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Journal ArticleDOI

Derivation of directional ocean‐wave spectra by integral inversion of second‐order radar echoes

Belinda J. Lipa
- 01 May 1977 - 
- Vol. 12, Iss: 3, pp 425-434
TLDR
In this paper, the inversion of a two-dimensional nonlinear integral equation is used to obtain the second-order radar cross-section in terms of the ocean-wave spectrum.
Abstract
The derivation of sea-state from a single decameter radio wave-scatter observation requires the inversion of a two-dimensional nonlinear integral equation which gives the second-order radar cross section in terms of the ocean-wave spectrum. The second-order structure is sensitive to the directional properties of waves moving slower than the wind and the total nondirectional energy spectrum. We show how these properties, together with the rms waveheight and the wind direction, may be obtained by inverting the integral equation. The inversion method depends on recognition of physical properties of the wave-wave interactions which allow linearization of the equation, followed by application of standard inversion methods. This method is tested by application to simulated Doppler spectra corresponding to known ocean wave spectra. For typical examples (radar frequency 30 MHz, Doppler resolution 0.01 Hz, with 20 range and 10 time cells averaged) the directional ocean-wave spectrum was reproduced to within 10%, the true wind direction obtained to within 5 deg, and the rms waveheight predicted to within 5%.

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Citations
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Journal ArticleDOI

Extraction of wave parameters from measured HF radar sea-echo Doppler spectra

Donald E. Barrick
- 01 May 1977 - 
TL;DR: In this paper, a closed-form inversion model for wave height and dominant wave period extraction from radar sea-echo Doppler spectra has been proposed and compared with the actual values input to the original equations for scatter.
Journal ArticleDOI

A relaxation method for integral inversion applied to HF radar measurement of the ocean wave directional spectrum

TL;DR: In this article, the Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency (HF) radio waves from the ocean surface.
Journal ArticleDOI

Operational Wave, Current, and Wind Measurements With the Pisces HF Radar

TL;DR: In this paper, the authors present results of a trial of a Pisces HF radar system aimed at assessing its use as a component of a wave-monitoring network being installed around the coasts of England and Wales.
Journal ArticleDOI

The ocean waveheight nondirectional spectrum from inversion of the HF sea-echo Doppler spectrum

TL;DR: In this paper, a simple inversion technique for obtaining the wave height non-directional spectrum is presented, independent of the wave directionality factor, the radar look direction, or the stage of development of wave height spectrum.
Journal ArticleDOI

Ship detection with high-resolution HF skywave radar

TL;DR: In this paper, the authors present an overview of ship detection by high-frequency (HF) skywave backscatter over-the-horizon radar (OTHR) that uses sufficient resolution in the radar spatial and Doppler frequency domains.
References
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Journal ArticleDOI

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

TL;DR: Here the authors will consider only nonsingular linear integral equations of the first kind, where the known functions h(x), K(x, y) and g(x) are assumed to be bounded and usually to be continuous.
Journal ArticleDOI

On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature

S. Twomey
- 01 Jan 1963 - 
TL;DR: The purpose of the present note is to show how the same result can be obtained in a way which requires the inversion of only one matrix, whereas the method described by Phillips involves the inversions of two matrices.
Journal ArticleDOI

Doppler Spectrum of Sea Echo at 13.56 Mc./s.

D. D. Crombie
- 01 Apr 1955 - 
TL;DR: The frequency of the principal component (as initially obtained by measurement of the length of individual cycles on the record) is surprisingly constant at about 0.38 c/s, irrespective of wind conditions and state of the sea as discussed by the authors.

Statistical and computational methods in data analysis

TL;DR: Contemporary physical mathematics has much to offer the physicist as it provides well-defined concepts and tehcniques for the study of physical systems, helps in the very formulation of the laws of physical system and brings a better understanding to physiscs.
Proceedings ArticleDOI

Remote sensing of sea state by radar

TL;DR: In this paper, the authors present several radar techniques which allow the remote measurement of certain parameters important in the description of sea state, such as the ocean wave height spectrum with several frequencies via firstorder Bragg scatter.