Entropy 2011, 13(1), 195-210; doi:10.3390/e13010195
Article

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

1 State Key Laboratory of Pollution Control and Resource Reuse, Department of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China 2 China Water International Engineering Consulting Co. Ltd., Beijing 100053, China 3 Hydrology Bureau of Yellow River Conservancy Committee of Ministry of Water Resources, Zhengzhou 450001, China
* Author to whom correspondence should be addressed.
Received: 1 December 2010; in revised form: 21 December 2010 / Accepted: 22 December 2010 / Published: 17 January 2011
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Abstract: In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the performances of four wavelet-based entropy measures used commonly, namely continuous wavelet entropy (CWE), continuous wavelet relative entropy (CWRE), discrete wavelet entropy (DWE) and discrete wavelet relative entropy (DWRE) respectively, were compared and discussed. Finally, according to the analytic results of various examples, some understanding and conclusions about the calculation of wavelet-based entropy values gained in this study have been summarized, and the corresponding suggestions have also been proposed, based on which the analytic results of complexity of hydrologic series data can be improved.
Keywords: time series analysis; complexity; wavelet; information theory; entropy; multi-temporal scale; noise; probability density function; trend

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MDPI and ACS Style

Sang, Y.-F.; Wang, D.; Wu, J.-C.; Zhu, Q.-P.; Wang, L. Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales. Entropy 2011, 13, 195-210.

AMA Style

Sang Y-F, Wang D, Wu J-C, Zhu Q-P, Wang L. Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales. Entropy. 2011; 13(1):195-210.

Chicago/Turabian Style

Sang, Yan-Fang; Wang, Dong; Wu, Ji-Chun; Zhu, Qing-Ping; Wang, Ling. 2011. "Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales." Entropy 13, no. 1: 195-210.

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