Abstract

A Monte Carlo code for ocean color simulations has been developed to model in-water radiometric fields of downward and upward irradiance (Ed and Eu), and upwelling radiance (Lu) in a two-dimensional domain with a high spatial resolution. The efficiency of the code has been optimized by applying state-of-the-art computing solutions, while the accuracy of simulation results has been quantified through benchmark with the widely used Hydrolight code for various values of seawater inherent optical properties and different illumination conditions. Considering a seawater single scattering albedo of 0.9, as well as surface waves of 5m width and 0.5m height, the study has shown that the number of photons required to quantify uncertainties induced by wave focusing effects on Ed, Eu, and Lu data products is of the order of 106, 109, and 1010, respectively. On this basis, the effects of sea-surface geometries on radiometric quantities have been investigated for different surface gravity waves. Data products from simulated radiometric profiles have finally been analyzed as a function of the deployment speed and sampling frequency of current free-fall systems in view of providing recommendations to improve measurement protocols.

© 2010 Optical Society of America

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2009 (4)

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Technol. 26, 91–106 (2009).
[CrossRef]

D. D’Alimonte, “Detection of mesoscale eddy-related structures through iso-SST patterns,” IEEE Geosci. Remote Sens. Lett. 6, 189–193 (2009).
[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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

J. Piskozub, D. Stramski, E. Terrill, and W. K. Melville, “Small-scale effects of underwater Bubble clouds on ocean reflectance: 3-D modeling results,” Opt. Express 17, 11747–11752(2009).
[CrossRef] [PubMed]

2008 (1)

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

2007 (4)

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]

G. R. Fournier, “Backscatter corrected Fournier-Forand phase function for remote sensing and underwater imaging performance evaluation,” Proc. SPIE 6615, 66150N (2007).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal Northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
[CrossRef] [PubMed]

W. Freda and J. Piskozub, “Improved method of Fournier–Forand marine phase function parameterization,” Opt. Express 15, 12763–12768 (2007).
[CrossRef] [PubMed]

2005 (2)

H. Wijesekera, W. S. Pegau, and T. Boyd, “Effect of surface waves on the irradiance distribution in the upper ocean,” Opt. Express 13, 9257–9264 (2005).
[CrossRef] [PubMed]

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 (3)

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

M. Gimond, “Description and verification of an aquatic optics Monte Carlo model,” Environ. Modeling Software 19, 1065–1076 (2004).
[CrossRef]

J. Piskozub, “Effect of ship shadow on in-water irradiance measurements,” Oceanologia 46, 103–112 (2004).

2003 (4)

2002 (3)

2001 (3)

1999 (1)

G. R. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[CrossRef]

1998 (1)

Y. M. Govaerts and M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–505 (1998).
[CrossRef]

1994 (1)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

1993 (1)

1991 (1)

1989 (1)

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]

1988 (1)

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy Mater. 40, 57–63 (1988).
[CrossRef]

1985 (1)

1979 (1)

K. Ueki and P. N. Stevens, “Variance reduction techniques using adjoint Monte Carlo method in shielding problem,” J. Nucl. Sci. Technol. 16, 117–131 (1979).
[CrossRef]

1975 (1)

1972 (1)

G. N. Plass and G. W. Kattawar, “Monte Carlo Calculations of radiative transfer in the Earth’s atmosphere-ocean system: I. Flux in the atmosphere and ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

1954 (1)

1949 (1)

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef] [PubMed]

1941 (1)

L. Henyey and J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Barnard, A.

Berthon, J.-F.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Technol. 26, 91–106 (2009).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal Northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
[CrossRef] [PubMed]

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

B. Bulgarelli, G. Zibordi, and J.-F. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef] [PubMed]

G. Zibordi, S. B. Hooker, J.-F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurement from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002).
[CrossRef]

Boss, E.

Boyd, T.

Brown, O. B.

Bulgarelli, B.

Casella, G.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods (Springer, 2004).

Coombes, C. A.

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy Mater. 40, 57–63 (1988).
[CrossRef]

Cox, C.

Cunha, J. C.

T. Kajiyama, D. D’Alimonte, J. C. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the geo-info project,” in Proceedings of the Eighth International Conference on Parallel Processing and Applied Mathematics,Lect. Notes Comput. Sci., R.Wyrzykowski, J.Dongarra, K.Karczewski, and J.Wasniewski, eds. (Springer, 2010), pp. 370–379.

D’Alimonte, D.

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Technol. 26, 91–106 (2009).
[CrossRef]

D. D’Alimonte, “Detection of mesoscale eddy-related structures through iso-SST patterns,” IEEE Geosci. Remote Sens. Lett. 6, 189–193 (2009).
[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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[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. Technol. 21, 1059–1073 (2004).
[CrossRef]

G. Zibordi, S. B. Hooker, J.-F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurement from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002).
[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 Proceedings of the Eighth International Conference on Parallel Processing and Applied Mathematics,Lect. Notes Comput. Sci., R.Wyrzykowski, J.Dongarra, K.Karczewski, and J.Wasniewski, eds. (Springer, 2010), pp. 370–379.

D. D’Alimonte and G. Zibordi, The JRC Data Processing System, Vol. 15 of SeaWiFS Technical Report Series, TM-2001-206892 (NASA Goddard Space Flight Center, 2001), pp. 52–56.

Davis, C. O.

R. A. Leathers, T. V. Downes, C. O. Davis, and C. D. Mobley, “Monte Carlo radiative transfer simulations for ocean optics: a practical guide,” Tech. Rep. (Naval Research Laboratory, Applied Optics Branch, 2004).

Downes, T. V.

R. A. Leathers, T. V. Downes, C. O. Davis, and C. D. Mobley, “Monte Carlo radiative transfer simulations for ocean optics: a practical guide,” Tech. Rep. (Naval Research Laboratory, Applied Optics Branch, 2004).

Doyle, J. P.

J. P. Doyle and G. Zibordi, “Monte Carlo modeling of optical transmission within 3-D shadowed field: application to large deployment structure,” Appl. Opt. 41, 4283–4306 (2002).
[CrossRef] [PubMed]

J. P. Doyle, S. B. Hooker, G. Zibordi, and D. vanderLinde, “Validation of an in-water, tower-shading correction scheme,” S.B.Hooker and E.R.Firestone, eds., NASA Tech. Note TM-2003-206892 (NASA Goddard Space Flight Center, 2002).
[CrossRef]

Escher, J.

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

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Fedkiw, R. P.

S. J. Osher and R. P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002).

Feng, H.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Fournier, G. R.

G. R. Fournier, “Backscatter corrected Fournier-Forand phase function for remote sensing and underwater imaging performance evaluation,” Proc. SPIE 6615, 66150N (2007).
[CrossRef]

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 2258, 194–201 (1994).
[CrossRef]

Freda, W.

Gentili, B.

Giles, D.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Gimond, M.

M. Gimond, “Description and verification of an aquatic optics Monte Carlo model,” Environ. Modeling Software 19, 1065–1076 (2004).
[CrossRef]

Gjerstad, K. I.

Gordon, H. R.

Govaerts, Y. M.

Y. M. Govaerts and M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–505 (1998).
[CrossRef]

Greenstein, J.

L. Henyey and J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Grenfell, T. C.

B. Light, G. A. Maykut, and T. C. Grenfell, “A two-dimensional Monte Carlo model of radiative transfer in sea ice,” J. Geophys. Res. 108, 3219–3227 (2003).
[CrossRef]

Haltrin, V. I.

Hamre, B.

Hanrahan, P.

M. Pharr and P. Hanrahan, “Monte Carlo evaluation of non-linear scattering equations for subsurface reflection,” in SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley., 2000), pp. 75–84.
[CrossRef]

Harrison, A. W.

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy Mater. 40, 57–63 (1988).
[CrossRef]

Henyey, L.

L. Henyey and J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Holben, B.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Hooker, S. B.

G. Zibordi, S. B. Hooker, J.-F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurement from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002).
[CrossRef]

J. P. Doyle, S. B. Hooker, G. Zibordi, and D. vanderLinde, “Validation of an in-water, tower-shading correction scheme,” S.B.Hooker and E.R.Firestone, eds., NASA Tech. Note TM-2003-206892 (NASA Goddard Space Flight Center, 2002).
[CrossRef]

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.

Jacobs, M. M.

Jin, Z.

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]

Kaitala, S.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Kajiyama, T.

T. Kajiyama, D. D’Alimonte, J. C. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the geo-info project,” in Proceedings of the Eighth International Conference on Parallel Processing and Applied Mathematics,Lect. Notes Comput. Sci., R.Wyrzykowski, J.Dongarra, K.Karczewski, and J.Wasniewski, eds. (Springer, 2010), pp. 370–379.

Kattawar, G. W.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

G. N. Plass and G. W. Kattawar, “Monte Carlo Calculations of radiative transfer in the Earth’s atmosphere-ocean system: I. Flux in the atmosphere and ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

Leathers, R. A.

R. A. Leathers, T. V. Downes, C. O. Davis, and C. D. Mobley, “Monte Carlo radiative transfer simulations for ocean optics: a practical guide,” Tech. Rep. (Naval Research Laboratory, Applied Optics Branch, 2004).

Lee, M. E.-G.

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]

Light, B.

B. Light, G. A. Maykut, and T. C. Grenfell, “A two-dimensional Monte Carlo model of radiative transfer in sea ice,” J. Geophys. Res. 108, 3219–3227 (2003).
[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]

Lotsberg, J. K.

Martín, I.

F. Pérez, I. Martín, F. X. Sillion, and X. Pueyo, “Acceleration of Monte Carlo path tracing in general environments,” in Proceedings of Pacific Graphics 2000 (2000).

Maykut, G. A.

B. Light, G. A. Maykut, and T. C. Grenfell, “A two-dimensional Monte Carlo model of radiative transfer in sea ice,” J. Geophys. Res. 108, 3219–3227 (2003).
[CrossRef]

Mélin, F.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Melville, W. K.

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef] [PubMed]

N. Metropolis, “The beginning of the Monte Carlo method,” Tech. Rep. (Stanford University, 1987).

Mobley, C. D.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

R. A. Leathers, T. V. Downes, C. O. Davis, and C. D. Mobley, “Monte Carlo radiative transfer simulations for ocean optics: a practical guide,” Tech. Rep. (Naval Research Laboratory, Applied Optics Branch, 2004).

C. D. Mobley and L. K. Sundman, “Hydrolight 5 and Ecolight 5 technical documentation,” Tech. Rep., Sequoia Scientific, Inc., 2700 Richards Road, Suite 107 Bellevue, Wash. 98005 (2010).

C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters (Academic, 1994).

Modest, M. F.

M. F. Modest, “Backward Monte Carlo simulations in radiative heat transfer,” J. Heat Transfer 125, 57–62 (2003).
[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. Methods 5, 317–327(2007).
[CrossRef]

Morel, A.

Munk, W.

Osher, S. J.

S. J. Osher and R. P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002).

Pegau, W. S.

Pérez, F.

F. Pérez, I. Martín, F. X. Sillion, and X. Pueyo, “Acceleration of Monte Carlo path tracing in general environments,” in Proceedings of Pacific Graphics 2000 (2000).

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep., SIO Reference 72–78 (Scripps Institution of Oceanography, 1972).

Pharr, M.

M. Pharr and P. Hanrahan, “Monte Carlo evaluation of non-linear scattering equations for subsurface reflection,” in SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley., 2000), pp. 75–84.
[CrossRef]

Piskozub, J.

Plass, G. N.

G. N. Plass and G. W. Kattawar, “Monte Carlo Calculations of radiative transfer in the Earth’s atmosphere-ocean system: I. Flux in the atmosphere and ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

Pueyo, X.

F. Pérez, I. Martín, F. X. Sillion, and X. Pueyo, “Acceleration of Monte Carlo path tracing in general environments,” in Proceedings of Pacific Graphics 2000 (2000).

Reinersman, P.

Robert, C. P.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods (Springer, 2004).

Schlurmann, T.

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

Schuster, G.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Shybanov, E.

Sillion, F. X.

F. Pérez, I. Martín, F. X. Sillion, and X. Pueyo, “Acceleration of Monte Carlo path tracing in general environments,” in Proceedings of Pacific Graphics 2000 (2000).

Slutsker, I.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

Stamnes, J. J.

Stamnes, K.

Stavn, R. H.

Stevens, P. N.

K. Ueki and P. N. Stevens, “Variance reduction techniques using adjoint Monte Carlo method in shielding problem,” J. Nucl. Sci. Technol. 16, 117–131 (1979).
[CrossRef]

Stramski, D.

Sundman, L. K.

C. D. Mobley and L. K. Sundman, “Hydrolight 5 and Ecolight 5 technical documentation,” Tech. Rep., Sequoia Scientific, Inc., 2700 Richards Road, Suite 107 Bellevue, Wash. 98005 (2010).

Terrill, E.

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]

Ueki, K.

K. Ueki and P. N. Stevens, “Variance reduction techniques using adjoint Monte Carlo method in shielding problem,” J. Nucl. Sci. Technol. 16, 117–131 (1979).
[CrossRef]

Ulam, S.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef] [PubMed]

Vandemark, D.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

vanderLinde, D.

J. P. Doyle, S. B. Hooker, G. Zibordi, and D. vanderLinde, “Validation of an in-water, tower-shading correction scheme,” S.B.Hooker and E.R.Firestone, eds., NASA Tech. Note TM-2003-206892 (NASA Goddard Space Flight Center, 2002).
[CrossRef]

Verstraete, M. M.

Y. M. Govaerts and M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–505 (1998).
[CrossRef]

Voss, K. J.

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]

Wijesekera, H.

Yan, B.

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]

Zaneveld, J. R.

Zaneveld, J. R. V.

Zibordi, G.

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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[CrossRef]

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Technol. 26, 91–106 (2009).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal Northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
[CrossRef] [PubMed]

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

B. Bulgarelli, G. Zibordi, and J.-F. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef] [PubMed]

J. P. Doyle and G. Zibordi, “Monte Carlo modeling of optical transmission within 3-D shadowed field: application to large deployment structure,” Appl. Opt. 41, 4283–4306 (2002).
[CrossRef] [PubMed]

G. Zibordi, S. B. Hooker, J.-F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurement from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002).
[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]

D. D’Alimonte and G. Zibordi, The JRC Data Processing System, Vol. 15 of SeaWiFS Technical Report Series, TM-2001-206892 (NASA Goddard Space Flight Center, 2001), pp. 52–56.

T. Kajiyama, D. D’Alimonte, J. C. Cunha, and G. Zibordi, “High-performance ocean color Monte Carlo simulation in the geo-info project,” in Proceedings of the Eighth International Conference on Parallel Processing and Applied Mathematics,Lect. Notes Comput. Sci., R.Wyrzykowski, J.Dongarra, K.Karczewski, and J.Wasniewski, eds. (Springer, 2010), pp. 370–379.

J. P. Doyle, S. B. Hooker, G. Zibordi, and D. vanderLinde, “Validation of an in-water, tower-shading correction scheme,” S.B.Hooker and E.R.Firestone, eds., NASA Tech. Note TM-2003-206892 (NASA Goddard Space Flight Center, 2002).
[CrossRef]

Appl. Opt. (11)

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

K. I. Gjerstad, J. J. Stamnes, B. Hamre, J. K. Lotsberg, B. Yan, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system,” Appl. Opt. 42, 2609–2622 (2003).
[CrossRef] [PubMed]

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

H. R. Gordon, “Ship perturbation of irradiance measurements at sea. 1: Monte Carlo simulations,” Appl. Opt. 24, 4172–4182(1985).
[CrossRef] [PubMed]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal Northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
[CrossRef] [PubMed]

J. P. Doyle and G. Zibordi, “Monte Carlo modeling of optical transmission within 3-D shadowed field: application to large deployment structure,” Appl. Opt. 41, 4283–4306 (2002).
[CrossRef] [PubMed]

B. Bulgarelli, G. Zibordi, and J.-F. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef] [PubMed]

V. I. Haltrin, “One-parameter two-term Henyey–Greenstein phase function for light scattering in seawater,” Appl. Opt. 41, 1022–1028 (2002).
[CrossRef] [PubMed]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. Henyey and J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Environ. Modeling Software (1)

M. Gimond, “Description and verification of an aquatic optics Monte Carlo model,” Environ. Modeling Software 19, 1065–1076 (2004).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

D. D’Alimonte, “Detection of mesoscale eddy-related structures through iso-SST patterns,” IEEE Geosci. Remote Sens. Lett. 6, 189–193 (2009).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

Y. M. Govaerts and M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–505 (1998).
[CrossRef]

J. Am. Stat. Assoc. (1)

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef] [PubMed]

J. Atmos. Ocean. Technol. (4)

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Technol. 26, 91–106 (2009).
[CrossRef]

G. Zibordi, S. B. Hooker, J.-F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurement from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002).
[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 ocean color primary radiometric products,” J. Atmos. Ocean. Technol. 26, 1634–1651(2009).
[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. Technol. 21, 1059–1073 (2004).
[CrossRef]

J. Geophys. Res. (1)

B. Light, G. A. Maykut, and T. C. Grenfell, “A two-dimensional Monte Carlo model of radiative transfer in sea ice,” J. Geophys. Res. 108, 3219–3227 (2003).
[CrossRef]

J. Heat Transfer (1)

M. F. Modest, “Backward Monte Carlo simulations in radiative heat transfer,” J. Heat Transfer 125, 57–62 (2003).
[CrossRef]

J. Nonlin. Math. Phys. (1)

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

J. Nucl. Sci. Technol. (1)

K. Ueki and P. N. Stevens, “Variance reduction techniques using adjoint Monte Carlo method in shielding problem,” J. Nucl. Sci. Technol. 16, 117–131 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

G. N. Plass and G. W. Kattawar, “Monte Carlo Calculations of radiative transfer in the Earth’s atmosphere-ocean system: I. Flux in the atmosphere and ocean,” J. Phys. Oceanogr. 2, 139–145 (1972).
[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. Methods 5, 317–327(2007).
[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]

Oceanologia (1)

J. Piskozub, “Effect of ship shadow on in-water irradiance measurements,” Oceanologia 46, 103–112 (2004).

Opt. Express (4)

Proc. SPIE (3)

G. R. Fournier, “Backscatter corrected Fournier-Forand phase function for remote sensing and underwater imaging performance evaluation,” Proc. SPIE 6615, 66150N (2007).
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G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 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. (1)

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]

Sol. Energy Mater. (1)

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy Mater. 40, 57–63 (1988).
[CrossRef]

Other (13)

J. P. Doyle, S. B. Hooker, G. Zibordi, and D. vanderLinde, “Validation of an in-water, tower-shading correction scheme,” S.B.Hooker and E.R.Firestone, eds., NASA Tech. Note TM-2003-206892 (NASA Goddard Space Flight Center, 2002).
[CrossRef]

R. A. Leathers, T. V. Downes, C. O. Davis, and C. D. Mobley, “Monte Carlo radiative transfer simulations for ocean optics: a practical guide,” Tech. Rep. (Naval Research Laboratory, Applied Optics Branch, 2004).

C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters (Academic, 1994).

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep., SIO Reference 72–78 (Scripps Institution of Oceanography, 1972).

D. D’Alimonte and G. Zibordi, The JRC Data Processing System, Vol. 15 of SeaWiFS Technical Report Series, TM-2001-206892 (NASA Goddard Space Flight Center, 2001), pp. 52–56.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods (Springer, 2004).

N. Metropolis, “The beginning of the Monte Carlo method,” Tech. Rep. (Stanford University, 1987).

F. Pérez, I. Martín, F. X. Sillion, and X. Pueyo, “Acceleration of Monte Carlo path tracing in general environments,” in Proceedings of Pacific Graphics 2000 (2000).

M. Pharr and P. Hanrahan, “Monte Carlo evaluation of non-linear scattering equations for subsurface reflection,” in SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley., 2000), pp. 75–84.
[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 Proceedings of the Eighth International Conference on Parallel Processing and Applied Mathematics,Lect. Notes Comput. Sci., R.Wyrzykowski, J.Dongarra, K.Karczewski, and J.Wasniewski, eds. (Springer, 2010), pp. 370–379.

MATLAB is a product and trademark of The Mathworks Incorporated, Natick, Mass., USA.

C. D. Mobley and L. K. Sundman, “Hydrolight 5 and Ecolight 5 technical documentation,” Tech. Rep., Sequoia Scientific, Inc., 2700 Richards Road, Suite 107 Bellevue, Wash. 98005 (2010).

S. J. Osher and R. P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002).

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Figures (11)

Fig. 1
Fig. 1

Dashed curve indicates the FF VSF. The distribution of sampled scattering angles (crosses) well matches the analytical expression of the FF probability density function (solid curve).

Fig. 2
Fig. 2

MOX simulation domain. 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 20 m deep and 10 m wide.

Fig. 3
Fig. 3

Virtual profiles from simulated radiometric fields. The sea-surface wave length and height are l = 5 m and h = 0.5 m , respectively, while the wave velocity is υ s 2.8 ms 1 . For an optical system deployed at υ s 0.25 ms 1 , the zenith angle of the virtual profile is θ p 80 ° [Eq. (10)]; see also the figure inset. Full-resolution sampling points along this virtual trajectory are plotted as dots (although the spatial resolution makes them appear as a line). Crosses indicate the location of sampling points assuming an acquisition frequency of 6 Hz .

Fig. 4
Fig. 4

Iso-depth contours displaying the surface wave gravity effects on the pressure gauge.

Fig. 5
Fig. 5

Coefficient of variation as a function of the photon population size N ph for E d , E u , and L u from top to bottom row panels. R ( 0 ) and K R are in the left and right column, respectively.

Fig. 6
Fig. 6

MOX and HYD radiometric profiles (black and red curves, respectively). Comparison details are given in Tables 3, 4, 5.

Fig. 7
Fig. 7

E d radiometric matrices, contours of iso-intensity, and virtual profiles in the left, central, and right column panels, respectively. Sea surfaces addressed from top to bottom row panels are (i) one harmonic component with height h = 0.5 m and width l = 5 m , (ii) one harmonic component with h = 0.05 m and l = 0.5 m , and (iii) the combined effects of (i) and (ii). Full-resolution virtual profiles are represented by black dots. Sampling data points for an acquisition frequency of 6 Hz and the related regression values are highlighted in green and red, respectively.

Fig. 8
Fig. 8

As in Fig. 7 but for E u .

Fig. 9
Fig. 9

As in Fig. 7 but for L u .

Fig. 10
Fig. 10

Left column panels show the coefficient of variation of subsurface radiometric quantities as a function of the sampling frequency and deployment speed of the optical system. Analogous statistical figures in the right column panels summarize the dependence of CV on the number of sampling points per meter at different acquisition frequencies. Results for E d , E u , and L u are shown in the top, central, and bottom row panels, respectively. Large black dots indicate estimates of uncertainties obtained from experimental data for a sampling frequency of 6 Hz with 32 samples per meter.

Fig. 11
Fig. 11

Parallel performance of MOX on TACC Ranger. The execution time was measured in units of seconds, with the number of processors varying from 1 to 2048. The number of traced photons is 10 8 in all cases.

Tables (5)

Tables Icon

Table 1 Summary of MOX Processing Parameters a

Tables Icon

Table 2 Processing Settings to Quantify the Effects of the Photon Population Size on the Uncertainty of Data Products Derived from Simulated Radiometric Fields

Tables Icon

Table 3 Comparison of MOX and Hydrolight using the FF VSF

Tables Icon

Table 4 Comparison of MOX and Hydrolight using the FF VSF (Additional Cases)

Tables Icon

Table 5 Execution Time Details of MOX Simulations on TACC Ranger Using 256 Processors a

Equations (17)

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

p ( τ ) = e τ ,
b = Ω β ( θ , ϕ ) d Ω ,
b = 0 π 2 π β ( θ ) sin ( θ ) d θ .
0 π 2 π β ˜ ( θ ) sin ( θ ) d θ = 1 ,
p ( θ ) = 2 π β ˜ ( θ ) sin ( θ ) ,
P ( θ ) = 0 θ 2 π β ˜ ( θ ) sin ( θ ) d θ .
β ( θ ) = 1 4 π ( 1 κ ) 2 κ ν ( [ ν ( 1 κ ) ( 1 κ ν ) ] + 4 u 2 [ κ ( 1 κ ν ) ν ( 1 κ ) ] ) ,
ν = 3 m 2 , κ = u 2 3 ( n 1 ) 2 , u = 2 sin ( θ / 2 ) ,
( δ z ) = ( 0 ) e K · δ z ,
v s = g · l 2 π ,
θ p = arctan υ s υ p .
z g ( x ) = z + cosh k ( z + δ b ) cosh k δ b z s ( x ) ,
CV = 1 M j M [ j ] 2 ,
= 1 M j M j .
ε = 100 · MOX HYD HYD ,
( δ z i ) = 1 J j = i J i ( δ z j ) ,
J = υ p Δ z ν p ,

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