A Compact Transportable HF Radar System for Directional Coastal Wave Field Measurements

Abstract

A low-powered transportable coastal radar system which can measure the first five angular Fourier coefficients of the wave height directional spectrum as a function of wave number is proposed and described. Operating at a single frequency in the upper HF region, the surface-wave radar employs a novel, stationary three-element receiving antenna to obtain angular information. The received signals from two crossed Zoop antennas and a monopole, all aligned along the same vertical axis and standing ~2 m high, are combined digitally to form and scan a broad cardioid beam. The second-order portion of the sea-echo Doppler spectrum is used to extract wave spectral information. This echo portion is described mathematically by a nonlinear integral equation. Trigonometric basis functions are used to represent the radar system output (both first and second order) as well as the wave height spectrum’s angular dependence.

The first-order echo is used to linearize the integral equation in an approximation valid at upper HF for higher sea states (e.g., at 25 MHz for rms sea wave heights greater than 0.4 m). A Fredholm linear integral equation in which the radar data and the desired wave data are five-element vectors or tensors is then obtained. Different inversion methods are employed for the echo region between the first-order peaks and for the region beyond these peaks. Inversion error is examined based upon N-sample averaging of the random sea-echo voltage, and a stabilization technique is introduced to circumvent the problem of ill-conditioning. The standard deviation of the five coefficients is obtained from simulations using a Phillips wave spectral model and error propagation theory. The accuracy of these radar-derived coefficients is compared with that obtained with a pitch-and-roll buoy over the same two-hour observing period and for the same frequency resolution. Near the spectral peak, typical radar inversion errors are 2–3% versus 13% buoy errors for the zero-order coefficient (i.e., the nondirectional wave height spectrum); the two first-harmonic coefficient accuracies are typically 2–4% for the radar, while they can be as high as 17% for the buoy. The Zess important second-harmonic coefficient comparisons are 2–4% for the radar and ~4% for the buoy. These accuracies are generally consistent with the inverse square-root relation to the number of independent samples; for the same observation time and frequency resolution, the radar observes many more samples from area averaging.