Abstract

A numerical model is developed for computation of the reflection of atmospheric-emitted IR radiance from a wind-roughened water body. The model assumes the Kirchhoff approximation for rough surface scattering. This allows application of the postulates of geometrical optics to determine the reflection of rays from an ensemble of wave facets. We performed the hemispherical integration with Gaussian quadrature by using an uplooking fast transmittance model. This calculation is simplified further through the concept of a reflection–diffusivity angle. The model compares favorably with observed radiance spectra obtained from the Marine-Atmospheric Emitted Radiance Interferometer during the Combined Sensor Program research cruise.

© 2001 Optical Society of America

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    [CrossRef]
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  34. R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.
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    [CrossRef]

2000 (1)

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

1998 (2)

N. R. Nalli, W. L. Smith, “Improved remote sensing of sea surface skin temperature using a physical retrieval method,” J. Geophys. Res. 103, 10527–10542 (1998).
[CrossRef]

C. J. R. Sheppard, “Imaging of random surfaces and inverse scattering in the Kirchhoff approximation,” Waves Random Media 8, 53–66 (1998).
[CrossRef]

1997 (3)

J. A. Shaw, J. H. Churnside, “Scanning-laser glint measurements of sea-surface slope statistics,” Appl. Opt. 36, 4202–4213 (1997).
[CrossRef] [PubMed]

X. Wu, W. L. Smith, “Emissivity of rough sea surface for 8–13 µm: modeling and validation,” Appl. Opt. 36, 1–11 (1997).

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

1996 (3)

X. Wu, W. L. Smith, “Sensitivity of sea surface temperature retrieval to sea surface emissivity, English translation,” Acta Meteorol. Sin. 10, 376–384 (1996).

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, N. R. Nalli, “Observations 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. Watts, M. Allen, T. Nightingale, “Sea surface emission and reflection for radiometric measurements made with the along-track scanning radiometer,” J. Atmos. Oceanic Technol. 13, 126–141 (1996).
[CrossRef]

1992 (1)

J. W. Salisbury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8-14 µm atmospheric window,” Remote Sens. Environ. 42, 83–106 (1992).
[CrossRef]

1989 (1)

1988 (2)

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sens. Environ. 24, 313–329 (1988).
[CrossRef]

J. R. Eyre, H. M. Woolf, “Transmittance of atmospheric gases in the microwave region: a fast model,” Appl. Opt. 27, 3244–3249 (1988).
[CrossRef] [PubMed]

1976 (1)

1969 (1)

1967 (2)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

A. Stogryn, “The apparent temperature of the sea at microwave frequencies,” IEEE Trans. Antennas Propag. 15, 278–286 (1967).
[CrossRef]

1955 (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

1954 (1)

1952 (1)

L. M. Brekhovskikh, “The diffraction of waves by a rough surface, part I,” Zh. Eksp. Teor. Fiz. 23, 275–289 (1952).

Allen, M.

P. Watts, M. Allen, T. Nightingale, “Sea surface emission and reflection for radiometric measurements made with the along-track scanning radiometer,” J. Atmos. Oceanic Technol. 13, 126–141 (1996).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electomagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

Best, F. A.

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

Brekhovskikh, L. M.

L. M. Brekhovskikh, “The diffraction of waves by a rough surface, part I,” Zh. Eksp. Teor. Fiz. 23, 275–289 (1952).

Brown, G. S.

G. S. Brown, “Quasi-specular scattering from the air–sea interface,” in Surface Waves and Fluxes: Volume II—Remote Sensing, Vol. 8 of Environmental Fluid Mechanics, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, 1990).
[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, N. R. Nalli, “Observations 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, N. R. Nalli, “Observations 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. B.

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

Churnside, J. H.

Cooper, D. I.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Cousins, D.

D. Cousins, W. L. Smith, “National Polar-orbiting Environmental Satellite System (NPOESS) Airborne Sounder Testbed-Interferometer (NAST-I),” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 323–331 (1997).
[CrossRef]

Cox, C.

Cox, C. S.

C. S. Cox, “Refraction and reflection of light at the sea surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974).

D’Aria, D. M.

J. W. Salisbury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8-14 µm atmospheric window,” Remote Sens. Environ. 42, 83–106 (1992).
[CrossRef]

Ecklund, W. L.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Emery, W. J.

G. L. Pickard, W. J. Emery, Descriptive Physical Oceanography: An Introduction, 5th ed. (Pergamon, New York, 1990).

Evans, R. H.

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

Eyre, J. R.

Fairall, C. W.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

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, N. R. Nalli, “Observations 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]

Friedman, D.

Hagan, D. E.

D. E. Hagan, N. R. Nalli, “Tropical water vapor correction for remotely sensed sea surface temperature: results using narrowband window radiance profiles from TOGA COARE,” J. Geophys. Res. (to be published).

Han, Y.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Hanafin, J. A.

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

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, N. R. Nalli, “Observations 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]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media: Multiple Scattering, Turbulence, Rough Surfaces, and Remote Sensing (Academic, New York, 1978), Vol. 2.

Jeynes, P. L. C.

P. L. C. Jeynes, “The scattering of electromagnetic radiation from irregular surfaces,” in Mathematics in Remote Sensing, S. R. Brooks, ed. (Clarendon, Oxford, 1989).

Kearns, E. J.

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

Knuteson, R.

R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.

Knuteson, R. O.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

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, N. R. Nalli, “Observations 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. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

R. O. Knuteson, Space Science and Engineering Center, University of Wisconsin-Madison, Madison, Wis. (personal communication, 1999).

Masuda, K.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sens. Environ. 24, 313–329 (1988).
[CrossRef]

McIntosh, R. E.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

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, N. R. Nalli, “Observations 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, N. R. Nalli, “Observations 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]

Minnett, P.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

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, N. R. Nalli, “Observations 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]

R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.

Minnett, P. J.

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

Munk, W.

Nalli, N. R.

N. R. Nalli, W. L. Smith, “Improved remote sensing of sea surface skin temperature using a physical retrieval method,” J. Geophys. Res. 103, 10527–10542 (1998).
[CrossRef]

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, N. R. Nalli, “Observations 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]

D. E. Hagan, N. R. Nalli, “Tropical water vapor correction for remotely sensed sea surface temperature: results using narrowband window radiance profiles from TOGA COARE,” J. Geophys. Res. (to be published).

N. R. Nalli, “Sea surface skin temperature retrieval using the high-resolution interferometer sounder,” M.S. thesis (University of Wisconsin-Madison, Madison, Wis., 1995).

N. R. Nalli, “A physical multispectral method for the retrieval of ocean and lake surface temperatures via scanning spectrometer,” Ph.D. dissertation (University of Wisconsin-Madison, Madison, Wis., 2000).

Nightingale, T.

P. Watts, M. Allen, T. Nightingale, “Sea surface emission and reflection for radiometric measurements made with the along-track scanning radiometer,” J. Atmos. Oceanic Technol. 13, 126–141 (1996).
[CrossRef]

Osborne, B. J.

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

Pickard, G. L.

S. Pond, G. L. Pickard, Introductory Dynamical Oceanography, 2nd ed. (Pergamon, New York, 1983).

G. L. Pickard, W. J. Emery, Descriptive Physical Oceanography: An Introduction, 5th ed. (Pergamon, New York, 1990).

Pinkley, L.

Pond, S.

S. Pond, G. L. Pickard, Introductory Dynamical Oceanography, 2nd ed. (Pergamon, New York, 1983).

Post, M. J.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Querry, M. R.

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

M. R. Querry, D. M. Wieliczka, D. J. Segelstein, “Water (H2O),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Boston, 1991).

Quinn, P. K.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Revercomb, H.

R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.

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, N. R. Nalli, “Observations 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]

Salisbury, J. W.

J. W. Salisbury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8-14 µm atmospheric window,” Remote Sens. Environ. 42, 83–106 (1992).
[CrossRef]

Saunders, P. M.

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

Segelstein, D. J.

M. R. Querry, D. M. Wieliczka, D. J. Segelstein, “Water (H2O),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Boston, 1991).

Sekelsky, S. M.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Shaw, J. A.

Sheppard, C. J. R.

C. J. R. Sheppard, “Imaging of random surfaces and inverse scattering in the Kirchhoff approximation,” Waves Random Media 8, 53–66 (1998).
[CrossRef]

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series, English edition translated by D. Oliver (American Institute of Physics, New York, 1988).

Smith, W.

R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.

Smith, W. L.

N. R. Nalli, W. L. Smith, “Improved remote sensing of sea surface skin temperature using a physical retrieval method,” J. Geophys. Res. 103, 10527–10542 (1998).
[CrossRef]

X. Wu, W. L. Smith, “Emissivity of rough sea surface for 8–13 µm: modeling and validation,” Appl. Opt. 36, 1–11 (1997).

X. Wu, W. L. Smith, “Sensitivity of sea surface temperature retrieval to sea surface emissivity, English translation,” Acta Meteorol. Sin. 10, 376–384 (1996).

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, N. R. Nalli, “Observations 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]

D. Cousins, W. L. Smith, “National Polar-orbiting Environmental Satellite System (NPOESS) Airborne Sounder Testbed-Interferometer (NAST-I),” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 323–331 (1997).
[CrossRef]

Snider, J. B.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electomagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

Stogryn, A.

A. Stogryn, “The apparent temperature of the sea at microwave frequencies,” IEEE Trans. Antennas Propag. 15, 278–286 (1967).
[CrossRef]

Takashima, T.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sens. Environ. 24, 313–329 (1988).
[CrossRef]

Takayama, Y.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sens. Environ. 24, 313–329 (1988).
[CrossRef]

Watts, P.

P. Watts, M. Allen, T. Nightingale, “Sea surface emission and reflection for radiometric measurements made with the along-track scanning radiometer,” J. Atmos. Oceanic Technol. 13, 126–141 (1996).
[CrossRef]

Weickmann, K. M.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Weng, S.

White, A. B.

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

Wieliczka, D. M.

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

M. R. Querry, D. M. Wieliczka, D. J. Segelstein, “Water (H2O),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Boston, 1991).

Williams, W.

Woolf, H. M.

Wu, X.

X. Wu, W. L. Smith, “Emissivity of rough sea surface for 8–13 µm: modeling and validation,” Appl. Opt. 36, 1–11 (1997).

X. Wu, W. L. Smith, “Sensitivity of sea surface temperature retrieval to sea surface emissivity, English translation,” Acta Meteorol. Sin. 10, 376–384 (1996).

Acta Meteorol. Sin. (1)

X. Wu, W. L. Smith, “Sensitivity of sea surface temperature retrieval to sea surface emissivity, English translation,” Acta Meteorol. Sin. 10, 376–384 (1996).

Appl. Opt. (5)

Bull. Am. Meteorol. Soc. (3)

M. J. Post, C. W. Fairall, J. B. Snider, Y. Han, A. B. White, W. L. Ecklund, K. M. Weickmann, P. K. Quinn, D. I. Cooper, S. M. Sekelsky, R. E. McIntosh, P. Minnett, R. O. Knuteson, “The Combined Sensor Program: an air–sea science mission in the central and western Pacific Ocean,” Bull. Am. Meteorol. Soc. 78, 2797–2815 (1997).
[CrossRef]

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, N. R. Nalli, “Observations 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]

E. J. Kearns, J. A. Hanafin, R. H. Evans, P. J. Minnett, O. B. Brown, “An independent assessment of Pathfinder AVHRR sea surface temperature accuracy using the marine atmosphere emitted radiance interferometer (MAERI),” Bull. Am. Meteorol. Soc. 81, 1525–1536 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Stogryn, “The apparent temperature of the sea at microwave frequencies,” IEEE Trans. Antennas Propag. 15, 278–286 (1967).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

P. Watts, M. Allen, T. Nightingale, “Sea surface emission and reflection for radiometric measurements made with the along-track scanning radiometer,” J. Atmos. Oceanic Technol. 13, 126–141 (1996).
[CrossRef]

J. Geophys. Res. (2)

N. R. Nalli, W. L. Smith, “Improved remote sensing of sea surface skin temperature using a physical retrieval method,” J. Geophys. Res. 103, 10527–10542 (1998).
[CrossRef]

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

J. Mar. Res. (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

J. Opt. Soc. Am. (2)

Remote Sens. Environ. (2)

J. W. Salisbury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8-14 µm atmospheric window,” Remote Sens. Environ. 42, 83–106 (1992).
[CrossRef]

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sens. Environ. 24, 313–329 (1988).
[CrossRef]

Waves Random Media (1)

C. J. R. Sheppard, “Imaging of random surfaces and inverse scattering in the Kirchhoff approximation,” Waves Random Media 8, 53–66 (1998).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

L. M. Brekhovskikh, “The diffraction of waves by a rough surface, part I,” Zh. Eksp. Teor. Fiz. 23, 275–289 (1952).

Other (16)

P. L. C. Jeynes, “The scattering of electromagnetic radiation from irregular surfaces,” in Mathematics in Remote Sensing, S. R. Brooks, ed. (Clarendon, Oxford, 1989).

G. S. Brown, “Quasi-specular scattering from the air–sea interface,” in Surface Waves and Fluxes: Volume II—Remote Sensing, Vol. 8 of Environmental Fluid Mechanics, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, 1990).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media: Multiple Scattering, Turbulence, Rough Surfaces, and Remote Sensing (Academic, New York, 1978), Vol. 2.

P. Beckmann, A. Spizzichino, The Scattering of Electomagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

D. Cousins, W. L. Smith, “National Polar-orbiting Environmental Satellite System (NPOESS) Airborne Sounder Testbed-Interferometer (NAST-I),” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 323–331 (1997).
[CrossRef]

S. Pond, G. L. Pickard, Introductory Dynamical Oceanography, 2nd ed. (Pergamon, New York, 1983).

P. J. Minnett, R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin, O. B. Brown, “The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a high-accuracy, sea-going infrared spectroradiometer,” J. Atmos. Oceanic Technol. (to be published).

R. Knuteson, P. Minnett, H. Revercomb, W. Smith, “High spectral resolution infrared observations at the ocean–atmosphere interface in the Tropical Western Pacific using a marine atmospheric emitted radiance interferometer (MAERI),” in Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 180–183.

R. O. Knuteson, Space Science and Engineering Center, University of Wisconsin-Madison, Madison, Wis. (personal communication, 1999).

N. R. Nalli, “A physical multispectral method for the retrieval of ocean and lake surface temperatures via scanning spectrometer,” Ph.D. dissertation (University of Wisconsin-Madison, Madison, Wis., 2000).

D. E. Hagan, N. R. Nalli, “Tropical water vapor correction for remotely sensed sea surface temperature: results using narrowband window radiance profiles from TOGA COARE,” J. Geophys. Res. (to be published).

N. R. Nalli, “Sea surface skin temperature retrieval using the high-resolution interferometer sounder,” M.S. thesis (University of Wisconsin-Madison, Madison, Wis., 1995).

C. S. Cox, “Refraction and reflection of light at the sea surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974).

M. R. Querry, D. M. Wieliczka, D. J. Segelstein, “Water (H2O),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Boston, 1991).

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series, English edition translated by D. Oliver (American Institute of Physics, New York, 1988).

G. L. Pickard, W. J. Emery, Descriptive Physical Oceanography: An Introduction, 5th ed. (Pergamon, New York, 1990).

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Figures (9)

Fig. 1
Fig. 1

Cartesian coordinate system for a sea surface wave facet under the Kirchhoff approximation. The z axis is the local zenith (vertical), and the horizontal x and y axes are chosen such that the reflected ray vector lies in the xz plane with zenith angle θ0. Θ i = Θ r is the incidence angle relative to the facet unit normal vector defined by zenith and azimuth angles θ n and φ (after Masuda et al.3 and Wu and Smith,5 with some modification).

Fig. 2
Fig. 2

Reflected surface emission geometry consistent with that of Fig. 1 (after Watts et al.4 and Wu and Smith,5 with some modification).

Fig. 3
Fig. 3

Reflection-diffusivity angle θ̅ ν versus zenith view angle θ0 and mean wind speed . The leftmost plots are for a limiting-case dry atmosphere, and the rightmost plots are for a limiting-case moist atmosphere. The bottom two plots are two-dimensional renderings of the top two plots.

Fig. 4
Fig. 4

Ray-trace schematic of reflection at a water surface. Ray widths indicate relative magnitudes in radiance. The top two panels are for a smooth surface, whereas the bottom two panels are for a wind-roughened, wavy surface. The leftmost panels are for a small zenith view angle, and the rightmost panels are for a large zenith view angle.

Fig. 5
Fig. 5

Reflection-diffusivity angle plotted as a function of wave number and zenith view angle for a moist limiting-case atmosphere and mean wind speed = 12.5 m/s.

Fig. 6
Fig. 6

Hourly weather observation photograph taken at approximately 00:13 UTC on 24 March 1996. Much of the scanning range of M-AERI (lower right) is visible. Note the presence of low-level cumulus and high-level cirrus clouds.

Fig. 7
Fig. 7

Model calculations derived from the RAOB launch at 22:18 UTC on 17 March 1996 versus the M-AERI observations for a 55° view angle. The locations of water-vapor absorption lines are apparent as spikes in the spectra.

Fig. 8
Fig. 8

Model calculations derived from the 22:18 UTC RAOB launch on 17 March 1996 versus M-AERI observations, 21.52–22.49 UTC (2.1° S, 179.9° W). Panels are for the 65°, 55°, 45°, and 35° ocean views. The mean wind speed and ship roll angle were, respectively, ≃ 4.9 m/s and ϑ̅ ≃ -1.08°.

Fig. 9
Fig. 9

Same as Fig. 8 except for the RAOB launch at 22:28 UTC on 9 April 1996 (7.32° N, 172.6° W). = 13.7 m/s and ϑ̅ = -0.45° for the observing period 22.09–22.83 UTC.

Tables (1)

Tables Icon

Table 1 Computed Values of x j,k and W j,k for use in the Gauss Formulaa

Equations (33)

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

Rνsθ0, φ0=02π0π/2 rνθ, φ; θ0, φ0Iνθ, φ×cosθsinθdθdφ,
ρNν, Θi=12|ρNν, Θi|2+|ρNν, Θi|2,
χ=2kR cosΘi  1.
Pzx, zy=12πσ2exp-zx2+zy22σ2.
Rνsθ0, φ0=1μ0-- ρNν, ΘiIνΘiPzx, zy×cosΘiμndzxdzy,
Pzx, zy=Pμn, σ2=12πσ2exp-1-μn22μn2σ2.
cosΘi=μ0μn+cosφ1-μ021-μn21/2.
dzxdzy=zx, zyμn, φdμndφ,
zx, zyμn, φ=sec2 θn cos φsin θntan θn sin φsec2 θn sin φsin θn-tan θn cos φ=- 1μn3.
cosβ1=cosθ0-cosθncosΘisinθnsinΘi.
μ=2μn cosΘiμ0, μn, φ-μ0.
Rνsμ0=2μ001Pμn, σ2μn40π ρNν, Θi×IνμΘi, μ0, μncosΘidφdμn,
ΣPμn, σ22μ001Pμn, σ2μn4×0πcosΘiμ0, μn, φdφdμn,
cosφ>-cotθ0cotθn.
φ2θ0, θn=π,-cot θ0 cot θn-1θ0=0°arccos-cot θ0 cot θn,-1<-cot θ0 cot θn1θ0>0°0,-cot θ0 cot θn>1θ0>0°.
P*μn, μ0, Θi, σ22μ0-1μn-4 cosΘiPμn, σ2ΣPμn, σ2,
010π P*μn, μ0, Θi, σ2dφdμn=1.
Rνsμ0=010φ2 ρNν, ΘiIνμΘi, μ0, μn×P*μn, μ0, Θi, σ2dφdμn.
*Nν, ΘiNν, Θi+1-Nν, ΘiPsθ¯sNν, θr.
Psθ0,θ<85°θ-85°225,85°θ90°1,θ>90°.
ρ*Nν, Θi=1-*Nν, Θi.
ρ*Nν, Θi=ρNν, Θi-ρNν, ΘiPsθ1-r¯sNν, θr,
r¯sNν, θr010φ2 ρNν, ΘiP*μn, μr, Θi, σ2dφdμn,
Rνsμ0=010φ2 ρ*Nν, ΘiIνμΘi, μ0, μn×P*μn, μ0, Θi, σ2dφdμn.
Iνθ¯νμn110φ2 ρ*IνθP*dφdμnμn110φ2 ρ*P*dφdμn,
Rνsθ0=Iνθ¯νμn110φ2 ρ*Nν, Θi×P*μn, μ0, Θi, σ2dφdμn=Iνθ¯νr¯νθ0, V¯,
-11 fxdxj=-mm Wjfxj.
Wj=1dP2mxdxxj-11P2mxx-xjdx,
ab fxdxb-a2j=-mm Wjfa+b2+b-a2 xj,
μn-4 exp-1-μn22μn2σ20
1μn14exp-1-μn122μn12σ2ε,
Rνsμ0=1-μn12j=-mjmj Wjφ2j2k=-mkmk Wkρj,k*Iνμj,kPj,k*,
ρj,k*ρ*Nν, Θij,k,μj,kμΘij,k, μ0, μnj,Pj,k*P*μnj, μ0, Θij,k, σ2,Θij,kΘiμ0, μnj, φk,φk=φ2/21+φk,μnj=μn1+1/2+1-n1/2μ

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