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

Document Type : Research Article

Authors

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

Abstract

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.

Keywords

Main Subjects

References

[1]. Honarbakhsh A, Karimian kakolaki R, shams Ghahfarokhi G, Davoudian Dehkordi A, Pajouhesh M. Flow modeling in a bend of a natural river based on different turbulence models (Case study: Doab Samsami River). Iranian Journal of Ecohydrology. 2018;5(3):907-916. (Persian)
[2]. Hashemi Golpayegani SMR. Chaos and its applications in engineering. Tehran: Amirkabir University of Technology; 2009. (Persian)
[3]. Seyedian S, Soleimani M, Kashani M. Predicting streamflow using data-driven model and time series. Iranian Journal of Ecohydrology. 2014; 1(3):167-179. (Persian)
[4]. Amiri E, Roudbari Mousavi M. Evaluation of IHACRES hydrological model for simulation of daily flow (case study Polrood and Shalmanrood rivers). Iranian Journal of Ecohydrology. 2016;3(4):533-543. (Persian)
[5]. Lorenz E. The essence of chaos. Seattle: University of Washington Press; 1993.
 
[6]. Porporato A, Ridolfi L. Nonlinear analysis of river flow time sequences. Water Resources Research. 1997;33(6):1353-1367.
[7]. Kantz H, Schreiber T. Nonlinear Time Series Analysis. UK: Cambridge University Press; 1997.
[8]. Sivakumar B, Phoon KK, Liong SY, Liaw CY. A systematic approach to noise reduction in chaotic hydrological time series. Journal of Hydrology. 1999;219(4):103-135.
[9]. Elshorbagy A, Simonovic SP, Panu US. Estimation of missing streamflow data using principles of chaos theory. Journal of Hydrology. 2002a; 255:123–133.
[10]. Ng W.W, Panu U.S, Lennox W.C. Chaos based analytical techniques for daily extreme hydrological observations. Journal of Hydrology. 2007;342:17-41.
[11]. Fattahi MH. Applying a noise reduction method to reveal chaos in the river flow time series. International Journal of Environmental, Ecological, Geological and Mining Engineering. 2014;8(8):524-531.
[12]. Rezaei H, Jabbari Gharabagh S. Noise reduction effect on chaotic analysis of Nazluchay River flow. Water and Soil Science. 2017;27(3):239-250. (Persian)
[13]. Iranmehr M, Pourmanafi S, Soffianian A. Ecological monitoring and assessment of spatial-temporal changes in land cover with an emphasis on agricultural water consumption in Zayandeh Rood region. Iranian Journal of Ecohydrology. 2015; 2(1):23-38. (Persian)
[14]. Takens F. Detecting strange attractors in turbulence. Berlin: SpringerVerlag. 1981.
 
[15]. Wang W, Vrijling JK, Van Gelder PH, Ma J. Testing for nonlinearity of streamflow processes at different time scales. Journal of Hydrology. 2006;322(1):247–268.
[16]. Dhanya CT, Kumar DN. Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate input. Journal of Hydrology. 2011;403:292-306.
[17]. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D. 1983;9:189-208.
[18]. Brock WA, Sayers CL. Is the business cycle characterized by deterministic chaos?. Journal of Monetary Economics. 1988;22(1):71-90.
[19]. Shang P, Li X, Kamae S. Chaotic analysis of traffic time series. Chaos, Solitons and Fractals. 2005;25:121-128.
[20]. Wolf A, Swift JB, Swinney HL, Vastano JA. Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena. 1985;16(3):285-317.
[21]. Rosenstein M.T, Collins J.J, De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena. 1993;65(1-2):117-134.
[22]. Scheriber T. Extremely simple nonlinear noise-reduction method. Physical Review. E. 1993;47(4):2401-2404.
[23]. Hegger R, Kantz H, Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1999;9(2):413-35.
Iranian journal of Ecohydrology
Volume 6, Issue 1
April 2019
Pages 15-27

Files

History

  • Receive Date: 22 May 2018
  • Revise Date: 04 November 2018
  • Accept Date: 04 November 2018
  • First Publish Date: 21 March 2019
  • Publish Date: 21 March 2019

Share

How to cite

Statistics