Abstract

Radiometric images taken in mid-wave and long-wave infrared bands are used as a basis for validating a sea surface bidirectional reflectance distribution function (BRDF) being implemented into MODTRAN 5 (Berk et al. [Proc. SPIE 5806, 662 (2005)]). The images were obtained during the MIRAMER campaign that took place in May 2008 in the Mediterranean Sea near Toulon, France. When atmosphere radiances are matched at the horizon to remove possible calibration offsets, the implementation of the BRDF in MODTRAN produces good sea surface radiance agreement, usually within 2% and at worst 4% from off-glint azimuthally averaged measurements. Simulations also compare quite favorably to glint measurements. The observed sea radiance deviations between model and measurements are not systematic, and are well within expected experimental uncertainties. This is largely attributed to proper radiative coupling between the surface and the atmosphere implemented using the DISORT multiple scattering algorithm.

© 2012 Optical Society of America

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  1. A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
    [CrossRef]
  2. A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7,” Tech. Rep. GL-TR-89-0122 (Air-Force Geophysics Lab., 1989).
  3. 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. A 22, 2442–2453 (2005).
    [CrossRef]
  4. V. Ross and D. Dion, “Sea surface slope statistics derived from Sun glint radiance measurements and their apparent dependence on sensor elevation,” J. Geophys. Res. 112, C09015 (2007).
    [CrossRef]
  5. K. Stamnes, S.-C. Tsay, K. Jayaweera, and W. Wiscombe, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
    [CrossRef]
  6. P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
    [CrossRef]
  7. J. L. Forand, “The L(W)WKD marine boundary layer model—version 7.09,” Tech. Rep. 1999-099 (Defence Research Establishment of Valcartier (DREV), 1999).
  8. J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
    [CrossRef]
  9. L. Gardenal and D. Dion, “Aerosol optical properties code (AeroProC),” Tech. Rep. (2006) (available via e-mail by submitting request to the authors).
  10. S. G. Gathman, G. Deleeuw, K. L. Davidson, and D. R. Jensen, eds., The Naval Oceanic Vertical Aerosol Model (1990).
  11. S. G. Gathman, “Optical properties of the marine aerosols as predicted by the navy aerosol model,” Opt. Eng. 22, 57–62 (1983).
  12. T. Saemundsson, “Atmospheric refraction,” Sky and Telescope 72, 70 (1986).
  13. T. Elfouhaily, B. Chapron, K. Katsaros, and V. D., “A unified directional spectrum for long and short wind-driven waves,” J. Geophys. Res. 102, 15781–15796 (1997).
    [CrossRef]
  14. J. A. Shaw, D. Cimini, E. R. Westwater, Y. Han, H. M. Zorn, and J. H. Churnside, “Scanning infrared radiometer for measuring the air-sea temperature difference,” Appl. Opt. 40, 4807–4815 (2001).
    [CrossRef]
  15. A. Goroch, S. Burk, and K. L. Davidson, “Stability effects on aerosol size and height distributions,” Tellus 32, 245 (1980).
    [CrossRef]
  16. G. Tedeschi and J. Piazzola, “Development of a 2D marine aerosol transport model: application to the influence of thermal stability in the marine atmospheric boundary layer,” Atmos. Res. 101, 469–479 (2011).
    [CrossRef]
  17. P. A. Hwang and O. H. Shemdin, “The dependence of sea surface slope on atmospheric stability and swell conditions,” J. Geophys. Res. 93, 13903–13912 (1988).
    [CrossRef]
  18. J. A. Shaw and J. H. Churnside, “Scanning-laser glint measurements of sea-surface slope statistics,” Appl. Opt. 36, 4202–4213 (1997).
    [CrossRef]
  19. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  20. C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  21. Y. Liu, X.-H. Yan, and P. A. Hwang, “The probability density function of the ocean surface slopes and its effects on radar backscatter,” J. Phys. Oceanogr. 27, 782–797 (1997).
    [CrossRef]
  22. W. J. Plant, “A new interpretation of sea-surface slope probability density functions,” J. Geophys. Res. 108, 3295–3298 (2003).
    [CrossRef]
  23. B. G. Smith, “Lunar surface roughness, shadowing and thermal emission,” J. Geophys. Res. 72, 4059–4067 (1967).
    [CrossRef]
  24. B. G. Smith, “Geometrical shadowing of a random rough surface,” IEEE Trans. Antennas Propag. 15, 668–671(1967).
    [CrossRef]

2011 (1)

G. Tedeschi and J. Piazzola, “Development of a 2D marine aerosol transport model: application to the influence of thermal stability in the marine atmospheric boundary layer,” Atmos. Res. 101, 469–479 (2011).
[CrossRef]

2007 (1)

V. Ross and D. Dion, “Sea surface slope statistics derived from Sun glint radiance measurements and their apparent dependence on sensor elevation,” J. Geophys. Res. 112, C09015 (2007).
[CrossRef]

2005 (2)

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

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. A 22, 2442–2453 (2005).
[CrossRef]

2003 (2)

J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
[CrossRef]

W. J. Plant, “A new interpretation of sea-surface slope probability density functions,” J. Geophys. Res. 108, 3295–3298 (2003).
[CrossRef]

2001 (1)

1999 (1)

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

1997 (3)

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

Y. Liu, X.-H. Yan, and P. A. Hwang, “The probability density function of the ocean surface slopes and its effects on radar backscatter,” J. Phys. Oceanogr. 27, 782–797 (1997).
[CrossRef]

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

1988 (2)

K. Stamnes, S.-C. Tsay, K. Jayaweera, and W. Wiscombe, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[CrossRef]

P. A. Hwang and O. H. Shemdin, “The dependence of sea surface slope on atmospheric stability and swell conditions,” J. Geophys. Res. 93, 13903–13912 (1988).
[CrossRef]

1986 (1)

T. Saemundsson, “Atmospheric refraction,” Sky and Telescope 72, 70 (1986).

1983 (1)

S. G. Gathman, “Optical properties of the marine aerosols as predicted by the navy aerosol model,” Opt. Eng. 22, 57–62 (1983).

1980 (1)

A. Goroch, S. Burk, and K. L. Davidson, “Stability effects on aerosol size and height distributions,” Tellus 32, 245 (1980).
[CrossRef]

1967 (2)

B. G. Smith, “Lunar surface roughness, shadowing and thermal emission,” J. Geophys. Res. 72, 4059–4067 (1967).
[CrossRef]

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

1954 (2)

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 glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

Acharya, P. K.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

Adler-Golden, S. M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Anderson, G. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

Berk, A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7,” Tech. Rep. GL-TR-89-0122 (Air-Force Geophysics Lab., 1989).

Bernstein, L. S.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7,” Tech. Rep. GL-TR-89-0122 (Air-Force Geophysics Lab., 1989).

Borel, C. C.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Bouchara, F.

J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
[CrossRef]

Burk, S.

A. Goroch, S. Burk, and K. L. Davidson, “Stability effects on aerosol size and height distributions,” Tellus 32, 245 (1980).
[CrossRef]

Chapron, B.

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

Chetwynd, J. H.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Churnside, J. H.

Cimini, D.

Cooley, T. W.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Cox, C.

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 glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

D., V.

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

Davidson, K. L.

A. Goroch, S. Burk, and K. L. Davidson, “Stability effects on aerosol size and height distributions,” Tellus 32, 245 (1980).
[CrossRef]

S. G. Gathman, G. Deleeuw, K. L. Davidson, and D. R. Jensen, eds., The Naval Oceanic Vertical Aerosol Model (1990).

de Leeuw, G.

J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
[CrossRef]

Deleeuw, G.

S. G. Gathman, G. Deleeuw, K. L. Davidson, and D. R. Jensen, eds., The Naval Oceanic Vertical Aerosol Model (1990).

Dion, D.

V. Ross and D. Dion, “Sea surface slope statistics derived from Sun glint radiance measurements and their apparent dependence on sensor elevation,” J. Geophys. Res. 112, C09015 (2007).
[CrossRef]

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. A 22, 2442–2453 (2005).
[CrossRef]

L. Gardenal and D. Dion, “Aerosol optical properties code (AeroProC),” Tech. Rep. (2006) (available via e-mail by submitting request to the authors).

Elfouhaily, T.

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

Forand, J. L.

J. L. Forand, “The L(W)WKD marine boundary layer model—version 7.09,” Tech. Rep. 1999-099 (Defence Research Establishment of Valcartier (DREV), 1999).

Fox, M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Gardenal, L.

L. Gardenal and D. Dion, “Aerosol optical properties code (AeroProC),” Tech. Rep. (2006) (available via e-mail by submitting request to the authors).

Gardner, J. A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Gathman, S. G.

S. G. Gathman, “Optical properties of the marine aerosols as predicted by the navy aerosol model,” Opt. Eng. 22, 57–62 (1983).

S. G. Gathman, G. Deleeuw, K. L. Davidson, and D. R. Jensen, eds., The Naval Oceanic Vertical Aerosol Model (1990).

Goroch, A.

A. Goroch, S. Burk, and K. L. Davidson, “Stability effects on aerosol size and height distributions,” Tellus 32, 245 (1980).
[CrossRef]

Han, Y.

Hoke, M. L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Hwang, P. A.

Y. Liu, X.-H. Yan, and P. A. Hwang, “The probability density function of the ocean surface slopes and its effects on radar backscatter,” J. Phys. Oceanogr. 27, 782–797 (1997).
[CrossRef]

P. A. Hwang and O. H. Shemdin, “The dependence of sea surface slope on atmospheric stability and swell conditions,” J. Geophys. Res. 93, 13903–13912 (1988).
[CrossRef]

Jayaweera, K.

Jensen, D. R.

S. G. Gathman, G. Deleeuw, K. L. Davidson, and D. R. Jensen, eds., The Naval Oceanic Vertical Aerosol Model (1990).

Katsaros, K.

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

Larsen, N. F.

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

Lee, J.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Lewis, P. E.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Liu, Y.

Y. Liu, X.-H. Yan, and P. A. Hwang, “The probability density function of the ocean surface slopes and its effects on radar backscatter,” J. Phys. Oceanogr. 27, 782–797 (1997).
[CrossRef]

Lockwood, R. B.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Munk, W.

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 glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

Muratov, L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, and P. E. Lewis, “MODTRAN 5: a reformulated atmospheric band model with auxiliary species and practical multiple scattering options: update,” Proc. SPIE 5806, 662–667 (2005).
[CrossRef]

Piazzola, J.

G. Tedeschi and J. Piazzola, “Development of a 2D marine aerosol transport model: application to the influence of thermal stability in the marine atmospheric boundary layer,” Atmos. Res. 101, 469–479 (2011).
[CrossRef]

J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
[CrossRef]

Plant, W. J.

W. J. Plant, “A new interpretation of sea-surface slope probability density functions,” J. Geophys. Res. 108, 3295–3298 (2003).
[CrossRef]

Potvin, G.

Robertson, D. C.

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7,” Tech. Rep. GL-TR-89-0122 (Air-Force Geophysics Lab., 1989).

Ross, V.

V. Ross and D. Dion, “Sea surface slope statistics derived from Sun glint radiance measurements and their apparent dependence on sensor elevation,” J. Geophys. Res. 112, C09015 (2007).
[CrossRef]

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. A 22, 2442–2453 (2005).
[CrossRef]

Saemundsson, T.

T. Saemundsson, “Atmospheric refraction,” Sky and Telescope 72, 70 (1986).

Shaw, J. A.

Shemdin, O. H.

P. A. Hwang and O. H. Shemdin, “The dependence of sea surface slope on atmospheric stability and swell conditions,” J. Geophys. Res. 93, 13903–13912 (1988).
[CrossRef]

Smith, B. G.

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

B. G. Smith, “Lunar surface roughness, shadowing and thermal emission,” J. Geophys. Res. 72, 4059–4067 (1967).
[CrossRef]

Stamnes, K.

Stamnes, K. H.

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

Tedeschi, G.

G. Tedeschi and J. Piazzola, “Development of a 2D marine aerosol transport model: application to the influence of thermal stability in the marine atmospheric boundary layer,” Atmos. Res. 101, 469–479 (2011).
[CrossRef]

Tsay, S.

P. K. Acharya, A. Berk, G. P. Anderson, G. P. Anderson, N. F. Larsen, S. Tsay, and K. H. Stamnes, “MODTRAN4: multiple scattering and bidirectional reflectance distribution function (BRDF) upgrades to MODTRAN,” Proc. SPIE 3756, 354–362 (1999).
[CrossRef]

Tsay, S.-C.

van Eijk, A. M. J.

J. Piazzola, F. Bouchara, G. de Leeuw, and A. M. J. van Eijk, “Development of the Mediterranean extinction code (MEDEX),” Opt. Eng. 42, 912–924 (2003).
[CrossRef]

Westwater, E. R.

Wiscombe, W.

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Figures (9)

Fig. 1.
Fig. 1.

Synthetic color background generated using MODTRAN (left) and the difference in path (atmospheric) radiance for the same scene from using a fully coupled BRDF as the bottom boundary condition instead of a Lambertian surface with equivalent albedo.

Fig. 2.
Fig. 2.

Band II camera response with no filter installed (full line) and with the N23 filter used for solar glint images (dotted line).

Fig. 3.
Fig. 3.

Band III camera with LP11 filter installed.

Fig. 4.
Fig. 4.

Sea slope variances derived from the Elfouhaily et al. [13] wave spectrum plotted against wind speed.

Fig. 5.
Fig. 5.

Variation in modeled radiance when taking into account wind speed and slope variance model variability for case 108 (trial 1262) in the BIII band. Percentile differences from radiance measurements are also plotted in the lower pane.

Fig. 6.
Fig. 6.

Vertical profiles averaged in azimuth for all nonglint case. From top to bottom: ATAL 89 (trial 1116) in band BIII, ATAL 95 (trial 1159) in band BII, ATAL 107 (trial 1255) in band BII (left) and BIII (right), ATAL 109 (trial 1267) in band BII (left) and BIII (right).

Fig. 7.
Fig. 7.

Vertical profile (A) and horizontal profile (B) obtained for glint case ATAL 145 (trial 1416) in band BII. The vertical profile is averaged on zone A of the reference image (top), while the horizontal profile is averaged on zone B. The sun is located at azimuth 0°.

Fig. 8.
Fig. 8.

Vertical profile (A) and horizontal profile (B) obtained for glint case ATAL 64 (trial 902) in band BII. The vertical profile is averaged on zone A of the reference image (top), while the horizontal profile is averaged on zone B. The sun is located at azimuth 0°.

Fig. 9.
Fig. 9.

Coordinate system and representation of relevant quantities: U n , facet Cartesian normal unit vector; U r , receiver Cartesian unit vector; U s , source Cartesian unit vector; ω , reflection angle; θ i , zenith angle of U i vector ( ( i = n , r , s ) ; ϕ i , azimuth angle of U i vector ( i = n , r , s ) from upwind direction ( W ); ζ x , facet slope in the upwind ( W ) direction; ζ y , facet slope in the crosswind direction.

Tables (1)

Tables Icon

Table 1. Parameters for Selected Casesa

Equations (14)

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α = 1 2 0 k 2 M E ( k ) d k , β = 1 4 0 k 2 M E ( k ) Δ E ( k ) d k ,
σ x 2 = α + β , σ y 2 = α β .
f ( Ψ s , Ψ r ) = π L r ( Ψ r ) E s ( Ψ s ) cos θ s ,
f ( Ψ s , Ψ r ) p ( ζ ) ,
p 0 ( ζ ) 1 2 π σ x σ y exp { 1 2 ( ζ x 2 σ x 2 + ζ y 2 σ y 2 ) } ,
p ( ζ ) p 0 ( ζ ) { 1 1 2 c 21 ( Y 2 1 ) X 1 6 c 03 ( X 3 3 X ) . + 1 24 c 40 ( Y 4 6 Y 2 + 3 ) + 1 4 c 22 ( Y 2 1 ) ( X 2 1 ) + 1 24 c 04 ( X 4 6 X 2 + 3 ) } ,
X = ζ x σ x , Y = ζ y σ y .
c 21 = 0.01 0.0086 U , c 03 = 0.04 0.033 U ,
c 40 = 0.40 , c 22 = 0.12 , c 04 = 0.23 .
f ( Ψ s , Ψ r ) = π r ( Ψ s , Ψ r ) q v n ( Ψ s , Ψ r ) 4 z n 3 ( U n · U r ) cos θ s ,
q v n ( Ψ s , Ψ r ) = p ( ζ ) W ( ζ , Ψ r ) H ζ ( ζ , Ψ r ) [ 1 + Λ ( v r ) + Λ ( v s ) ] cos θ r ,
W ( ζ , Ψ r ) = U n · U r z n ,
H ζ ( ζ , Ψ r ) = ϒ ( U n · U r ) ,
Λ ( v ) = exp ( v 2 ) v r π erfc ( v ) 2 v π , v = cot ( θ ) 2 σ ( ϕ ) , σ ( ϕ ) = σ x 2 cos 2 ϕ + σ y 2 sin 2 ϕ .

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