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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 44, Iss. 11 — Nov. 1, 1954
  • pp: 838–850

Measurement of the Roughness of the Sea Surface from Photographs of the Sun’s Glitter

CHARLES COX and WALTER MUNK  »View Author Affiliations

JOSA, Vol. 44, Issue 11, pp. 838-850 (1954)

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A method is developed for interpreting the statistics of the sun’s glitter on the sea surface in terms of the statistics of the slope distribution. The method consists of two principal phases: (1) of identifying, from geometric considerations, any point on the surface with the particular slope required for the reflection of the sun’s rays toward the observer; and (2) of interpreting the average brightness of the sea surface in the vicinity of this point in terms of the frequency with which this particular slope occurs. The computation of the probability of large (and infrequent) slopes is limited by the disappearance of the glitter into a background consisting of (1) the sunlight scattered from particles beneath the sea surface, and (2) the skylight reflected by the sea surface.

The method has been applied to aerial photographs taken under carefully chosen conditions in the Hawaiian area. Winds were measured from a vessel at the time and place of the aerial photographs, and cover a range from 1 to 14 m sec-1. The effect of surface slicks, laid by the vessel, are included in the study. A two-dimensional Gram-Charlier series is fitted to the data. As a first approximation the distribution is Gaussian and isotropic with respect to direction. The mean square slope (regardless of direction) increases linearly with the wind speed, reaching a value of (tan 16°)2 for a wind speed of 14 m sec-1. The ratio of the up/downwind to the crosswind component of mean square slope varies from 1.0 to 1.9. There is some up/downwind skewness which increases with increasing wind speed. As a result the most probable slope at high winds is not zero but a few degrees, with the azimuth of ascent pointing downwind. The measured peakedness which is barely above the limit of observational error, is such as to make the probability of very large and very small slopes greater than Gaussian. The effect of oil slicks covering an area of one-quarter square mile is to reduce the mean square slopes by a factor of two or three, to eliminate skewness, but to leave peakedness unchanged.

CHARLES COX and WALTER MUNK, "Measurement of the Roughness of the Sea Surface from Photographs of the Sun’s Glitter," J. Opt. Soc. Am. 44, 838-850 (1954)

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  1. J. Spooner, Corresp. Astro. du Baron de Zach, 6 (1822).
  2. E. O. Hulbert, J. Opt. Soc. Am. 24, 35 (1934).
  3. V. V. Shuleikin, Fizika Moria (Physics of the Sea) (Izdatelstvo Akad. Nauk. U.S.S.R., Moscow, 1941).
  4. M. Minnaert, Physica 9, 925 (1942).
  5. J. S. Van Wieringen, Proc. Koninkl. Ned. Akad. Wetenschap. 50, 952 (1947).
  6. Carl Eckart, The sea surface and its effect on the reflection of sound and light. University of Calif. Div. of War Research No. M407, March 20, 1946 (unpublished). The horizontal extent of the glitter pattern is assumed small compared to the distance from the observer.
  7. C. Cox and W. H. Munk, Scripps Inst. of Oceanogr. Bull. (to be published).
  8. C. Eckart, J. Acoust. Soc. Am. 25, 566 (1953). Here the linearized equations are developed for the case where the incoming radiation is not necessarily short compared to the ocean waves. For the limiting case of short-wave radiation, Eckart obtains essentially p=4ρ-1(N cosµ/H).
  9. For example, Harald Cramer, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946). This gives a general account, but the development in two dimensions could not be found in the literature. Details are given in reference 7.
  10. This accounts for the fact that one rarely sees distant trees, dunes, or ships reflected in the sea. The reason, as pointed out by Minnaert [M. Minnaert, Light and Colour in the Upper Air (G. Bell and Sons, London, 1940)], is that "at a great distance one sees only the sides of waves turned toward us. This makes it seem as if we saw all the objects … reflected in a slanting mirror." For the same reason, the reflection of low, distant clouds is displaced toward the horizon.
  11. S. Q. Duntley, "The visibility of submerged objects." Part I, Optical Effects of Water Waves. Mass. Inst. Tech. Report, Dec. 15, 1950, on U. S. Office of Naval Research Report NO N5 ori-07831.
  12. A. H. Schooley, J. Opt. Soc. Am. 44, 37 (1954).

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