Abstract

The phenomenon of sunglint, well known in satellite remote sensing, lacks a fundamental characterization under controlled laboratory conditions. Exploiting an apparatus specifically assembled for the purpose, we examine the signal collected by a photopolarimeter, pointed at a wavy water surface with measurable statistics and illuminated by a laser source. We also analyze the wave slope distributions, retrieved with an imaging system, and correlate them with the time series of glints. More particularly, we investigate the link between the occurrence of glints and that of the slopes from which they originate. In this context, the results obtained by applying the Hilbert–Huang transform technique to the slope time series are compared with those obtained through a traditional Fourier transform. This novel study first identifies the individual atomic glints as Fresnel reflection originating from a single wave facet. It then discusses the periodic character of a sequence of glints generated by a gravity wave state, as opposed to the erratic behavior of glints typical of capillary wave states. In mixed gravity–capillary conditions, it is shown that the glint properties are governed mainly by the capillary regime.

© 2008 Optical Society of America

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  1. Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
    [CrossRef]
  2. R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
    [CrossRef]
  3. 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]
  4. C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).
  5. C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 401-488 (1956).
  6. S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
    [CrossRef]
  7. P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
    [CrossRef]
  8. B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
    [CrossRef]
  9. S. R. Massel, Ocean Surface Waves: Their Physics and Prediction, Vol. 11 of Advanced Series on Ocean Engineering (World Scientific, 1996).
    [CrossRef]
  10. M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
    [CrossRef]
  11. N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
    [CrossRef]
  12. L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
    [CrossRef]
  13. N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
    [CrossRef]
  14. N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
    [CrossRef]
  15. N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
    [CrossRef]
  16. M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).
  17. S. Long, “NASA Wallops flight facility air-sea interaction research facility,” NASA Ref. Pub. 1277 (NASA Wallops, 1992).
  18. R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Optic. 29, 685-689 (1982).
  19. R. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” J. Mod. Optic. 32, 1407-1412 (1985).
  20. S. Long and J. Klinke, A Closer Look at Short Waves Generated by Wave Interactions with Adverse Currents Vol. 127 of Geophysics Monograph Series: Gas Transfer at Water Surfaces (American Geophysical Union, 2002), pp. 121-128.
  21. S. Long, “A self-zeroing capacitance probe for water wave measurements,” NASA Ref. Pub. 1278 (NASA Wallops, 1992).
  22. O. M. Phillips, Dynamics of the Upper Ocean, 2nd ed.(Cambridge U. Press, 1977),
  23. H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
    [CrossRef]
  24. S. Long, “Applications of HHT in image analysis, in The Hilbert-Huang Transform and its Applications, N. Huang and S. Shen, eds. (World Scientific, 2005), Vol. 5, p. 289.
    [CrossRef]

2006

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

2005

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

2003

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

2002

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
[CrossRef]

2000

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

1999

N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
[CrossRef]

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

1998

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

1997

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

1989

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

1985

R. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” J. Mod. Optic. 32, 1407-1412 (1985).

1982

R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Optic. 29, 685-689 (1982).

1956

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 401-488 (1956).

1954

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

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]

Azzam, R.

R. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” J. Mod. Optic. 32, 1407-1412 (1985).

R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Optic. 29, 685-689 (1982).

Banner, M.

M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
[CrossRef]

Bouffiès, S.

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

Brackett, V.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Bréon, F. M.

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

Bréon, F.-M.

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

Brito, A. Salas

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

Browell, E.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Cox, C.

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 401-488 (1956).

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).

Deuzé, J.-L.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

Dubuisson, P.

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

Eide, H.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Fan, K. L.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Farmer, D.

M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
[CrossRef]

Ferrare, R.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Gao, B.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Gemmrich, J.

M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
[CrossRef]

Gérard, B.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Gloersen, P.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Goloub, P.

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

Hara, E.

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

Herman, M.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

Huang, N.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Huang, N. E.

N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
[CrossRef]

Hwang, P.

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

Ismail, S.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Kaufman, Y.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Kaufman, Y. J.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

Kleidman, R.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Klinke, J.

S. Long and J. Klinke, A Closer Look at Short Waves Generated by Wave Interactions with Adverse Currents Vol. 127 of Geophysics Monograph Series: Gas Transfer at Water Surfaces (American Geophysical Union, 2002), pp. 121-128.

Koskulics, J.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Lallart, P.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Liu, H. H.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Long, S.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

S. Long, “NASA Wallops flight facility air-sea interaction research facility,” NASA Ref. Pub. 1277 (NASA Wallops, 1992).

S. Long, “A self-zeroing capacitance probe for water wave measurements,” NASA Ref. Pub. 1278 (NASA Wallops, 1992).

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

S. Long, “Applications of HHT in image analysis, in The Hilbert-Huang Transform and its Applications, N. Huang and S. Shen, eds. (World Scientific, 2005), Vol. 5, p. 289.
[CrossRef]

S. Long and J. Klinke, A Closer Look at Short Waves Generated by Wave Interactions with Adverse Currents Vol. 127 of Geophysics Monograph Series: Gas Transfer at Water Surfaces (American Geophysical Union, 2002), pp. 121-128.

Long, S. R.

N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
[CrossRef]

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Lotsberg, J. K.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Marchand, A.

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

Marken, E.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Martins, J. V.

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

Massel, S. R.

S. R. Massel, Ocean Surface Waves: Their Physics and Prediction, Vol. 11 of Advanced Series on Ocean Engineering (World Scientific, 1996).
[CrossRef]

Munk, W.

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 401-488 (1956).

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).

Nielsen, K.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Ottaviani, M.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Oudard, C.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Phillips, O. M.

O. M. Phillips, Dynamics of the Upper Ocean, 2nd ed.(Cambridge U. Press, 1977),

Qu, W.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Remer, L.

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

Remer, L. A.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

Roger, B.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Schoeberl, M. R.

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

Scott, N.

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

Shen, S.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Shen, Z.

N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
[CrossRef]

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Shih, H. H.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Six, B.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

Stamnes, J. J.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Stamnes, K.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Stamnes, K. H.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Su, W.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Tanré, D.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

Tung, C. C.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Vargas, C.

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

Vicente, L.

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

Walsh, T.

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

Wiscombe, W.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

Wu, M.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Wu, M.-C.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Yamasoe, M. A.

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

Yen, N.-C.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Yépez, H. Núñez

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

Zhao, L.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Zheng, Q.

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Annu. Rev. Fluid Mech.

N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annu. Rev. Fluid Mech. 31, 417-457 (1999).
[CrossRef]

Bull. Scripps Inst. Oceanogr.

C. Cox and W. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 401-488 (1956).

Eur. J. Phys.

H. Núñez Yépez, A. Salas Brito, C. Vargas, and L. Vicente, “Chaos in a dripping faucet,” Eur. J. Phys. 10, 99-105 (1989).
[CrossRef]

Geophys. Res. Lett.

Y. J. Kaufman, J. V. Martins, L. A. Remer, M. R. Schoeberl, and M. A. Yamasoe, “Satellite retrieval of aerosol absorption over the oceans using sunglint,” Geophys. Res. Lett. 29, 1928, doi:10.1029/2002GL015403 (2002).
[CrossRef]

R. Kleidman, Y. Kaufman, B. Gao, L. Remer, V. Brackett, R. Ferrare, E. Browell, and S. Ismail, “Remote sensing of total precipitable water vapor in the near-IR over ocean glint,” Geophys. Res. Lett. 27, 2657-2660 (2000).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

P. Goloub, D. Tanré, J.-L. Deuzé, M. Herman, A. Marchand, and F.-M. Bréon, “Validation of the first algorithm applied for deriving the aerosol properties over ocean using the POLDER/ADEOS measurements,” IEEE Trans. Geosci. Remote Sens. 37, 1586-1596 (1999).
[CrossRef]

J. Atmos. Ocean. Technol.

M. Ottaviani, K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe, “Light reflection off water waves: suitable setup for a polarimetric investigation under controlled laboratory conditions,” J. Atmos. Ocean. Technol. (to be published).

J. Atmos. Oceanic Technol.

N. Scott, E. Hara, T. Walsh, and P. Hwang, “Observations of steep wave statistics in open ocean waters,” J. Atmos. Oceanic Technol. 22, 258-271 (2005).
[CrossRef]

J. Geophys. Res.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, “Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean,” J. Geophys. Res. 110, D24211 (2005).
[CrossRef]

S. Bouffiès, F. M. Bréon, D. Tanré, and P. Dubuisson, “Atmospheric water vapor estimate by a differential absorption technique with the polarisation and directionality of the Earth reflectances (POLDER) instrument,” J. Geophys. Res. 102, 3831-3842 (1997).
[CrossRef]

J. Mar. Res.

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

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R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Optic. 29, 685-689 (1982).

R. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” J. Mod. Optic. 32, 1407-1412 (1985).

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M. Banner, J. Gemmrich, and D. Farmer, “Multiscale measurements of ocean wave breaking probability,” J. Phys. Oceanogr. 32, 3364-3375 (2002).
[CrossRef]

Opt. Eng.

L. Zhao, K. Nielsen, J. K. Lotsberg, E. Marken, J. J. Stamnes, and K. H. Stamnes, “New versatile setup for goniometric measurements of spectral radiance,” Opt. Eng. 45, 053606 (2006).
[CrossRef]

Proc. R. Soc. London A

N. Huang, Z. Shen, S. R. Long, M.-C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-steady time series analysis,” Proc. R. Soc. London A 454, 903-995 (1998).
[CrossRef]

Proc. R. Soc., Lond. A.

N. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc., Lond. A. 459, 2317-2345 (2003).
[CrossRef]

Other

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S. Long, “Applications of HHT in image analysis, in The Hilbert-Huang Transform and its Applications, N. Huang and S. Shen, eds. (World Scientific, 2005), Vol. 5, p. 289.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Block diagram of our glint-measurement apparatus. Wave states in the tank are created by using any combination of the tank control units for wind, wave, and current. The 1 m radius, rainbow-shaped rail with source and detector is here rendered with AutoCAD, and shows the instrumentation positioned at the Brewster configuration (source and detector both at 53.1 ° from the vertical). The 12-channel datalogger records reflected light (intensity and polarization components, 3 channels), glintometer temperature, reference detector signal, instrument tilt (pitch and roll of both source and glintometer, 4 channels), and wave elevation on capacitance wires spaced 1 cm apart near the glint area (3 channels). Images of the portion of surface under investigation are captured by an imaging system (support not shown for simplicity) and stored in a separate personal computer. Water and air temperature and wind speed are also monitored in each experiment.

Fig. 2
Fig. 2

Measured and theoretical Fresnel reflectance components for a flat water surface. The theoretical curves assume a water refractive index of 1.34. The data are normalized to a reference detector that samples the beam before it leaves the source.

Fig. 3
Fig. 3

The flat surface is disturbed as paddle-driven waves (thick black curve) start running down the tank. The axis on the left refers to surface elevation measured with capacitance wires and that on the right to the reflectance values measured by the glintometer. There is no wind and therefore no capillary waves in this case. With source and detector at equal angles, the reflected beam enters the FOV only when reflecting from a zero slope (in this case, a crest or a trough). Here only the s-polarization intensity (light gray) is shown, since the p-polarized intensity is basically zero because of the Brewster-angle geometry. Glints whose peaks do not reach the Fresnel reflectance value are due to occasional non-1D waves reflecting partially or totally off the detector FOV.

Fig. 4
Fig. 4

Glint-to-glint interval distributions for the glints collected under the gravity, capillary, and mixed wave state. The histograms are normalized to 1, so that the ordinate values correspond to the probability of occurrence. Note the dominance of peaks at 0.3, 0.5, and 0.8    s in the discrete spectrum of gravity glints, and the similarity of the two lower panels (capillary and gravity–capillary glints) with the exception of the peak at 0.07 s in the capillary wave state.

Fig. 5
Fig. 5

Normalized probabilities for the glint durations sampled in the three considered wave states. Most of the captured capillary glints last 0.002 ± 0.001     s . The peak in the distribution is well separated from that of gravity glints, which exhibit a broader range of values centered at 0.008     s . The mixed state shows essentially the same behavior as the capillary state.

Fig. 6
Fig. 6

Schematic illustration of the gravity wave state, as derived from the imaging data. The overall wave profile is pseudosinusoidal, with a virtually constant crest-to-crest period mirroring the 1.25 Hz driving frequency of the paddle. A secondary, higher-frequency wave component can interpose an inflection point (with near-zero slope) at a slightly variable location between a trough and a crest and cause variation in the position of the troughs relative to the crests. Source and detector are positioned at the same angle: including the crest and the trough, there are therefore three points per wave period which can potentially generate a glint. However, due to nonzero cross-tank slopes or other variations in the wave profile, glints may not always occur. One possible sequence is shown by the series marked “G”. Intervals between adjacent glints are marked along the abscissae. The variability of intervals created by the secondary component is represented by dashed lines and a “∼” preceding the duration. In an attractor plot (see Fig. 7), the points contributed by this glint pattern would be ( 0.5 , 0.8), (0.8, 0.8), (0.8, 0.3 ), ( 0.3 , 0.5 ), ( 0.5 , 0.3 ), ( 0.3 , 0.3 ).

Fig. 7
Fig. 7

Attractor plot for glints generated by a gravity wave state. The driving frequency of the hydraulic unit is 1.25 Hz . A total of 1482 glints belong to the dataset. High-density regions are labeled with the fraction of points (intervals) present in the cluster relative to the total number of points in the dataset. A large portion of the intervals (26%) occurs in a 0.5–0.3–0.5 s sequence.

Fig. 8
Fig. 8

Attractor plot for glints generated by a capillary wave state. The wind speed is 3.1 m/s . The majority of the 1912 collected glints are scattered throughout the whole interval space below 2     s : only very few intervals (5) were found overlapping at some point. Although the distribution favors shorter intervals, the randomness in the correlation between consecutive capillary glints is evident.

Fig. 9
Fig. 9

Attractor plot for glints generated by the overlap between the previous two wave states. The total number of collected glints is 2645, and the scatter plot is essentially indistinguishable from that in Fig. 8.

Fig. 10
Fig. 10

Normalized wave slope distributions for the wave states under analysis. Note the two predominant peaks in the gravity waves, with an abundance of positive slopes. The capillary and the mixed wave states distributions encompass a wider range of slopes and are practically indistinguishable.

Fig. 11
Fig. 11

15 s of the 10 components extracted from the gravity slope time series with the HHT technique. The ordinate axes are in slope units, and adding all these components yields the complete time series (see text). Note the periodic oscillations found in component c3 and c4.

Fig. 12
Fig. 12

Same as in Fig. 11, but for the capillary slopes time series.

Fig. 13
Fig. 13

Same as in Figs. 11, 12, but for the gravity–capillary slopes time series.

Fig. 14
Fig. 14

Comparison of the HHT (dashed curve, right y axis) and the Fourier transform (solid curve, left y axis) of the slope data. The distinct features of the gravity wave wave state (upper panel) contrast with the more uniform distribution typical of capillary waves (lower panel). The central panel represents the overlap between the two states. The arrows report the value of the peaks out of scale.

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