Comparison between phase space-based local chaotic models for riverflow forecasting

Generally، The dynamics which is observed in time series of a hydrologic system variable have been considered as complex and random behavior. During last decades، using various artificial intelligence approaches such as chaos theory to analyze and prediction of hydrologic systems have been increased. In chaos theory viewpoint، complexity and random-like behavior of a system can be resulted from a simple and hidden determinism. Therefore، systems such as dominant hydrologic system which controls flow in a river can have this kind of determinism. If such determinism is existed، can be observed through system phase space، which can be reconstructed using a time series by lags method. Based on such a pattern that formed in reconstructed phase space، various prediction models can be used to forecast system behavior in future. Hence، chaotic behavior of the Kashkan river daily discharge time series have been studied using False Nearest Neighbors and Lyapunov Exponent methods which evaluated fractal attractor and sensitivity to initial condition as two major characteristics of a chaotic system. Average Mutual Information method was used to determine optimal delay time in phase space reconstruction by delay method. In this paper، it has been suggested to use first global minimum of mutual information function as standard to select optimal delay time. According to the results which have been obtain by these methods، chaotic behavior in daily runoff time series of the Kashkan river have been observed. In False Nearest Neighbors method، the percent of false neighbors have been significantly decreased due to rising embedding dimension of phase space، which have been shown the existence of a fractal attractor in system phase space. In lyapunov exponent method، the sensitivity to initial condition has been evaluated through reconstructed phase space and positive lyapunov exponent has been obtained. Hence، chaos theory-based models can be used to forecast daily runoff in this system. Various local models were used to make prediction based on reconstructed phase space and the results have been compared. Local Average and Local Polynomial was among local models that employed in this study. In addition، as a new hybrid approach، Multi Layer Prespetron Artificial Neural Networks have been used to local modeling based on phase space. All prediction results show appropriate quality of local prediction models in base of attractor pattern in phase space of dominant system of the Kashkan river flow. The accuracy which have been resulted from local hybrid model with Artificial Neural Networks، have been not shown significant difference with other current local models such as Local Average and Local Polynomial prediction methods. However، the Local Polynomial model has been shown better forecasting accuracy in compare with other methods. Totally، Local chaotic methods are suggested to make daily prediction of runoff in the Kashkan river.