# An Algorithm for the Extraction of Ocean Wave Information from Bistatic HF Ground Wave Radar Data: A Simulation

The factors affecting error bounds on ocean surface currents derived from the first-order Doppler spectra of high frequency (HF) radar have received significant attention for nearly three decades. Barrick derived a valid approach to the determination of the standard deviation of the centroid frequencies of the Bragg peaks as a measure of such errors. Zhang et al. presented a method of modeling the centroid variability by incorporating Pierson's model for a stationary Gaussian process as a sea-surface descriptor into the ocean cross section models for a pulsed dipole source.

However, to fundamentally examine the physical basis for this variability it is necessary to revisit the time domain electric field equations. The Fourier surface coefficients, which typically appear as generic Gaussian random variables in these equations, must be explicitly cast as functions of the surface wave vectors to which are attached random phases. Unlike the plane wave assumption of earlier theoretical analyses in which a unique ocean wave number gives rise to sharp (delta-function) Bragg peaks, for a pulsed sinusoidal source there are a range of ocean waves which are responsible for the first-order scatter. Here, the random phase associated with each wave vector within this range is explicitly entered into the first-order electric field equation. When the resulting time series is partitioned and each portion is Fourier transformed, individual realizations of the power spectrum are shown to have a random variation about a mean value. Consequently, the estimated centroid frequencies are also randomly distributed.

The main differences between this approach and earlier analyses are that (1) a finite source is assumed and (2) the dependence of the surface Fourier coefficients as functions of wave vectors with random phases is explicitly entered into the electric field equations before any other statistical averaging is carried out. This approach emphasizes the physical processes which underlie the observed variability of the HF sea echo over short time periods. It is hoped that such insights will provide an improved understanding of the errors associated with surface parameter estimation.

Thesis (M.Eng.) - MUN 2004