Abstract

Time series of laser glint counts from the ocean surface exhibit fractal behavior. Glint-count histogram widths do not follow Gaussian statistics, and histogram shapes are approximately log normal. Fractal dimensions for the statistically self-similar glint-count time series are found from the power spectra, which have an inverse power-law form. Glint counts in one spatial dimension from a linearly scanning laser and glint counts in two spatial dimensions from a laser glint imager behave similarly. In both sets of data, spectral density peaks exist at frequencies corresponding to swell and long wind waves. This implies that the glint-count process contains information related to long-wave modulation of surface roughness.

© 1997 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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1995

A. J. Palmer, R. A. Kropfli, C. W. Fairall, “Signatures of deterministic chaos in radar sea clutter and ocean surface winds,” CHAOS 5, 613–616 (1995).
[CrossRef] [PubMed]

1994

V. Y. Raizer, V. M. Novikov, T. Y. Bocharova, “The geometrical and fractal properties of visible radiances associated with breaking waves in the ocean,” Ann. Geophysicae 12, 1229–1233 (1994).

V. V. Zosimov, K. A. Naugolnykh, “Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data,” CHAOS 4, 21–24 (1994).
[CrossRef] [PubMed]

1993

J. Leung, T. Lo, “Chaotic radar signal-processing over the sea,” IEEE Trans. Ocean. Eng. 18, 287–295 (1993).

1991

M. Stiassnie, Y. Agnon, L. Shemer, “Fractal dimensions of random water surfaces,” Physica D 47, 341–352 (1991).
[CrossRef]

Y. Agnon, M. Stiassnie, “Remote sensing of the roughness of a fractal sea surface,” J. Geophys. Res. 96(C7), 12773–12779 (1991).
[CrossRef]

1990

V. Y. Rayzer, V. M. Novikov, “Fractal structure of breaking zones for surface waves in the ocean,” Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 26, 491–494 (1990).

B. J. West, “Sensing scaled scintillations,” J. Opt. Soc. Am. A 7, 1074–1100 (1990).
[CrossRef]

1989

B. J. West, M. F. Shlesinger, “On the ubiquity of 1/f noise,” Int. J. Mod. Phys. B 3, 795–820 (1989).
[CrossRef]

S. Elgar, G. Mayer-Kress, “Observations of the fractal dimension of deep- and shallow-water ocean surface gravity waves,” Physica D 37, 104–108 (1989).
[CrossRef]

1987

G. M. Zaslavskii, E. A. Sharkov, “Fractal properties of breaking zones of sea surface waves,” Sov. Phys. Dokl. 32, 499–501 (1987).

1982

E. W. Montroll, M. F. Shlesinger, “On 1/f noise and distributions with long tails,” Proc. Natl. Acad. Sci. USA 79, 3380–3387 (1982).
[CrossRef]

1960

Agnon, Y.

Y. Agnon, M. Stiassnie, “Remote sensing of the roughness of a fractal sea surface,” J. Geophys. Res. 96(C7), 12773–12779 (1991).
[CrossRef]

M. Stiassnie, Y. Agnon, L. Shemer, “Fractal dimensions of random water surfaces,” Physica D 47, 341–352 (1991).
[CrossRef]

Bocharova, T. Y.

V. Y. Raizer, V. M. Novikov, T. Y. Bocharova, “The geometrical and fractal properties of visible radiances associated with breaking waves in the ocean,” Ann. Geophysicae 12, 1229–1233 (1994).

Churnside, J. H.

J. A. Shaw, J. H. Churnside, “Ocean ripple statistics measured with a scanning-laser glint sensor,” in Proceedings of the International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1328–1330.

Elgar, S.

S. Elgar, G. Mayer-Kress, “Observations of the fractal dimension of deep- and shallow-water ocean surface gravity waves,” Physica D 37, 104–108 (1989).
[CrossRef]

Fairall, C. W.

A. J. Palmer, R. A. Kropfli, C. W. Fairall, “Signatures of deterministic chaos in radar sea clutter and ocean surface winds,” CHAOS 5, 613–616 (1995).
[CrossRef] [PubMed]

Feder, J.

J. Feder, Fractals (Plenum, New York, 1988).

Kropfli, R. A.

A. J. Palmer, R. A. Kropfli, C. W. Fairall, “Signatures of deterministic chaos in radar sea clutter and ocean surface winds,” CHAOS 5, 613–616 (1995).
[CrossRef] [PubMed]

Leung, J.

J. Leung, T. Lo, “Chaotic radar signal-processing over the sea,” IEEE Trans. Ocean. Eng. 18, 287–295 (1993).

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995), pp. 76–79.

Lo, T.

J. Leung, T. Lo, “Chaotic radar signal-processing over the sea,” IEEE Trans. Ocean. Eng. 18, 287–295 (1993).

Longuet-Higgins, M. S.

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995), pp. 76–79.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).

Mayer-Kress, G.

S. Elgar, G. Mayer-Kress, “Observations of the fractal dimension of deep- and shallow-water ocean surface gravity waves,” Physica D 37, 104–108 (1989).
[CrossRef]

Minnaert, M. M.

M. M. Minnaert, Light and Color in the Open Air (Dover, New York, 1954).

Montroll, E. W.

E. W. Montroll, M. F. Shlesinger, “On 1/f noise and distributions with long tails,” Proc. Natl. Acad. Sci. USA 79, 3380–3387 (1982).
[CrossRef]

Naugolnykh, K.

K. Naugolnykh, NOAA/ETL/ET1, 325 Broadway, Boulder, Colorado 80303 (personal communication, June1996).

Naugolnykh, K. A.

V. V. Zosimov, K. A. Naugolnykh, “Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data,” CHAOS 4, 21–24 (1994).
[CrossRef] [PubMed]

Novikov, V. M.

V. Y. Raizer, V. M. Novikov, T. Y. Bocharova, “The geometrical and fractal properties of visible radiances associated with breaking waves in the ocean,” Ann. Geophysicae 12, 1229–1233 (1994).

V. Y. Rayzer, V. M. Novikov, “Fractal structure of breaking zones for surface waves in the ocean,” Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 26, 491–494 (1990).

Palmer, A. J.

A. J. Palmer, R. A. Kropfli, C. W. Fairall, “Signatures of deterministic chaos in radar sea clutter and ocean surface winds,” CHAOS 5, 613–616 (1995).
[CrossRef] [PubMed]

Raizer, V. Y.

V. Y. Raizer, V. M. Novikov, T. Y. Bocharova, “The geometrical and fractal properties of visible radiances associated with breaking waves in the ocean,” Ann. Geophysicae 12, 1229–1233 (1994).

Rayzer, V. Y.

V. Y. Rayzer, V. M. Novikov, “Fractal structure of breaking zones for surface waves in the ocean,” Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 26, 491–494 (1990).

Schroeder, M.

M. Schroeder, Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise (Freeman, New York, 1991).

Sharkov, E. A.

G. M. Zaslavskii, E. A. Sharkov, “Fractal properties of breaking zones of sea surface waves,” Sov. Phys. Dokl. 32, 499–501 (1987).

Shaw, J. A.

J. A. Shaw, J. H. Churnside, “Ocean ripple statistics measured with a scanning-laser glint sensor,” in Proceedings of the International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1328–1330.

Shemer, L.

M. Stiassnie, Y. Agnon, L. Shemer, “Fractal dimensions of random water surfaces,” Physica D 47, 341–352 (1991).
[CrossRef]

Shlesinger, M. F.

B. J. West, M. F. Shlesinger, “On the ubiquity of 1/f noise,” Int. J. Mod. Phys. B 3, 795–820 (1989).
[CrossRef]

E. W. Montroll, M. F. Shlesinger, “On 1/f noise and distributions with long tails,” Proc. Natl. Acad. Sci. USA 79, 3380–3387 (1982).
[CrossRef]

Stiassnie, M.

Y. Agnon, M. Stiassnie, “Remote sensing of the roughness of a fractal sea surface,” J. Geophys. Res. 96(C7), 12773–12779 (1991).
[CrossRef]

M. Stiassnie, Y. Agnon, L. Shemer, “Fractal dimensions of random water surfaces,” Physica D 47, 341–352 (1991).
[CrossRef]

West, B. J.

B. J. West, “Sensing scaled scintillations,” J. Opt. Soc. Am. A 7, 1074–1100 (1990).
[CrossRef]

B. J. West, M. F. Shlesinger, “On the ubiquity of 1/f noise,” Int. J. Mod. Phys. B 3, 795–820 (1989).
[CrossRef]

Zaslavskii, G. M.

G. M. Zaslavskii, E. A. Sharkov, “Fractal properties of breaking zones of sea surface waves,” Sov. Phys. Dokl. 32, 499–501 (1987).

Zosimov, V. V.

V. V. Zosimov, K. A. Naugolnykh, “Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data,” CHAOS 4, 21–24 (1994).
[CrossRef] [PubMed]

Ann. Geophysicae

V. Y. Raizer, V. M. Novikov, T. Y. Bocharova, “The geometrical and fractal properties of visible radiances associated with breaking waves in the ocean,” Ann. Geophysicae 12, 1229–1233 (1994).

CHAOS

A. J. Palmer, R. A. Kropfli, C. W. Fairall, “Signatures of deterministic chaos in radar sea clutter and ocean surface winds,” CHAOS 5, 613–616 (1995).
[CrossRef] [PubMed]

V. V. Zosimov, K. A. Naugolnykh, “Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data,” CHAOS 4, 21–24 (1994).
[CrossRef] [PubMed]

IEEE Trans. Ocean. Eng.

J. Leung, T. Lo, “Chaotic radar signal-processing over the sea,” IEEE Trans. Ocean. Eng. 18, 287–295 (1993).

Int. J. Mod. Phys. B

B. J. West, M. F. Shlesinger, “On the ubiquity of 1/f noise,” Int. J. Mod. Phys. B 3, 795–820 (1989).
[CrossRef]

Izv. Acad. Sci. USSR, Atmos. Oceanic Phys.

V. Y. Rayzer, V. M. Novikov, “Fractal structure of breaking zones for surface waves in the ocean,” Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 26, 491–494 (1990).

J. Geophys. Res.

Y. Agnon, M. Stiassnie, “Remote sensing of the roughness of a fractal sea surface,” J. Geophys. Res. 96(C7), 12773–12779 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Physica D

M. Stiassnie, Y. Agnon, L. Shemer, “Fractal dimensions of random water surfaces,” Physica D 47, 341–352 (1991).
[CrossRef]

S. Elgar, G. Mayer-Kress, “Observations of the fractal dimension of deep- and shallow-water ocean surface gravity waves,” Physica D 37, 104–108 (1989).
[CrossRef]

Proc. Natl. Acad. Sci. USA

E. W. Montroll, M. F. Shlesinger, “On 1/f noise and distributions with long tails,” Proc. Natl. Acad. Sci. USA 79, 3380–3387 (1982).
[CrossRef]

Sov. Phys. Dokl.

G. M. Zaslavskii, E. A. Sharkov, “Fractal properties of breaking zones of sea surface waves,” Sov. Phys. Dokl. 32, 499–501 (1987).

Other

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).

J. Feder, Fractals (Plenum, New York, 1988).

M. Schroeder, Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise (Freeman, New York, 1991).

J. A. Shaw, J. H. Churnside, “Ocean ripple statistics measured with a scanning-laser glint sensor,” in Proceedings of the International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1328–1330.

K. Naugolnykh, NOAA/ETL/ET1, 325 Broadway, Boulder, Colorado 80303 (personal communication, June1996).

M. M. Minnaert, Light and Color in the Open Air (Dover, New York, 1954).

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995), pp. 76–79.

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Figures (6)

Fig. 1
Fig. 1

Two time series from a 2-Hz scanning-laser glint meter of glint counts within ±10° of nadir. (a), 5 min of 10-s samples; (b), 50 min of 10-s samples.

Fig. 2
Fig. 2

Glint-count histograms for the time series in Fig. 1. With an order-of-magnitude increase of sample and time-series durations, the histogram width decreased by less than a factor of 2.

Fig. 3
Fig. 3

Typical scanning-laser glint-count power spectrum computed from a 75-min time series of 2-Hz samples (U5 m s-1, 2–3 m swell). The slope chosen for the low-frequency region is indicated by a dashed line segment.

Fig. 4
Fig. 4

Video glint count histogram (glint counts from 9000 30-Hz video frames) and the corresponding best-fit log-normal function.

Fig. 5
Fig. 5

Video glint-count power spectrum for a 5-min time series of 30-Hz samples (U1 m s-1, 1–1.5 m swell). The intersection of the low- and high-frequency regions occurs at the dominant wind-wave frequency. Dashed-line segments indicate the slopes chosen for these two regions.

Fig. 6
Fig. 6

Scatter plot of spectral exponents for blob and pixel counting. Crosses represent low-frequency exponents; circles represent high-frequency exponents. The exponents become smaller with a rougher ocean surface (see text).

Tables (1)

Tables Icon

Table 1 Summary of Glint-Count Fractal Dimensions

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

D=E+3-β2.
T=2πUg,
pg=45002π(1.20)ngexp-[ln(ng)-4.73]22(1.20).

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