Long-term persistence and multifractality of streamflow dynamics in the Godavari River Basin, India

The study of multifractality for a given time series has become extremely important to detect non-stationarities, disturbances and hidden regularity. As known, the physical mechanism that governs any river dynamics varies on both temporal as well as on spatial scales. As the number of physical processes increases, the complexity of the system increases, thereby its non-linearity. Multifractal detrended fluctuation analysis (MFDFA), is one of the effective methods being used for detecting the presence of long-term correlation and multifractality in the system dynamics. The multifractal behaviour and temporal correlations of streamflow at the hydrological stations, Polavaram and Perur in the Godavari River Basin, are examined over a period of 31 years using the Multifractal detrended fluctuation analysis (MFDFA) and Wavelet methods. The wavelet spectrum for the data clearly shows the presence of a significant and dominating strong annual and semi-annual cycles. The multifractal response at both stations, indicates a crossover point at approximately one year (12 months), thereby indicating the presence of seasonality within the streamflow variations. To estimate the scaling properties, the data has been deseasonalized and then reconstructed, which was used for further analysis. The MFDFA analysis for the deseasonalized data shows long-range correlation, indicating the presence of long-term persistence in the data. The study shows a strong dependence of generalized Hurst exponent suggesting the presence of multifractal structure in the streamflow oscillations. The entropy analysis determines the degree of complexity and uncertainty present in the data. The analyses show scaling and multifractality in the data, over a considerable range of scales.