Inter-comparison of wave skewness and asymmetry estimation using wavelet, Fourier and statistical methods. (15th January 2023) - Cao, Xiangming; Shi, Jian; Zhang, Chi; Zheng, Jinhai
Abstract: The traditional definition of wavelet bispectrum does not give the quantification of the bispectral content of an area of frequency–frequency space and bicoherence for signals exhibiting rapidly changing amplitudes and limited length can be misleading. To overcome these drawbacks, this research applies a newly defined quantitative wavelet bispectrum to the analysis of wave skewness and asymmetry over typical coastal topographies. Comparing with statistical methods and the Fourier-based bispectrum, the quantitative wavelet bispectrum with a lognormal mother wavelet is validated and can be used to calculate wave skewness and asymmetry. Parameters that can influence the wavelet transform is analyzed. For laboratory cases, number of voices n v = 8 is adequate to discretize the interested frequency band with sufficient resolution. The influence of wavelet peak frequency is analyzed. The magnitude of wavelet derived skewness ( S k ) and asymmetry ( A s ) increases with an increasing f 0 . Based on the analysis results, procedures to carry out wavelet transform to analyze wave records is suggested. Highlights: A newly defined quantitative wavelet bispectrum is applied to overcome the drawbacks of traditional definition of wavelet bispectrum. The quantitative wavelet bispectrum with a lognormal mother wavelet is validated with laboratory datasets. The magnitude of wavelet derived skewness and asymmetry increases with an increasing wavelet peak frequency.