Wave-Height Mapping From Second-Order Harmonic Peaks of Wide-Beam HF Radar Backscatter Spectra

Compact high-frequency surface wave radar has been widely applied to the measurement of sea surface current, but its accuracy and direction resolution of wave parameter estimation are always limited due to the wide beam of the antenna. In this article, a novel wave-height mapping method based on the second-order harmonic peak (SHP) of radar Doppler spectra is proposed to address this concern. The characteristic of the SHP at the Doppler frequency of <inline-formula> <tex-math notation="LaTeX">$\sqrt {2}$ </tex-math></inline-formula> times the Bragg frequency is studied through the theoretical derivation and numerical simulation. A relationship between the ratio (<inline-formula> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula>) of the SHP power to the Bragg peak power and significant wave height (<inline-formula> <tex-math notation="LaTeX">$H_{s}$ </tex-math></inline-formula>) is derived. Furthermore, the <inline-formula> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$H_{s}$ </tex-math></inline-formula> model is improved by incorporating influences, such as background noise and antenna beamwidth. With this improved model, a wave-height mapping algorithm based on the direction finding technique is presented. This approach enables the significant wave-height map extraction using a broad-beam radar. Finally, wave-height maps obtained at different sea states are depicted and analyzed, and the wave heights appearing on the maps are compared with buoy data over a one-month experiment to verify the validity and robustness of the algorithm. During this period, the significant wave height varies from about 0.5 to 4.5 m, and the radar measured wave heights at different range/distance bins show an overall root-mean-square error (RMSE) of 0.33–0.77 m and a correlation coefficient (CC) of 0.78–0.94, with respect to the buoy measurements.