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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 11 — Nov. 1, 2005
  • pp: 2442–2453

Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface

Vincent Ross, Denis Dion, and Guy Potvin  »View Author Affiliations

JOSA A, Vol. 22, Issue 11, pp. 2442-2453 (2005)

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A statistical sea surface specular BRDF (bidirectional reflectance distribution function) model is developed that includes mutual shadowing by waves, wave facet hiding, and projection weighting. The integral form of the model is reduced to an analytical form by making minor and justifiable approximations. The new form of the BRDF thus allows one to compute sea reflected radiance more than 100 times faster than the traditional numerical solutions. The repercussions of the approximations used in the model are discussed. Using the analytical form of the BRDF, an analytical approximation is also obtained for the reflected sun radiance that is always good to within 1% of the numerical solution for sun elevations of more than 10° above the horizon. The model is validated against measured sea radiances found in the literature and is shown to be in very good agreement.

© 2005 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(030.6600) Coherence and statistical optics : Statistical optics
(080.2720) Geometric optics : Mathematical methods (general)

ToC Category:
Atmospheric and ocean optics

Original Manuscript: January 31, 2005
Manuscript Accepted: March 18, 2005
Published: November 1, 2005

Vincent Ross, Denis Dion, and Guy 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)

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  1. R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Oceanogr. 16, 1293–1316 (1986). [CrossRef]
  2. C. Bourlier, J. Saillard, G. Berginc, “Effect of correlation between shadowing and shadowed points on the Wagner and Smith monostatic one-dimensional shadowing function,” IEEE Trans. Antennas Propag. 48, 437–446 (2000). [CrossRef]
  3. C. Bourlier, G. Berginc, “Microwave analytical backscattering models from randomly rough anisotropic sea surface—comparison with experimental data in C and Ku bands,” Electromagn. Waves 37, 31–78 (2002). [CrossRef]
  4. B. Henderson, J. Theiler, P. V. Villeneuve, “The polarized emissivity of a wind-roughened sea surface: a Monte-Carlo model,” Remote Sens. Environ. 88, 453–467 (2003). [CrossRef]
  5. W. Su, T. Charlock, K. Rutledge, “Observations of reflectance distribution around sunglint from a coastal ocean platform,” Appl. Opt. 41, 7369–7383 (2002). [CrossRef] [PubMed]
  6. C. R. Zeisse, “Radiance of the Ocean Horizon,” Tech. Rep. NCCOSC RDT&E TR-1660 (Naval Command, Control and Ocean Surveillance Center, RDT&E Division, San Diego, Calif., 1994).
  7. C. R. Zeisse, “Radiance of the ocean horizon,” J. Opt. Soc. Am. A 12, 2022–2030 (1995). [CrossRef]
  8. M. Mermelstein, E. Shettle, E. Takken, R. Priest, “Infrared radiance and solar glint at the ocean-sky horizon,” Appl. Opt. 33, 6022–6034 (1994). [CrossRef] [PubMed]
  9. D. Vaitekunas, “Technical manual for SHIPIR/NTCS (2.9),” Document A912-002 (Davis Engineering Limited, Ottawa, Ontario, Canada, 2002).
  10. C. Cox, 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]
  11. C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  12. J. Wu, “Sea-surface slope and equilibrium wind-wave spectra,” Phys. Fluids 13, 741–747 (1972). [CrossRef]
  13. J. Wu, “Mean squared slopes of the wind-disturbed water surface, their magnitude, directionality, and composition,” Radio Sci. 25, 37–48 (1990). [CrossRef]
  14. M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium range in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92, 4971–5029 (1987). [CrossRef]
  15. J. R. Apel, “An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter,” J. Geophys. Res. 99, 269–16 291 (1994).
  16. V. Ross, D. Dion, “Assessment of sea slope statistical models using a detailed micro-facet BRDF and upwelling radiance measurements,” in Proc. SPIE 5572, 112–122 (2004). [CrossRef]
  17. Y. Liu, M.-Y. Su, X.-H. Yan, W. T. Liu, “The mean-square slope of ocean surface waves and its effects on radar backscatter,” J. Atmos. Ocean. Technol. 17, 1092–1105 (2000). [CrossRef]
  18. P. A. Hwang, O. H. Shemdin, “The dependence of sea surface slope on atmospheric stability and swell conditions,” J. Geophys. Res. 93, 13,903–13,912 (1988). [CrossRef]
  19. J. A. Shaw, J. H. Churnside, “Scanning-laser glint measurements of sea-surface slope statistics,” Appl. Opt. 36, 4202–4213 (1997). [CrossRef] [PubMed]
  20. G. Plass, G. Kattawar, J. Guinn, “Radiative transfer in earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt. 14, 1924–1936 (1975). [CrossRef] [PubMed]
  21. B. G. Smith, “Lunar surface roughness, shadowing and thermal emission,” J. Geophys. Res. 72, 4059–4067 (1967). [CrossRef]
  22. B. G. Smith, “Geometrical shadowing of a random rough surface,” IEEE Trans. Antennas Propag. 15, 668–671 (1967). [CrossRef]
  23. R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Opt. Soc. Am. 41, 138–147 (1966).
  24. M. I. Sancer, “Shadow-corrected electromagnetic scattering from a randomly rough surface,” IEEE Trans. Antennas Propag. 17, 577–585 (1969). [CrossRef]
  25. Z. Jin, T. Charlock, K. Rutledge, “Analysis of Broadband Solar Radiation and Albedo over the Ocean Surface at COVE,” Bull. Am. Meteorol. Soc. 19, 1585–1601 (2002).
  26. W. J. Plant, “A new interpretation of sea-surface slope probability density functions,” J. Geophys. Res. 108, 3295–3298 (2003). [CrossRef]
  27. D. Rutan, F. Rose, N. Smith, T. Charlock, “Validation data set for CERES surface and atmospheric radiation budget (SARB),” World Climate Research Programme Global Energy and Water Cycle Experiment (WCRP/GEWEX) Newsletter 11, 11–12 (International GEWEX Project Office, Silver Spring, Maryland, 2001).
  28. J. L. Forand, “The L(W)WKD Marine Boundary Layer Model - Version 7.09,” Technical Report 1999-099 (Defence Research Establishment of Valcartier (DREV), Valcartier, Quebec, Canada, 1999).
  29. A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN7,” Technical Report GL-TR-89-0122 (Air Force Geophysics Laboratory, Bedford, Mass., 1989).
  30. P. K. Acharya, A. Berk, G. P. Anderson, N. F. Larsen, S.-C. Tsay, K. H. Stamnes, “MODTRAN4: Multiple Scattering and Bi-Directional Reflectance Distribution Function (BRDF) Upgrades to MODTRAN,” in Proc. SPIE 3756, 19–21 (1999).
  31. D. Dion, L. Gardenal, J. L. Forand, M. Duffy, G. Potvin, S. Daigle, “IR Boundary Layer Effects Model (IRBLEM), IRBLEM5.1 documentation, DRDC-RDDC Valcartier, Quebec, Canada (2004). (Available via e-mail by submitting request to the authors.)
  32. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988). [CrossRef]
  33. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993). [CrossRef] [PubMed]

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