Abstract

Radiance and degree of linear polarization of the upwelling and the downwelling radiation just above and below a ruffled ocean surface in a model atmosphere–ocean system are computed at the wavelengths of 0.5 and 0.75 μm with the doubling–adding method. Computational results show that: (1) maximum degree of polarization (Pmax) and radiance in the corresponding direction (Rmax) of the upwelling radiation below the ocean surface are strongly dependent on the oceanic condition and that Pmax is affected by the atmospheric condition. The effect of surface wind is negligible. (2) Pmax and Rmax of the downwelling radiation just above the ocean surface are strongly dependent on the atmospheric condition, but are little affected by oceanic and surface conditions. A combined measurement of Pmax and Rmax is expected to provide useful information to infer atmospheric and oceanic conditions.

© 1988 Optical Society of America

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References

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  1. E. Raschke, “Multiple Scattering Calculation of the Transfer of Solar Radiation in an Atmosphere–Ocean System,” Beitr. Phys. Atmos. 45, 1 (1972).
  2. G. N. Plass, G. W. Kattawar, J. A. Guinn, “Radiative Transfer in the Earth’s Atmosphere and Ocean: Influence of Ocean Waves,” Appl. Opt. 14, 1924 (1975).
    [CrossRef] [PubMed]
  3. G. N. Plass, T. J. Humphreys, G. W. Kattawar, “Ocean–Atmosphere Interface: Its Influence on Radiation,” Appl. Opt. 20, 917 (1981).
    [CrossRef] [PubMed]
  4. T. Nakajima, M. Tanaka, “Effect of Wind-Generated Waves on the Transfer of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 29, 521 (1983).
    [CrossRef]
  5. G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo Calculations of the Polarization in the Earth’s Atmosphere–Ocean System,” J. Phys. Oceanogr. 3, 353 (1973).
    [CrossRef]
  6. T. Takashima, “Polarization Effect on Radiative Transfer in Planetary Composite Atmospheres with Interacting Interface,” Earth, Moon, Planets 33, 59 (1985).
    [CrossRef]
  7. K. Masuda, T. Takashima, “Computational Accuracy of Radiation Emerging from the Ocean Surface in the Model Atmosphere-Ocean System,” Pap. Meteorol. Geophys. 37, 1 (1986).
    [CrossRef]
  8. T. Takashima, K. Masuda, “Degree of Radiance and Polarization of the Upwelling Radiation from an Atmosphere–Ocean System,” Appl. Opt. 24, 2423 (1985).
    [CrossRef] [PubMed]
  9. F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran5,” Air Force Geophysics Laboratory, AFGL-TR-80-0067 (1980).
  10. IAMAP, “A Preliminary Cloudless Standard Atmosphere for Radiation Computation,” Section 2, 78–107, Boulder, CO (1982).
  11. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  12. J. E. A. Selby, R. M. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code lowtran2,” Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1972).
  13. C. Cox, W. Munk, “Some Problems in Optical Oceanography,” J. Mar. Res. 14, 63 (1955).
  14. A. Morel, “Optical Properties of Pure Water and Pure Sea Water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 1.
  15. G. M. Hale, M. R. Querry, “Optical Constants of Water in the 200-nm to 200-μm Wavelength Region,” Appl. Opt. 12, 555 (1973).
    [CrossRef] [PubMed]
  16. M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
    [CrossRef]
  17. A. Ivanoff, “Polarization Measurements in the Sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 8.

1986 (1)

K. Masuda, T. Takashima, “Computational Accuracy of Radiation Emerging from the Ocean Surface in the Model Atmosphere-Ocean System,” Pap. Meteorol. Geophys. 37, 1 (1986).
[CrossRef]

1985 (2)

T. Takashima, K. Masuda, “Degree of Radiance and Polarization of the Upwelling Radiation from an Atmosphere–Ocean System,” Appl. Opt. 24, 2423 (1985).
[CrossRef] [PubMed]

T. Takashima, “Polarization Effect on Radiative Transfer in Planetary Composite Atmospheres with Interacting Interface,” Earth, Moon, Planets 33, 59 (1985).
[CrossRef]

1983 (1)

T. Nakajima, M. Tanaka, “Effect of Wind-Generated Waves on the Transfer of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 29, 521 (1983).
[CrossRef]

1981 (1)

1980 (1)

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran5,” Air Force Geophysics Laboratory, AFGL-TR-80-0067 (1980).

1977 (1)

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

1975 (1)

1973 (2)

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo Calculations of the Polarization in the Earth’s Atmosphere–Ocean System,” J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

G. M. Hale, M. R. Querry, “Optical Constants of Water in the 200-nm to 200-μm Wavelength Region,” Appl. Opt. 12, 555 (1973).
[CrossRef] [PubMed]

1972 (2)

E. Raschke, “Multiple Scattering Calculation of the Transfer of Solar Radiation in an Atmosphere–Ocean System,” Beitr. Phys. Atmos. 45, 1 (1972).

J. E. A. Selby, R. M. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code lowtran2,” Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1972).

1955 (1)

C. Cox, W. Munk, “Some Problems in Optical Oceanography,” J. Mar. Res. 14, 63 (1955).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Cox, C.

C. Cox, W. Munk, “Some Problems in Optical Oceanography,” J. Mar. Res. 14, 63 (1955).

Guinn, J. A.

G. N. Plass, G. W. Kattawar, J. A. Guinn, “Radiative Transfer in the Earth’s Atmosphere and Ocean: Influence of Ocean Waves,” Appl. Opt. 14, 1924 (1975).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo Calculations of the Polarization in the Earth’s Atmosphere–Ocean System,” J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

Hale, G. M.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Humphreys, T. J.

Ivanoff, A.

A. Ivanoff, “Polarization Measurements in the Sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 8.

Kattawar, G. W.

Kneizys, F. X.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran5,” Air Force Geophysics Laboratory, AFGL-TR-80-0067 (1980).

Masuda, K.

K. Masuda, T. Takashima, “Computational Accuracy of Radiation Emerging from the Ocean Surface in the Model Atmosphere-Ocean System,” Pap. Meteorol. Geophys. 37, 1 (1986).
[CrossRef]

T. Takashima, K. Masuda, “Degree of Radiance and Polarization of the Upwelling Radiation from an Atmosphere–Ocean System,” Appl. Opt. 24, 2423 (1985).
[CrossRef] [PubMed]

McClatchey, R. M.

J. E. A. Selby, R. M. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code lowtran2,” Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1972).

Morel, A.

A. Morel, “Optical Properties of Pure Water and Pure Sea Water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 1.

Munk, W.

C. Cox, W. Munk, “Some Problems in Optical Oceanography,” J. Mar. Res. 14, 63 (1955).

Nakajima, T.

T. Nakajima, M. Tanaka, “Effect of Wind-Generated Waves on the Transfer of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 29, 521 (1983).
[CrossRef]

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

Plass, G. N.

Querry, M. R.

Raschke, E.

E. Raschke, “Multiple Scattering Calculation of the Transfer of Solar Radiation in an Atmosphere–Ocean System,” Beitr. Phys. Atmos. 45, 1 (1972).

Selby, J. E. A.

J. E. A. Selby, R. M. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code lowtran2,” Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1972).

Takashima, T.

K. Masuda, T. Takashima, “Computational Accuracy of Radiation Emerging from the Ocean Surface in the Model Atmosphere-Ocean System,” Pap. Meteorol. Geophys. 37, 1 (1986).
[CrossRef]

T. Takashima, K. Masuda, “Degree of Radiance and Polarization of the Upwelling Radiation from an Atmosphere–Ocean System,” Appl. Opt. 24, 2423 (1985).
[CrossRef] [PubMed]

T. Takashima, “Polarization Effect on Radiative Transfer in Planetary Composite Atmospheres with Interacting Interface,” Earth, Moon, Planets 33, 59 (1985).
[CrossRef]

Tanaka, M.

T. Nakajima, M. Tanaka, “Effect of Wind-Generated Waves on the Transfer of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 29, 521 (1983).
[CrossRef]

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1)

J. E. A. Selby, R. M. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code lowtran2,” Air Force Cambridge Research Laboratory, AFCRL-72-0745 (1972).

Air Force Geophysics Laboratory, AFGL-TR-80-0067 (1)

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran5,” Air Force Geophysics Laboratory, AFGL-TR-80-0067 (1980).

Appl. Opt. (4)

Beitr. Phys. Atmos. (1)

E. Raschke, “Multiple Scattering Calculation of the Transfer of Solar Radiation in an Atmosphere–Ocean System,” Beitr. Phys. Atmos. 45, 1 (1972).

Earth, Moon, Planets (1)

T. Takashima, “Polarization Effect on Radiative Transfer in Planetary Composite Atmospheres with Interacting Interface,” Earth, Moon, Planets 33, 59 (1985).
[CrossRef]

J. Mar. Res. (1)

C. Cox, W. Munk, “Some Problems in Optical Oceanography,” J. Mar. Res. 14, 63 (1955).

J. Phys. Oceanogr. (1)

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo Calculations of the Polarization in the Earth’s Atmosphere–Ocean System,” J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

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

T. Nakajima, M. Tanaka, “Effect of Wind-Generated Waves on the Transfer of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 29, 521 (1983).
[CrossRef]

M. Tanaka, T. Nakajima, “Effects of Oceanic Turbidity and Index of Refraction of Hydrosols on the Flux of Solar Radiation in the Atmosphere–Ocean System,” J. Quant. Spectrosc. Radiat. Transfer 18, 93 (1977).
[CrossRef]

Pap. Meteorol. Geophys. (1)

K. Masuda, T. Takashima, “Computational Accuracy of Radiation Emerging from the Ocean Surface in the Model Atmosphere-Ocean System,” Pap. Meteorol. Geophys. 37, 1 (1986).
[CrossRef]

Other (4)

A. Morel, “Optical Properties of Pure Water and Pure Sea Water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 1.

IAMAP, “A Preliminary Cloudless Standard Atmosphere for Radiation Computation,” Section 2, 78–107, Boulder, CO (1982).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. Ivanoff, “Polarization Measurements in the Sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, Eds. (Academic, London, 1974), Chap. 8.

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Figures (6)

Fig. 1
Fig. 1

Phase function and degree of polarization for single scattering for (a) and (b) aerosols and (c) and (d) hydrosols, respectively, at λ = 0.5 μm. ω0 and 〈cosθ〉 are the albedo for single scattering and the asymmetry factor, respectively.

Fig. 2
Fig. 2

Angular distributions of the degree of polarization at depths of (a) 10 m and (b) 15 m in the principal plane. Measurements are shown by dashed curves, which are reproduced from Ivanoff.17 Parameters in our computations are λ = 0.5 μm and θ0 = 14.4° and 72.4°, the oceanic aerosols in the clear condition, v = 5 m/s, oceanic models of H 1.16 C (light curves) and H 1.16 M (heavy curves). Symbols S, C, (O1, O2), and A denote the direction of the sun after its refraction at the ocean surface, critical angles, and maximum degree of polarization caused by oceanic constituents and that caused by atmospheric constituents, respectively. Region of negative degree of polarization is indicated by shading.

Fig. 3
Fig. 3

Radiance and degree of polarization of upwelling radiation just above the ocean surface (light curves) and below the ocean surface at a depth of 10 m (heavy curves) in the atmosphere–ocean system at λ = 0.5 μm in the principal plane for the solar zenith angles θ0 = 66.5°, 38.2°, and 6.3°. Abscissa denotes the nadir angle of observation (θ) with the solar plane on the left (ϕ = 0°) and the antisolar plane on the right (ϕ = 180°). The atmosphere is in the clear condition with the oceanic aerosols and the ocean surface wind is 5 m/s. Three ocean models, H0 (○), H 1.16 M ( + ), and H 1.07 M ( × ), are compared. Symbol O1 is the same as in Fig. 2. θref is explained in the text. The incident flux per unit area normal to itself is normalized to 1 at the top.

Fig. 4
Fig. 4

Dependence of the maximum degree of polarization (Pmax) and the radiance in the corresponding direction (Rmax) of the upwelling radiation below the ocean surface on atmospheric and oceanic conditions at a depth of 10 m at λ = 0.5 μm. The reference point is shown by a circle where the atmosphere is in the clear condition with the oceanic aerosols and the oceanic condition is H0. For changes of the oceanic condition, the atmospheric condition is fixed and vice versa.

Fig. 5
Fig. 5

Same as Fig. 3, but for downwelling radiation. Symbols S, C, O2, and A are the same as in Fig. 2.

Fig. 6
Fig. 6

Dependence of the maximum degree of polarization (Pmax) and the radiance in the corresponding direction (Rmax) of the down-welling radiation just above the ocean surface at λ = 0.5 and 0.75 μm on atmospheric condition. For θ0 = 6.3°, Pmax did not appear in three cases for the hazy condition. Therefore, values in the same directions as for the clear condition are shown in parentheses.

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Table I Atmospheric Optical Thicknesses

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