Effect of Denoise Reduction of Time Series on Its Analysis using Chaos Theory (Case Study: Zayandehrud River)

Document Type : Research Article


1 PhD Student, Faculty of Civil Engineering, Semnan University, Semnan, Iran

2 Assistant Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran

3 Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran


In the present study, nonlinear characteristics of the monthly flow of Zayandehrud River in both pre and post noise reduction were evaluated using chaos theory during 43 years (1971- 2013) in four hydrometric stations. To determine the chaotic or randomness of the Zayandehrud River flow, the phase space was first reconstructed. Therefore, the optimal delay time and embedding dimension are calculated using the average mutual information and the nearest false neighbors. The possibility of chaos in the monthly flow, in the original and denoised time series, has been investigated using the correlation dimension. Based on the results, the correlation dimension for the denoised time series at Eskandari, Ghale Shahrokh, Pole Zaman Khan and Pole Koleh stations is estimated to be 5.94, 4.63, 2.89 and 3.30, respectively. The non-integer value of this dimension shows the chaotic behavior of monthly flow of the Zayandehrud River at these stations. The absence of correlation dimension in the original time series indicates the randomness of the system. Sensitivity to the initial conditions of the system, as a characteristic of chaotic systems, was investigated using the Liapunov exponent. Thereafter, the horizons of forecasting the current flow at the denoised stations were determined to be 36, 41, 45 and 44 months, respectively. One of the strategies for managing water scarcity and water crisis is to predict surface water discharge. By using the simulated monthly data of Zayandehrud River, it is possible to predict the flow by applying different methods, which was not possible for the original time series.


Main Subjects

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Volume 6, Issue 1
April 2019
Pages 15-27
  • Receive Date: 22 May 2018
  • Revise Date: 04 November 2018
  • Accept Date: 04 November 2018
  • First Publish Date: 21 March 2019