• Bijwarrd, H., , Spakman W. , , and Engdahl E. R. , 1998: Closing the gap between regional and global travel time tomography. J. Geophys. Res., 103 , 3005530078.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bogden, P. S., , and O'Donnell J. , 1998: Generalized inverse of ship-board current measurements: Tidal and non-tidal flows in Long Island Sound. J. Mar. Res., 56 , 9951027.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bruce, A., , and Gao H-Y. , 1996: Applied Wavelet Analysis with S-Plus. Springer, 338 pp.

  • Candela, J., , Beardsley R. C. , , and Limeburner R. , 1990: Removing tides from ship-mounted ADCP data, with application to the Yellow Sea. Proc. IEEE Fourth Working Conf. on Current Measurements, Airlie, VA, Institute of Electrical and Electronics Engineers, 258–266.

    • Search Google Scholar
    • Export Citation
  • Candela, J., , Beardsley R. C. , , and Limeburner R. , 1992: Seperation of tidal and subtidal currents in ship-mounted acoustic Doppler current profiler observations. J. Geophys. Res., 97 , 769788.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chiao, L-Y., , and Kuo B-Y. , 2001: Multiscale seismic tomography. Geophys. J. Int., 145 , 517527.

  • Chiao, L-Y., , and Liang W-T. , 2003: Multiresolution parameterization for geophysical inverse problems. Geophysics,. 68 , 199209.

  • Cohen, A., , Daubechies I. , , and Feauveau J-C. , 1992: Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math., 45 , 485560.

  • Dowd, M., , and Thompson K. R. , 1996: Extraction of tidal streams from a ship-borne acoustic Doppler current profiler using a statistical–dynamical model. J. Geophys. Res., 101 , 89438956.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Foreman, M. G. G., , and Freeland H. J. , 1991: A comparison of techniques for tide removal from ship-mounted acoustic Doppler measurements along the southwest coast of Vancouver Island. J. Geophys. Res., 96 , 1700717021.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Geyer, R., , and Signell R. , 1990: Tidal flow measurements around a headland with shipboard acoustic Doppler current profiler. J. Geophys. Res., 95 , 31893197.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gualtiero, B., , and Vesnaver A. L. , 1999: In quest of the grid. Geophysics, 64 , 1161125.

  • Jan, S., , Wang Y-H. , , Chao S-Y. , , and Wang D-P. , 2001: Development of a nowcast system for the Taiwan Strait. Ocean Polar Res., 22 , 195203.

    • Search Google Scholar
    • Export Citation
  • Kirby, M., 2001: Geometric Data Analysis—An Empirical Approach to Dimensionality Reduction and the Study of Patterns. John Wiley and Sons, 363 pp.

    • Search Google Scholar
    • Export Citation
  • Lines, L. R., , and Treitel S. , 1983: Tutorial: A review of least-squares inversion and its application to geophysical problems. Geophys. Prospect., 32 , 159186.

    • Search Google Scholar
    • Export Citation
  • Mallat, S., 1989a: A theory of multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern An. Mach. Intell., 11 , 674693.

  • Mallat, S., 1989b: Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc., 315 , 6988.

  • Mallat, S., 1998: A Wavelet Tour of Signal Processing. Academic Press, 577 pp.

  • Meyerholtz, K. A., , Pavlis G. L. , , and Szpakowski S. A. , 1989: Convolutional quelling in seismic tomography. Geophysics, 54 , 570580.

  • Münchow, A., 2000: Detiding three-dimensional velocity survey data in coastal waters. J. Atmos. Oceanic Technol., 17 , 736748.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Paige, C. C., , and Saunders M. A. , 1982: LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8 , 4371.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Press, W. H., , Teukolsky S. A. , , Vetterling W. T. , , and Flannery B. P. , 1992: Numerical Recipes in FORTRAN: The Art of Scientific Computing. 2d. ed. Cambridge University Press, 963 pp.

    • Search Google Scholar
    • Export Citation
  • Sandwell, D. T., 1987: Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data. Geophys. Res. Lett., 14 , 139142.

  • Simpson, J. H., , Mitchelson-Jacob E. G. , , and Hill A. E. , 1990: Flow structure in a channel from an acoustic Doppler current profiler. Cont. Shelf Res., 10 , 589603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tikhonov, A. N., , and Goncharsky A. V. , 1987: Ill-posed Problems in the Natural Sciences. Mir Publishers, 344 pp.

  • Wang, Y-H., , Jan S. , , and Wang D-P. , 2003: Transports through Taiwan Strait from shipboard ADCP observations (1999–2001). Estuarine Coastal Mar. Sci.,. 57 , 195201.

    • Search Google Scholar
    • Export Citation
  • Wessel, J. K., , and Smith H. F. , 1991: Free software helps map and display data. Eos, Trans. Amer. Geophys. Union, 72 , 441,. 445446.

  • Wesseling, P., 1991: An Introduction to Multigrid Methods. John Wiley and Sons, 284 pp.

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Multiresolution Interpolation and Detiding of the ADCP Data

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  • 1 Institute of Oceanography, National Taiwan University, Taipei, Taiwan
  • | 2 National Center for Ocean Research, Taipei, Taiwan
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Abstract

To account for the uneven sampling of current measurements collected by acoustic Doppler current profilers (ADCPs), a robust, three-dimensional interpolation scheme based on the multiresolution representation of the regional mean and tidal current fields is proposed. Instead of reconstructing the tidal field by getting bin-averaged time series that rely on heavy sampling or invoking radial basis function expansions, such as using the biharmonic splines with subjectively selected knots, the resolving capability of the proposed scheme relies fundamentally on the scale hierarchy of the resolvable local information constrained by the data. It is demonstrated that the proposed scheme flexibly incorporates the merits of the two conventional techniques. It enforces the resolution of model information while accommodating the local sampling density. Since it is based on a knots network defined by regular grids, attempts at experimentally and subjectively constructing the proper number and locations of controlling nodes are avoided. Constructing multiresolution representation of the current fields in terms of the three-dimensional wavelet basis is implemented by the computationally effective discrete wavelet transform of coefficients of the interpolation equations. Applications of the proposed multiresolution scheme on artificial as well as field datasets of the ADCP measurements demonstrate that it is a promising approach.

Corresponding author address: Ling-Yun Chiao, Institute of Oceanography, National Taiwan University, Taipei, Taiwan. Email: chiao@ccms.ntu.edu.tw

Abstract

To account for the uneven sampling of current measurements collected by acoustic Doppler current profilers (ADCPs), a robust, three-dimensional interpolation scheme based on the multiresolution representation of the regional mean and tidal current fields is proposed. Instead of reconstructing the tidal field by getting bin-averaged time series that rely on heavy sampling or invoking radial basis function expansions, such as using the biharmonic splines with subjectively selected knots, the resolving capability of the proposed scheme relies fundamentally on the scale hierarchy of the resolvable local information constrained by the data. It is demonstrated that the proposed scheme flexibly incorporates the merits of the two conventional techniques. It enforces the resolution of model information while accommodating the local sampling density. Since it is based on a knots network defined by regular grids, attempts at experimentally and subjectively constructing the proper number and locations of controlling nodes are avoided. Constructing multiresolution representation of the current fields in terms of the three-dimensional wavelet basis is implemented by the computationally effective discrete wavelet transform of coefficients of the interpolation equations. Applications of the proposed multiresolution scheme on artificial as well as field datasets of the ADCP measurements demonstrate that it is a promising approach.

Corresponding author address: Ling-Yun Chiao, Institute of Oceanography, National Taiwan University, Taipei, Taiwan. Email: chiao@ccms.ntu.edu.tw

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