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A Modified Multifractal Detrended Fluctuation Analysis (MFDFA) Approach for Multifractal Analysis of Precipitation in Dongting Lake Basin, China

1
Key Laboratory for Digital Dongting Lake Basin of Hunan Province, Central South University of Forestry and Technology, Changsha 410004, China
2
School of Municipal and Mapping Engineering, Hunan City University, Yiyang 413000, China
3
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
4
School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
5
State Grid XinYuan Company Ltd., Maintenance Branch, Beijing 100068, China
6
Shenzhen Garden Management Center, Shenzhen 518000, China
*
Authors to whom correspondence should be addressed.
Water 2019, 11(5), 891; https://doi.org/10.3390/w11050891
Received: 28 March 2019 / Revised: 21 April 2019 / Accepted: 26 April 2019 / Published: 28 April 2019
(This article belongs to the Section Hydrology)
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Abstract

Multifractal detrended fluctuation analysis (MFDFA) method can examine higher-dimensional fractal and multifractal characteristics hidden in time series. However, removal of local trends in MFDFA is based on discontinuous polynomial fitting, resulting in pseudo-fluctuation errors. In this paper, we propose a two-stage modified MFDFA for multifractal analysis. First, an overlap moving window (OMW) algorithm is introduced to divide time series of the classic MFDFA method. Second, detrending by polynomial fitting local trend in traditional MFDFA is replaced by ensemble empirical mode decomposition (EEMD)-based local trends. The modified MFDFA is named OMW-EEMD-MFDFA. Then, the performance of the OMW-EEMD-MFDFA method is assessed by extensive numeric simulation experiments based on a p-model of multiplicative cascading process. The results show that the modified OMW-EEMD-MFDFA method performs better than conventional MFDFA and OMW-MFDFA methods. Lastly, the modified OMW-EEMD-MFDFA method is applied to explore multifractal characteristics and multifractal sources of daily precipitation time series data at the Mapoling and Zhijiang stations in Dongting Lake Basin. Our results showed that the scaling properties of the daily precipitation time series at the two stations presented a long-range correlation, showing a long-term persistence of the previous state. The strong q-dependence of H ( q ) and τ ( q ) indicated strong multifractal characteristics in daily precipitation time series data at the two stations. Positive Δ f values demonstrate that precipitation may have a local increasing trend. Comparing the generalized Hurst exponent and the multifractal strength of the original precipitation time series data with its shuffled and surrogate time series data, we found that the multifractal characteristics of the daily precipitation time series data were caused by both long-range correlations between small and large fluctuations and broad probability density function, but the broad probability density function was dominant. This study may be of practical and scientific importance in regional precipitation forecasting, extreme precipitation regulation, and water resource management in Dongting Lake Basin. View Full-Text
Keywords: precipitation; multifractal detrend fluctuation analysis (MFDFA); overlap moving window (OMW); ensemble empirical mode decomposition (EEMD); Dongting Lake Basin precipitation; multifractal detrend fluctuation analysis (MFDFA); overlap moving window (OMW); ensemble empirical mode decomposition (EEMD); Dongting Lake Basin
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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 (CC BY 4.0).
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Zhang, X.; Zhang, G.; Qiu, L.; Zhang, B.; Sun, Y.; Gui, Z.; Zhang, Q. A Modified Multifractal Detrended Fluctuation Analysis (MFDFA) Approach for Multifractal Analysis of Precipitation in Dongting Lake Basin, China. Water 2019, 11, 891.

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