Wave Height Inversion on the Sea Surface Coupled With Broken-Short Waves and Free Waves Using a Fully Coherent <i>X</i>-Band Radar

Fully coherent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i>-band radar is a rapidly emerging tool for wave measurement. This article introduces a method for wave height inversion based on the sea surface coupled with broken-short waves and free waves using a fully coherent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i>-band radar. Initially, the Doppler spectrum characteristics from the coupled sea surface under vertical polarization are analyzed to obtain spatial–temporal velocity data. Subsequently, a 2-D Fourier transform is applied to the spatial–temporal matrix of velocities to estimate the wave number–frequency spectrum. The energy component produced by broken-short waves in the wave number–frequency spectrum is analyzed and partly filtered. Then, the processed wave number–frequency spectrum is integrated over the wave number domain to obtain the 1-D velocity spectrum. Subsequently, no calibration is required, and the wave height spectrum is estimated from the 1-D velocity spectrum. Finally, significant wave heights are derived from the zeroth moment of the wave height spectra. The method is validated through simulations and real data. An approximately 3-day data set that was collected using a shore-based fully coherent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i>-band radar, deployed along the coast of Shandong Province, China, is reanalyzed. Comparisons between the measurements of the radar and from the European Centre for Medium-Range Weather Forecasts (ECMWF) are conducted, and the radar-measured and the ECMWF's wave heights are in a reasonable agreement with a coherence coefficient of over 0.94. The results indicate that the proposed method is effective for wave height measurements under the coupled sea surface conditions using a coherent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i>-band radar.