• Barrick, D. E., , and Weber B. L. , 1977: On the nonlinear theory for gravity waves on the ocean’s surface. Part II: Interpretation and applications. J. Phys. Oceanogr., 7 , 1121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barrick, D. E., , and Lipa B. J. , 1986: The second-order shallow-water hydrodynamic coupling coefficient in interpretation of HF radar sea echo. IEEE J. Oceanic Eng., 11 , 310315.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, M., 1992: Large scale singular value computations. Int. J. Supercomput. Appl., 6 , 1349.

  • Byrne, C., 2000: Block-iterative interior point optimization methods for reconstruction from limited data. Inverse Problems, 16 , 14051419.

  • Censor, Y., 1981: Row-action methods for huge and sparse systems and their applications. SIAM Rev., 23 , 444466.

  • Chahine, M. T., 1968: Determination of the temperature profile in an atmosphere from its outgoing radiance. J. Opt. Soc. Amer., 58 , 16341637.

  • Colton, D., , and Kress R. , 1998: Inverse Acoustic and Electromagnetic Scattering Theory. 2d ed., Vol. 93, Applied Mathematical Sciences, Springer, 334 pp.

    • Search Google Scholar
    • Export Citation
  • Engl, H. W., , Hanke M. , , and Neubauer A. , 2000: Regularization of Inverse Problems. Vol. 374, Mathematics and Its Applications, Kluwer Academic, 321 pp.

    • Search Google Scholar
    • Export Citation
  • Fleming, H. E., 1990: Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems. Linear Algebra Appl., 130 , 133150.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gordon, R., , Bender R. , , and Hermann G. T. , 1970: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. J. Theoret. Biol., 29 , 471481.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Green, J. J., 2002: Approximation with the radial basis functions of Lewitt. Algorithms for Approximation IV, J. Leversley, I. Anderson, and J. C. Mason, Eds., University of Huddersfield, 212–219.

    • Search Google Scholar
    • Export Citation
  • Green, J. J., 2003: Discretising Barrick’s equations. Proceedings of Wind over Waves II: Forecasting and Fundamentals of Applications, S. G. Sajjadi and J. C. R. Hunt, Eds., IMA and Horwood, 219–232.

    • Search Google Scholar
    • Export Citation
  • Gurgel, K-W., , Antonischki G. , , Essen H-H. , , and Schlick T. , 1999: Wellen Radar (WERA): A new ground-wave based HF radar for ocean remote sensing. Coastal Eng., 37 , 219234.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hansen, P. C., 1998: Rank-Deficient and Discrete Ill-Posed Problems. Monographs on Mathematical Modeling and Computation, Vol. 4, SIAM, 247 pp.

    • Crossref
    • Export Citation
  • Hounsfield, G. N., 1973: Computerized transverse axial scanning (tomography). I: Description of system. Brit. J. Radiol., 46 , 10161022.

  • Lewitt, R. M., 1990: Multidimensional digital image representations using generalized Kaiser–Bessel window functions. J. Opt. Soc. Amer., 7A , 18341846.

    • Search Google Scholar
    • Export Citation
  • Lipa, B. J., , and Barrick D. E. , 1986: Extraction of sea state from HF radar sea echo: Mathematical theory and modeling. Radio Sci., 21 , 81100.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Natterer, F., , and Wübbeling F. , 2001: Mathematical Methods in Image Reconstruction. Monographs on Mathematical Modeling and Computation, Vol. 5, SIAM, 216 pp.

    • Search Google Scholar
    • Export Citation
  • Tucker, M. J., 1991: Waves in Ocean Engineering: Measurement, Analysis, Interpretation. Ellis Horwood, 431 pp.

  • Twomey, S., 1996: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements. Dover, 243 pp.

  • Watson, G. N., 1944: A Treatise on the Theory of Bessel Functions. 2d ed. Cambridge University Press, 804 pp.

  • Weber, B. L., , and Barrick D. E. , 1977: On the nonlinear theory for gravity waves on the ocean’s surface. Part I: Derivations. J. Phys. Oceanogr., 7 , 310.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wyatt, L. R., 1986: The measurement of the ocean wave directional spectrum from H.F. radar Doppler spectra. Radio Sci., 21 , 473485.

  • Wyatt, L. R., 1990: A relaxation method for integral inversion applied to HF radar measurement of the ocean wave directional spectrum. Int. J. Remote Sens., 11 , 14811494.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wyatt, L. R., , Thompson S. P. , , and Burton R. R. , 1999: Evaluation of HF radar wave measurement. Coastal Eng., 37 , 259282.

  • Wyatt, L. R., and Coauthors, 2003: Validation and intercomparisons of wave measurements and models during the EuroROSE experiments. Coastal Eng., 48 , 128.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Row-Action Inversion of the Barrick–Weber Equations

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  • 1 Department of Applied Mathematics, University of Sheffield, Sheffield, United Kingdom
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Abstract

The Barrick–Weber equations describe the interaction of radar signals with the dynamic ocean surface, and so provide a mathematical basis for oceanic remote sensing. This report considers the inversion of these equations with several of the row-action methods commonly used to solve large linear systems with unstructured sparsity. It is found that the performance of the methods in inverting both synthetic and measured Doppler spectral data is comparable, with the method of Chahine–Twomey–Wyatt offering a slight advantage in the reliability of the recovery of the full directional wave spectrum and of parameters derived from its integration. Some remarks and open questions on the ill-posedness of the inversion problem conclude the paper.

Corresponding author address: J. J. Green, Dept. of Applied Mathematics, University of Sheffield, Hicks Bldg., Hounsfield Rd., Sheffield S3 7RH, United Kingdom. Email: j.j.green@shef.ac.uk

Abstract

The Barrick–Weber equations describe the interaction of radar signals with the dynamic ocean surface, and so provide a mathematical basis for oceanic remote sensing. This report considers the inversion of these equations with several of the row-action methods commonly used to solve large linear systems with unstructured sparsity. It is found that the performance of the methods in inverting both synthetic and measured Doppler spectral data is comparable, with the method of Chahine–Twomey–Wyatt offering a slight advantage in the reliability of the recovery of the full directional wave spectrum and of parameters derived from its integration. Some remarks and open questions on the ill-posedness of the inversion problem conclude the paper.

Corresponding author address: J. J. Green, Dept. of Applied Mathematics, University of Sheffield, Hicks Bldg., Hounsfield Rd., Sheffield S3 7RH, United Kingdom. Email: j.j.green@shef.ac.uk

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