Multifractal Description of Streamflow and Suspended Sediment Concentration Data from Indian River Basins

📝 Abstract

This study investigates the multifractality of streamflow data of 192 stations located in 13 river basins in India using the Multifractal Detrended Fluctuation Analysis (MF-DFA). The streamflow datasets of different river basins displayed multifractality and long term persistence with a mean exponent of 0.585. The streamflow records of Krishna basin displayed least persistence and that of Godavari basin displayed strongest multifractality and complexity. Subsequently, the streamflow-sediment links of five major river basins are evaluated using the novel Multifractal Cross Correlation Analysis (MFCCA) method of cross correlation studies. The results showed that the joint persistence of streamflow and total suspended sediments (TSS) is approximately the mean of the persistence of individual series. The streamflow displayed higher persistence than TSS in 60 % of the stations while in majority of stations of Godavari basin the trend was opposite. The annual cross correlation is higher than seasonal cross correlation in majority of stations but at these time scales strength of their association differs with river basin.

💡 Analysis

This study investigates the multifractality of streamflow data of 192 stations located in 13 river basins in India using the Multifractal Detrended Fluctuation Analysis (MF-DFA). The streamflow datasets of different river basins displayed multifractality and long term persistence with a mean exponent of 0.585. The streamflow records of Krishna basin displayed least persistence and that of Godavari basin displayed strongest multifractality and complexity. Subsequently, the streamflow-sediment links of five major river basins are evaluated using the novel Multifractal Cross Correlation Analysis (MFCCA) method of cross correlation studies. The results showed that the joint persistence of streamflow and total suspended sediments (TSS) is approximately the mean of the persistence of individual series. The streamflow displayed higher persistence than TSS in 60 % of the stations while in majority of stations of Godavari basin the trend was opposite. The annual cross correlation is higher than seasonal cross correlation in majority of stations but at these time scales strength of their association differs with river basin.

📄 Content

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Multifractal Description of Streamflow and Suspended Sediment Concentration Data from Indian River Basins Adarsh S1*, Drisya S Dharan1, Nandhu AR1, Anand Vishnu B1, Vysakh K Mohan1, M Wątorek2 1 TKM College of Engineering Kollam, Kerala, India 1*Corresponding author, Adarsh S, Ph.D., Associate Professor, TKM College of Engineering Kollam, Kerala, India adarsh_lce@yahoo.co.in; adarsh1982@tkmce.ac.in Mob :+91-9446915388 2Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Kraków, Poland

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Multifractal Description of Streamflow and Suspended Sediment Concentration Data from Indian River Basins Adarsh S, Drisya S Dharan, Nandhu AR, Anand Vishnu B, Vysakh K Mohan, M Wątorek Abstract This study investigates the multifractality of streamflow data of 192 stations located in 13 river basins in India using the Multifractal Detrended Fluctuation Analysis (MF-DFA). The streamflow datasets of different river basins displayed multifractality and long term persistence with a mean exponent of 0.585. The streamflow records of Krishna basin displayed least persistence and that of Godavari basin displayed strongest multifractality and complexity. Subsequently, the streamflow-sediment links of five major river basins are evaluated using the novel Multifractal Cross Correlation Analysis (MFCCA) method of cross correlation studies. The results showed that the joint persistence of streamflow and total suspended sediments (TSS) is approximately the mean of the persistence of individual series. The streamflow displayed higher persistence than TSS in 60 % of the stations while in majority of stations of Godavari basin the trend was opposite. The annual cross correlation is higher than seasonal cross correlation in majority of stations but at these time scales strength of their association differs with river basin. Keywords: streamflow, multifractal, sediment, persistence, correlation
Introduction The estimation of local fluctuations and long term dependency of hydrologic time series is a long standing problem in hydrology. Hurst exponent (Hurst 1951) is perhaps one of the most debated properties of hydro-meteorological datasets, which is mainly used to elucidate the persistence of the time series. Mandelbrot (1982) paved the way of existence of fractal geometry of geophysical fields. Over the years, a large number of methods evolved for estimation of dependency structure and fractal behavior of hydrologic time series. It includes the rescaled range analysis, double trace moments (Tessier et al. 1996), Fourier spectral analysis (Hurst et al. 1965; Pandey et al. 1998), extended self similarity principles (Dahlstedt and Jensen 2005), Wavelet Transform Modula Maxima (WTMM) (Muzy et al. 1991), arbitrary order Hilbert spectral analysis

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(AOHSA) (Huang et al. 2009; Adarsh et al. 2018a). Peng et al. (1994) proposed an efficient method namely Detrended Fluctuation Analysis (DFA) to perform the fractal analysis based on a detrending procedure. Kantelhardt et al. (2002) proposed the multifractal extension of DFA procedure now popularly known as multifractal DFA (MF-DFA). Multifractal is the appropriate framework for scaling fields of time series and thus can provide the natural framework for analysing and modelling various geophysical processes. For hydrological time series multifractal description can be regarded as a ‘fingerprint’ and it serves as an efficient nontrivial test bed for the performance of state-of-the-art precipitation-runoff models Kantelhardt et al. (2006). Therefore DFA or MF-DFA was successfully applied for characterization of various hydro- meteorological time series (Yuan et al. 2010; Yu et al. 2014; Baranowski et al. 2011; Krzyszczak et al. 2019; Adarsh et al. 2019). Kantelhardt et al. (2003) applied the MF-DFA procedure for runoff and precipitation from different parts of globe and compared the results with WTMM method. Koscielny-Bunde et al. (2003) applied DFA, MF-DFA and wavelet analysis to discharge records from 41 hydrological stations around the globe for investigating their temporal correlations and multifractal properties. The study found that the daily runoff records were long-term correlated above some crossover time in the order of weeks, and they were characterized by a correlation function that follow a power law behaviour with exponents varying between 0.1 to 0.9. Kantelhardt et al. (2006) studied the multifractal behaviour of 99 long term daily precipitation records and 42 long term daily runoff records from different parts of the world. They found that the precipitation records generally show short term persistence while runoff records showed long term persistence with a mean exponent of 0.73. Zhang et al. (2008) applied the MF-DFA procedure to analyse the multifractal characteristics of streamflow from four gauging stations in Yang

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