Investigating the Multifractal Properties of Significant Wave Height Time Series Using a Wavelet-Based Approach
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137, Issue 1
Abstract
Singularities play a significant role in the characterization of time series. The temporal characteristics of fluctuating significant wave height time series are investigated in this study. The hourly time series from 24 stations located off the west coast of the United States are used for the analysis. The multifractal nature of these time series is unveiled by employing a wavelet-based method. The wavelet transform modulus maxima method is applied to obtain the multifractal spectra (singularity spectrum) of the significant wave height series. The multifractal spectra and their parameters such as peak, min and max Hölder exponents, skewness coefficients, and support lengths are calculated. The peak Hölder exponent ranged from 0.30 to 0.46 throughout the study area. Hölder exponents that are less than 0.5 indicate that the time series exhibits an antipersistent random walk. The spatial variation of parameters is depicted through kriging maps. Different spatial variation patterns can be seen from the maps. It is clear that deep offshore stations have relatively higher Hölder exponents than coastal areas. This change can be related to the wave generation mechanism, by way of physical interpretations. Since the stations located in the deep offshore can receive more swell waves than coastal zones and are open to large-scale storms, they may tend to be more persistent and have greater Hölder exponents. Also, the type of the singularities occurring in deep offshore and in the coastal zones is assessed by considering the wave generating mechanisms.
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Acknowledgments
The writer gratefully acknowledges the editor, Vijay Pangchang, and three anonymous reviewers who contributed to the improvement of this paper.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137 • Issue 1 • January 2011
Pages: 34 - 42
Copyright
© 2011 ASCE.
History
Received: Jul 10, 2009
Accepted: Jun 7, 2010
Published online: Jun 10, 2010
Published in print: Jan 2011
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