Editorial Type:
Article
Article Type:
Research Article

Directional Wavelet Analysis of Inhomogeneity in the Surface Wave Field from Aerial Laser Scanning Data

Richard M. Gorman National Institute of Water and Atmospheric Research, Hamilton, New Zealand

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D. Murray Hicks National Institute of Water and Atmospheric Research, Christchurch, New Zealand

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Print Publication:
01 Jun 2005
DOI:
https://doi.org/10.1175/JPO2728.1
Page(s):
949–963
Restricted access

Abstract

Modern measurement techniques such as aerial laser scanning allow for rapid determination of the spatial variation of sea surface elevation. Wave fields obtained from such data show spatial inhomogeneity associated with the presence of wave groups. A method based on two-dimensional directional wavelet analysis is described by which such inhomogeneity can be characterized in the spatial and wavenumber domains. The directional wavelet method has been applied to aerial laser scanning measurements of nearshore wave conditions off the east coast of New Zealand’s South Island. A high level of spatial variability was observed, with evidence of ensembles of wave-group envelopes of quasi-Gaussian form. These envelopes occur, with variations in spatial location, across a range of wavelet scales and directions.

Corresponding author address: Dr. Richard Gorman, NIWA, P.O. Box 11115, Hamilton, New Zealand. Email: r.gorman@niwa.co.nz

Abstract

Modern measurement techniques such as aerial laser scanning allow for rapid determination of the spatial variation of sea surface elevation. Wave fields obtained from such data show spatial inhomogeneity associated with the presence of wave groups. A method based on two-dimensional directional wavelet analysis is described by which such inhomogeneity can be characterized in the spatial and wavenumber domains. The directional wavelet method has been applied to aerial laser scanning measurements of nearshore wave conditions off the east coast of New Zealand’s South Island. A high level of spatial variability was observed, with evidence of ensembles of wave-group envelopes of quasi-Gaussian form. These envelopes occur, with variations in spatial location, across a range of wavelet scales and directions.

Corresponding author address: Dr. Richard Gorman, NIWA, P.O. Box 11115, Hamilton, New Zealand. Email: r.gorman@niwa.co.nz

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  • Abramowitz, M., and I. A. Stegun, 1970: Handbook of Mathematical Functions. 9th ed. Dover, 1046 pp.

  • Antoine, J-P., and R. Murenzi, 1996: Two-dimensional directional wavelets and the scale-angle representation. Signal Proc., 52 , 259–281.

    • Search Google Scholar
    • Export Citation

  • Antoine, J-P., R. Murenzi, and P. Vandergheynst, 1996: Two-dimensional directional wavelets in image processing. Int. J. Imaging Syst. Technol., 7 , 152–165.

    • Search Google Scholar
    • Export Citation

  • Argoul, F., A. Arneodo, J. Elezgaray, G. Grasseau, and R. Murenzi, 1989: Wavelet transform of fractal aggregates. Phys. Lett. A, 135 , 327–336.

    • Search Google Scholar
    • Export Citation

  • Chui, C. K., L. Montefusco, and L. Puccio, 1994: Wavelets: Theory, algorithms, and applications. Vol. 5. Wavelet Analysis and Its Applications, Academic Press, 627 pp.

    • Search Google Scholar
    • Export Citation

  • Daubechies, I., 1990: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory, 36 , 961–1005.

  • Daubechies, I., 1992: Ten Lectures on Wavelets. SIAM, 357 pp.

  • Donelan, M. A., W. M. Drennan, and A. K. Magnusson, 1996: Nonstationary analysis of the directional properties of propagating waves. J. Phys. Oceanogr., 26 , 1901–1914.

    • Search Google Scholar
    • Export Citation

  • Farge, M., 1990: Transformée en ondelettes continue et application à la turbulence. Publication de la Societé de Mathématique de France, 17–62.

  • Farge, M., E. Goirand, and T. Philipovitch, 1993: Wavelets and wavelet packets to analyse, filter and compress two-dimensional turbulent flows. Probability Concepts in Physical Oceanography, P. Müller, Ed., Hawaii University Press, 131–159.

    • Search Google Scholar
    • Export Citation

  • Gabor, D., 1946: Theory of communication. J. Inst. Elect. Eng., 93 , 429–457.

  • Goupillaud, P., A. Grossmann, and J. Morlet, 1984: Cycle-octave and related transforms in seismic signal analysis. Geoexploration, 23 , 85–102.

    • Search Google Scholar
    • Export Citation

  • Grossmann, A., and J. Morlet, 1984: Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal., 15 , 723–736.

    • Search Google Scholar
    • Export Citation

  • Hicks, D. M., J. Rice, S. Williams, and D. Turton, 2001: ALS stops the flow of water. Scanning the Horizons, No. 11, AAM Geoscan, Queensland, Australia, 1–3.

    • Search Google Scholar
    • Export Citation

  • Hicks, D. M., M. J. Duncan, U. Shankar, M. Wild, and J. R. Walsh, 2003: Project Aqua: Lower Waitaki River geomorphology and sediment transport. NIWA Client Rep. CHC01 (115), 171 pp.

  • Hui, W. H., and J. Hamilton, 1979: Exact solutions of a three-dimensional nonlinear Schrödinger equation applied to gravity waves. J. Fluid Mech., 93 , 117–133.

    • Search Google Scholar
    • Export Citation

  • Liu, P. C., 2000a: Is the wind wave frequency spectrum outdated? Ocean Eng., 27 , 577–588.

  • Liu, P. C., 2000b: Wavelet transform and new perspective on coastal and ocean engineering data analysis. Advances in Coastal and Ocean Engineering, P. L.-F. Liu, Ed., Vol. 6, World Scientific Publishing, 57–101.

    • Search Google Scholar
    • Export Citation

  • Mollo-Christensen, E., and A. Ramamonjiarisoa, 1978: Modeling the presence of wave groups in a random wave field. J. Geophys. Res., 83 , 4117–4122.

    • Search Google Scholar
    • Export Citation

  • Murenzi, R., 1989: Wavelet transforms associated to the n-dimensional Euclidean group with dilations: Signals in more than one dimension. Wavelets, Time-Frequency Methods and Phase Space, J.-M. Combes, A. Grossmann, and P. Tchamitchian, Eds., Springer-Verlag, 239–246.

    • Search Google Scholar
    • Export Citation

  • Nelder, J. A., and R. Mead, 1965: A simplex method for function minimization. Comput. J., 7 , 308–313.

  • Spedding, G. R., F. K. Browand, N. E. Huang, and S. R. Long, 1993: A 2-D complex wavelet analysis of an unsteady wind-generated surface wave field. Dyn. Atmos. Oceans, 20 , 55–77.

    • Search Google Scholar
    • Export Citation

  • Torrence, C., and G. P. Compo, 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79 , 61–78.

  • Williams, S., and D. Jonas, 2001: Heights accurate enough for drainage analysis: Ellipsoidal to orthometric heights. Scanning the Horizons, No. 11, AAM Geoscan, Queensland, Australia, 3–4.

    • Search Google Scholar
    • Export Citation
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