Abstract

Above-water radiometry depends on estimates of the reflectance factor ρ of the sea surface to compute the in situ water-leaving radiance. The Monte Carlo code for ocean color simulations MOX is used in this study to analyze the effect of different environmental components on ρ values. A first aspect is examining the reflectance factor without and by accounting for the sky-radiance polarization. The influence of the sea-surface statistics at discrete grid points is then considered by presenting a new scheme to define the variance of the waves slope. Results at different sun elevations and sensor orientations indicate that the light polarization effect on ρ simulations reduces from ∼17 to ∼10% when the wind speed increases from 0 to 14m s−1. An opposite tendency characterizes the modeling of the sea-surface slope variance, with ρ differences up to ∼12% at a wind speed of 10m s−1. The joint effect of polarization and the the sea-surface statistics displays a less systematic dependence on the wind speed, with differences in the range ∼13 to ∼18%. The ρ changes due to the light polarization and the variance of the waves slope become more relevant at sky-viewing geometries respectively lower and higher than 40° with respect to the zenith. An overall compensation of positive and negative offsets due to light polarization is finally documented when considering different sun elevations. These results address additional investigations which, by combining the modeling and experimental components of marine optics, better evaluate specific measurement protocols for collecting above-water radiometric data in the field.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (3)

2014 (1)

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 (4)

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, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27 (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, 11 (2013).
[Crossref]

J. Piskozub and W. Freda, “Signal of single scattering albedo in water leaving polarization,” J. Eur. Opt. Soc. Rapid Publ. 8, 13056 (2013).
[Crossref]

2012 (3)

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[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]

2011 (2)

Z. Xu, D. K. P. Yue, L. Shen, and K. J. Voss, “Patterns and statistics of in-water polarization under conditions of linear and nonlinear ocean surface waves,” J. Geophys. Res. Oc. 116, C00H12 (2011).

S. Kay, J. Hedley, S. Lavender, and A. Nimmo-Smith, “Light transfer at the ocean surface modeled using high resolution sea surface realizations,” Opt. Express 19, 6493–6504 (2011).
[Crossref] [PubMed]

2010 (2)

C. Cornet, L. C-Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111, 174–186 (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 (2)

G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
[Crossref]

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]

2007 (1)

R. W. Goosmann and C. M. Gaskell, “Modeling optical and UV polarization of AGNs. I. Imprints of individual scattering regions,” Astron. Astrophys. 465, 129–145 (2007).
[Crossref]

2005 (4)

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express 13, 10392–10405 (2005).
[Crossref] [PubMed]

B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations—description and examples of use,” Atmos. Chem. Phys. 5, 1855–1877 (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]

J. Ramella-Roman, S. Prahl, and S. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420–4438 (2005).
[Crossref] [PubMed]

2003 (1)

B. G. Henderson, J. Theiler, and P. Villeneuve, “The polarized emissivity of a wind-roughened sea surface: A Monte Carlo model,” Remote Sens. Environ. 88, 453–467 (2003).
[Crossref]

1999 (2)

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
[Crossref]

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Optics 38, 7442–7455 (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. 102, 15781 (1997).

1996 (1)

S. Bianchi, A. Ferrara, and C. Giovanardi, “Monte Carlo simulations of dusty spiral galaxies: Extinction and polarization properties,” Astrophys. J. 465, 127–144 (1996).
[Crossref]

1989 (2)

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: Effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[Crossref]

G. Zibordi and K. J. Voss, “Geometrical and spectral distribution of sky radiance—comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[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)

1954 (1)

1951 (1)

J. von Neumann, “Various techniques used in connection with random digits. Monte Carlo methods,” Nat. Bureau Standards 12, 36–38 (1951).

Adams, C. N.

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: Effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[Crossref]

Ahmed, S.

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
[Crossref]

Arnone, R.

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
[Crossref]

Bailey, S. W.

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]

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]

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, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
[Crossref]

Bianchi, S.

S. Bianchi, A. Ferrara, and C. Giovanardi, “Monte Carlo simulations of dusty spiral galaxies: Extinction and polarization properties,” Astrophys. J. 465, 127–144 (1996).
[Crossref]

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).

Bulgarelli, B.

B. Bulgarelli and D. D’Alimonte, Optical radiometry for oceans climate measurements (Elsevier, 2014), chap. Simulation of in situ visible radiometric measurements, p. 43, Experimental Methods in Physical Sciences. ISBN-10::0124170110.

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]

Cairns, B.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

Cameron, B. D.

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
[Crossref]

Canuti, E.

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]

Cartwright, D. E.

M. S. Longuet-Higgins, D. E. Cartwright, and N. D. Smith, “Observations of the directional spectrum of sea waves using the motions of a floating buoy,” in “Ocean Wave Spectra, proceedings of a conference, Easton, Maryland,” National Academy of Sciences (Prentice-Hall, 1963), pp. 111–136.

Chami, M.

Chandrasekhar, S.

S. Chandrasekhar, Radiative transfer (Dover Publications, Inc., 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. 102, 15781 (1997).

Chowdhary, J.

M. Chami, B. Lafrance, B. Fougnie, J. Chowdhary, T. Harmel, and F. Waquet, “OSOAA: a vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean,” Opt. Express 23, 27829–27852 (2015).
[Crossref] [PubMed]

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

C-Labonnote, L.

C. Cornet, L. C-Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111, 174–186 (2010).
[Crossref]

Cornet, C.

C. Cornet, L. C-Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111, 174–186 (2010).
[Crossref]

Coté, G. L.

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
[Crossref]

Cox, C.

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, Lecture notes in computer science,” vol. 6068, R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068, pp. 370–379.
[Crossref]

Cunha, J. C.

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,” (Singapore, 2011), vol. 4, pp. 2186–2195.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Statistical performance tuning of parallel Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012), pp. 761–766.

D’Alimonte, D.

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, “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, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27 (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]

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).
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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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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,” (Singapore, 2011), vol. 4, pp. 2186–2195.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Statistical performance tuning of parallel Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012), pp. 761–766.

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, Lecture notes in computer science,” vol. 6068, R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068, pp. 370–379.
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T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 102, 15781 (1997).

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).
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Fabbri, B. E.

G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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J. Piskozub and W. Freda, “Signal of single scattering albedo in water leaving polarization,” J. Eur. Opt. Soc. Rapid Publ. 8, 13056 (2013).
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T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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T. Huynh, G. Hou, J. Wang, M. Hou, and M. Kotinis, “A hybrid virtual reality simulation system for wave energy conversion,” International Journal of Computational Engineering Research 5, 50–60 (2015).

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Jacques, S. L.

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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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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, “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, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27 (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]

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. 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,” vol. 6068, 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,” (Singapore, 2011), vol. 4, pp. 2186–2195.

T. Kajiyama, D. D’Alimonte, and J. C. Cunha, “Statistical performance tuning of parallel Monte Carlo ocean color simulations,” in “Parallel and Distributed Computing, Applications and Technologies 2012,” (Beijing, China, 2012), pp. 761–766.

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T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. Oc. 102, 15781 (1997).

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M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
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Kotinis, M.

T. Huynh, G. Hou, J. Wang, M. Hou, and M. Kotinis, “A hybrid virtual reality simulation system for wave energy conversion,” International Journal of Computational Engineering Research 5, 50–60 (2015).

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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).
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B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations—description and examples of use,” Atmos. Chem. Phys. 5, 1855–1877 (2005).
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M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
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J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
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M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
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Rastegar, S.

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
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J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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Seppälä, J.

G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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Shybanov, E. B.

D. D’Alimonte, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27 (2013).
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G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
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M. S. Longuet-Higgins, D. E. Cartwright, and N. D. Smith, “Observations of the directional spectrum of sea waves using the motions of a floating buoy,” in “Ocean Wave Spectra, proceedings of a conference, Easton, Maryland,” National Academy of Sciences (Prentice-Hall, 1963), pp. 111–136.

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B. G. Henderson, J. Theiler, and P. Villeneuve, “The polarized emissivity of a wind-roughened sea surface: A Monte Carlo model,” Remote Sens. Environ. 88, 453–467 (2003).
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T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
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J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: Analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
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G. Zibordi and K. J. Voss, “Geometrical and spectral distribution of sky radiance—comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
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T. Huynh, G. Hou, J. Wang, M. Hou, and M. Kotinis, “A hybrid virtual reality simulation system for wave energy conversion,” International Journal of Computational Engineering Research 5, 50–60 (2015).

Wang, L. V.

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
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[Crossref]

Weidemann, A.

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
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Yue, D. K. P.

Z. Xu, D. K. P. Yue, L. Shen, and K. J. Voss, “Patterns and statistics of in-water polarization under conditions of linear and nonlinear ocean surface waves,” J. Geophys. Res. Oc. 116, C00H12 (2011).

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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, “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, E. B. Shybanov, G. Zibordi, and T. Kajiyama, “Regression of in-water radiometric profile data,” Opt. Express 21, 27 (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]

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, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Mélin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A network for the validation of ccean color primary radiometric products,” J. Atmos. Oceanic Tech. 26, 1634–1651 (2009).
[Crossref]

G. Zibordi and K. J. Voss, “Geometrical and spectral distribution of sky radiance—comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[Crossref]

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, Lecture notes in computer science,” vol. 6068, R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Wasniewski, eds. (Springer, 2010), vol. 6068, pp. 370–379.
[Crossref]

Appl. Opt. (1)

Appl. Optics (4)

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]

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Optics 38, 7442–7455 (1999).
[Crossref]

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Optics 51, 8324–8340 (2012).
[Crossref]

M. J. Raković, G. W. Kattawar, M. Mehrűbeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: Theory and experiment,” Appl. Optics 38, 3399–3408 (1999).
[Crossref]

Astron. Astrophys. (1)

R. W. Goosmann and C. M. Gaskell, “Modeling optical and UV polarization of AGNs. I. Imprints of individual scattering regions,” Astron. Astrophys. 465, 129–145 (2007).
[Crossref]

Astrophys. J. (1)

S. Bianchi, A. Ferrara, and C. Giovanardi, “Monte Carlo simulations of dusty spiral galaxies: Extinction and polarization properties,” Astrophys. J. 465, 127–144 (1996).
[Crossref]

Atmos. Chem. Phys. (1)

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IEEE Geosci. Remote Sens. Lett. (1)

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Figures (13)

Fig. 1
Fig. 1 Example of above-water radiometric measurements. The sensors orientation is that adopted for AERONET-OC [2].
Fig. 2
Fig. 2 The Stokes vector is at first referenced to the initial meridian plane specified by the base Vι = {ι, ι}. Before applying the Muller transformation, light polarization needs to be expressed in the basis Vκ = {κ, κ}, where the κ vector is within the change-of-direction plane. The new polarization state has afterwards to be formulated in the basis Vχ = {χ, χ}, where χ is in the final meridian plane. Each change of base is a rotation with a different Euler angle. The figure refers to the reflection of light at a facet of the sea surface (θi indicate both the incident and the reflection angle with respect to the normal n). The schematic for the photon scattering is analogous.
Fig. 3
Fig. 3 Sky-radiance simulations in the panels from left to right refer to θs = 0°, 30° and 60°, respectively. The I, Q, U Stokes parameters (in units of W m−2 nm−1 sr−1) and the polarization degree P (in percent) are presented from the top to the bottom row. Results are scaled so that the total irradiance is 1 Wm−2 nm−1 for θs =0°.
Fig. 4
Fig. 4 Schematic of photon tracing and an example of sea-surface generated at the grid points of the simulation domain (vw =10m s−1) in panel (a) and (b), respectively.
Fig. 5
Fig. 5 Elevation and slope variance of sea surfaces generated for wind speed values in the range 2–14 m s−1 are in the left and right panel, respectively. The legend acronyms are defined as follows: Trg denotes target quantities; Hws and Gps refers to the high-wavenumbers statistics and to the grid-points statistics, respectively; Raw indicates the case where no correction is applied.
Fig. 6
Fig. 6 Simulations of ρ values for vw in the range 0–14m s−1. Panels from left to right refer to θs = 0°, 30° and 60°, respectively. Panels from top to bottom correspond instead to the HwsUnp, HwsPol, GpsUnp and GpsPol case (Table 3).
Fig. 7
Fig. 7 Tendency of ρ values when increasing the wind speed (based on Fig. 6).
Fig. 8
Fig. 8 Scatter plots for different ρ simulation settings. The benchmark case is HwsUnp. The ρ variations induced by the light polarization (HwsPol), the use of the novel iterative algorithm for the sea-surface generation (GpsUnp), and their combined effect (GpsPol) are highlighted in panel (a), (b) and (c), respectively. Colors identify results at different wind speed values as in Fig. 6.
Fig. 9
Fig. 9 Summary of ρ variations when considering the θv = 40° viewing geometry and averaging results for θs = 0°, 30° and 60°. Effects due to the light polarization, the sea-surface statistics, and their combination are presented in panel(a), (b) and (c), respectively. Colors identify results at different wind speed values as in Fig. 6.
Fig. 10
Fig. 10 Comparisons of ρ simulations for wind speed values between 2 and 6 m s−1. Results for the HwsUnp&GpsUnp, HwsUnp&HwsPol, and HwsUnp&GpsPol case are addressed in the panels from the top to the bottom row. Column panels from left to right are addressed to θs = 0°, 30° and 60°, respectively.
Fig. 11
Fig. 11 Summary of ρ variations by averaging results for vw =2, 4 and 6 ms−1. The effect of light polarization, sea-surface statistics and their composition are considered in panel (a), (b) and (c), respectively.
Fig. 12
Fig. 12 Execution times for simulating the reflectance factor as a function of θs and vw. Results refer to the tracing of 109 photons for production runs of the HwsUnp case using 24 CPU cores on the Navigator supercomputer, University of Coimbra, Portugal.
Fig. 13
Fig. 13 Example of ρ simulations for θs = 0°, vw = 0 m s−1 and θv = 0° by including the direct light contribution to Li. The symbol and color scheme for results at different wind speed vw values are the same as in Fig. 6. See text for details.

Tables (3)

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Table 1 MOX parameters for simulating the sky-radiance distribution at λ =490nm.

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Table 2 MOX parameters for simulating the reflectance factor ρ.

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Table 3 Test cases to evaluate the variability of ρ simulation results.

Equations (28)

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= E ι + E ι
E ( l , t ) = A exp [ i ( ε + 2 π λ l ) ]
E ( l , t ) = A exp [ i ( ε + 2 π λ l ) ] ,
S ι = [ A 2 + A 2 A 2 A 2 2 A A cos δ 2 A A sin δ ] = [ I Q U V ] ,
R ( α ) = [ 1 0 0 1 0 cos ( 2 α ) sin ( 2 α ) 0 0 sin ( 2 α ) cos ( 2 α ) 0 0 0 0 1 ] .
S χ = R κ ˜ , χ ( ψ * ) M κ ( θ * ) R ι , κ ( ϕ * ) S ι .
l = log ( u ) / c atm
w new = w old ω atm
r tot = E sky E tot
r dir = E sky E sun ,
r dir = r tot 1 r tot .
M RLG ( θ * ) = Δ [ 3 4 ( 1 + cos 2 ( θ * ) ) 3 4 sin 2 ( θ * ) 0 0 3 4 sin 2 ( θ * ) 3 4 ( 1 + cos 2 ( θ * ) ) 0 0 0 0 3 2 cos ( θ * ) 0 0 0 0 Δ 3 2 cos ( θ * ) ] + ( 1 Δ ) [ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] ,
Δ = 1 δ 1 + δ / 2 and Δ = 1 2 δ 1 δ
M MIE ( θ * ) = [ 1 2 ( | 𝒮 1 | 2 + | 𝒮 2 | 2 ) 1 2 ( | 𝒮 1 | 2 | 𝒮 2 | 2 ) 0 0 1 2 ( | 𝒮 1 | 2 | 𝒮 2 | 2 ) 1 2 ( | 𝒮 1 | 2 + | 𝒮 2 | 2 ) 0 0 0 0 1 2 ( 𝒮 2 * 𝒮 1 + 𝒮 2 𝒮 1 * ) i 2 ( 𝒮 1 𝒮 2 * 𝒮 2 𝒮 1 * ) 0 0 i 2 ( 𝒮 1 𝒮 2 * 𝒮 2 𝒮 1 * ) 1 2 ( 𝒮 2 * 𝒮 1 + 𝒮 2 𝒮 1 * ) ] ,
ρ sky = α α + 1
α = r dir W sun W sky ,
W sun = cos ( θ s )
W sky = 0 2 π d ϕ 0 π / 2 L sky ( θ , ϕ ) sin ( θ ) cos ( θ ) d θ .
z ( r , s ) = 1 N u N v u = 1 N u v = 1 N v z ^ ( u , v ) e i ( r u / N u + s v / N v ) ,
M RFL ( θ + , θ ) = 1 2 ( tan ( θ ) sin ( θ + ) ) 2 [ cos 2 ( θ ) + cos 2 ( θ + ) cos 2 ( θ ) cos 2 ( θ + ) 0 0 cos 2 ( θ ) cos 2 ( θ + ) cos 2 ( θ ) + cos 2 ( θ + ) 0 0 0 0 2 cos ( θ + ) cos ( θ ) 0 0 0 0 2 cos ( θ + ) cos ( θ ) ] .
[ σ TRG ELE ] 2 k FND k H 𝒮 ( k ) d k
[ σ TRG SLP ] 2 k FND k H k 2 𝒮 ( k ) d k
𝒮 ^ ( k ) = [ 1 + δ ^ HWS ( k ) ] 𝒮 ( k ) ,
δ ^ HWS ( k ) = { 0 if k k P δ NYQ ( k k P k NYQ k P ) otherwise
δ NYQ = k NYQ k H k 2 𝒮 ( k ) d k k P k NYQ k 2 ( k k P k NYQ k P ) 𝒮 ( k ) d k ,
k FND k NYQ k 2 𝒮 ^ ( k ) d k = [ σ TRG SLP ] 2 .
[ σ HWS SLP ] 2 = 1 N x 1 N y { r = 1 N x 1 s = 1 N y [ Δ x z ( r , s ) ] 2 + r = 1 N x s = 1 N y 1 [ Δ y z ( r , s ) ] 2 } ,
ε = 100 1 N i = 1 N | y i x i | x i and δ = 100 1 N i = 1 N y i x i x i ,

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