky and a wind-driven sea surface. The deployment speed is vprf =0.2ms−1. Ed, Eu and Lu are in the row panels from top to bottom. Full resolution points are denoted by the + symbol in shade of gray. The integrated values are labeled as Δ, ∇ and ○ for the Fst, Lst, and Wgt depths, respectively.
Fig. 16
Fig. 16 As in Fig. 15, but adopting the multi-cast scheme with 10 independent casts combined into a single profile.
Fig. 17
Fig. 17 As in Fig. 14, but adopting the multi-cast scheme with 10 optical profiles.

Tables (12)

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Table 1 Parameters for Simulating the Sky-radiance Distribution at λ =490nm.

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Table 2 Parameters Determining the Clear Sky and Overcast Illumination Conditions.

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Table 3 Examples of Sea-surface Statistical Figures.

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Table 4 Settings of In-water Radiometric Simulations.

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Table 5 Inherent Optical Properties (Absorption a, Attenuation c and Single Scattering Albedo ω) as well as Properties of the Virtual Bottom (Depth zb and Reflectance Value Rb) Adopted to Perform Monte Carlo Simulations for Different Marine Optical Cases. The Coefficients of the Fournier-Forand Volume Scattering Function [34,35] are: Slope of the Junge Distribution m =3.5835 and Refraction Index n =1.34.

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Table 6 Values of the Integration Time for Ed and Lu [see also Fig. 6]. The Intervals for Eu are the Same as for Ed. These Intervals were Determined to Mimic those Actually Implemented in HyperOCR Radiometers Manufactured by Satlantic (Halifax, NS, Canada).

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Table 7 List of Symbols of the Data Products Analyzed in this Study.

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Table 8 Values of Differences δ (Indicating both δ 0 or δ K ) Determined with Eq. (15) and Values of the Related Standard Deviations σ (i.e., σ or σK), from Fig. 11 for the Avg and Wgt Depths. Values are Provided for the Different Water Types, Deployment Speeds and Regression Methods (i.e., NL and LN). The Number of Measurements per Unit Depth (i.e., Meas. Density) Refers to the Extrapolation Interval.

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Table 9 Values of the Signal-to-noise-ratio (SNR) Characterizing the Sub-surface Radiometric Quantities Simulated for Different Water Types and for 16- and 24-bit Systems.

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Table 10 Ed Regression Determined Products Accounting for 16-bit ADC, Latency Time of 250ms and Dark-signal Recording. Both the Single-cast and the Multicast Profiles (the Latter Built with 5 or alternatively 10 casts) are Considered. Statistical Figures are Provided for the Sole Wgt Depths, both the NL and the LN Regression Methods, the Various Water Types and Deployment Speeds of 0.2, 0.6 and 1.0 ms−1. Symbols µ, CV, δ and σ Refer to the Mean of Regression Products, their Coefficient of Variation, the Percent Differences with Respect to Reference Values Determined with Eq. 15 and the Related Standard Deviations, respectively. It is further Mentioned that Results Refer to a Pool of 10 Samples for each Case. The Mean Density of Measurements is also Reported to Identify cases Leading to a Better Determination of Regression Products.

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Table 11 As in Fig. 12, but for Eu Data Regression Products.

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Table 12 As in Fig. 10, but for Lu Data Regression Products.

Equations (15)

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˜ ( z i * ) = 1 Δ z z i z i + Δ z ( z ) d z ,
l = log ( u ) / c atm
w new = w old ω atm ,
z ( s ) = 1 N u u = 1 N u z ^ ( u ) e i ( s u / N u ) ,
v wav = g l wav 2 π ,
θ prf = arctg v wav v prf
z g ( x ) = z + e z k wav z s ( x ) ,
˜ z i z i + Δ z = 1 Δ z z i z i + Δ z e K z d z = e ( K z i + Δ z ) e K z i K Δ z ,
e K z i * = e K ( z i + Δ z ) e K z i K Δ z ,
z i * = 1 K ln ( ˜ z i z i + Δ 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 NL ( 0 , K ) = i = 1 N [ ˜ ( z i * ) 0 e K z i * ] 2
{ [ δ J ] FST LN } S = 100 1 N n = 1 N { [ J ] FST LN } n S { [ J ] FULL NL } n S { [ J ] FULL NL } n S ,

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