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

Abstract

This paper presents arbitrary-order Hilbert spectral analysis (AOHSA) and multifractal detrended fluctuation analysis (MF-DFA) approaches to describe the multifractality of daily streamflows from four stations, namely Tilga, Jeraikela, Gomlai and Jenapur of Brahmani river basin in India. In the former method, the spectral slopes of Hilbert spectra for different moment orders depict the multifractality, and in this study, AOHSA method detected the scale invariance between synoptic to intra-seasonal scales (3 days–3 months approximately) in the daily streamflows of all the four stations. The MF-DFA method detected a crossover within 80–110 days (~ 3 months) in the four time series in addition to the crossover at annual scale. The robust estimates of Hurst exponents made by following the adaptive detrending method of pre-processing detrending operation ranged between 0.7 and 0.73 for the four time series which confirmed the universal multifractal properties within Brahmani river basin. The behaviour of spectral slope plot of AOHSA, the characteristics of scaling exponent plot, mass exponent plot and multifractal spectra confirmed that the highest multifractal degree is for the streamflow records of Tilga station which is having the smallest drainage area, and it may be attributed to the faster response of this sub-catchment to local precipitation events. The multifractality of all the four streamflow time series is found to be due to the dominant influence of correlation properties than due to the broadness of probability density function.