Rapid wavelet-based bathymetry inversion method for nearshore X-band radars

A wavelet based method for bathymetry retrieval from X-band radar images is proposed. The method combines traditional Fast Fourier Transform techniques for retrieving peak frequency maps by evaluating the spectral peaks in the time domain, and a localized 2D Continuous Wavelet Transform for retrieving the corresponding peak wavenumbers. The main improvements of the new method compared to conventional FFT-based methods are as follows: a) the wavelet-based approach is localized - naturally fitting the inhomogeneous conditions typically found in the nearshore environment; b) it is continuous and uses wave phase information providing smooth bathymetry maps with good accuracy (RMSE in the range 2.6-6.6% of the maximum water depth); c) it requires relatively small number of successive images without the limitation of requiring a uniform time step. In order to verify the proposed method, 2D simulations of wave shoaling and refraction were performed for different sea conditions and over several bottom topographies. A radar image model including tilt and shadowing modulations together with speckle noise was applied to the simulated surface elevations to provide synthetic radar images. The method's ability to reconstruct the original bathymetry is shown to be robust in intermediate to shallow water depths (k(p)h < 1) for all cases. The method was also applied to real data acquired in Sylt island (Germany). A comparison between a bathymetric survey held prior to a storm and a radar reconstructed one during the storm shows very good agreement. These results reassure the high capability of this new method to be used in operational settings.