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

Xike Zhang,Gui Zhang,Yurong Sun,Bo Zhang,Luo Qiu,Qiuwen Zhang,Zifan Gui

doi:10.3390/w11050891

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.

Highlights

Precipitation is arguably the most important variable in water cycle and land–atmosphere systems accountable for shaping the climatic state and variability of water on the land surface, in soil, and in the atmosphere [1]
The results show that the modified overlap moving window (OMW)-ensemble empirical mode decomposition (EEMD)-Multifractal detrended fluctuation analysis (MFDFA) method performs better than conventional
In order to solve the problem of discontinuity of data segmentation, in this study we introduced the overlap moving window (OMW) algorithm

Summary

Introduction

Precipitation is arguably the most important variable in water cycle and land–atmosphere systems accountable for shaping the climatic state and variability of water on the land surface, in soil, and in the atmosphere [1]. Hydrological processes and the water cycle have been greatly affected by human activities during the past century, such as deforestation, emission of carbon dioxide, exploitation of water resources, and so forth, which has led to evident global climate change [2]. A better understanding of the evolution law of precipitation is crucial to further grasp land surface hydrological processes for hydrometeorological modeling, flood control, water resources management, and ecological conservation. Long-range correlation of precipitation time series data is a useful characteristic for future forecasting. Many scholars studied scaling properties and long-range correlations of time series data [12,13,14,15,16,17,18,19,20,21]. DFA was common and widely employed to study long-range correlation and fractal scaling properties of hydrometeorological variable time series data. Matsoukas et al [20]

Methods

Results

Conclusion