Wavelet-Based 2-D Sea Surface Reconstruction Method From Nearshore X-Band Radar Image Sequences

A 2-D wavelet-based radar analysis method for sea surface reconstruction is presented. The wavelet-based sea surface reconstruction (WSSR) method resolves the traditional limitations of the Fourier analysis, such as the requirement of the homogeneity and the periodicity of the analyzed image sequences, which is hardly found in nearshore wave shoaling conditions. The method is based on a filtration of the corresponding 2-D wavelet spectra of the radar images in the pseudo-wavevector domain and includes bandpass filtration and phase correction as well as the application of an empirical modulation transfer function. In extending the method to 2-D images, the main numerical and computational challenge is to realize the inverse wavelet transform. This challenge is overcome by using the Dirac delta function as a mother wavelet in the synthesis step to reduce the computational requirements of the integration procedures via an analytical solution. A statistical comparison between the original and the reconstructed surface elevations shows the mean absolute error on the level of 6%–14% of the significant wave height, which is quite an improvement when compared with conventional 2-D Fourier-based techniques (
$\approx 27$
% for the tested case). Another main advantage of the WSSR method is its near real-time capabilities, as it can work on a single or a small number of images unlike conventional methods, which require a few minutes of integration time. In addition to various synthetic data consistency checks, the WSSR was employed on real radar data collected in Haifa bay, Israel, with good qualitative agreements in comparison with a near wave buoy.