Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Abstract

Based on a monthly drought index, the Standardized Precipitation Index (SPI), we investigate the multifractality of monthly drought areas in seven major regions in China from 1961 to 2012 using multifractal detrended fluctuation analysis. The results show that multifractality is evident in the monthly time series for all seven regions, but its strength varies between areas. From the numerical results, we further examine the stationarity and persistence of the time series in the seven drought areas. The characteristics of the variance of big and small fluctuations are also analyzed. The characteristics of multifractal spectra are used to distinguish the features of the singularity of all the data, as well as the large and small fluctuations and the spread of the changes of fractal patterns, and so on, in the monthly drought area time series for the different regions. Finally, we investigate the possible source(s) of multifractality in the drought series by random shuffling as well as surrogating the original series for each region.

Unravelling the scaling characteristics of daily streamflows of Brahmani river basin, India, using arbitrary-order Hilbert spectral and detrended fluctuation analyses

“…The plot between h(q) versus q is helpful to assess the multifractality [13]. To represent the scaling exponent, one unit addition is necessary by the relation (q) = h(q) + 1 , where the behaviour of the plot remains the same.…”

“…Asymmetric index (R) is a useful parameter for multifractal analysis [13], which can be derived from the multifractal spectrum. It is obtained by following relation: value is positive, which shows that the largest fluctuations are more frequent than smallest fluctuations in the streamflow series of all stations.…”

“…If both long-range correlation and broadness of PDFs are responsible for multifractality, the shuffled and surrogated series will show lower multifractality than the original series. The details of shuffling and the procedure for generating surrogate series through phase randomization can be found elsewhere [13,37,38,43]. The plots of shuffled surrogated and original estimates of generalized Hurst exponent are provided in Fig.…”

Multifractal characterization of meteorological drought in India using detrended fluctuation analysis

“…As the drought indices are quantified based on hydro‐meteorological variables like precipitation, evapotranspiration and streamflow, it is logical to suspect fractal properties in such derived indices also. However, the multifractal analysis of hydrological extremes like floods or droughts is really scarce in literature while in the past decade, few studies in this direction were reported (Hou et al , ; ; Zhang et al , ). Tatli () determined persistence in the PDSI of 1966–2010 period over Turkey by determination of scaling (Hurst, H) exponent using classical rescaled range analysis, but did not estimate other multifractal properties of the series.…”

“…The high values of the Hurst exponent in all the regions were attributed to the possible association between drought and the large‐scale atmospheric circulations. Hou et al () performed multifractal characterization of drought from seven regions in China considering the SPI series, based on monthly rainfall data of 1961–2012 period. The SPI series of North and North West regions of China showed short‐term persistency while in the remaining regions, the SPI showed LTP.…”