Abstract

The upward radiance just above the ocean surface and at the top of the atmosphere is calculated for a realistic model including an ocean surface with waves. The separate contributions of the sun glitter, the reflected sky radiance, and the upwelling photons from the ocean are calculated. The Monte Carlo method takes account of both Rayleigh scattering by the molecules and Mie scattering by the aerosols as well as molecular and aerosol absorption in the atmosphere. Similarly, in the ocean, both Rayleigh scattering by the water molecules and Mie scattering by the hydrosols as well as absorption by the water molecules and hydrosols are considered. Separate single-scattering functions are used for the aerosols and hydrosols calculated from the Mie theory. Both the reflected and refracted rays, as well as the rays that undergo total internal reflection, are followed at the ocean surface. The wave slope is chosen from the Cox-Munk distribution. The upward radiance just above the ocean surface outside of the sun glitter region is dominated by the reflected sky radiation from the horizon to a nadir angle of observation of from 68° to 23° depending on the azimuthal angle and the solar zenith angle; the upwelling photons from the ocean dominate over the remainder of the hemisphere, except in the region of the sun glitter which centers around the mirror image of the sun on a calm ocean. It is possible to answer various questions about the interaction of light with the ocean from the quantitative results presented here.

© 1976 Optical Society of America

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References

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  1. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954).
  2. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).
  3. N. G. Jerlov, E. S. Nielsen, Eds., Optical Aspects of Oceanography (Academic, New York, 1974).
  4. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [CrossRef] [PubMed]
  5. G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
    [CrossRef]
  6. G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
    [CrossRef] [PubMed]
  7. G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
    [CrossRef]
  8. G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
    [CrossRef]
  9. G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
    [CrossRef]
  10. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
    [CrossRef] [PubMed]
  11. E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972).
  12. H. R. Gordon, O. B. Brown, Appl. Opt. 12, 1549 (1973).
    [CrossRef] [PubMed]
  13. C. Cox, W. Munk, J. Opt. Soc. Am. 44, 838 (1954).
    [CrossRef]

1975 (1)

1973 (2)

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

H. R. Gordon, O. B. Brown, Appl. Opt. 12, 1549 (1973).
[CrossRef] [PubMed]

1972 (3)

E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972).

G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
[CrossRef]

1971 (1)

G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
[CrossRef]

1969 (1)

1968 (1)

1954 (1)

Brown, O. B.

Cox, C.

Gordon, H. R.

Guinn, J. A.

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

Jerlov, N. G.

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

Kattawar, G. W.

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
[CrossRef]

G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
[CrossRef] [PubMed]

Minnaert, M.

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954).

Munk, W.

Plass, G. N.

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
[CrossRef]

G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
[CrossRef] [PubMed]

Raschke, E.

E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972).

Appl. Opt. (4)

Beitr. Phys. Atmos. (1)

E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972).

J. Atmos. Sci. (1)

G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (3)

G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

Other (3)

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954).

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

N. G. Jerlov, E. S. Nielsen, Eds., Optical Aspects of Oceanography (Academic, New York, 1974).

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Figures (7)

Fig. 1
Fig. 1

Total upwelling radiance at the top of the atmosphere (crosses) and just above the ocean surface (solid curve) as a function of the nadir angle of observation for the sun at the zenith. The three contributions to the upward radiance just above the ocean surface are shown separately: (1) sun glitter (open circles); (2) reflected sky radiance (triangles); (3) upwelling photons from ocean (solid circles). Waves appropriate for a 20-knot (37.1-km/h) wind are assumed. A wavelength of 0.46 μm is assumed.

Fig. 2
Fig. 2

Same as Fig. 1, except solar zenith angle is 15°. The solar horizon is at the left of the figure, the nadir at the center, and the antisolar horizon at the right edge. These curves are for the principal plane (ϕ = 0° and 180°).

Fig. 3
Fig. 3

Same as Fig. 1, except solar zenith angle is 32°.

Fig. 4
Fig. 4

Same as Fig. 1, except solar zenith angle is 57°.

Fig. 5
Fig. 5

Same as Fig. 1, except solar zenith angle is 80°.

Fig. 6
Fig. 6

The right half of the figure indicates the dominant terms in the upwelling radiance for a solar zenith angle θ0 = 15°, while the left half is for θ0 = 32°. The nadir is at the center of the figure, while the horizon is at the edge. The position of the reflected sun is indicated. The word sun indicates that the sun glitter dominates, sky that the reflected sky radiance dominates, and ocean that the upwelling photons from the ocean dominate. In the sun glitter region, the next most important term contributing to the total radiance is also indicated.

Fig. 7
Fig. 7

Same as Fig. 6, except for θ0 = 57° and 80°.

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