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Entropy 2011, 13(1), 241-253; doi:10.3390/e13010241
Article

Wavelet-Based Multi-Scale Entropy Analysis of Complex Rainfall Time Series

Received: 10 December 2010 / Revised: 7 January 2011 / Accepted: 8 January 2011 / Published: 20 January 2011
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Abstract

This paper presents a novel framework to determine the number of resolution levels in the application of a wavelet transformation to a rainfall time series. The rainfall time series are decomposed using the à trous wavelet transform. Then, multi-scale entropy (MSE) analysis that helps to elucidate some hidden characteristics of the original rainfall time series is applied to the decomposed rainfall time series. The analysis shows that the Mann-Kendall (MK) rank correlation test of MSE curves of residuals at various resolution levels could determine the number of resolution levels in the wavelet decomposition. The complexity of rainfall time series at four stations on a multi-scale is compared. The results reveal that the suggested number of resolution levels can be obtained using MSE analysis and MK test. The complexity of rainfall time series at various locations can also be analyzed to provide a reference for water resource planning and application.
Keywords: wavelet transform; multi-scale entropy; rainfall time series wavelet transform; multi-scale entropy; rainfall time series
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.

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Chou, C.-M. Wavelet-Based Multi-Scale Entropy Analysis of Complex Rainfall Time Series. Entropy 2011, 13, 241-253.

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