Analysis and Prediction of the Kashkan River Flow using Chaos Theory

In this paper, flow of the Kashkan River was analyzed through chaotic viewpoint regarding the daily discharge time series. At first, time series noise level was evaluated by the Gaussian Kernel estimation and wavelet transform methods. In addition, statistical behavior of time series was studied using autocorrelation and partial autocorrelation functions. Then, in phase space reconstruction by lags method, Average Mutual Information and False Nearest Neighbors methods were used to recognize the optimal delay time and embedding dimension, respectively. Subsequently, fractal dimension of system had been estimated using the correlation dimension method. In addition, sensitivity to initial conditions examined by Lyapunov exponent method and finally, prediction has been made using the local approximation method. Decrease of false neighbors due to increasing the embedding dimension, shows the existence of fractal attractor in system's phase space, which beside positive Lyapunov exponent obtained, suggests the condition of a chaotic system for river flow in the Kashkan basin. Following these results, forecasting had been made using local approximation method in the base of reconstructed phase space and satisfactory accuracy obtained, indicate the usefulness of chaos theorybased methods to analysis and prediction of river flow in the Kashkan basin. This efficiency was emphasized using comparison between local approximation and genetic programming results.