Abstract

The water-leaving radiance field above a sea surface polluted by an oil film has been modelled using a Monte Carlo radiative transfer technique with large numbers of photons incident at a selected zenith angle. The calculated radiance was recorded for each of the 240 sectors of equal solid angle the upper hemisphere had been divided into. The results are presented in the form of a bi-directional reflectance distribution function (BRDF) and as a contrast function parameterised by observation angle for various angles of incident sunlight and for various states of the sea surface roughness. The conditions for observing maximal and minimal contrast are described.

© 2001 Optical Society of America

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References

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  1. Z. Otremba, “The impact on the reflectance in VIS of a type of crude oil film floating on the water surface,” Opt. Express 7, 129–134 (2000), http://www.opticsexpress.org/oearchive/source/23002.htm
    [Crossref] [PubMed]
  2. P.J. Flatau, J. Piskozub, and J.R. Zaneveld, “Asymptotic light field in the presence of a bubble-layer,” Opt. Express 5, 120–123 (1999), http://www.opticsexpress.org/oearchive/source/11948.htm
    [Crossref] [PubMed]
  3. J. Piskozub, A.R. Weeks, J.N. Schwarz, and I.S. Robinson, “Self-shading of upwelling irradiance for an instrument with sensors on a sidearm,” Appl. Opt. 39, 1872–1878 (2000)
    [Crossref]
  4. R. Leathers, T. Downes, and C. Mobley, “Self-shading correction for upwelling sea-surface radiance measurements made with buoyed instruments” Opt. Express 8, 561 (2001), http://www.opticsexpress.org/oearchive/source/32933.htm
    [Crossref] [PubMed]
  5. C. Cox and W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter”, Scripps. Inst. Oceanogr. Bul. 6, 9 (1956)
  6. Siegel and Seifert, Influence of sea bottom on spectral reflectance in the Oder bank region, Beit. Meer., 52, 65–71(1985)
  7. A. Morel and L. Prieur, “Analysis of variation in ocean colour,” Limnol. Oceanol.,  22, 709–721 (1977)
    [Crossref]
  8. T. Petzold, “Volume scattering functions for selected ocean waters. In: Light in the sea, J.E. Tyler (Ed) Dowden, (Hithinsons and Ross Inc., Strounburg, Pensylvania, 1977) pp.152–174

2001 (1)

2000 (2)

1999 (1)

1977 (1)

A. Morel and L. Prieur, “Analysis of variation in ocean colour,” Limnol. Oceanol.,  22, 709–721 (1977)
[Crossref]

1956 (1)

C. Cox and W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter”, Scripps. Inst. Oceanogr. Bul. 6, 9 (1956)

Cox, C.

C. Cox and W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter”, Scripps. Inst. Oceanogr. Bul. 6, 9 (1956)

Downes, T.

Flatau, P.J.

Leathers, R.

Mobley, C.

Morel, A.

A. Morel and L. Prieur, “Analysis of variation in ocean colour,” Limnol. Oceanol.,  22, 709–721 (1977)
[Crossref]

Munk, W. H.

C. Cox and W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter”, Scripps. Inst. Oceanogr. Bul. 6, 9 (1956)

Otremba, Z.

Petzold, T.

T. Petzold, “Volume scattering functions for selected ocean waters. In: Light in the sea, J.E. Tyler (Ed) Dowden, (Hithinsons and Ross Inc., Strounburg, Pensylvania, 1977) pp.152–174

Piskozub, J.

Prieur, L.

A. Morel and L. Prieur, “Analysis of variation in ocean colour,” Limnol. Oceanol.,  22, 709–721 (1977)
[Crossref]

Robinson, I.S.

Schwarz, J.N.

Weeks, A.R.

Zaneveld, J.R.

Appl. Opt. (1)

Limnol. Oceanol. (1)

A. Morel and L. Prieur, “Analysis of variation in ocean colour,” Limnol. Oceanol.,  22, 709–721 (1977)
[Crossref]

Opt. Express (3)

Scripps. Inst. Oceanogr. Bul. (1)

C. Cox and W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter”, Scripps. Inst. Oceanogr. Bul. 6, 9 (1956)

Other (2)

Siegel and Seifert, Influence of sea bottom on spectral reflectance in the Oder bank region, Beit. Meer., 52, 65–71(1985)

T. Petzold, “Volume scattering functions for selected ocean waters. In: Light in the sea, J.E. Tyler (Ed) Dowden, (Hithinsons and Ross Inc., Strounburg, Pensylvania, 1977) pp.152–174

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Figures (3)

Fig. 1.
Fig. 1.

BRDF for various angles of incidence (0°, 20°, 50°) and various sea surface states (related to the wind speeds (0 m/s, 2 m/s, 5 m/s, 10 m/s)

Fig. 2.
Fig. 2.

BRDF for the exemplary incidence angles (0° and 50°) and various sea surface states (as in Fig. 1), however at a limited scale of BRDF. Left — a clean surface, right — a polluted surface

Fig. 3.
Fig. 3.

Contrast of an oil film at various light incidence angles (0° — upper, 20° — middle, 50° — lower) and at various wind speeds (0 m/s, 2 m/s, 5 m/s, 10 m/s)

Tables (1)

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Table 1. Conversion points (angle of observations when contrast appears zero) for various angle of incidence and various wind speed

Equations (5)

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r ( θ r , φ r , θ i , φ i ) = L ( θ r , φ r ) E ( θ i , φ i )
L ( θ r , φ r ) = 0 π 2 0 2 π r ( θ i , φ i , θ r , φ r ) L ( θ i , φ i ) sin θ i d φ i d θ i
c ( θ r , φ r , λ ) = L p ( θ r , φ r , λ ) L c ( θ r , φ r , λ ) L c ( θ r , φ r , λ )
c ( θ r , φ r , θ i , φ i , λ ) = r p ( θ r , φ r , θ i , φ i , λ ) r c ( θ r , φ r , θ i , φ i , λ ) r c ( θ r , φ r , θ i , φ i , λ )
c ( θ r , θ i ) = N p ( θ r , θ i ) N c ( θ r , θ i ) N c ( θ r , θ i )

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