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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 12, Iss. 9 — Sep. 1, 1995
  • pp: 2022–2030

Radiance of the ocean horizon

C. R. Zeisse  »View Author Affiliations

JOSA A, Vol. 12, Issue 9, pp. 2022-2030 (1995)

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Cox and Munk used aerial photographs of Sun glint to determine the statistical distribution of ocean capillary wave slopes as a function of wind velocity [ J. Opt. Soc. Am. 44, 838 ( 1954)]. When their equation connecting the slope distribution with Sun glint is used on the horizon, however, an infinite glint is predicted even though Sun glint never exceeds solar radiance. An integral equation connecting the capillary wave slope distribution with ocean radiance is derived. The integral predicts a finite Sun glint on the ocean horizon and, away from the horizon, reduces to the algebraic form used by Cox and Munk.

© 1995 Optical Society of America

Original Manuscript: December 16, 1994
Revised Manuscript: April 21, 1995
Manuscript Accepted: April 26, 1995
Published: September 1, 1995

C. R. Zeisse, "Radiance of the ocean horizon," J. Opt. Soc. Am. A 12, 2022-2030 (1995)

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  1. R. E. Walker, Marine Light Field Statistics (Wiley, New York, 1994), Chap. 7, pp. 297–343.
  2. M. S. Longuet-Higgins, “On the statistical distribution of the heights of sea waves,” J. Mar. Res. 11, 245–266 (1952).
  3. S. Q. Duntley, “Measurements of the distribution of water wave slopes,” J. Opt. Soc. Am. 44, 574–575 (1954). [CrossRef]
  4. C. Cox, 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]
  5. C. Cox, W. Munk, “Slopes of the sea surface deduced from photographs of Sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).
  6. G. Plass, G. Kattawar, J. Guinn, “Radiative transfer in the Earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt. 14, 1924–1946 (1975). [CrossRef] [PubMed]
  7. J. Gordon, “Directional radiance (luminance) of the sea surface,” Scripps Inst. Oceanogr. Visibility Lab. Rep.69–20, 1–50 (Scripps Institution of Oceanography, San Diego, Calif., 1969).
  8. R. Preisendorfer, Surfaces, Vol. 6 of Hydrologic Optics (National Oceanic and Atmospheric Administration, U.S. Dept. of Commerce, Honolulu, Hawaii, 1976), pp. 263 ff.
  9. C. R. Zeisse, “Radiance of the ocean horizon,” Naval Command, Control and Ocean Surveillance Center Research, Development, Test and Evaluation Division Tech. Rep.1660, 1–30 (1994). This reference also contains the fortran code for evaluating the equations used throughout this paper and for generating ASCII files to create many of these figures. The source code is available on disk through correspondence with the author, whose e-mail address is zeisse@nosc.mil.
  10. The tolerance ellipse contains all those slopes capable of reflecting a ray from any part of the solar disk into the receiver.
  11. One can see that this is the case by imagining a receiver on the shore looking directly into a Sun whose center is exactly on the far horizon. Only the upper half of the Sun’s disk would be visible. A facet with nearly zero slope would be required for reflection of the very top of this half-disk into the receiver, but facets with infinite slope would be required if one wished to reflect into the receiver those sides of the half-disk that touch the horizon.
  12. C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).
  13. P. Saunders, “Radiance of sea and sky in the infrared window 800–1200 cm−1,” J. Opt. Soc. Am. 58, 645–652 (1968). [CrossRef]

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