Abstract

In this paper, we derive the unpolarized infrared (IR) emissivity of thin oil films over anisotropic Gaussian seas from a refined physical surface spectrum model of damping due to oil. Since the electromagnetic wavelength is much smaller than the surface mean curvature radius and than the surface root mean square height, the Kirchhoff–tangent plane approximation, reduced to the geometric optics approximation, can be used. The surface can then be replaced by its local infinite tangent plane at each point of each rough surface. The multiple reflections at each interface are ignored (i.e., for both the upper air/oil interface and the lower oil/sea interface of the contaminated sea). Nevertheless, the multiple reflections between the upper and the lower interfaces of the oil film are taken into account, by assuming a locally flat and planar thin oil film, which forms a local Fabry–Perot interferometer. This means that the Fresnel reflection coefficient of a single interface can be substituted for the equivalent Fresnel reflection coefficient of the air/oil/sea film, calculated by considering an infinite number of reflections inside the layer. Comparisons of the emissivity between a clean sea and a contaminated sea are presented, with respect to emission angle, wind speed, wind direction, oil film thickness, oil type, and wavelength. Thus, oil de tection, characterization, and quantization are investigated in the IR window regions.

© 2010 Optical Society of America

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2008

2007

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. PIER-76, 95-126(2007).
[CrossRef]

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

I. Fuks and V. Zavorotny, “Polarization dependence of radar contrast for sea surface oil slicks,” IEEE Radar Conf. 503-508 (2007).
[CrossRef]

2006

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

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

2005

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

M. Migliaccio, M. Tranfaglia, and S. Ermakov, “A physical approach for the observation of oil spills in SAR images,” IEEE J. Oceanic Eng. 30, 496-507 (2005).
[CrossRef]

2004

2003

Z. Otremba and J. Piskozub, “Modeling the remotely sensed optical contrast caused by oil suspended in the sea water column,” Opt. Express 11, 2-6 (2003).

R. D. Roo and C.-T. Tai, “Plane wave reflection and refraction involving a finitely conducting medium,” IEEE Antennas Propag. Mag. 45, 54-61 (2003).
[CrossRef]

B. 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]

2002

G. Kara, “Remote sensing of oil films on the sea surface,” Turkish J. Mar. Sci. 8, 27-40 (2002).

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

2001

C. Bourlier, G. Berginc, and J. Saillard, “Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect,” IEEE Trans. Geosci. Remote Sensing 39, 379-392(2001).
[CrossRef]

Z. Otremba and J. Piskozub, “Modelling of the optical contrast of an oil film on a sea surface,” Opt. Express 9, 411-416(2001).
[CrossRef]

2000

H. A. Espedal and O. M. Johannessen, “Detection of oil spills near offshore installations using synthetic aperture radar (SAR),” Int. J. Remote Sensing 21, 2141-2144 (2000).
[CrossRef]

1999

V. Osadchy, K. Shifrin, and I. Gurevich, “The airborne identification of oil films at the Caspian sea surface using CO2 lidar,” Oceanol. Acta 22, 51-56 (1999).
[CrossRef]

C. R. Zeisse, C. P. McGrath, K. M. Littfin, and H. G. Hughes, “Infrared radiance of the wind-ruffled sea,” J. Opt. Soc. Am. A 16, 1439-1452 (1999).
[CrossRef]

1998

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

1997

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]

D. E. Freund, R. I. Joseph, D. J. Donohue, and K. T. Constantikes, “Numerical computations of rough sea surface emissivity using the interaction probability density,” J. Opt. Soc. Am. A 14, 1836-1849 (1997).
[CrossRef]

A. Jenkins and S. Jacobs, “Wave damping by a thin layer of viscous fluid,” Phys. Fluids 9, 1256-1264 (1997).
[CrossRef]

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

1996

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

1992

S. Ermakov, S. Salashin, and A. Panchenko, “Film slicks on the sea surface and some mechanisms of their formation,” Dyn. Atmos. Oceans 16, 279-304 (1992).
[CrossRef]

1991

J. Wu, “Effects of atmospheric stability on ocean ripples: A comparison between optical and microwave measurements,” J. Geophys. Res. 96, 7265-7269 (1991).
[CrossRef]

1989

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

W. Alpers and H. Huhnerfuss, “The damping of ocean waves by surface films: a new look at an old problem,” J. Geophys. Res. 94, 6251-6265 (1989).
[CrossRef]

D. Wieliczka, S. Weng, and M. Querry, “Wedge shaped cell for highly absorbent liquids: infrared optical constants of water,” Appl. Opt. 28, 1714-1719 (1989).
[CrossRef]

1987

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

1982

W. Plant, “A relationship between wind stress and wave slope,” J. Geophys. Res. 87, 1961-1967 (1982).
[CrossRef]

1978

R. Cini and P. Lombardini, “Damping effect of monolayers on surface wave motion in a liquid,” J. Colloid Interface Sci. 65, 387-389 (1978).
[CrossRef]

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

1973

1969

1966

L. Pontier and C. Dechambenoy, “Détermination des constantes optiques de l'eau liquide entre 1 et 40 μm. application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633-641 (1966).

1956

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bulletin of the Scripps Institution of Oceanograpy of the University of California 6, 401-488(1956).

1954

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun's glitter,” J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

Al'perovich, L.

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

Alpers, W.

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

W. Alpers and H. Huhnerfuss, “The damping of ocean waves by surface films: a new look at an old problem,” J. Geophys. Res. 94, 6251-6265 (1989).
[CrossRef]

Andrews, A. B.

Ayari, M.

M. Ayari, A. Coatanhay, and A. Khenchaf, “The influence of ripple damping on electromagnetic bistatic scattering by sea surface,” in Proceedings of the 2005 International Geoscience and Remote Sensing Symposium (IEEE, 2005), pp. 1345-1348.

Berginc, G.

C. Bourlier, G. Berginc, and J. Saillard, “Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect,” IEEE Trans. Geosci. Remote Sensing 39, 379-392(2001).
[CrossRef]

C. Bourlier and G. Berginc, “Microwave analytical backscattering models from randomly anisotropic sea surface--comparison with experimental data in C and Ku bands,” in Progress in Electromagnetics Research, D.J. A.Kong, ed. (EMW Publishing, 2002), Vol. 37, pp. 31-78.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Bourlier, C.

N. Pinel, N. Déchamps, and C. Bourlier, “Modeling of the bistatic electromagnetic scattering from sea surfaces covered in oil for microwave applications,” IEEE Trans. Geosci. Remote Sensing 46, 385-392 (2008).
[CrossRef]

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. PIER-76, 95-126(2007).
[CrossRef]

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

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

C. Bourlier, G. Berginc, and J. Saillard, “Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect,” IEEE Trans. Geosci. Remote Sensing 39, 379-392(2001).
[CrossRef]

N. de Beaucoudrey, P. Schott, and C. Bourlier, “Detection of oil slicks on sea surface depending on layer thickness and sensor frequency,” in Proceedings of the 2003 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2003), pp. 2741-2743.

C. Bourlier and G. Berginc, “Microwave analytical backscattering models from randomly anisotropic sea surface--comparison with experimental data in C and Ku bands,” in Progress in Electromagnetics Research, D.J. A.Kong, ed. (EMW Publishing, 2002), Vol. 37, pp. 31-78.

Brown, J.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Byfield, V.

V. Byfield, “Optical remote sensing of oil in the marine environment,” Ph.D. thesis (School of Ocean and Earth Science, University of Southampton, 1998).

Cappa, C.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

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]

Cini, E.

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

Cini, R.

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

R. Cini and P. Lombardini, “Damping effect of monolayers on surface wave motion in a liquid,” J. Colloid Interface Sci. 65, 387-389 (1978).
[CrossRef]

Coatanhay, A.

M. Ayari, A. Coatanhay, and A. Khenchaf, “The influence of ripple damping on electromagnetic bistatic scattering by sea surface,” in Proceedings of the 2005 International Geoscience and Remote Sensing Symposium (IEEE, 2005), pp. 1345-1348.

Combes, P.-F.

P.-F. Combes, Micro-Ondes--Cours et Exercices avec Solutions. Tome 1: Lignes, Guides et Cavités (Dunod, 1996).

Constantikes, K. T.

Cox, C.

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bulletin of the Scripps Institution of Oceanograpy of the University of California 6, 401-488(1956).

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun's glitter,” J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

de Beaucoudrey, N.

N. de Beaucoudrey, P. Schott, and C. Bourlier, “Detection of oil slicks on sea surface depending on layer thickness and sensor frequency,” in Proceedings of the 2003 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2003), pp. 2741-2743.

Dechambenoy, C.

L. Pontier and C. Dechambenoy, “Détermination des constantes optiques de l'eau liquide entre 1 et 40 μm. application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633-641 (1966).

Déchamps, N.

N. Pinel, N. Déchamps, and C. Bourlier, “Modeling of the bistatic electromagnetic scattering from sea surfaces covered in oil for microwave applications,” IEEE Trans. Geosci. Remote Sensing 46, 385-392 (2008).
[CrossRef]

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

Donohue, D. J.

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]

Ermakov, S.

M. Migliaccio, M. Tranfaglia, and S. Ermakov, “A physical approach for the observation of oil spills in SAR images,” IEEE J. Oceanic Eng. 30, 496-507 (2005).
[CrossRef]

S. Ermakov, S. Salashin, and A. Panchenko, “Film slicks on the sea surface and some mechanisms of their formation,” Dyn. Atmos. Oceans 16, 279-304 (1992).
[CrossRef]

S. Ermakov, “Possibilities of identification of oil films using radar probing of the sea surface,” in Proceedings of the 2008 IEEE/OES US/EU-Baltic International Symposium (BALTIC) (IEEE, 2008), pp. 1-6.

I. Sergievskaya and S. Ermakov, “On wave damping due to oil films,” in Proceedings of the 2008 IEEE/OES US/EU-Baltic International Symposium (BALTIC) (IEEE, 2008), pp. 1-6.

Espedal, H. A.

H. A. Espedal and O. M. Johannessen, “Detection of oil spills near offshore installations using synthetic aperture radar (SAR),” Int. J. Remote Sensing 21, 2141-2144 (2000).
[CrossRef]

Feltz, W.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Fiscella, B.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

Franceschetti, G.

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

Freund, D. E.

Friedman, D.

Fuks, I.

I. Fuks and V. Zavorotny, “Polarization dependence of radar contrast for sea surface oil slicks,” IEEE Radar Conf. 503-508 (2007).
[CrossRef]

Gade, M.

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

Garrett, W.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

Gurevich, I.

V. Osadchy, K. Shifrin, and I. Gurevich, “The airborne identification of oil films at the Caspian sea surface using CO2 lidar,” Oceanol. Acta 22, 51-56 (1999).
[CrossRef]

Hale, G.

Henderson, B.

B. 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]

Howell, H.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Hughes, H. G.

Huhnerfuss, H.

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

W. Alpers and H. Huhnerfuss, “The damping of ocean waves by surface films: a new look at an old problem,” J. Geophys. Res. 94, 6251-6265 (1989).
[CrossRef]

Hühnerfuss, H.

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

Iodice, A.

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

Jacobs, S.

A. Jenkins and S. Jacobs, “Wave damping by a thin layer of viscous fluid,” Phys. Fluids 9, 1256-1264 (1997).
[CrossRef]

Jenkins, A.

A. Jenkins and S. Jacobs, “Wave damping by a thin layer of viscous fluid,” Phys. Fluids 9, 1256-1264 (1997).
[CrossRef]

Johannessen, O. M.

H. A. Espedal and O. M. Johannessen, “Detection of oil spills near offshore installations using synthetic aperture radar (SAR),” Int. J. Remote Sensing 21, 2141-2144 (2000).
[CrossRef]

Joseph, R. I.

Kara, G.

G. Kara, “Remote sensing of oil films on the sea surface,” Turkish J. Mar. Sci. 8, 27-40 (2002).

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]

Khenchaf, A.

M. Ayari, A. Coatanhay, and A. Khenchaf, “The influence of ripple damping on electromagnetic bistatic scattering by sea surface,” in Proceedings of the 2005 International Geoscience and Remote Sensing Symposium (IEEE, 2005), pp. 1345-1348.

Knuteson, R.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Komarova, A.

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

Lamkaouchi, K.

K. Lamkaouchi, “Water: a dielectric standard. permittivity of water-petrol mixtures at microwave frequencies,” Ph.D. thesis (Bordeaux I University, 1992) (in French).

Lange, A.

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

Levich, V. G.

V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, 1962).

V. G. Levich, “The theory of waves by surface-active materials,” (in Russian) Zh. Eksp. Teor. Fiz., 10, 1296-1304 (1940). English translation, Acta Physicochimica URSS, 14, 307-328 (1941).

Littfin, K. M.

Lombardini, P.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

R. Cini and P. Lombardini, “Damping effect of monolayers on surface wave motion in a liquid,” J. Colloid Interface Sci. 65, 387-389 (1978).
[CrossRef]

Manfredi, C.

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

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).
[CrossRef]

McGrath, C. P.

McKeown, W.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Migliaccio, M.

M. Migliaccio, M. Tranfaglia, and S. Ermakov, “A physical approach for the observation of oil spills in SAR images,” IEEE J. Oceanic Eng. 30, 496-507 (2005).
[CrossRef]

Minnett, P.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Munk, W.

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bulletin of the Scripps Institution of Oceanograpy of the University of California 6, 401-488(1956).

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun's glitter,” J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

Nalli, N.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Narziev, B.

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

Osadchy, V.

V. Osadchy, K. Shifrin, and I. Gurevich, “The airborne identification of oil films at the Caspian sea surface using CO2 lidar,” Oceanol. Acta 22, 51-56 (1999).
[CrossRef]

Otremba, Z.

Panchenko, A.

S. Ermakov, S. Salashin, and A. Panchenko, “Film slicks on the sea surface and some mechanisms of their formation,” Dyn. Atmos. Oceans 16, 279-304 (1992).
[CrossRef]

Pinel, N.

N. Pinel, N. Déchamps, and C. Bourlier, “Modeling of the bistatic electromagnetic scattering from sea surfaces covered in oil for microwave applications,” IEEE Trans. Geosci. Remote Sensing 46, 385-392 (2008).
[CrossRef]

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. PIER-76, 95-126(2007).
[CrossRef]

Piskozub, J.

Plant, W.

W. Plant, “A relationship between wind stress and wave slope,” J. Geophys. Res. 87, 1961-1967 (1982).
[CrossRef]

Pontier, L.

L. Pontier and C. Dechambenoy, “Détermination des constantes optiques de l'eau liquide entre 1 et 40 μm. application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633-641 (1966).

Pushkarev, V.

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

Querry, M.

Revercomb, H.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Riccio, D.

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

Roo, R. D.

R. D. Roo and C.-T. Tai, “Plane wave reflection and refraction involving a finitely conducting medium,” IEEE Antennas Propag. Mag. 45, 54-61 (2003).
[CrossRef]

Ruello, G.

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

Saillard, J.

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. PIER-76, 95-126(2007).
[CrossRef]

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

C. Bourlier, G. Berginc, and J. Saillard, “Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect,” IEEE Trans. Geosci. Remote Sensing 39, 379-392(2001).
[CrossRef]

Salashin, S.

S. Ermakov, S. Salashin, and A. Panchenko, “Film slicks on the sea surface and some mechanisms of their formation,” Dyn. Atmos. Oceans 16, 279-304 (1992).
[CrossRef]

Schott, P.

N. de Beaucoudrey, P. Schott, and C. Bourlier, “Detection of oil slicks on sea surface depending on layer thickness and sensor frequency,” in Proceedings of the 2003 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2003), pp. 2741-2743.

Sergievskaya, I.

I. Sergievskaya and S. Ermakov, “On wave damping due to oil films,” in Proceedings of the 2008 IEEE/OES US/EU-Baltic International Symposium (BALTIC) (IEEE, 2008), pp. 1-6.

Shifrin, K.

V. Osadchy, K. Shifrin, and I. Gurevich, “The airborne identification of oil films at the Caspian sea surface using CO2 lidar,” Oceanol. Acta 22, 51-56 (1999).
[CrossRef]

Shih, W.-C.

Siviero, R.

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

Smith, W.

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

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Tai, C.-T.

R. D. Roo and C.-T. Tai, “Plane wave reflection and refraction involving a finitely conducting medium,” IEEE Antennas Propag. Mag. 45, 54-61 (2003).
[CrossRef]

Theiler, J.

B. 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]

Tranfaglia, M.

M. Migliaccio, M. Tranfaglia, and S. Ermakov, “A physical approach for the observation of oil spills in SAR images,” IEEE J. Oceanic Eng. 30, 496-507 (2005).
[CrossRef]

Trivero, P.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

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).
[CrossRef]

Villeneuve, P.

B. 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]

Weng, S.

Wieliczka, D.

Wismann, V.

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Wu, J.

J. Wu, “Effects of atmospheric stability on ocean ripples: A comparison between optical and microwave measurements,” J. Geophys. Res. 96, 7265-7269 (1991).
[CrossRef]

Wu, X.

Zavorotny, V.

I. Fuks and V. Zavorotny, “Polarization dependence of radar contrast for sea surface oil slicks,” IEEE Radar Conf. 503-508 (2007).
[CrossRef]

Zeisse, C. R.

Ann. Geophys.

L. Pontier and C. Dechambenoy, “Détermination des constantes optiques de l'eau liquide entre 1 et 40 μm. application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633-641 (1966).

Appl. Opt.

Bull. Am. Meteorol. Soc.

W. Smith, R. Knuteson, H. Revercomb, W. Feltz, H. Howell, W. Menzel, N. Nalli, O. Brown, J. Brown, P. Minnett, and W. McKeown, “Observations of the infrared radiative 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]

Bulletin of the Scripps Institution of Oceanograpy of the University of California

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bulletin of the Scripps Institution of Oceanograpy of the University of California 6, 401-488(1956).

Dyn. Atmos. Oceans

S. Ermakov, S. Salashin, and A. Panchenko, “Film slicks on the sea surface and some mechanisms of their formation,” Dyn. Atmos. Oceans 16, 279-304 (1992).
[CrossRef]

IEEE Antennas Propag. Mag.

R. D. Roo and C.-T. Tai, “Plane wave reflection and refraction involving a finitely conducting medium,” IEEE Antennas Propag. Mag. 45, 54-61 (2003).
[CrossRef]

IEEE J. Oceanic Eng.

M. Migliaccio, M. Tranfaglia, and S. Ermakov, “A physical approach for the observation of oil spills in SAR images,” IEEE J. Oceanic Eng. 30, 496-507 (2005).
[CrossRef]

IEEE Radar Conf.

I. Fuks and V. Zavorotny, “Polarization dependence of radar contrast for sea surface oil slicks,” IEEE Radar Conf. 503-508 (2007).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing

G. Franceschetti, A. Iodice, D. Riccio, G. Ruello, and R. Siviero, “SAR raw signal simulation of oil slicks in ocean environments,” IEEE Trans. Geosci. Remote Sensing 40, 1935-1949(2002).
[CrossRef]

C. Bourlier, G. Berginc, and J. Saillard, “Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect,” IEEE Trans. Geosci. Remote Sensing 39, 379-392(2001).
[CrossRef]

N. Pinel, N. Déchamps, and C. Bourlier, “Modeling of the bistatic electromagnetic scattering from sea surfaces covered in oil for microwave applications,” IEEE Trans. Geosci. Remote Sensing 46, 385-392 (2008).
[CrossRef]

Int. J. Remote Sensing

V. Wismann, M. Gade, W. Alpers, and H. Hühnerfuss, “Radar signature of marine mineral oil spills measured by an airborne multi-radar,” Int. J. Remote Sensing 19, 3607-3623(1998).
[CrossRef]

H. A. Espedal and O. M. Johannessen, “Detection of oil spills near offshore installations using synthetic aperture radar (SAR),” Int. J. Remote Sensing 21, 2141-2144 (2000).
[CrossRef]

J. Appl. Spectrosc.

L. Al'perovich, A. Komarova, B. Narziev, and V. Pushkarev, “Optical constants of petroleum samples in the 0.25-25 μ range,” J. Appl. Spectrosc. 28, 491-494 (1978).
[CrossRef]

J. Atmos. Ocean. Technol.

P. Lombardini, B. Fiscella, P. Trivero, C. Cappa, and W. Garrett, “Modulation of the spectra of short gravity waves by sea surface films: slick detection and characterization with a microwave probe,” J. Atmos. Ocean. Technol. 6, 882-890(1989).
[CrossRef]

J. Colloid Interface Sci.

R. Cini and P. Lombardini, “Damping effect of monolayers on surface wave motion in a liquid,” J. Colloid Interface Sci. 65, 387-389 (1978).
[CrossRef]

R. Cini, P. Lombardini, C. Manfredi, and E. Cini, “Ripples damping due to monomolecular films,” J. Colloid Interface Sci. 119, 74-80 (1987).
[CrossRef]

J. Geophys. Res.

W. Alpers and H. Huhnerfuss, “The damping of ocean waves by surface films: a new look at an old problem,” J. Geophys. Res. 94, 6251-6265 (1989).
[CrossRef]

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]

W. Plant, “A relationship between wind stress and wave slope,” J. Geophys. Res. 87, 1961-1967 (1982).
[CrossRef]

J. Wu, “Effects of atmospheric stability on ocean ripples: A comparison between optical and microwave measurements,” J. Geophys. Res. 96, 7265-7269 (1991).
[CrossRef]

J. Mar. Res.

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Oceanol. Acta

V. Osadchy, K. Shifrin, and I. Gurevich, “The airborne identification of oil films at the Caspian sea surface using CO2 lidar,” Oceanol. Acta 22, 51-56 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Fluids

A. Jenkins and S. Jacobs, “Wave damping by a thin layer of viscous fluid,” Phys. Fluids 9, 1256-1264 (1997).
[CrossRef]

Prog. Electromagn. Res.

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. PIER-76, 95-126(2007).
[CrossRef]

Remote Sens. Environ.

M. Gade, W. Alpers, H. Huhnerfuss, V. Wismann, and A. Lange, “On the reduction of the radar backscatter by oceanic surface films: scatterometer measurements and their theoretical interpretation,” Remote Sens. Environ. 66, 52-70(1998).
[CrossRef]

B. 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]

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

Turkish J. Mar. Sci.

G. Kara, “Remote sensing of oil films on the sea surface,” Turkish J. Mar. Sci. 8, 27-40 (2002).

Waves Random Complex Media

N. Pinel, N. Déchamps, C. Bourlier, and J. Saillard, “Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect,” Waves Random Complex Media 17, 283-303(2007).
[CrossRef]

Other

P.-F. Combes, Micro-Ondes--Cours et Exercices avec Solutions. Tome 1: Lignes, Guides et Cavités (Dunod, 1996).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

C. Bourlier and G. Berginc, “Microwave analytical backscattering models from randomly anisotropic sea surface--comparison with experimental data in C and Ku bands,” in Progress in Electromagnetics Research, D.J. A.Kong, ed. (EMW Publishing, 2002), Vol. 37, pp. 31-78.

V. G. Levich, “The theory of waves by surface-active materials,” (in Russian) Zh. Eksp. Teor. Fiz., 10, 1296-1304 (1940). English translation, Acta Physicochimica URSS, 14, 307-328 (1941).

V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, 1962).

K. Lamkaouchi, “Water: a dielectric standard. permittivity of water-petrol mixtures at microwave frequencies,” Ph.D. thesis (Bordeaux I University, 1992) (in French).

Z. Otremba, “Selected results of light field modeling above the sea surface covered by thin oil film,” in Computer Simulation and Boundary Field Problems, Environmental Simulations (Riga Technical University, 1999), Vol. 41.

V. Byfield, “Optical remote sensing of oil in the marine environment,” Ph.D. thesis (School of Ocean and Earth Science, University of Southampton, 1998).

M. Ayari, A. Coatanhay, and A. Khenchaf, “The influence of ripple damping on electromagnetic bistatic scattering by sea surface,” in Proceedings of the 2005 International Geoscience and Remote Sensing Symposium (IEEE, 2005), pp. 1345-1348.

S. Ermakov, “Possibilities of identification of oil films using radar probing of the sea surface,” in Proceedings of the 2008 IEEE/OES US/EU-Baltic International Symposium (BALTIC) (IEEE, 2008), pp. 1-6.

I. Sergievskaya and S. Ermakov, “On wave damping due to oil films,” in Proceedings of the 2008 IEEE/OES US/EU-Baltic International Symposium (BALTIC) (IEEE, 2008), pp. 1-6.

N. de Beaucoudrey, P. Schott, and C. Bourlier, “Detection of oil slicks on sea surface depending on layer thickness and sensor frequency,” in Proceedings of the 2003 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2003), pp. 2741-2743.

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Figures (13)

Fig. 1
Fig. 1

Illustration of the multiple reflections inside the flat and planar thin film of thickness H with incidence angle χ (local oil film).

Fig. 2
Fig. 2

Unpolarized power reflection coefficient (dB) versus the local incidence angle χ (°) for λ = 10 μm , H = 50 μm , and for a heavy petroleum.

Fig. 3
Fig. 3

Same parameters as in Fig. 2, except for λ = 3.4 μm .

Fig. 4
Fig. 4

Isotropic part of the slope spectrum of clean and contaminated sea surfaces versus the surface wavenumber k. For the contaminated sea, two cases of the Lombardini et al. damping model are compared with two cases of the MLB, with a heavy oil of viscosity 0.5 cm 2 / s having a film thickness of H = 100 μm or H = 500 μm . The wind speed is u 10 = 6 m / s .

Fig. 5
Fig. 5

RMS slopes in the x and y directions, σ s x and σ s y , of clean and contaminated sea surfaces [with the same parameters as in Fig. 4] versus the wind speed u 10 in the range 2 10 m / s : comparison with the Cox and Munk experimental model.

Fig. 6
Fig. 6

Emissivity with multiple reflection from the contaminated sea: representation of the first three scattered fields E r , 1 , E r , 2 , and E r , 3

Fig. 7
Fig. 7

(a) Unpolarized emissivity of clean and contaminated seas and (b) emissivity contrast between clean and contaminated seas versus the emission angle θ for λ = 10 μm , u 10 = 6 m / s , ϕ = 0 . The contaminated sea is a heavy oil film of thickness H = 50 μm , described by the MLB. A comparison is also made with the case of flat interfaces, corresponding to u 10 = 0 m / s .

Fig. 8
Fig. 8

Same parameters as in Fig. 7, except for the wavelength is λ = 3.4 μm .

Fig. 9
Fig. 9

(a) Unpolarized emissivity of clean and contaminated seas and (b) emissivity contrast between clean and contaminated seas versus the emission angle θ for λ = 10 μm , u 10 = 4 m / s , and ϕ = 0 . The contaminated sea is a heavy oil film of thicknesses H = { 0 , 10 , 50 , 100 , 500 } μm , described by the MLB.

Fig. 10
Fig. 10

Same parameters as in Fig. 9, except for the wind speed is u 10 = 8 m / s .

Fig. 11
Fig. 11

Same parameters as in Fig. 10, except for the wavelength is λ = 3.4 μm .

Fig. 12
Fig. 12

(a) Unpolarized emissivity of contaminated seas and (b) emissivity contrast between clean and contaminated seas versus the emission angle θ for u 10 = 6 m / s , ϕ = 0 , and λ = { 3.4 , 10 } μm , and for both light and heavy fuel oils. The contaminated sea is of thickness H = 50 μm , described by the MLB.

Fig. 13
Fig. 13

Unpolarized emissivity of clean and contaminated seas versus the observation direction ϕ for θ = 80 ° , u 10 = { 4 , 8 } m / s , and λ = 10 μm . The contaminated sea is a heavy fuel oil of thickness H = 50 μm , described by the MLB.

Tables (2)

Tables Icon

Table 1 Refractive Indices of Seawater (Taken from Refractive Index of Pure Water by Hale and Querry [24] with Salinity Adjustment from Friedman [25]) and Oil [26, 27] for λ = { 3.4 ; 10 } μm , Respectively

Tables Icon

Table 2 Values of Physical Parameters P P Obtained from Laboratory and Field Experiments with Oil, Used in Numerical Simulations Presented Here

Equations (50)

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ϵ flat ( χ ) = 1 R ( χ ) .
R ( χ ) = | r V ( χ ) | 2 + | r H ( χ ) | 2 2 ,
{ r 1 = r 12 r p = t 12 t 21 r 21 p 2 r 23 p 1 e + j ( p 1 ) ψ ̲ p 2 ,
ψ ̲ = 2 k 0 n ̲ 2 H cos χ ̲ m .
r α β ( χ α ) = { n α cos χ β n β cos χ α n α cos χ β + n β cos χ α ( V   polarization ) n α cos χ α n β cos χ β n α cos χ α + n β cos χ β ( H   polarization ) ,
t α β ( χ α ) = { [ 1 r α β ( χ α ) ] n α n β ( V   polarization ) 1 + r α β ( χ α ) ( H   polarization ) .
n 1 sin χ = n ̲ 2 sin χ ̲ m .
tan χ m phys = sin χ p ,
p = e ( n ̲ 2 cos χ ̲ m ) = 1 2 [ ( ϵ r 2 sin 2 χ ) 2 + ϵ r 2 2 + ( ϵ r 2 sin 2 χ ) ] 1 2 ,
ψ = e ( ψ ̲ ) = 2 k 0 H p , with     p = e ( n ̲ 2 cos χ ̲ m ) ,
ψ = m ( ψ ̲ ) = 2 k 0 H q , with     q = m ( n ̲ 2 cos χ ̲ m ) .
δ skin 0 = 1 / ( k 0 n 2 ) .
d skin ( χ ) = 1 2 k 0 q , with     q = m ( n ̲ 2 cos χ ̲ m ) ,
{ R P ( χ ) = r 12 + p = 2 P ( 1 r 12 2 ) r 21 p 2 r 23 p 1 e + j ( p 1 ) ψ R ( χ ) = r 12 + r 23 e + j ψ 1 + r 12 r 23 e + j ψ ,
R P ( χ ) = | R P , V ( χ ) | 2 + | R P , H ( χ ) | 2 2 .
R R 2 = r 12 + ( 1 r 12 2 ) r 23 e + j ψ .
y Lomb ( k ; E 0 , ω D ) = 1 ± 2 τ + 2 τ 2 X + Y ( X + τ ) 1 ± 2 τ + 2 τ 2 2 X + 2 X 2 ,
τ = ( ω D 2 ω ) 1 / 2 X = E 0 k 2 ρ ( 2 ν ω 3 ) 1 / 2 Y = E 0 k 4 ν ρ ω ,
ω = ( ζ k 3 / ρ + g k ) 1 / 2 ,
S cont,Lomb ( k ; u 10 , ϕ , E 0 , ω D ) = S clean ( k ; u 10 , ϕ ) y Lomb , s ( k ; E 0 , ω D ) .
y Lomb , s = ( 1 F + F / y Lomb ) 1 ,
S clean ( k ; u 10 , ϕ ) = M ( k ) [ 1 + Δ ( k ) cos ( 2 ϕ ) ] / ( 2 π ) ,
y MLB = S clean ( k ; u 10 , ϕ ) S cont ( k ; u 10 , ϕ , H , P P ) = [ β ( u * , k ) γ clean ( k ) β ( u * , k ) γ cont ( k , H , P P ) ] n , with     { n = + 1 if     β > γ , n = 1 if     β < γ ,
γ cont = 2 ν k 2 × y Lomb ( k , E 0 , ω D ) .
S cont,MLB ( k ; u 10 , ϕ , H , P P ) = S clean ( k ; u 10 , ϕ ) y MLB .
σ s X 2 = α + β cos ( 2 ϕ ) ,
α = 1 2 0 + M ( k ) y k 2 d k , β = 1 4 0 + M ( k ) Δ ( k ) y k 2 d k ,
σ s x = α + β , σ s y = α β ,
{ σ s x 2 = 0.005 + 0.78 × 10 3 u 12 ± 0.002 σ s y 2 = 0.003 + 0.84 × 10 3 u 12 ± 0.002 ,
ϵ ( θ , ϕ ) = 1 1 + Λ ( θ , ϕ ) + μ d γ X + [ 1 R ( χ ) ] p s ( γ x , γ y ) ( 1 γ X μ ) d γ Y ,
cos χ ( θ , ϕ , γ x , γ y ) = ( 1 γ X μ ) cos θ ( 1 + γ X 2 + γ Y 2 ) 1 2 .
p s ( γ x , γ x ) = 1 2 π σ s x σ s y exp ( γ x 2 2 σ s x 2 γ y 2 2 σ s y 2 ) .
{ γ X = + γ x cos ϕ + γ y sin ϕ γ Y = γ x sin ϕ + γ y cos ϕ .
Λ ( v ) = exp ( v 2 ) v π erfc ( v ) 2 v π , with     v = | cot θ | 2 [ ( σ s x cos ϕ ) 2 + ( σ s y sin ϕ ) 2 ] 1 / 2 .
ϵ ( θ , ϕ ) 1 1 + Λ ( θ , ϕ ) + μ [ 1 R ( χ ) ] p s ( γ X ) ( 1 γ X μ ) d γ X .
ϵ ( θ , ϕ ) ϵ 0 ( θ ) + ϵ 1 ( θ ) cos ( ϕ ) + ϵ 2 ( θ ) cos ( 2 ϕ ) ,
ϵ 0 ( θ ) = [ ϵ ( θ , 0 ) + ϵ ( θ , π ) + 2 ϵ ( θ , π / 2 ) ] / 4 ,
ϵ 1 ( θ ) = [ ϵ ( θ , 0 ) ϵ ( θ , π ) ] / 2 ,
ϵ 2 ( θ ) = [ ϵ ( θ , 0 ) + ϵ ( θ , π ) 2 ϵ ( θ , π / 2 ) ] / 4.
U x + W z = 0 ,
U t + P x = ν 2 U ,
W t + P z = ν 2 W ,
W + = Z + t ,
ρ + ν + ( U + z + W + x ) = E + ξ x x + μ + ξ x x t ,
P + g Z 2 ν + W + z + ( σ + / ρ + ) Z x x = 0 ,
U + = ξ t ,
W + = W = H t ,
U + = U ,
ρ + ν + ( U + z + W + x ) + E ξ x x + μ ξ x x t = ρ ν ( U z + W z ) ,
ρ + ( P + g Z 2 ν + W + z ) = ρ ( P g H 2 ν W z ) + σ H x x ,

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