Abstract

An analytical model of sea optical properties has been developed in order to generate sea surface images, as seen by an infrared sensor. This model is based on a statistical approach and integrates the spatial variability of a wind-roughened sea surface whose variability ranges from a 1-m to a kilometer scale. It also takes into account submetric variability. A two-scale approach has been applied by superimposing small scale variability (smaller than the pixel footprint) to larger ones. Introducing multiresolution in the sensor field of view allows the requirement of any observational configuration, including nadir as well as grazing view geometry. The physical background of the methods has been tested against theoretical considerations. We also obtained a good agreement with dataset collections at our disposal and taken from the literature, such that a bias shows up at grazing angles, mainly explained by not taking into account multiple reflections. Applied to the generation of synthetic sea surface radiance images, our model leads to good quality ocean scenes, whatever the contextual conditions.

© 2007 Optical Society of America

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  1. P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).
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  16. T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, "A unified directional spectrum for long and short wind-driven waves," J. Geophys. Res. 102, 15781-15796 (1997).
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  20. V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
    [CrossRef]
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    [CrossRef]
  23. W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
    [CrossRef]
  24. X. Wu and W. L. Smith, "Emissivity of a rough sea surface for 8-13 μm: modeling and verification," Appl. Opt. 36, 2609-2619 (1997).
    [CrossRef] [PubMed]
  25. P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
    [CrossRef]
  26. C. Bourlier, "Unpolarized emissivity with shadow and multiple reflections from random rough surfaces in the geometric optics approximation. Application to Gaussian sea surfaces in the infrared band," Appl. Opt. 45, 6241-6254 (2006).
    [PubMed]
  27. K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).
  28. F. Losasso and H. Hoppe, "Geometry clipmaps: terrain rendering using nested regular grids," ACM SIGGRAPH Trans. Graph. 23, 769-776 (2004).

2006 (4)

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
[CrossRef]

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).

C. Bourlier, "Unpolarized emissivity with shadow and multiple reflections from random rough surfaces in the geometric optics approximation. Application to Gaussian sea surfaces in the infrared band," Appl. Opt. 45, 6241-6254 (2006).
[PubMed]

2005 (2)

C. Bourlier, "Unpolarized infrared emissivity with shadow from anisotropic rough sea surfaces with non-Gaussian statistics," Appl. Opt. 44, 4335-4349 (2005).
[CrossRef] [PubMed]

V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
[CrossRef]

2004 (1)

F. Losasso and H. Hoppe, "Geometry clipmaps: terrain rendering using nested regular grids," ACM SIGGRAPH Trans. Graph. 23, 769-776 (2004).

2003 (2)

C. Bourlier and G. Berginc, "Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations," Waves Random Media 13, 27-58 (2003).
[CrossRef]

B. G. Henderson, J. Theiler, and P. V. Villeneuve, "The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model," Rem. Sens. Environ. 88, 453-467 (2003).
[CrossRef]

2001 (1)

C. Bourlier, J. Saillard, and G. Berginc, "Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effects," IEEE Trans. Geosci. Remote Sens. 39, 319-392 (2001).
[CrossRef]

2000 (1)

C. Bourlier, J. Saillard, and G. Berginc, "Intrinsic infrared radiation of the sea surface," in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, 2000), Vol. 27, pp. 185-335.
[CrossRef]

1997 (4)

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, "A unified directional spectrum for long and short wind-driven waves," J. Geophys. Res. 102, 15781-15796 (1997).
[CrossRef]

J. Theiler and B. G. Henderson, "Geometrical constraint on shadowing in rough surface," in Infrared Spaceborne Remote Sensing V, M. Strojnik and B. F. Andresen, eds., Proc. SPIE 3122, 271-279 (1997).

X. Wu and W. L. Smith, "Emissivity of a rough sea surface for 8-13 μm: modeling and verification," Appl. Opt. 36, 2609-2619 (1997).
[CrossRef] [PubMed]

K. Yoshimori, K. Itoh, and Y. Ichioka, "Optical characteristics of a wind-roughened water surface:a two-dimensional theory," Appl. Opt. 34, 6236-6247 (1997).
[CrossRef]

1996 (2)

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
[CrossRef]

1995 (1)

1994 (1)

1989 (1)

F. Poirion and C. Soize, "Simulation numérique de champs vectoriels stochastiques gaussiens homogènes et non homogènes," Rech. Aérosp. 1, 41-61 (1989).

1986 (2)

A. Fournier and W. T. Reeves, "A simple model of ocean waves," ACM SIGGRAPH Comput. Graph. 20, 75-82 (1986).
[CrossRef]

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

1982 (1)

R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics," ACM Trans. Graphics 1, 7-24 (1982).
[CrossRef]

1975 (1)

B. T. Phong, "Illumination for computer generated pictures," Commun. ACM 18, 311-377 (1975).
[CrossRef]

1967 (1)

B. G. Smith, "Geometrical shadowing of random rough surface," IEEE Trans. Antennas Propag. 15, 668-671 (1967).
[CrossRef]

1966 (1)

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138-147 (1966).
[CrossRef]

1965 (1)

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Antennas Propag. 13, 384-388 (1965).
[CrossRef]

1954 (1)

Allen, M. R.

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
[CrossRef]

Beckmann, P.

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Antennas Propag. 13, 384-388 (1965).
[CrossRef]

Berginc, G.

C. Bourlier and G. Berginc, "Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations," Waves Random Media 13, 27-58 (2003).
[CrossRef]

C. Bourlier, J. Saillard, and G. Berginc, "Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effects," IEEE Trans. Geosci. Remote Sens. 39, 319-392 (2001).
[CrossRef]

C. Bourlier, J. Saillard, and G. Berginc, "Intrinsic infrared radiation of the sea surface," in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, 2000), Vol. 27, pp. 185-335.
[CrossRef]

Berton, R.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Bourlier, C.

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
[CrossRef]

C. Bourlier, "Unpolarized emissivity with shadow and multiple reflections from random rough surfaces in the geometric optics approximation. Application to Gaussian sea surfaces in the infrared band," Appl. Opt. 45, 6241-6254 (2006).
[PubMed]

C. Bourlier, "Unpolarized infrared emissivity with shadow from anisotropic rough sea surfaces with non-Gaussian statistics," Appl. Opt. 44, 4335-4349 (2005).
[CrossRef] [PubMed]

C. Bourlier and G. Berginc, "Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations," Waves Random Media 13, 27-58 (2003).
[CrossRef]

C. Bourlier, J. Saillard, and G. Berginc, "Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effects," IEEE Trans. Geosci. Remote Sens. 39, 319-392 (2001).
[CrossRef]

C. Bourlier, J. Saillard, and G. Berginc, "Intrinsic infrared radiation of the sea surface," in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, 2000), Vol. 27, pp. 185-335.
[CrossRef]

Brown, J.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Brown, O.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Caillault, K.

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
[CrossRef]

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

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. 102, 15781-15796 (1997).
[CrossRef]

Cook, R. L.

R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics," ACM Trans. Graphics 1, 7-24 (1982).
[CrossRef]

Cox, C. S.

Dion, D.

V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
[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. 102, 15781-15796 (1997).
[CrossRef]

Fauqueux, S.

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
[CrossRef]

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Feltz, W.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Fournier, A.

A. Fournier and W. T. Reeves, "A simple model of ocean waves," ACM SIGGRAPH Comput. Graph. 20, 75-82 (1986).
[CrossRef]

Henderson, B. G.

B. G. Henderson, J. Theiler, and P. V. Villeneuve, "The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model," Rem. Sens. Environ. 88, 453-467 (2003).
[CrossRef]

J. Theiler and B. G. Henderson, "Geometrical constraint on shadowing in rough surface," in Infrared Spaceborne Remote Sensing V, M. Strojnik and B. F. Andresen, eds., Proc. SPIE 3122, 271-279 (1997).

Hoppe, H.

F. Losasso and H. Hoppe, "Geometry clipmaps: terrain rendering using nested regular grids," ACM SIGGRAPH Trans. Graph. 23, 769-776 (2004).

Howell, H. B.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Huet, T.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Ichioka, Y.

Itoh, K.

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. 102, 15781-15796 (1997).
[CrossRef]

Knuteson, R. O.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Krapez, J. C.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Labarre, L.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Losasso, F.

F. Losasso and H. Hoppe, "Geometry clipmaps: terrain rendering using nested regular grids," ACM SIGGRAPH Trans. Graph. 23, 769-776 (2004).

Malherbe, C.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Martin, C.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Masuda, K.

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).

McKeown, W.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Menzel, W. P.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Miesch, C.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Minnett, P.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Mobley, C. D.

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

Munk, W. H.

Nalli, N. R.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Nightingale, T. J.

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
[CrossRef]

Phong, B. T.

B. T. Phong, "Illumination for computer generated pictures," Commun. ACM 18, 311-377 (1975).
[CrossRef]

Poirion, F.

F. Poirion and C. Soize, "Simulation numérique de champs vectoriels stochastiques gaussiens homogènes et non homogènes," Rech. Aérosp. 1, 41-61 (1989).

Potvin, G.

V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

Reeves, W. T.

A. Fournier and W. T. Reeves, "A simple model of ocean waves," ACM SIGGRAPH Comput. Graph. 20, 75-82 (1986).
[CrossRef]

Revercomb, H. E.

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

Roblin, A.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

Ross, V.

V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
[CrossRef]

Saillard, J.

C. Bourlier, J. Saillard, and G. Berginc, "Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effects," IEEE Trans. Geosci. Remote Sens. 39, 319-392 (2001).
[CrossRef]

C. Bourlier, J. Saillard, and G. Berginc, "Intrinsic infrared radiation of the sea surface," in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, 2000), Vol. 27, pp. 185-335.
[CrossRef]

Simoneau, P.

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
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Smith, B. G.

B. G. Smith, "Geometrical shadowing of random rough surface," IEEE Trans. Antennas Propag. 15, 668-671 (1967).
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Smith, W. L.

X. Wu and W. L. Smith, "Emissivity of a rough sea surface for 8-13 μm: modeling and verification," Appl. Opt. 36, 2609-2619 (1997).
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W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
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Soize, C.

F. Poirion and C. Soize, "Simulation numérique de champs vectoriels stochastiques gaussiens homogènes et non homogènes," Rech. Aérosp. 1, 41-61 (1989).

Theiler, J.

B. G. Henderson, J. Theiler, and P. V. Villeneuve, "The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model," Rem. Sens. Environ. 88, 453-467 (2003).
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J. Theiler and B. G. Henderson, "Geometrical constraint on shadowing in rough surface," in Infrared Spaceborne Remote Sensing V, M. Strojnik and B. F. Andresen, eds., Proc. SPIE 3122, 271-279 (1997).

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R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics," ACM Trans. Graphics 1, 7-24 (1982).
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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. 102, 15781-15796 (1997).
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Villeneuve, P. V.

B. G. Henderson, J. Theiler, and P. V. Villeneuve, "The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model," Rem. Sens. Environ. 88, 453-467 (2003).
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Wagner, R. J.

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138-147 (1966).
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Watts, P. D.

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
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Yoshimori, K.

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A. Fournier and W. T. Reeves, "A simple model of ocean waves," ACM SIGGRAPH Comput. Graph. 20, 75-82 (1986).
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ACM Trans. Graphics (1)

R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics," ACM Trans. Graphics 1, 7-24 (1982).
[CrossRef]

Appl. Opt. (4)

Bull. Am. Meteorol. Soc. (1)

W. L. Smith, R. O. Knuteson, H. E. Revercomb, J. Brown, O. Brown, W. Feltz, H. B. Howell, W. McKeown, W. P. Menzel, P. Minnett, and N. R. Nalli, "Observation of the infrared properties of the ocean--implications for the measurement of sea surface temperature via satellite remote sensing," Bull. Am. Meteorol. Soc. 77, 41-51 (1996).
[CrossRef]

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B. T. Phong, "Illumination for computer generated pictures," Commun. ACM 18, 311-377 (1975).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Antennas Propag. 13, 384-388 (1965).
[CrossRef]

B. G. Smith, "Geometrical shadowing of random rough surface," IEEE Trans. Antennas Propag. 15, 668-671 (1967).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

C. Bourlier, J. Saillard, and G. Berginc, "Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effects," IEEE Trans. Geosci. Remote Sens. 39, 319-392 (2001).
[CrossRef]

J. Acoust. Soc. Am. (1)

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138-147 (1966).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the Along Track Scanning Radiometer," J. Atmos. Oceanic Technol. 13, 126-141 (1996).
[CrossRef]

J. Geophys. Res. (1)

T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, "A unified directional spectrum for long and short wind-driven waves," J. Geophys. Res. 102, 15781-15796 (1997).
[CrossRef]

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C. S. Cox and W. H. Munk, "Measurements of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954).
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V. Ross, D. Dion, and G. Potvin, "Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface," J. Opt. Soc. Am. 22, 2442-2453 (2005).
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J. Opt. Soc. Am. A (2)

J. Phys. Oceanogr. (1)

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

Proc. SPIE (1)

K. Caillault, S. Fauqueux, C. Bourlier, and P. Simoneau, "Infrared multiscale sea surface modeling," Proc. SPIE 6360, 636006 (2006).
[CrossRef]

Rech. Aérosp. (1)

F. Poirion and C. Soize, "Simulation numérique de champs vectoriels stochastiques gaussiens homogènes et non homogènes," Rech. Aérosp. 1, 41-61 (1989).

Rem. Sens. Environ. (1)

B. G. Henderson, J. Theiler, and P. V. Villeneuve, "The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model," Rem. Sens. Environ. 88, 453-467 (2003).
[CrossRef]

Waves Random Media (1)

C. Bourlier and G. Berginc, "Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations," Waves Random Media 13, 27-58 (2003).
[CrossRef]

Other (5)

C. Bourlier, J. Saillard, and G. Berginc, "Intrinsic infrared radiation of the sea surface," in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, 2000), Vol. 27, pp. 185-335.
[CrossRef]

J. Theiler and B. G. Henderson, "Geometrical constraint on shadowing in rough surface," in Infrared Spaceborne Remote Sensing V, M. Strojnik and B. F. Andresen, eds., Proc. SPIE 3122, 271-279 (1997).

P. Simoneau, R. Berton, K. Caillault, S. Fauqueux, T. Huet, J. C. Krapez, L. Labarre, C. Malherbe, C. Martin, C. Miesch, and A. Roblin, "MATISSE, Version 1.2 and future developments," in Twenty-seventh Annual Review of Atmospheric Transmission Models (National Heritage Museum, Lexington, Mass. 2006).

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).

F. Losasso and H. Hoppe, "Geometry clipmaps: terrain rendering using nested regular grids," ACM SIGGRAPH Trans. Graph. 23, 769-776 (2004).

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Figures (10)

Fig. 1
Fig. 1

Normalized omnidirectional Elfouhaily spectrum for wind velocity at 10 m above average ocean surface u 10 = 8   m .s 1 and infinite fetch. The vertical dashed line indicates the location of the cutoff wavenumber k c .

Fig. 2
Fig. 2

Schematic representation of a mono-dimensional sea surface. In the upper part, bold line indicates the sea surface. It is decomposed into intersected rough areas (IRAs) related to pixels solid angles. In the lower part, a decomposition of the sea surface is shown: small scale waves (dashed lines) are superimposed on large scale waves (plain lines) on the n IRAs. The size of the orthogonal projection of the IRAs is given by L 1 , L 2 , , L n . Stochastic processes describing slopes are given by γ < L i and γ L i ( i = 1 , , n ) for the small and large scales respectively.

Fig. 3
Fig. 3

Geometry definition: (0xyz) is the coordinate system relative to the upwind direction x and crosswind direction y; u o b s and u i n c are observation and incident directions respectively, defined by their zenith and azimuth angles ( θ o b s , ϕ o b s ) and ( θ i n c , ϕ i n c ) relative to the (Oxyz) coordinate system; n is the facet normal; ψ is the angle between facet normal n and observation direction u o b s .

Fig. 4
Fig. 4

Verification of the conservation of energy. Wind speed is u 10 = 10   m .s 1 , wavelength is λ = 4 μ m and four IRA projection sizes are presented: (a) L = 1   m , (b) L = 8   m , (c) L = 32   m , and (d) L = 128   m .

Fig. 5
Fig. 5

Effective emissivity as a function of surface size, expressed as L = 2 x 1   m , x = 1 , , 11 , for λ = 4 μ m , two wind speeds u 10 = 5 and 20   m .s 1 and ( θ obs = 80 ° ; ϕ obs = 0 ° ) . Dotted and solid lines refer to calculations done with low resolution (LR) and high resolution (HR) expressions respectively.

Fig. 6
Fig. 6

Effective reflectivity as a function of surface size, expressed as L = 2 x 1   m , x = 1 , , 11 , for λ = 4 μ m , two wind speeds u 10 = 5 and 20   m .s 1 and for ( θ inc = 80 ° ; ϕ inc = 0 ° ) and ( θ obs = 80 ° ; ϕ obs = 0 ° ) . Dotted and solid lines refer to calculations done with low resolution (LR) and high resolution (HR) expressions respectively.

Fig. 7
Fig. 7

Image of sea surface radiance at 4 μ m composed of 500 × 500 pixels. The sensor is located at an altitude of 0.389 km and looks at nadir. The sun is at zenith. The wind speed is u 10 = 10   m .s 1 .

Fig. 8
Fig. 8

Same as Fig. 7 but with the sensor located at an altitude of 0.5 km. Sensor observation angles are ( θ obs = 36 ° ; ϕ obs = 0 ° ) and sun angles are ( θ inc = 40 ° ; ϕ inc = 180 ° ) . The wind speed is u 10 = 15   m .s 1 .

Fig. 9
Fig. 9

Same as Fig. 8 but with the sensor located at an altitude of 1.5 km.

Fig. 10
Fig. 10

Levels of spatial resolution associated with images of sea surface radiance. Sizes of each domain and related spatial resolutions are also indicated. Diagrams (a), (b), and (c) give domains and sizes related to Figs. 7, 8, and 9, respectively.

Tables (1)

Tables Icon

Table 1 Slope Means Upwind (mx) and Crosswind (my) Relative to the Surface Sizes Presented in Fig. 4

Equations (34)

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ρ ( θ inc ) = 1 2 ( sin 2 ( θ inc θ t ) sin 2 ( θ inc + θ t ) + tan 2 ( θ inc θ t ) tan 2 ( θ inc + θ t ) ) ,
n a   sin   θ inc = n w   sin   θ t ,
ε ( θ inc ) = 1 ρ ( θ inc ) .
ε ˜ ( θ obs , ϕ obs ) = + + [ 1 ρ ( ψ ) ] × P m , C ( γ x , γ y ) × g ( θ obs , ϕ obs ; γ x , γ y ) × cos   θ obs × S m , C ε ( θ obs , ϕ obs ; γ x , γ y ) d γ x d γ y + + P m , C ( γ x , γ y ) × g ( θ obs , ϕ obs ; γ x , γ y ) × cos   θ obs × S m , C ε ( θ obs , ϕ obs ; γ x , γ y ) d γ x d γ y ,
m = ( m x , m y ) T ,
C = ( σ x 2 σ xy 2 σ xy 2 σ y 2 ) .
γ Xobs = γ x   cos   ϕ obs + γ y   sin   ϕ obs
γ Yobs = γ x   sin   ϕ obs + γ y   cos   ϕ obs .
ε ˜ ( θ obs , ϕ obs ) = + + [ 1 ρ ( ψ ) ] × P m obs , C obs ( γ Xobs , γ Yobs ) × g ( θ obs , ϕ obs ; γ Xobs , γ Yobs ) × S m Xobs , σ Xobs ε ( θ obs ; γ Xobs ) d γ Xobs d γ Yobs + + P m obs , C obs ( γ Xobs , γ Yobs ) × g ( θ obs , ϕ obs ; γ Xobs , γ Yobs ) × S m Xobs , σ Xobs ε ( θ obs ; γ Xobs ) d γ Xobs d γ Yobs .
A ϕ = ( cos   ϕ sin   ϕ sin   ϕ cos   ϕ ) .
ψ = cos 1 [ 1 1 + γ Xobs 2 + γ Yobs 2 ( cos   θ obs γ Xobs   sin   θ obs ) ] ,
g ( θ obs , ϕ obs ; γ Xobs , γ Yobs ) = 1 γ Xobs   tan   θ obs .
S m , σ ε ( θ ; γ ) = { ( ; cotan   θ ] ( γ ) 1 + Λ m , σ ( θ ) if   θ 0 [ cotan   θ ; + ) ( γ ) 1 + Λ m , σ ( θ ) if   θ 0 ,
I ( x ) = { 1 if   x I 0 otherwise ,
where  I = { ( ;   cotan   θ ] if   θ 0 [ cotan   θ ;  + ) if   θ 0 ,
Λ m , σ ( θ ) = { cotan   θ + ( γ   tan   θ 1 ) P m , σ ( γ ) d γ if   θ 0 cotan   θ ( γ   tan   θ 1 ) P m , σ ( γ ) d γ if   θ 0 .
D = 1 m Xobs   tan ( θ obs ) 1 + Λ m Xobs , σ Xobs ( θ obs ) .
cos ( ψ ) cos ( ψ ) = 1 1 + γ Xobs 2 + m Y obs 2 × ( cos   θ obs γ Xobs   sin   θ obs ) .
ε ˜ ( θ obs , ϕ obs ) + [ 1 ρ ( ψ ) ] × P m Xobs , σ Xobs ( γ Xobs ) × ( 1 γ Xobs   tan   θ obs ) × S m Xobs , σ Xobs ε ( θ obs ; γ Xobs ) d γ Xobs 1 m Xobs   tan ( θ obs ) 1+ Λ m Xobs , σ Xobs ( θ obs ) .
ρ ˜ ( θ inc , ϕ inc ; θ obs , ϕ obs ) = ρ [ ψ ( θ obs , ϕ obs ; γ x 0 , γ y 0 ) ] × P m , C ( γ x0 , γ y0 ) × g ( θ obs , ϕ obs ; γ x0 , γ y0 ) × S m , C ρ ( θ inc , ϕ inc ; θ obs , ϕ obs ; γ x0 , γ y0 ) × | J | 1 m Xobs   tan ( θ obs ) 1+ Λ m Xobs , σ Xobs ( θ obs ) .
γ x 0 = sin   θ obs   cos   ϕ obs + sin   θ inc   cos   ϕ inc cos   θ inc + cos   θ obs ,
γ y 0 = sin   θ obs   sin   ϕ obs + sin   θ inc   sin   ϕ inc cos   θ inc + cos   θ obs .
S m X , σ X ρ ( θ inc ; θ obs ; γ Xobs , γ Xinc ) =
1 1 + Λ m Xobs , σ obs ( θ obs ) + Λ m Xinc , σ inc ( θ inc ) ,
J = 1 + cos   θ inc   cos   θ obs + sin   θ inc   sin   θ obs   cos ( ϕ obs ϕ inc ) ( cos   θ inc + cos   θ obs ) 3 .
σ x 2 = 0 + π π k 2 cos 2 θ S ( k,   θ ) d θ dk, σ y 2 = 0 + π π k 2 sin 2 θ S ( k,   θ ) d θ dk, σ x y 2 = 0 ,
γ = γ L + γ < L .
    m < L = 0 , σ x ; < L 2 = k c + π π k 2 cos 2 ( θ ) S ( k , θ ) d θ dk, σ y ; < L 2 = k c + π π k 2 sin 2 ( θ ) S ( k , θ ) d θ dk , σ x y ; < L 2 = 0.
m = m L + m < L = m L , C = C L + C < L = C < L .
m = m Δ + m < Δ , C = C Δ + C < Δ .
ρ ˜ ( θ i , ϕ i ; θ o , ϕ o ) = f ( θ i , ϕ i ; θ o , ϕ o ) × cos   θ i .
ε ˜ ( θ inc , ϕ inc ) + π / 2 π / 2 0 π ρ ˜ ( θ , ϕ ; θ inc , ϕ inc ) sin   θ d θ d ϕ = 1 ,
L ( θ obs , ϕ obs ) = Ω sun f ( θ sun , ϕ sun ; θ obs , ϕ obs ) · cos   θ sun · L sun ( θ sun , ϕ sun ) · d Ω sun + Ω + f ( θ + , ϕ + ; θ obs , ϕ obs ) · cos   θ + · L atm ( θ + , ϕ + ) · d Ω + + ε ˜ ( θ obs , ϕ obs ) · L BB ( T sea ) .
L ( θ obs , ϕ obs ) = ρ ˜ ( θ sun , ϕ sun ; θ obs , ϕ obs ) · L sun ( θ sun , ϕ sun ) + [ 1 ε ˜ ( θ obs , ϕ obs ) ] · L ¯ atm + ε ˜ ( θ obs , ϕ obs ) · L B B ( T s e a ) ,

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