A nonlinear approach to ocean wave spectrum extraction from bistatic HF-radar data

Silva, Murilo Teixeira (2017) A nonlinear approach to ocean wave spectrum extraction from bistatic HF-radar data. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this thesis, a new approach to the extraction of the directional ocean wave spectrum from bistatic high frequency (HF) radar data is proposed. The proposed method relies on the simplification of the second-order bistatic radar cross-section, analogous to the one presented by Shahidi and Gill [1] for the monostatic case, to facilitate the use of nonlinear optimization methods, such as regularized nonlinear least-squares. Initially, the historic development of the techniques related to the extraction of the ocean wave spectrum from HF radar data is provided in order to contextualize the work of this thesis. Then, an overview of the theory related to ocean waves and the bistatic radar cross-section is shown. Later, the nonlinear optimization method used in this thesis, Tikhonov regularization in Hilbert spaces, is explained, as well as the theoretical background necessary to understand the method. Once the theory is laid out, the simplification of the second-order bistatic HF radar cross section is presented. The simplification consists of a change of variables that allow the use of the “sifting” property of the Dirac delta function. This reduces the dependence of the second-order bistatic cross-section to a single variable. After the simplification process is shown, the methodology for extracting the directional ocean wave spectrum from bistatic HF radar data is discussed. As a proof-of-concept, the method is initially applied to the second-order bistatic cross section, without the presence of noise. The method successfully extracted the directional ocean wave spectrum without assuming any function model for the nondirectional ocean wave spectrum, and assuming a cosine-power model for the directional spreading function. Next, the first-order bistatic HF radar cross section is added to the second-order cross section, and the proposed method is applied, still without noise present. The proposed method was also able to extract the directional ocean wave spectrum and very low error is added by the inclusion of the first-order cross section. Finally, different levels of noise are added to the cross section including the first and second- orders, and the presented method is applied for the extraction. Again, the method yields good results, with acceptable levels of error for the different noise levels. This new approach to the extraction of the directional ocean wave spectrum from bistatic HF radar data presents, to the author’s knowledge, the first nonlinear extraction method for bistatic HF radar data. Further developments of the technique, such as the use of different nonlinear extraction methods, or a general directional spreading function, are suggested.

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