Two-dimensional continuous wavelet transform of simulated spatial images of waves on a slowly varying topography

The wavelet transform (WT) is now recognized as a useful, flexible, and efficient technique to analyze intermittent, non-stationary and inhomogeneous signals as well as images which are obtained from experimental or in situ measurements. In this study, the two-dimensional continuous wavelet transform (2-D CWT) was introduced to analyze the spatial image of waves. The numerical algorithm of 2-D CWT was developed and testified in simulated wave field of regular and random waves. Some more simulated wave fields of various wave conditions and sea bed slopes were then assumed to verify the analytical accuracy of this new technique. The comparisons of estimations to theoretical values for several wave parameters show that the 2-D CWT is capable of identifying the directional spectra and wave properties in shallow water.