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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 3148257, 18 pages
Research Article

Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

1School of Automation, Huazhong University of Science & Technology, Wuhan 430074, China
2Hubei Province Key Laboratory of Intelligent Robot, Wuhan Institute of Technology, Wuhan 430073, China
3School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China
4School of Science, Wuhan University of Technology, Wuhan 430070, China

Correspondence should be addressed to Liang Wu; moc.liamg@enihsgnailuw

Received 14 February 2017; Revised 26 August 2017; Accepted 25 September 2017; Published 31 October 2017

Academic Editor: David Arroyo

Copyright © 2017 Tongzhou Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the multifractal properties of water level with a high-frequency and massive time series using wavelet methods (estimation of Hurst exponents, multiscale diagram, and wavelet leaders for multifractal analysis (WLMF)) and multifractal detrended fluctuation analysis (MF-DFA). The dataset contains more than two million records from 10 observation sites at a northern China river. The multiscale behaviour is observed in this time series, which indicates the multifractality. This multifractality is detected via multiscale diagram. Then we focus on the multifractal analysis using MF-DFA and WLMF. The two methods give the same conclusion that at most sites the records satisfy the generalized binomial multifractal model, which is robust for different times (morning, afternoon, and evening). The variation in the detailed characteristic parameters of the multifractal model indicates that both human activities and tributaries influence the multifractality. Our work is useful for building simulation models of the water level of local rivers with many observation sites.