Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China

Multifractal detrended fluctuation analysis (MFDFA) can provide information about inner regularity, randomness and long-range correlation of time series, promoting the knowledge of their evolution regularity. The MFDFA are applied to detect long-range correlations and multifractal behavior of streamflow series at four hydrological stations (Toudaoguai, Longmen, Huangfu and Ganguyi) in the main channel and tributaries of the Yellow River. The results showed that there was one crossover point in the log−log curve of the fluctuation function Fq(s) versus s. The location for the crossover point is approximately one year, implying an unchanged annual periodicity within the streamflow variations. The annual periodical feature of streamflow was removed by using seasonal trend decomposition based on locally weighted regression (STL). All the decomposed streamflow series were characterized by long-term persistence in the study areas. Strong dependence of the generalized Hurst exponent h(q) on q exhibited multifractal behavior in streamflow time series at four stations in the Yellow River basin. The reduction of dependence of h(q) on q for shuffled time series showed that the multifractality of streamflow series was responsible for the correlation properties, as well as the probability density function of the streamflow series