Abstract

The radiation field for an atmosphere–ocean system is calculated by a Monte Carlo method. In the atmosphere, both Rayleigh scattering by the molecules and Mie scattering by the aerosols and water droplets, when present, as well as molecular and aerosol absorption are included in the model. 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 scattering functions are calculated from the Mie theory for the water droplets in clouds, the aerosols, and the hydrosols with an appropriate and different size distribution in each case. The photon path is followed accurately in three dimensions with new scattering angles determined from the appropriate scattering function including the strong forward scattering peak. Both the reflected and refracted rays, as well as the rays that undergo total internal reflection, are followed at the ocean surface, which is assumed smooth. The ocean floor is represented by a Lambert surface. The radiance and flux are given for two wavelengths, three solar angles, shallow and deep oceans, various albedos of ocean floor, various depths in atmosphere and ocean, and with and without clouds in the atmosphere.

© 1969 Optical Society of America

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References

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  1. T. H. Waterman, W. E. Westell, J. Marine Res. 15, 149 (1956).
  2. A. Ivanoff, T. H. Waterman, J. Marine Res. 16, 283 (1958).
  3. R. W. Preisendorfer, J. Marine Res. 18, 1 (1959).
  4. Z. Sekera, in Union Géodésique et Géophysique Internationale, Monograph 10, N. G. Jerlov, Ed. (l’Institut Géographique National, Paris, 1961), pp. 66–72.
  5. G. Neuman, R. Hollman, Symposium on Radiant Energy in the Sea, Int. Assoc. Phys. Oceanography73 (1960).
  6. S. Q. Duntley, J. Opt. Soc. Amer. 53, 214 (1963).
    [Crossref]
  7. R. S. Fraser, W. H. Walker, J. Opt. Soc. Amer. 58, 1636 (1963).
  8. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [Crossref] [PubMed]
  9. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 1129 (1968).
    [Crossref] [PubMed]
  10. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [Crossref]
  11. L. Elterman, in Handbook of Geophysics and Space Environments, S. L. Valley, Ed. (McGraw-Hill Book Company, Inc., New York, 1965).
  12. G. W. Kattawar, G. N. Plass, Appl. Opt. 7, 869 (1968).
    [Crossref] [PubMed]
  13. Y. LeGrand, Ann. Inst. Ocean. 19, 393 (1939).
  14. E. O. Hulburt, J. Opt. Soc. Amer. 35, 698 (1945).
    [Crossref]
  15. W. R. G. Atkins, H. H. Poole, Proc. Roy. Soc. London B140, 321 (1952).
  16. W. V. Burt, Tellus 6, 229 (1954).
    [Crossref]
  17. G. F. Beardsley, J. Opt. Soc. Amer. 58, 52 (1968).
    [Crossref]

1968 (4)

1964 (1)

1963 (2)

S. Q. Duntley, J. Opt. Soc. Amer. 53, 214 (1963).
[Crossref]

R. S. Fraser, W. H. Walker, J. Opt. Soc. Amer. 58, 1636 (1963).

1960 (1)

G. Neuman, R. Hollman, Symposium on Radiant Energy in the Sea, Int. Assoc. Phys. Oceanography73 (1960).

1959 (1)

R. W. Preisendorfer, J. Marine Res. 18, 1 (1959).

1958 (1)

A. Ivanoff, T. H. Waterman, J. Marine Res. 16, 283 (1958).

1956 (1)

T. H. Waterman, W. E. Westell, J. Marine Res. 15, 149 (1956).

1954 (1)

W. V. Burt, Tellus 6, 229 (1954).
[Crossref]

1952 (1)

W. R. G. Atkins, H. H. Poole, Proc. Roy. Soc. London B140, 321 (1952).

1945 (1)

E. O. Hulburt, J. Opt. Soc. Amer. 35, 698 (1945).
[Crossref]

1939 (1)

Y. LeGrand, Ann. Inst. Ocean. 19, 393 (1939).

Atkins, W. R. G.

W. R. G. Atkins, H. H. Poole, Proc. Roy. Soc. London B140, 321 (1952).

Beardsley, G. F.

G. F. Beardsley, J. Opt. Soc. Amer. 58, 52 (1968).
[Crossref]

Burt, W. V.

W. V. Burt, Tellus 6, 229 (1954).
[Crossref]

Deirmendjian, D.

Duntley, S. Q.

S. Q. Duntley, J. Opt. Soc. Amer. 53, 214 (1963).
[Crossref]

Elterman, L.

L. Elterman, in Handbook of Geophysics and Space Environments, S. L. Valley, Ed. (McGraw-Hill Book Company, Inc., New York, 1965).

Fraser, R. S.

R. S. Fraser, W. H. Walker, J. Opt. Soc. Amer. 58, 1636 (1963).

Hollman, R.

G. Neuman, R. Hollman, Symposium on Radiant Energy in the Sea, Int. Assoc. Phys. Oceanography73 (1960).

Hulburt, E. O.

E. O. Hulburt, J. Opt. Soc. Amer. 35, 698 (1945).
[Crossref]

Ivanoff, A.

A. Ivanoff, T. H. Waterman, J. Marine Res. 16, 283 (1958).

Kattawar, G. W.

LeGrand, Y.

Y. LeGrand, Ann. Inst. Ocean. 19, 393 (1939).

Neuman, G.

G. Neuman, R. Hollman, Symposium on Radiant Energy in the Sea, Int. Assoc. Phys. Oceanography73 (1960).

Plass, G. N.

Poole, H. H.

W. R. G. Atkins, H. H. Poole, Proc. Roy. Soc. London B140, 321 (1952).

Preisendorfer, R. W.

R. W. Preisendorfer, J. Marine Res. 18, 1 (1959).

Sekera, Z.

Z. Sekera, in Union Géodésique et Géophysique Internationale, Monograph 10, N. G. Jerlov, Ed. (l’Institut Géographique National, Paris, 1961), pp. 66–72.

Walker, W. H.

R. S. Fraser, W. H. Walker, J. Opt. Soc. Amer. 58, 1636 (1963).

Waterman, T. H.

A. Ivanoff, T. H. Waterman, J. Marine Res. 16, 283 (1958).

T. H. Waterman, W. E. Westell, J. Marine Res. 15, 149 (1956).

Westell, W. E.

T. H. Waterman, W. E. Westell, J. Marine Res. 15, 149 (1956).

Ann. Inst. Ocean. (1)

Y. LeGrand, Ann. Inst. Ocean. 19, 393 (1939).

Appl. Opt. (4)

J. Marine Res. (3)

T. H. Waterman, W. E. Westell, J. Marine Res. 15, 149 (1956).

A. Ivanoff, T. H. Waterman, J. Marine Res. 16, 283 (1958).

R. W. Preisendorfer, J. Marine Res. 18, 1 (1959).

J. Opt. Soc. Amer. (4)

S. Q. Duntley, J. Opt. Soc. Amer. 53, 214 (1963).
[Crossref]

R. S. Fraser, W. H. Walker, J. Opt. Soc. Amer. 58, 1636 (1963).

E. O. Hulburt, J. Opt. Soc. Amer. 35, 698 (1945).
[Crossref]

G. F. Beardsley, J. Opt. Soc. Amer. 58, 52 (1968).
[Crossref]

Proc. Roy. Soc. London (1)

W. R. G. Atkins, H. H. Poole, Proc. Roy. Soc. London B140, 321 (1952).

Symposium on Radiant Energy in the Sea (1)

G. Neuman, R. Hollman, Symposium on Radiant Energy in the Sea, Int. Assoc. Phys. Oceanography73 (1960).

Tellus (1)

W. V. Burt, Tellus 6, 229 (1954).
[Crossref]

Other (2)

Z. Sekera, in Union Géodésique et Géophysique Internationale, Monograph 10, N. G. Jerlov, Ed. (l’Institut Géographique National, Paris, 1961), pp. 66–72.

L. Elterman, in Handbook of Geophysics and Space Environments, S. L. Valley, Ed. (McGraw-Hill Book Company, Inc., New York, 1965).

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Figures (24)

Fig. 1
Fig. 1

Single scattering function for the hydrosols as a function of the cosine of the scattering angle for particles with n1 = 1.15 and n2 = 0.001 and the size distribution given in the text. The inset in the upper left corner shows the function near a scattering angle of 0° (forward scattering).

Fig. 2
Fig. 2

Downward radiance as a function of μ, cosine of zenith angle, at λ = 0.65 μm and for μ0 (cosine of solar zenith angle) = −1. The value of A (albedo of ocean floor) is zero for the curves on the left and unity for those on the right. The optical depth τ of the atmosphere is 0.217 and of the ocean is unity. Thus, τ = 0.2165 is just above the ocean surface, τ = 0.2175 is just below, and τ = 1.217 is on the ocean floor. The incident flux is included in the radiance by the assumption that it is recorded by a detector with an acceptance half-angle such that Δμ = 0.025. The solar flux is normalized to unity in all figures.

Fig. 3
Fig. 3

Upward radiance as a function of μ for μ0 = −1, λ = 0.65 μ, and A = 0 and 1. See caption to Fig. 2.

Fig. 4
Fig. 4

Downard radiance as a function of μ for μ0 = −0.5, λ = 0.65 μm, and A = 1. The optical depth τ of the atmosphere is 0.217 and of the ocean is unity. The solar horizon is on the left of all graphs, the zenith or nadir is at the center, and the antisolar horizon is at the right. The radiance for each interval has been averaged over all azimuthal angles within 90° of the incident plane.

Fig. 5
Fig. 5

Upward radiance as a function of μ for μ0 = −0.5, λ = 0.65 μm, and A = 1. See caption to Fig. 4.

Fig. 6
Fig. 6

Downward radiance as a function of μ for μ0 = −0.1, λ = 0.65 μm, and A = 1. See caption to Fig. 4.

Fig. 7
Fig. 7

Upward radiance as a function of μ for μ0 = −0.1, λ = 0.65 μm, and A = 1. See caption to Fig. 4.

Fig. 8
Fig. 8

Downward and upward radiance as a function of μ for μ0 = −1, A = 0, and λ = 0.65 μm. The optical depth of the atmosphere is 0.217 and the ocean is 10. Thus τ = 0.2165 is just above the ocean surface, τ = 0.2175 is just below, and τ = 10.217 is on the ocean floor.

Fig. 9
Fig. 9

Downward and upward radiance as a function of μ for μ0 = −1, A = 0 and λ = 0.65 μm. Values are shown for an ocean–atmosphere model, for an ocean model with no atmosphere, and for an atmosphere model with a Lambert surface having A = 0.0298. See caption to Fig. 8.

Fig. 10
Fig. 10

Downward radiance as a function of μ for μ0 = −0.55 and λ = 0.65 μm. See caption to Fig. 8.

Fig. 11
Fig. 11

Upward radiance as a function of μ for μ0 = −0.55 and λ = 0.65 μm. See caption to Fig. 8.

Fig. 12
Fig. 12

Downward radiance as a function of μ for μ0 = −0.15 and λ = 0.65 μm. See caption to Fig. 8.

Fig. 13
Fig. 13

Upward radiance as a function of μ for μ0 = −0.15 and λ = 0.65 μm. See caption to Fig. 8.

Fig. 14
Fig. 14

Downward and upward radiance as a function of μ for μ0 = −1, A = 0, and λ = 0.46 μm. The optical depth of the atmosphere is 0.5768 and of the ocean is 10. Thus, τ = 0.5767 is just above the ocean surface, τ = 0.5769 is just below, and τ = 10.577 is on the ocean floor.

Fig. 15
Fig. 15

Downward and upward radiance as a function of μ for μ0 = −1, A = 0, and λ = 0.46 μm. Values are shown for an ocean–atmosphere model, for an ocean model with no atmosphere, and for an atmosphere model with a Lambert surface having A = 0.09822. See caption to Fig. 14.

Fig. 16
Fig. 16

Downward radiance as a function of μ for μ0 = −0.55 and λ = 0.46 μm. See caption to Fig. 14.

Fig. 17
Fig. 17

Upward radiance as a function of μ for μ0 = −0.55 and λ = 0.46 μm. See caption to Fig. 14.

Fig. 18
Fig. 18

Downward radiance as a function of μ for μ0 = −0.15 and λ = 0.46 μm. See caption to Fig. 14.

Fig. 19
Fig. 19

Upward radiance as a function of μ for μ0 = −0.15 and λ = 0.46 μm. See caption to Fig. 14.

Fig. 20
Fig. 20

Downward and upward radiance for μ0 = −1 and λ = 0.65 μm with a nimbostratus cloud of optical depth 10. The atmospheric optical depth without cloud is 0.217 and the oceanic optical depth is 10. Thus, τ = 10.2165 is just the above ocean surface, τ = 12.2175 is just below the ocean surface, and τ = 20.217 is on the ocean floor.

Fig. 21
Fig. 21

Downward and upward radiance for μ0 = −1 and λ = 0.46 μm with a nimbostratus cloud of optical depth 10. The atmospheric optical depth without cloud is 0.5768 and the oceanic optical depth is 10. Thus, τ = 10.5767 is just above the ocean surface, τ = 10.5769 is just below the ocean surface, and τ = 20.5768 is on the ocean floor.

Fig. 22
Fig. 22

Downward and upward flux as a function of the optical depth τ from the top of the atmosphere at λ = 0.65 μm. The ocean surface is at τ = 0.217 and the ocean floor is at τ = 1.217. Curves are shown for various values of the albedo A of the ocean floor and for various solar zenith angles.

Fig. 23
Fig. 23

Downward and upward flux as a function of the optical depth from the top of the atmosphere at λ = 0.65 μm. The ocean surface is at τ = 0.217 and the ocean floor is at λ = 10.217. Curves are shown for μ0 = −1, −0.55, and −0.15.

Fig. 24
Fig. 24

Downward and upward flux as a function of the optical depth from the top of the atmosphere at λ = 0.46 μm. The ocean surface is at τ = 0.5768 and the ocean floor is at τ = 10.577. Curves are shown for μ0 = −1, −0.55, and −0.15 and for μ0 = −1 with nimbostratus clouds. The last curve is adjusted so that the ocean surface has the same τ value as the other curves.

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