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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17528–17538

A model for the probability density function of downwelling irradiance under ocean waves

Meng Shen, Zao Xu, and Dick K. P. Yue  »View Author Affiliations

Optics Express, Vol. 19, Issue 18, pp. 17528-17538 (2011)

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We present a statistical model that analytically quantifies the probability density function (PDF) of the downwelling light irradiance under random ocean waves modeling the surface as independent and identically distributed flat facets. The model can incorporate the separate effects of surface short waves and volume light scattering. The theoretical model captures the characteristics of the PDF, from skewed to near-Gaussian shape as the depth increases from shallow to deep water. The model obtains a closed-form asymptotic for the probability that diminishes at a rate between exponential and Gaussian with increasing extreme values. The model is validated by comparisons with existing field measurements and Monte Carlo simulation.

© 2011 OSA

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.5620) Atmospheric and oceanic optics : Radiative transfer

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: June 29, 2011
Revised Manuscript: August 10, 2011
Manuscript Accepted: August 12, 2011
Published: August 22, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Meng Shen, Zao Xu, and Dick K. P. Yue, "A model for the probability density function of downwelling irradiance under ocean waves," Opt. Express 19, 17528-17538 (2011)

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  1. W. McFarland and E. Loew, “Wave produced changes in underwater light and their relations to vision,” Environ. Biol. Fish 8, 173–184 (1983). [CrossRef]
  2. W. C. Brown and A. K. Majumdar, “Point-spread function associated with underwater imaging through a wavy air-water interface: theory and laboratory tank experiment,” Appl. Opt. 31(36), 7650–7659 (1992). [CrossRef] [PubMed]
  3. J. R. V. Zaneveld and P. A. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express 9(6), 260–266 (2001). [CrossRef] [PubMed]
  4. R. L. Snyder and J. Dera, “Wave-induced light-field fluctuations in sea,” J. Opt. Soc. Am. B 60(8), 1072–1083 (1970). [CrossRef]
  5. H. R. Gordon, J. S. Smith, and O. B. Brown, “Spectra of underwater light-field fluctuations in the photic zone,” Bull. Mar. Sci 21, 466–470 (1971).
  6. J. Dera and D. Stramski, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).
  7. D. Stramski and L. Legendre, “Laboratory simulation of light focusing by water surface waves,” Mar. Biol 114, 341–348 (1992). [CrossRef]
  8. J. Dera, S. Sagan, and D. Stramski, “Focusing of sunlight by sea surface waves: new results from the Black Sea,” Oceanologia 34, 13–25 (1993).
  9. H. W. Wijesekera, W. S. Pegau, and T. J. Boyd, “Effect of surface waves on the irradiance distribution in the upper ocean,” Opt. Express 13(23), 9257–9264 (2005). [CrossRef] [PubMed]
  10. P. Gernez and D. Antoine, “Field characterization of wave-induced underwater light field fluctuations,” J. Geophys. Res. 114(15), C06025 (2009). [CrossRef]
  11. Y. You, D. Stramski, M. Darecki, and G. W. Kattawar, “Modeling of wave-induced irradiance fluctuations at near-surface depths in the ocean: a comparison with measurements,” Appl. Opt. 49(6), 1041–1053 (2010). [CrossRef] [PubMed]
  12. P. Gernez, D. Stramski, and M. Darecki, “Vertical changes in the probability distribution of downwelling irradiance within the near-surface ocean under clear sky conditions,” presented at Ocean Optics XX, Anchorage, Alaska, 27 September 2010.
  13. C. D. Mobley, Light and Water Radiative Transfer in Natural Waters (Academic Press, 1994).
  14. J. W. McLean and J. D. Freeman, “Effects of ocean waves on airborne lidar imaging,” Appl. Opt.35(18), 3261–3269 (1996). [CrossRef] [PubMed]
  15. J. R. V. Zaneveld and E. Boss, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40(9), 1442–1449 (2001). [CrossRef]
  16. J. Hedley, “A three-dimensional radiative transfer model for shallow water environments,” Opt. Express 16(26), 21887–21902 (2008). [CrossRef] [PubMed]
  17. P. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method,” Appl. Opt. 47, 1037–1047 (2008). [CrossRef] [PubMed]
  18. P. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. II. the hybrid matrix operator-Monte Carlo method,” Appl. Opt. 47, 1063–1071 (2008). [CrossRef] [PubMed]
  19. V. L. Veber, “On the spatial fluctuations of underwater illumination,” Izv. Atmos. Oceanic Phys. 18, 735–741 (1982).
  20. V. I. Shevernev, “Statistical structure of the illumination field under a wavy surface,” Izv. Atmos. Oceanic Phys. 18, 735–741 (1973).
  21. B. R. Frieden, Probability, Statistical Optics, and Data Testing: A Problem Solving Approach (Springer, 1983). [CrossRef]
  22. C. Cox and W. H. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. B 44(11), 838–850 (1954). [CrossRef]
  23. R. G. Gallager, Discrete Stochastic Processes (Springer, 1996).
  24. R. E. Walker, Marine Light Field Statistics (Wiley-Interscience, 1994).
  25. Z. Xu, “A DNS capability for obtaining underwater light field and retrieving upper ocean conditions via in-water light measurements,” thesis (MIT, 2011).

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