Abstract

Irradiance fluctuations in the natural underwater light field close to the sea surface have an amplitude that is of the same order of magnitude as the mean irradiance. A principal source of these fluctuations, differential refraction by surface waves, is examined in this paper, and some experimental data obtained at an experimental site in the Bight of Abaco, Bahamas, are presented. A first-order single-ray theory is developed and the predictions of this theory are compared with the data. The theory identifies five refractive effects, the most important of which is the focusing and defocusing of light beams by fluctuations of surface curvature.

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  1. The reader is forewarned of an unavoidable duplication of terminology in the optical and geophysical aspects of this paper. Some confusion may result if this duplication is not borne in mind. Here, the terms "frequency" and "wavenumber" refer to the geophysical distribution of irradiance in the sea, not to the wave-mechanical properties of light.
  2. Y. Le Grand, Ann. Inst. Oceanogr. 19, 393 (1939).
  3. W. V. Burt, J. Meteorol. 11, 283 (1959).
  4. C. Cox and W. Munk, Bull. Scripps Inst. Oceanogr. 6, 401 (1956).
  5. K. Hishida and M. Kishino, J. Oceanogr. Soc. Japan 27, 748 (1965).
  6. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).
  7. Y. Mullamaa, Izv. Akad. Nauk. USSR. Sev. Geofiz. 8, 1232 (1964).
  8. H. Schenck, J. Opt. Soc. Am. 47, 653 (1957).
  9. J. Dera and H. R. Gordon, Linmnol. Oceanogr. 13, 697 (1968).
  10. J. Dera and J. Olszewski, Acta Geophys. Polon. 15, 351 (1967).
  11. In this paper, the terms "spectrum" and "spectra" are not optical terms, but refer to a time-series analysis of a random fluctuation.
  12. z is taken positive upwards with z = 0 at the mean water surface.
  13. Boldface letters will denote two-dimensional (horizontal) vector quantities. (h, ν) will denote a three-dimensional vector quantity with horizontal projection h and vertical component ν.
  14. This calculation assumes that the mean irradiance field is entirely the result of direct sun rays. The observations of Dera and Olszewski suggest that this assumption is only crudely satisfied. The value of the resulting attenuation coefficient is probably more representative of a downwelling-irradiance attenuation coefficient than it is of a beam-attenuation coefficient.
  15. As evidenced in the coordinate transformation (3) in Sec. III.
  16. The expansion parameter is essentially the rms surface-wave slope.
  17. The variables ξ and η here have a meaning different from their previous meaning.

Burt, W. V.

W. V. Burt, J. Meteorol. 11, 283 (1959).

Cox, C.

C. Cox and W. Munk, Bull. Scripps Inst. Oceanogr. 6, 401 (1956).

Dera, J.

J. Dera and H. R. Gordon, Linmnol. Oceanogr. 13, 697 (1968).

J. Dera and J. Olszewski, Acta Geophys. Polon. 15, 351 (1967).

Gordon, H. R.

J. Dera and H. R. Gordon, Linmnol. Oceanogr. 13, 697 (1968).

Grand, Y. Le

Y. Le Grand, Ann. Inst. Oceanogr. 19, 393 (1939).

Hishida, K.

K. Hishida and M. Kishino, J. Oceanogr. Soc. Japan 27, 748 (1965).

Jerlov, N. G.

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).

Kishino, M.

K. Hishida and M. Kishino, J. Oceanogr. Soc. Japan 27, 748 (1965).

Mullamaa, Y.

Y. Mullamaa, Izv. Akad. Nauk. USSR. Sev. Geofiz. 8, 1232 (1964).

Munk, W.

C. Cox and W. Munk, Bull. Scripps Inst. Oceanogr. 6, 401 (1956).

Olszewski, J.

J. Dera and J. Olszewski, Acta Geophys. Polon. 15, 351 (1967).

Schenck, H.

H. Schenck, J. Opt. Soc. Am. 47, 653 (1957).

Other (17)

The reader is forewarned of an unavoidable duplication of terminology in the optical and geophysical aspects of this paper. Some confusion may result if this duplication is not borne in mind. Here, the terms "frequency" and "wavenumber" refer to the geophysical distribution of irradiance in the sea, not to the wave-mechanical properties of light.

Y. Le Grand, Ann. Inst. Oceanogr. 19, 393 (1939).

W. V. Burt, J. Meteorol. 11, 283 (1959).

C. Cox and W. Munk, Bull. Scripps Inst. Oceanogr. 6, 401 (1956).

K. Hishida and M. Kishino, J. Oceanogr. Soc. Japan 27, 748 (1965).

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).

Y. Mullamaa, Izv. Akad. Nauk. USSR. Sev. Geofiz. 8, 1232 (1964).

H. Schenck, J. Opt. Soc. Am. 47, 653 (1957).

J. Dera and H. R. Gordon, Linmnol. Oceanogr. 13, 697 (1968).

J. Dera and J. Olszewski, Acta Geophys. Polon. 15, 351 (1967).

In this paper, the terms "spectrum" and "spectra" are not optical terms, but refer to a time-series analysis of a random fluctuation.

z is taken positive upwards with z = 0 at the mean water surface.

Boldface letters will denote two-dimensional (horizontal) vector quantities. (h, ν) will denote a three-dimensional vector quantity with horizontal projection h and vertical component ν.

This calculation assumes that the mean irradiance field is entirely the result of direct sun rays. The observations of Dera and Olszewski suggest that this assumption is only crudely satisfied. The value of the resulting attenuation coefficient is probably more representative of a downwelling-irradiance attenuation coefficient than it is of a beam-attenuation coefficient.

As evidenced in the coordinate transformation (3) in Sec. III.

The expansion parameter is essentially the rms surface-wave slope.

The variables ξ and η here have a meaning different from their previous meaning.

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