Abstract

The color of the ocean is calculated from a model that realistically takes into account the various types of scattering and absorption events that occur in both the atmosphere and ocean. Solar photons are followed through the atmosphere and into the ocean by a Monte Carlo technique. The reflection and refraction at the ocean surface are included in the calculation. The upward and downward flux is calculated at several different heights in the atmosphere, at thirteen different wavelengths from 0.4 μm to 0.7 μm. These results are compared with two approximate theories: (1) one-dimensional; (2) single scattering. The first of these theories gives results which are accurate within 10% in most cases and are easy to calculate. The chromaticity coordinates as well as the dominant wavelength and purity of the color are calculated from the Monte Carlo results for the variation of upward flux with wavelength. The ocean color near the horizon is almost entirely determined by the color of the sky reflected by the ocean surface. The upwelling light from the ocean can be observed near the nadir if precautions are taken to exclude as much light as possible reflected from the ocean surface. The color of this upwelling light from the ocean contains much information about the hydrosol, chlorophyll, and yellow substance amounts in the ocean water. The model calculations show how the ocean color changes from a deep blue of high purity for relatively pure water to a greenish blue and then to green of low purity as the cholorphyll and yellow substance amounts increase. Further increases in these substances cause the color to change to yellow green of a higher purity. A large increase in the hydro-sol amount usually causes a marked decrease in the purity of the color.

© 1978 Optical Society of America

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References

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  1. R. Bunsen, Jahresber, Fortschr. Chem. 1847, 1236 (1847).
  2. H. Sainte-Claire Deville, Ann. Chem. Phys. (3) 23, 32 (1848).
  3. J. Tyndall, Naturforscher 4, 1 (1871).
  4. J. Aitken, Proc. R. Soc. Edinburgh 11, 472 (1882).
  5. J. W. Strutt, Nature 83, 48 (1910).
    [CrossRef]
  6. W. D. Bancroft, J. Franklin Inst. 187, 249, 459 (1917).
    [CrossRef]
  7. C. V. Raman, Proc. R. Soc. London Ser. A 101, 64, (1922).
    [CrossRef]
  8. K. R. Ramanathan, London, Edinburgh, Dublin Philos. Mag. J. Sci. 46, 543 (1923).
    [CrossRef]
  9. W. Shuleiken, Phys. Rev. 22, 85 (1923).
    [CrossRef]
  10. J. Lenoble, C. R. Acad. Sci. 242, 662 (1956).
  11. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1974).
  12. N. G. Jerlov, E. S. Nielsen, Eds., Optical Aspects of Oceanography (Academic, New York: 1974).
  13. W. R. McCluney, Appl. Opt. 13, 2422 (1974).
    [CrossRef] [PubMed]
  14. A. Morel, L. Caloumenos, Tethys 6, 93 (1974).
  15. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [CrossRef] [PubMed]
  16. G. N. Plass, G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971).
    [CrossRef]
  17. G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
    [CrossRef] [PubMed]
  18. G. N. Plass, G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972).
    [CrossRef]
  19. G. W. Kattawar, G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972).
    [CrossRef]
  20. G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
    [CrossRef]
  21. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
    [CrossRef] [PubMed]
  22. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 15, 3161 (1976).
    [CrossRef] [PubMed]
  23. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 16, 643 (1977).
    [CrossRef] [PubMed]
  24. L. Elterman, UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968, Air Force Cambridge Research Laboratories Report AFCRL-68-D153 (1968);Appl. Opt. 8, 893 (1969).
    [PubMed]
  25. G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065 (1973).
    [CrossRef]
  26. A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
    [CrossRef]
  27. G. A. Maul, H. R. Gordon, Remote Sensing Environ. 4, 95 (1975).
    [CrossRef]

1977 (2)

1976 (1)

1975 (2)

1974 (2)

W. R. McCluney, Appl. Opt. 13, 2422 (1974).
[CrossRef] [PubMed]

A. Morel, L. Caloumenos, Tethys 6, 93 (1974).

1973 (2)

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 (1973).
[CrossRef]

1972 (2)

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)

1956 (1)

J. Lenoble, C. R. Acad. Sci. 242, 662 (1956).

1923 (2)

K. R. Ramanathan, London, Edinburgh, Dublin Philos. Mag. J. Sci. 46, 543 (1923).
[CrossRef]

W. Shuleiken, Phys. Rev. 22, 85 (1923).
[CrossRef]

1922 (1)

C. V. Raman, Proc. R. Soc. London Ser. A 101, 64, (1922).
[CrossRef]

1917 (1)

W. D. Bancroft, J. Franklin Inst. 187, 249, 459 (1917).
[CrossRef]

1910 (1)

J. W. Strutt, Nature 83, 48 (1910).
[CrossRef]

1882 (1)

J. Aitken, Proc. R. Soc. Edinburgh 11, 472 (1882).

1871 (1)

J. Tyndall, Naturforscher 4, 1 (1871).

1848 (1)

H. Sainte-Claire Deville, Ann. Chem. Phys. (3) 23, 32 (1848).

1847 (1)

R. Bunsen, Jahresber, Fortschr. Chem. 1847, 1236 (1847).

Aitken, J.

J. Aitken, Proc. R. Soc. Edinburgh 11, 472 (1882).

Bancroft, W. D.

W. D. Bancroft, J. Franklin Inst. 187, 249, 459 (1917).
[CrossRef]

Bunsen, R.

R. Bunsen, Jahresber, Fortschr. Chem. 1847, 1236 (1847).

Caloumenos, L.

A. Morel, L. Caloumenos, Tethys 6, 93 (1974).

Elterman, L.

L. Elterman, UV, Visible, and IR Attenuation 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.

G. A. Maul, H. R. Gordon, Remote Sensing Environ. 4, 95 (1975).
[CrossRef]

Guinn, J. A.

Jahresber,

R. Bunsen, Jahresber, Fortschr. Chem. 1847, 1236 (1847).

Kattawar, G. W.

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 16, 643 (1977).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 15, 3161 (1976).
[CrossRef] [PubMed]

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

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

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]

Lenoble, J.

J. Lenoble, C. R. Acad. Sci. 242, 662 (1956).

Maul, G. A.

G. A. Maul, H. R. Gordon, Remote Sensing Environ. 4, 95 (1975).
[CrossRef]

McCluney, W. R.

Minnaert, M.

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1974).

Morel, A.

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

A. Morel, L. Caloumenos, Tethys 6, 93 (1974).

Plass, G. N.

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 16, 643 (1977).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 15, 3161 (1976).
[CrossRef] [PubMed]

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

G. W. Kattawar, G. N. Plass, J. Quant. Spectrosc. Radiat. Transfer 13, 1065 (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. 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]

Prieur, L.

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

Raman, C. V.

C. V. Raman, Proc. R. Soc. London Ser. A 101, 64, (1922).
[CrossRef]

Ramanathan, K. R.

K. R. Ramanathan, London, Edinburgh, Dublin Philos. Mag. J. Sci. 46, 543 (1923).
[CrossRef]

Sainte-Claire Deville, H.

H. Sainte-Claire Deville, Ann. Chem. Phys. (3) 23, 32 (1848).

Shuleiken, W.

W. Shuleiken, Phys. Rev. 22, 85 (1923).
[CrossRef]

Strutt, J. W.

J. W. Strutt, Nature 83, 48 (1910).
[CrossRef]

Tyndall, J.

J. Tyndall, Naturforscher 4, 1 (1871).

Ann. Chem. Phys. (1)

H. Sainte-Claire Deville, Ann. Chem. Phys. (3) 23, 32 (1848).

Appl. Opt. (6)

C. R. Acad. Sci. (1)

J. Lenoble, C. R. Acad. Sci. 242, 662 (1956).

Dublin Philos. Mag. J. Sci. (1)

K. R. Ramanathan, London, Edinburgh, Dublin Philos. Mag. J. Sci. 46, 543 (1923).
[CrossRef]

Fortschr. Chem. (1)

R. Bunsen, Jahresber, Fortschr. Chem. 1847, 1236 (1847).

J. Atmos. Sci. (1)

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

J. Franklin Inst. (1)

W. D. Bancroft, J. Franklin Inst. 187, 249, 459 (1917).
[CrossRef]

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]

J. Quant. Spectrosc. Radiat. Transfer (1)

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

Limnol. Oceanogr. (1)

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

Nature (1)

J. W. Strutt, Nature 83, 48 (1910).
[CrossRef]

Naturforscher (1)

J. Tyndall, Naturforscher 4, 1 (1871).

Phys. Rev. (1)

W. Shuleiken, Phys. Rev. 22, 85 (1923).
[CrossRef]

Proc. R. Soc. Edinburgh (1)

J. Aitken, Proc. R. Soc. Edinburgh 11, 472 (1882).

Proc. R. Soc. London Ser. A (1)

C. V. Raman, Proc. R. Soc. London Ser. A 101, 64, (1922).
[CrossRef]

Remote Sensing Environ. (1)

G. A. Maul, H. R. Gordon, Remote Sensing Environ. 4, 95 (1975).
[CrossRef]

Tethys (1)

A. Morel, L. Caloumenos, Tethys 6, 93 (1974).

Other (3)

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1974).

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

L. Elterman, UV, Visible, and IR Attenuation 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 (16)

Fig. 1
Fig. 1

Attenuation coefficient (m−1) as a function of wavelength (μm). The coefficients for scattering and absorption are shown for pure water and for hydrosols as well as the absorption coefficients for chlorophyll and yellow substance. The chlorophyll amount (C) is assumed to be 1 mg/m3, while the hydrosol (H) and yellow substance (Y) amounts are taken equal to unity (on the arbitrary scale used here).

Fig. 2
Fig. 2

Total attenuation coefficient cM for particles and dissolved substances at a wavelength of 0.655 μm as a function of the same quantity at 0.38 μm. Curves are shown for various values of chlorophyll amount, C (mg/m3), and yellow substance amount Y (arbitrary scale). The hydrosol amount H at various points on the curves is indicated. The crosses indicate measured points.

Fig. 3
Fig. 3

Total attenuation coefficient cM as a function of the scattering coefficient bM. The left graph is for a wavelength of 0.38 μm and the right one for 0.655 μm. The circles indicate measured points.

Fig. 4
Fig. 4

Upwelling flux from the ocean observed just above the ocean surface as a function of wavelength (μm). The cosine of the solar zenith angle, μ0 = 1. The values of the hydrosol (H), chlorophyll (C), and yellow substance (Y) amounts are indicated for each curve. The flux at each wavelength is relative to unit incident flux on a horizontal surface at the top of the atmosphere. These curves must be multiplied by the actual solar flux at each wavelength in order to obtain actual fluxes.

Fig. 5
Fig. 5

Upwelling flux from the ocean observed just above the ocean surface as a function of wavelength.

Fig. 6
Fig. 6

Upwelling flux from the ocean observed just above the ocean surface as a function of wavelength. Curves are given for solar zenith angles of 0° and 81.4° (μ0 = 1 and 0.15).

Fig. 7
Fig. 7

Fraction of photons scattered by Rayleigh type processes R as a function of hydrosol concentration at various wavelengths.

Fig. 8
Fig. 8

The single-scattering albedo ω0 as a function of hydrosol concentration at various wavelengths. It is assumed that H = C = Y.

Fig. 9
Fig. 9

The single-scattering albedo as a function of hydrosol concentration at a wavelength of 0.40 μm.

Fig. 10
Fig. 10

The single-scattering albedo as a function of hydrosol concentration at a wavelength of 0.48 μm.

Fig. 11
Fig. 11

The single-scattering albedo as a function of hydrosol concentration at a wavelength of 0.67 μm.

Fig. 12
Fig. 12

The upwelling flux from the ocean observed just above the ocean surface as a function of hydrosol amount H. It is assumed that H = C = Y. Curves are given for four wavelengths and for three different assumptions about attenuation coefficients, A, B, and C (see text). The curves in this figure were calculated from the one-dimensional approximation and assume unit downwelling flux at the ocean surface.

Fig. 13
Fig. 13

Color of upwelling light from the ocean. The purity is shown as a function of the dominant wavelength (μm). The three curves are for H = 0.1, 1, 10. The chlorophyll amount varies along each curve with particular values indicated by the symbols. It is assumed that Y = C and that μ0 = 1 (sun at zenith).

Fig. 14
Fig. 14

Color of upwelling light from the ocean. The three curves are for Y = 0.1C, Y = C, Y = 10C. The chlorophyll amount varies along each curve with particular values indicated by the symbols. It is assumed that H = 1 and μ0 = 1.

Fig. 15
Fig. 15

Color of upwelling light from the ocean. The seven curves are for C = 0.01, 1, 2, 5, 10, 20, 50. The yellow substance varies along each curve with particular values indicated by the symbols. It is assumed that H = 1 and μ0 = 1.

Fig. 16
Fig. 16

Color of upwelling light from the ocean. The two longer curves are for μ0 = 1 and 0.15. The chlorphyll amount varies along each curve with particular values indicated by the symbols. It is assumed that H = 1 and Y = C. In the lower left corner is shown the color derived from the upwelling light from the ocean plus the sky radiation reflected by the ocean surface. Another curve shows the color derived from these two contributions plus the radiation from the direct solar beam after reflection by the ocean surface.

Tables (3)

Tables Icon

Table I Upwelling Flux from Ocean

Tables Icon

Table II Upwelling and Downwelling Flux

Tables Icon

Table III Dominant Wavelength and Purity of Light from the Ocean

Equations (7)

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R = [ 1 + ( b H / b R ) H ] 1 .
ω 0 = ( b R + b H H ) ( c R + c H H + a C C + a Y Y ) 1 .
F = B { 1 ω 0 + B + [ ( 1 ω 0 ) 2 + 2 B ( 1 ω 0 ) ] 1 / 2 } 1 ,
B = ω 0 ( 0.177 R + 0.0029 ) .
F = 1 2 B ( 1 ω 0 + B ) 1 ,
F = 0.180 b S ( a + 0.360 b S ) 1 ,
F = 0.333 b S ( a + 0.360 b S ) 1 .

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