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Journal of Atmospheric and Oceanic Technology

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Editorial Type:
Article
Article Type:
Research Article

Row-Action Inversion of the Barrick–Weber Equations

J. J. GreenDepartment of Applied Mathematics, University of Sheffield, Sheffield, United Kingdom

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L. R. WyattDepartment of Applied Mathematics, University of Sheffield, Sheffield, United Kingdom

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Print Publication:
01 Mar 2006
DOI:
https://doi.org/10.1175/JTECH1854.1
Page(s):
501–510
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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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