Abstract

The sunglint geometrical optics equations of a statistically faceted sea, supported by the so-called interaction probability density and employing an averaging hybrid of the Cox–Munk and Mermelstein slope statistics, was successful in simulating 0.5 μm sunglint region characteristics. The results match independent experimental data, and good agreement is reported for various sea conditions and Sun locations, on sunglint amplitude, sunglint location, and azimuth range. In particular, the peak reflectance shift from the specular direction toward the horizon is correctly predicted, and it is found that the physical mechanism responsible for the shift is the accumulation of contributing facets near the horizon.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. J. A. Shaw and J. H. Churnside, "Scanning-laser glint measurements of sea-surface slope statistics," Appl. Opt. 36, 4202-4213 (1997).
    [CrossRef] [PubMed]
  13. B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
    [CrossRef]
  14. Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
    [CrossRef]
  15. Y. G. Trokhimovski, "Gravity-capillary wave curvature spectrum and mean-square slope retrieved from microwave radiometric measurements (Coastal Ocean Probing Experiment)," J. Atmos. Ocean. Technol. 17, 1259-1270 (2000).
    [CrossRef]
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  19. F. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4 , 767-773 (1965).
  20. F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

2002 (1)

2000 (2)

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

Y. G. Trokhimovski, "Gravity-capillary wave curvature spectrum and mean-square slope retrieved from microwave radiometric measurements (Coastal Ocean Probing Experiment)," J. Atmos. Ocean. Technol. 17, 1259-1270 (2000).
[CrossRef]

1999 (1)

1997 (2)

1995 (1)

1994 (1)

1988 (1)

P. A. Hwang and O. H. Shemdin, "The dependence of sea surface slope on atmospheric stability and swell conditions," J. Geophys. Res. 93, 13903-13912 (1988).
[CrossRef]

1987 (1)

M. A. Donelan and W. J. Pierson, Jr., "Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry," J. Geophys. Res. 92, 4971-5028 (1987).
[CrossRef]

1985 (1)

S. P. Haimbach and J. Wu, "Field trials of an optical scanner for studying sea-surface fine structures," IEEE J. Ocean. Eng. OE-10, 451-453 (1985).
[CrossRef]

1977 (1)

B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
[CrossRef]

1975 (1)

1973 (1)

1965 (1)

F. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4 , 767-773 (1965).

1960 (1)

1954 (2)

C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Anderson, G. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Bell, E. E.

Chappell, R. W.

B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
[CrossRef]

Charlock, T. P.

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Churnside, J. H.

Clough, S. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Constantikes, K. T.

Cox, C.

C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

Donelan, M. A.

M. A. Donelan and W. J. Pierson, Jr., "Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry," J. Geophys. Res. 92, 4971-5028 (1987).
[CrossRef]

Donohue, D. J.

Eisner, L.

Freund, D. E.

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Grant, H. L.

B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
[CrossRef]

Guinn, J.

Haimbach, S. P.

S. P. Haimbach and J. Wu, "Field trials of an optical scanner for studying sea-surface fine structures," IEEE J. Ocean. Eng. OE-10, 451-453 (1985).
[CrossRef]

Hale, G. M.

Hughes, B. A.

B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
[CrossRef]

Hughes, H. G.

Hwang, P. A.

P. A. Hwang and O. H. Shemdin, "The dependence of sea surface slope on atmospheric stability and swell conditions," J. Geophys. Res. 93, 13903-13912 (1988).
[CrossRef]

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Macmillan, 1964).

Joseph, R. I.

Kattawar, G.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Littfin, K. M.

Liu, W. T.

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

Liu, Y.

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

McGrath, C. P.

Mermelstein, M. D.

Munk, W.

C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

Nicodemus, F.

F. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4 , 767-773 (1965).

Oetjen, R. A.

Pierson, W. J.

M. A. Donelan and W. J. Pierson, Jr., "Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry," J. Geophys. Res. 92, 4971-5028 (1987).
[CrossRef]

Plass, G.

Priest, R. G.

Querry, M. R.

Rutledge, K.

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Shaw, J. A.

Shemdin, O. H.

P. A. Hwang and O. H. Shemdin, "The dependence of sea surface slope on atmospheric stability and swell conditions," J. Geophys. Res. 93, 13903-13912 (1988).
[CrossRef]

Shettle, E. P.

M. D. Mermelstein, E. P. Shettle, E. H. Takken, and R. G. Priest, "Infrared radiance and solar glint at the ocean-sky horizon," Appl. Opt. 33, 6022-6034 (1994).
[CrossRef] [PubMed]

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

Su, M.-Y.

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

Su, W.

Takken, E. H.

Trokhimovski, Y. G.

Y. G. Trokhimovski, "Gravity-capillary wave curvature spectrum and mean-square slope retrieved from microwave radiometric measurements (Coastal Ocean Probing Experiment)," J. Atmos. Ocean. Technol. 17, 1259-1270 (2000).
[CrossRef]

Wu, J.

S. P. Haimbach and J. Wu, "Field trials of an optical scanner for studying sea-surface fine structures," IEEE J. Ocean. Eng. OE-10, 451-453 (1985).
[CrossRef]

Yan, X.-H.

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

Young, J.

Zeisse, C. R.

Appl. Opt. (5)

Appl. Opt. 4 (1)

F. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4 , 767-773 (1965).

Deep-Sea Res. (1)

B. A. Hughes, H. L. Grant, and R. W. Chappell, "A fast response surface-wave slope meter and measured wind-wave moments," Deep-Sea Res. 24, 1211-1223 (1977).
[CrossRef]

IEEE J. Ocean. Eng. (1)

S. P. Haimbach and J. Wu, "Field trials of an optical scanner for studying sea-surface fine structures," IEEE J. Ocean. Eng. OE-10, 451-453 (1985).
[CrossRef]

J. Atmos. Ocean. Technol. (2)

Y. Liu, M.-Y. Su, X.-H. Yan, and W. T. Liu, "The mean-square slope of ocean surface waves and its effects on radar backscatter," J. Atmos. Ocean. Technol. 17, 1092-1105 (2000).
[CrossRef]

Y. G. Trokhimovski, "Gravity-capillary wave curvature spectrum and mean-square slope retrieved from microwave radiometric measurements (Coastal Ocean Probing Experiment)," J. Atmos. Ocean. Technol. 17, 1259-1270 (2000).
[CrossRef]

J. Geophys. Res. (2)

P. A. Hwang and O. H. Shemdin, "The dependence of sea surface slope on atmospheric stability and swell conditions," J. Geophys. Res. 93, 13903-13912 (1988).
[CrossRef]

M. A. Donelan and W. J. Pierson, Jr., "Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry," J. Geophys. Res. 92, 4971-5028 (1987).
[CrossRef]

J. Mar. Res. (1)

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Other (2)

D. S. Jones, The Theory of Electromagnetism (Macmillan, 1964).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, and S. A. Clough, User's Guide to LOWTRAN 7, Rep. AFGL-TR-88-0177 (Air Force Geophysics Laboratory, 1988).

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Figures (8)

Fig. 1
Fig. 1

Normalized sunglint contribution (reflectance) in the central plane (view azimuth ∼180°) corresponding to a 59.3° SZA and a Sun azimuth ∼180°, with a mean wind speed of 4.9 m∕s, and direction of 244.5°N. Our simulated data comprised CM, M, and CM&M statistics and is compared with measurements by Su et al. [Ref. 6, Fig. 6(a)].

Fig. 2
Fig. 2

Full simulated normalized sunglint contribution (reflectance) corresponding to a 59.3° SZA and a mean wind speed of 4.9 m∕s, and direction of 244.5°N. This was obtained by use of the average CM&M statistics and is found to compare very favorably with the measurements of Su et al. [Ref. 6, Fig. 6(a)].

Fig. 3
Fig. 3

Normalized sunglint contribution (reflectance) in the central plane (view azimuth ∼188°) corresponding to a 58° SZA and a Sun azimuth of ∼188°, with a mean wind speed of 4.8 m∕s. Our simulated data comprised CM, M, and CM&M statistics and is compared with measurements by Su et al. [Ref. 6, Fig. 10(a)].

Fig. 4
Fig. 4

Full simulated normalized sunglint contribution (reflectance) corresponding to a 58° SZA and a mean wind speed of 4.8 m∕s was obtained by use of the average CM&M statistics and is found to compare very favorably with the measurements of Su et al. [Ref. 6, Fig. 10(a)].

Fig. 5
Fig. 5

Normalized sunglint contribution (reflectance) in the central plane (azimuth ∼188°) corresponding to a 58° SZA and a Sun azimuth of ∼188°, with a mean wind speed of 0.6 m∕s. Our simulated data comprises (a) CM, (b) M, and (c) CM&M statistics, and is compared with measurements by Su et al. [Ref. 6; Fig 10(b)]. Although only five wind directions in one quadrant are considered explicitly, the data correspond to all quadrants in view of the symmetries about the downwind and crosswind directions.

Fig. 6
Fig. 6

Full simulated normalized sunglint contribution (reflectance) corresponding to a 58° SZA and a mean wind speed of 0.6 m∕s was obtained via use of the average CM&M statistics and is found to compare favorably with the measurements of Su et al. [Ref. 6, Fig. 10(b)].

Fig. 7
Fig. 7

Normalized sunglint contribution (reflectance) in the central plane corresponding to the Sun just above the horizon, with 83.1° SZA, a Sun azimuth of ∼128°, and a mean wind speed of 5.8 m∕s. Our simulated data comprises CM, M, and CM&M statistics, all with and without a transmittance multiplicative factor of 0.15. The simulated data are compared with measurement data read from Su et al. [Ref. 6, Fig. 5(a)], and decent agreement is observed for the case of CM&M with transmissivity and look-down angles larger than the measure of the Sun elevation above the horizon.

Fig. 8
Fig. 8

Qualitative description of reflectance. (a) Geometry involving a contributing (specular) facet at angle θ. The qualitative picture provided by Eq. (12) is represented in the reflectance curves (b), for CM statistics, several wind speed conditions, and Sun elevation at θ0 = 40° (the arrow denotes the specular angle). For a rough sea, and as θ → 0, the angular density of contributing facets increases significantly, leading to a shift of the reflectivity peak toward the horizon. The effect increases as the seas become rougher.

Equations (17)

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p ( x , y ) = 1 2 π σ x σ y exp [ 1 2 ( x 2 σ x     2 + y 2 σ y     2 ) ]
σ x = 0.00 + 0.00316 W   downwind,
σ y = 0.003 + 0.00192 W   crosswind .
σ x = 0.091 + 0.019 W 0.00046 W 2   downwind,
σ y = 0.059 + 0.021 W 0.00055 W 2   crosswind .
N ( θ , ϕ ) = 1 4 C ( θ , ϕ ) Sky ρ ( ω ) N inc ( θ , ϕ ) ×   p ( x , y ) ( 1 + x 2 + y 2 ) 2 d Ω ,
x ( θ , ϕ , θ , ϕ ) = sin ( θ ) cos ( ϕ ) + sin ( θ ) cos ( ϕ ) cos ( θ ) + cos ( θ ) ,
y ( θ , ϕ , θ , ϕ ) = sin ( θ ) sin ( ϕ ) + sin ( θ ) sin ( ϕ ) cos ( θ ) + cos ( θ ) .
ω ( θ , ϕ , θ , ϕ ) =
cos 1 { cos ( θ ) sin ( θ ) [ x cos ( ϕ ) + y sin ( ϕ ) ] 1 + x 2 + y 2 } ,
C ( θ , ϕ ) = q ( θ , ϕ , x , y ) p ( x , y ) d x d y ,
q ( θ , ϕ , x , y ) = { cos ( θ ) sin ( θ ) [ x cos ( ϕ ) + y sin ( ϕ ) ] } u ( π 2 ω ) ,
N ( θ , ϕ ) = Sky R ( θ , ϕ , θ , ϕ ) N Sky ( θ , ϕ ) d Ω ,
R ( θ , ϕ , θ , ϕ )
= ρ ( ω ) N inc ( θ , ϕ ) p ( x , y ) ( 1 + x 2 + y 2 ) 2 4 C ( θ , ϕ ) ,
ρ ( θ , ϕ ) = π d 2 N ( θ , ϕ ) d 0     2 cos ( θ Sun ) E s 0 ,
N ( θ ) ρ [ tan ( β ) ] cos ( u ) ρ ( u ) / sin ( θ ) 2 .

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