Indian Institute of Technology Roorkee 247667
Prof. Abhey Ram Bansal
CSIR-National Geophysical Research Institute, Hyderabad, Telangana-500007
Complexity and predictability quantification is important for evaluating the impact of different hydrological parameters on the hydrological process. The classification of complexity of the hydrological process based on the wavelet entropy function was studied. A reference wavelet entropy function was established by calculating the wavelet entropy of the white noise. The gauged daily flow data of the Findhorn river, Scotland was analyzed using Discrete wavelet transform(DWT). The wavelet entropy function was computed from the coefficients of the DWT and compared with the energy distribution of the white noise. The degree of absolute complexity of the hydrological time series system cannot be objectively evaluated. We found that complexity and predictability of the time series can be graded into Lower, Middle and High ranks based on the difference in the energy distribution of the series. We also estimated autocorrelation and Hurst coefficient of the gauged flow data for further quantifications of the complexity.MATLAB codes were developed for the estimation of Hurst coefficients, autocorrelation, wavelet energy function, and wavelet entropy function. The value of Hurst coefficients was found to vary from 0.6-0.7 indicating self-affine nature of the series containing predictable component in it. The preliminary results indicate that the Lower, Middle and High ranks approximately correspond to the deterministic, stochastic and random system, respectively. The result of complexity gradation is useful for modeling of hydrological dataset.
Keywords: wavelet entropy, rank, deterministic, stochastic, random, hurst coefficient