Abstract

The radiance in the earth's atmosphere and ocean is calculated for a realistic model including an ocean surface with waves. Individual photons are followed in a Monte Carlo calculation. In the atmosphere, both Rayleigh scattering by the molecules and Mie scattering by the aerosols as well as molecular and aerosol absorption are taken into account. 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 which are calculated separately for the aerosols and the hydrosols from the Mie theory with appropriate and different size distributions in each case. The scattering angles are determined from the appropriate scattering function including the strong forward-scattering peak when there is aerosol or hydrosol scattering. 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. Graphs show the influence of the waves on the upward radiance at the top of the atmosphere and just above the ocean surface and on the downward radiance just below the ocean surface as well as deeper within the ocean. The radiance changes are sufficient at the top of the atmosphere to determine the sea state from satellite measurements. Within the ocean the waves smooth out the abrupt transition that occurs at the edge of the allowed cone for radiation entering a calm ocean. The influence of the waves on the contrast between the sky and sea at the horizon is discussed. It is shown that the downward flux just below the surface increases with wind speed at all solar angles.

© 1975 Optical Society of America

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References

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  1. G. N. Plass, G. W. Kattawar, F. E. Catchings, Appl. Opt. 12, 314, 1071 (1973).
    [CrossRef] [PubMed]
  2. G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065, 1081 (1973);J. Quant. Spectrosc. Radiat. Transfer 15, 61 (1975).
    [CrossRef]
  3. G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (1973).
    [CrossRef]
  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. E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972).
  11. H. R. Gordon, O. B. Brown, Appl. Opt. 12, 1549 (1973).
    [CrossRef] [PubMed]
  12. L. Elterman, UV, Visible, and IR Attenuation for for Altitudes to 50 km, 1968, Air Force Cambridge Research Laboratories Report AFCRL-68-D153 (1968);Appl. Opt. 8, 893 (1969).
    [PubMed]
  13. C. Cox, W. Munk, J. Opt. Soc. Am. 44, 838 (1954).
    [CrossRef]
  14. C. S. Cox, in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, New York, 1974).

1973 (5)

G. N. Plass, G. W. Kattawar, F. E. Catchings, Appl. Opt. 12, 314, 1071 (1973).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065, 1081 (1973);J. Quant. Spectrosc. Radiat. Transfer 15, 61 (1975).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (1973).
[CrossRef]

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)

Binststock, J.

G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (1973).
[CrossRef]

Brown, O. B.

Catchings, F. E.

G. N. Plass, G. W. Kattawar, F. E. Catchings, Appl. Opt. 12, 314, 1071 (1973).
[CrossRef] [PubMed]

Cox, C.

Cox, C. S.

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

Elterman, L.

L. Elterman, UV, Visible, and IR Attenuation for for Altitudes to 50 km, 1968, Air Force Cambridge Research Laboratories Report AFCRL-68-D153 (1968);Appl. Opt. 8, 893 (1969).
[PubMed]

Gordon, H. R.

Guinn, J. A.

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

Kattawar, G. W.

G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (1973).
[CrossRef]

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

G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065, 1081 (1973);J. Quant. Spectrosc. Radiat. Transfer 15, 61 (1975).
[CrossRef]

G. N. Plass, G. W. Kattawar, F. E. Catchings, Appl. Opt. 12, 314, 1071 (1973).
[CrossRef] [PubMed]

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]

Munk, W.

Plass, G. N.

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

G. N. Plass, G. W. Kattawar, F. E. Catchings, Appl. Opt. 12, 314, 1071 (1973).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065, 1081 (1973);J. Quant. Spectrosc. Radiat. Transfer 15, 61 (1975).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (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]

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. (1)

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

J. Phys. Oceanogr. (2)

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]

J. Quant. Spectrosc. Radiat. Transfer (2)

G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065, 1081 (1973);J. Quant. Spectrosc. Radiat. Transfer 15, 61 (1975).
[CrossRef]

G. N. Plass, G. W. Kattawar, J. Binststock, J. Quant. Spectrosc. Radiat. Transfer 13, 1081 (1973).
[CrossRef]

Other (2)

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

L. Elterman, UV, Visible, and IR Attenuation for for Altitudes to 50 km, 1968, Air Force Cambridge Research Laboratories Report AFCRL-68-D153 (1968);Appl. Opt. 8, 893 (1969).
[PubMed]

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Figures (28)

Fig. 1
Fig. 1

Upward radiance at top of atmosphere as a function of nadir angle of observation for θ0 = 57° and 80° (solar zenith angle), λ = 0.46 μm, and a wind speed of 20 knots (37.1 km/h). Each curve is averaged over a range of azimuthal angles ϕ as shown in the legend.

Fig. 2
Fig. 2

Upward radiance at top of atmosphere for θ0 = 32° (lower curves) and 57° and a wind speed of 5 knots (9.3 km/h).

Fig. 3
Fig. 3

Upward radiance just above ocean surface for θ0 = 57° and wind speeds of 0 knots and 5 knots (9.3 km/h).

Fig. 4
Fig. 4

Upward radiance just above ocean surface for θ0 = 57° and a wind speed of 20 knots (37.1 km/h).

Fig. 5
Fig. 5

Upward radiance just above ocean surface for θ0 = 32° and wind speed of 0 knots and 5 knots (9.3 km/h).

Fig. 6
Fig. 6

Downward radiance just below ocean surface as a function of zenith angle of observation for θ0 = 80° and a wind speed of 0 knots.

Fig. 7
Fig. 7

Downward radiance just below ocean surface for θ0 = 32° and 57° and a wind speed of 0 knots.

Fig. 8
Fig. 8

Downward radiance just below ocean surface for θ0 = 80° and a wind speed of 5 knots (9.3 km/h).

Fig. 9
Fig. 9

Downward radiance just below ocean surface for θ0 = 57° and a wind speed of 5 knots (9.3 km/h).

Fig. 10
Fig. 10

Downward radiance just below ocean surface for θ0 = 32° and a wind speed of 5 knots (9.3 km/h).

Fig. 11
Fig. 11

Downward radiance just below ocean surface for θ0 = 80° and a wind speed of 20 knots (37.1 km/h).

Fig. 12
Fig. 12

Downward radiance just below ocean surface for θ0 = 57° and a wind speed of 20 knots (37.1 km/h).

Fig. 13
Fig. 13

Downward radiance just below ocean surface for θ0 = 32° and a wind speed of 20 knots (37.1 km/h).

Fig. 14
Fig. 14

Upward radiance at top of atmosphere as function of nadir angle of observation for θ0 = 0° and the principal plane. Curves are given for six wind speeds from 0 knots to 30 knots. The upper curves are for the direct solar beam only. The lower curves show the total (direct plus diffuse) radiance.

Fig. 15
Fig. 15

Upward radiance just above ocean surface for θ0 = 0° and the principal plane. See legend for Fig. 14.

Fig. 16
Fig. 16

Downward radiance just below ocean surface as function of zenith angle of observation for θ0 = 0° and the principal plane. See legend for Fig. 14.

Fig. 17
Fig. 17

Upward radiance at top of atmosphere as function of nadir angle of observation for θ0 = 57° and the principal plane. Curves are given for four wind speeds from 0 knots to 20 knots. The lower curves are for the direct solar beam only. The upper curves show the total (direct plus diffuse) radiance.

Fig. 18
Fig. 18

Upward radiance just above ocean surface for θ0 = 57° and the principal plane. See legend for Fig. 17.

Fig. 19
Fig. 19

Downward radiance just below ocean surface as function of zenith angle of observation for θ0 = 57° and the principal plane. See legend for Fig. 17.

Fig. 20
Fig. 20

Upward radiance at top of atmosphere as function of nadir angle of observation for θ0 = 57°, λ = 0.7 μm, and the principal plane. Curves are given for three wind speeds from 0 knots to 20 knots. The lower curves are for the direct solar beam only. The upper curves show the total (direct plus diffuse) radiance.

Fig. 21
Fig. 21

Upward radiance just above ocean surface for θ0 = 57° and the principal plane. See legend for Fig. 20.

Fig. 22
Fig. 22

Downward radiance just below ocean surface as function of zenith angle of observation for θ0 = 57°, λ = 0.7 μm, and the principal plane. See legend for Fig. 20.

Fig. 23
Fig. 23

Downward radiance at various depths within the ocean as a function of zenith angle of observation for θ0 = 0°. The curves on the right are for a wind speed of 0 knots, while those on the left are for 20 knots (37.1 km/h). Curves are given for the radiance at various optical depths beneath the surface from 0 to 10. The inset on the right shows the radiance for a calm ocean for zenith angles from 35° to 65°.

Fig. 24
Fig. 24

Same as Fig. 23 except θ0 = 32°.

Fig. 25
Fig. 25

Same as Fig. 23 except θ0 = 80°.

Fig. 26
Fig. 26

Downward radiance at optical depths of 1 and 8 below the ocean surface for θ0 = 57° and a wind speed of 10 knots (18.5 km/h). Curves are given for various values of the azimuthal angle.

Fig. 27
Fig. 27

Upward radiance (on left) and downward radiance (on right) in order to show variation of radiance across horizon (at center). The top curves are for θ0 = 0° and the bottom curves for θ0 = 57°. Curves are given for various wind speeds.

Fig. 28
Fig. 28

Upward radiance just above ocean surface as a function of nadir angle for θ0 = 80° (at left) and 32° (at right) and a wind speed of 20 knots (37.1 km/h). The four curves show the total radiance, the radiance from the direct solar beam as reflected by the ocean surface, the radiance from scattered photons (sky radiation) reflected by the ocean surface, and the radiance from upwelling photons from beneath the ocean surface.

Tables (1)

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Table I Flux Just below Surface and Albedo of Surface

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p ( cos θ i ) / ( A cos θ f ) ,

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