Abstract

Oceanic waves have been found to contribute enhanced back-scattering in the direction of the illumination source in studies that assumed the ocean surface to be a random sum of waves. Here we investigate enhanced back-scattering by coherent capillary-gravity wave trains that co-exist near the crests of short gravity waves in the ocean. We find that the enhanced back-scattering effect is intensified relative to that of a random surface and that the effect is observed at larger angles. This effect may not only affect active sensors such as lidar, which have a viewing angle close to that of the source but possibly passive sensors as well. This effect is likely to result in biases when attempting closure between radiative transfer models that do not include realistic representation of the ocean surface and observed water leaving radiance.

© Optical Society of America

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References

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  1. See SeaWiFS and MODIS remote sensing programs on the NASA website: http://www.earth.nasa.gov/
  2. A.G. Luchinin, �Influence of wind waves on the characteristics of the light field backscattered by the bottom and the intervening water,� Izv. Atmos. Oceanic Phys. 15, 531-534 (1979).
  3. A.G. Luchinin, �The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,� Izv. Atmos. Oceanic Phys. 18, 431-434 (1982) .
  4. R.E. Walker, Marine Light Field Statistics, (Wiley, New York, 1994).
  5. M.D. Cox and W. H. Munk, �Statistics of the sea surface derived from sun glitter,� J. Mar. Res. 13, 198. (1954).
  6. W.J. Pierson and L. Moskowitz , �A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitigorodski,� J. Geophys. Res. 69, 5181-5190, (1964).
    [CrossRef]
  7. P.A. Hwang, S. Atakturk, M.. Sletten and D. B. Trizna, �A study of the wavenumber spectra of short water waves in the ocean,� J. Phys. Oceanogr. 26, 1266-1285 (1996).
    [CrossRef]
  8. M.S. Longuet-Higgins, �The generation of capillary gravity waves by steep gravity waves,� J. Fluid Mech. 16, 138-159 (1963).
    [CrossRef]
  9. M.S. Longuet-Higgins, �A non-linear mechanism for the generation of sea waves,� Proc. Roy. Soc. Ser. A 311, 529. (1969).
  10. J. R. V. Zaneveld, E. S. J. Boss and A. Barnard, �Influence of surface waves on measured and modeled irradiance profiles,� Appl. Optics 40, 1442-1449 (2001).
    [CrossRef]
  11. M.S. Longuet-Higgins, �Capillary rollers and bores,� J. Fluid Mech., 240, 659-679 (1992).
    [CrossRef]
  12. C.S. Cox, �Measurements of slopes of high-frequency wind waves,� J. Mar. Res. 16, 199-225 (1958).
  13. P.A. Hwang, D. B. Trizna and J. Wu, �Spatial measurements of short wind waves using a scanning slope sensor,� Dyna. Atmos. and Oceans 20, 1-23 (1993).
    [CrossRef]
  14. P.A. Hwang, �Microstructure of ocean surface roughness: A study of spatial measurement and laboratory investigation of modulation analysis,� J. Atmos. and Oceanic Tech. 16, 1619-1629 (1999).
    [CrossRef]
  15. N.G. Jerlov, Marine Optics, (Elsevier, Amsterdam, 1976, p. 9).

Other

See SeaWiFS and MODIS remote sensing programs on the NASA website: http://www.earth.nasa.gov/

A.G. Luchinin, �Influence of wind waves on the characteristics of the light field backscattered by the bottom and the intervening water,� Izv. Atmos. Oceanic Phys. 15, 531-534 (1979).

A.G. Luchinin, �The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,� Izv. Atmos. Oceanic Phys. 18, 431-434 (1982) .

R.E. Walker, Marine Light Field Statistics, (Wiley, New York, 1994).

M.D. Cox and W. H. Munk, �Statistics of the sea surface derived from sun glitter,� J. Mar. Res. 13, 198. (1954).

W.J. Pierson and L. Moskowitz , �A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitigorodski,� J. Geophys. Res. 69, 5181-5190, (1964).
[CrossRef]

P.A. Hwang, S. Atakturk, M.. Sletten and D. B. Trizna, �A study of the wavenumber spectra of short water waves in the ocean,� J. Phys. Oceanogr. 26, 1266-1285 (1996).
[CrossRef]

M.S. Longuet-Higgins, �The generation of capillary gravity waves by steep gravity waves,� J. Fluid Mech. 16, 138-159 (1963).
[CrossRef]

M.S. Longuet-Higgins, �A non-linear mechanism for the generation of sea waves,� Proc. Roy. Soc. Ser. A 311, 529. (1969).

J. R. V. Zaneveld, E. S. J. Boss and A. Barnard, �Influence of surface waves on measured and modeled irradiance profiles,� Appl. Optics 40, 1442-1449 (2001).
[CrossRef]

M.S. Longuet-Higgins, �Capillary rollers and bores,� J. Fluid Mech., 240, 659-679 (1992).
[CrossRef]

C.S. Cox, �Measurements of slopes of high-frequency wind waves,� J. Mar. Res. 16, 199-225 (1958).

P.A. Hwang, D. B. Trizna and J. Wu, �Spatial measurements of short wind waves using a scanning slope sensor,� Dyna. Atmos. and Oceans 20, 1-23 (1993).
[CrossRef]

P.A. Hwang, �Microstructure of ocean surface roughness: A study of spatial measurement and laboratory investigation of modulation analysis,� J. Atmos. and Oceanic Tech. 16, 1619-1629 (1999).
[CrossRef]

N.G. Jerlov, Marine Optics, (Elsevier, Amsterdam, 1976, p. 9).

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Figures (5)

Fig.1.
Fig.1.

Ray pattern beneath a sinusoidal wave with a wavelength of 1m and amplitude of 10 cm.

Fig. 2.
Fig. 2.

An example of calculated irradiance relative to the irradiance just above the sea surface. The absorption coefficient is 0.07 m-1 and the scattering coefficient is 0.39 m-1; the wave surface is wavelength L=[1.1 0.55 0.05] m and amplitude A=[0.05 0.01 0.0008]m. The beam is 0.8 m wide and enters vertically. Fig.3a shows the beam entering near the trough of a wave, generating a divergent beam. On Fig.3b the light enters near the crest of a wave, generating a convergent beam with a focal area.

Fig. 3.
Fig. 3.

The dependence of the remote sensing reflectance on wave amplitude for a wave of wavelength of 0.01 m and on the angle of separation between the light source and the light detector, normalized to the reflectance for a flat sea surface just below the sea surface. The amplitude of the wave is given in the legend box in cm.

Fig. 4.
Fig. 4.

Source rays in red and detector rays in blue for a sine wave with wavelength of 0.01m and amplitude of 0.003m. The source detector separation is 15 degrees. Horizontal and vertical axes are not to the same scale. When the wave is steep, the primary focal point is “trapped” in the wave. The source and detector focal points are then further apart the larger the separation angle. This results in a steadily decreasing reflectance as a function of separation angle as can be seen in Fig. 3 for the steeper waves (curves 1and 2 in Fig. 3).

Fig. 5.
Fig. 5.

Same as for Fig.5, but for wave amplitude of 0.0001 m. Note different vertical scale. When the wave is less steep there can be multiple locations where the source and receiver focal points overlap. This sets up a periodic response function (curves 5-7 in Fig.3).

Equations (1)

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Z f L = 2 A L + L ( 8 A )

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