Assessing memory signal of time-series and simulation of rainfall-runoff process, using neural networks and wavelet-neural hybrid models

In this study, long-term memory and dynamic behavior of daily flow time-series of Khorramabad River, which its basin is mountainous and has urban land use, is investigated by Hurst exponent. The Hurst exponent of runoff signal of Khorramabad River during 1991-2014 period was obtained as 0.8. This value shows long-term memory and nonlinear, dynamic signal of this river’s runoff. By applying neural network and wavelet transforms, the rainfall-runoff time-series of this river was simulated. In this respect, by taking the time-series of rainfall and rainfall-runoff as input to the artificial neural network and wavelet-neural network hybrid, four models including: 1) rainfall, neural network, 2) rainfall-runoff, neural network, 3) rainfall, wavelet-neural network and 4) rainfall-runoff, wavelet-neural network were developed. In the hybrid models of wavelet-neural network, time-series of rainfall and runoff were decomposed to high-frequency and low-frequency sub-signals. Results of evaluating the accuracy and efficiency of the four models showed that the wavelet–neural network model correctly simulated the runoff behavior with the best efficiency at 99% confidence level. Comparison of the results of wavelet–neural network model to the neural network model, using Morgan-Granger-Newbold, showed significant superiority of the first model. Also, results of evaluating signal error of the four implemented models, using two tests of Von-Neumann and Buishand test, showed that there is a significant substitution point in the signal error of the neural network model and signal of rainfall-runoff model. Therefore, existence of very different monthly and periodical fluctuations in 1991-1998 and 1999-2014 in the behavior of rainfall-runoff leads to reduction of efficiency and precision coefficient of neural network model. While, in the hybrid model of wavelet-neural network, allocation of relative weight to each sub-signal, has effectively reduced the short-term, average and long-term fluctuations in modeling error.