Analysing the multifractality and cross correlations of river stage records using detrended fluctuation principles

Abstract

This study presents the application of Multifractal detrended fluctuation analysis (MFDFA) for analyzing the multifractal properties of river stage time series of Indian rivers. Initially, the MFDFA method was applied to detect long-range correlations and multifractal behaviour of river stage time series of 81 locations from 11 basins of Peninsular India. The study found that all the Hurst exponent (H) values are found to be more than 0.5 indicating the long-range power law correlations in the stage data of Indian rivers. The different datasets indicated strong multifractal degree and a strong association between H and Holder exponent supported by a strong correlation over 0.98. Most of the multifractal spectra (93 %) indicated a positive asymmetry showing the frequent low fluctuations and localized high fluctuations. Basin wise analysis showed the strongest long-term persistence (LTP) and highest degree of multifractality for the datasets of Cauvery basin. In order to get an insight on the multifractality, MFDFA was applied to the daily data of corresponding period as that of stage observations. The analysis indicated that unlike the case of stage data 68 % of the data showed LTP while rest of the data displayed STP in the analysis. The multifractality of stage series is more than that of stream flow series at all river basins in India. Multifractal cross correlation analysis performed between daily river stage data and discharge data of same period indicated a strong correlation (>0.8) in majority of cases for different scales, despite the absence of a definite pattern in the correlation behavior for the data of different stations. This analysis is proven to be a very essential and useful prerequisite for developing stage-discharge relationships in a multifractal perspective, which may eventually help in proper flood management of Indian basins' changing climate scenario. Keywords: Persistence, multifractality, Stage, Streamflow, Correlation, Scale