Monthly flow analysis of Sefidrood River using Chaos theory

Document Type : Research/Original/Regular Article

Authors

1 Professor/ Department of Water Engineering, Faculty of Agriculture, Urmia University, Urmia, Iran.

2 Graduated M.Sc. student/ Department of Water Engineering, Faculty of Agriculture, Urmia University, Urmia, Iran

3 Graduated Ph.D. student/ Department of Water Engineering, Faculty of Agriculture, Urmia University, Urmia, Iran

4 Associate Professor/ Department of Water Engineering, Faculty of Agriculture, University of Shahrkord, Shahrkord, Iran

Abstract

Introduction
Measuring complexity and ways to reduce it in organizations and decision-making processes has become one of the topics of the day. The chaos theory was proposed in the 1960s, and the most effective and most successful effort was made by Edward Lorenz. Towards this, the flow rate of Sefidrood River as the most important river in Guilan Province and the second-longest river in Iran was studied using Chaos theory.
Materials and Methods
The study area in this research is a sub-basin of the Sefidrood River Basin. After collecting the monthly and annual discharge data of Sefidrood River, the following items were investigated:
1- chaotic dynamic systems, 2- phase space reconstruction, 3- determining the time delay, 4- determining the embedding dimension, 5- determining the correlation dimension, and 6- determining the Lyapunov and Hurst exponents.
Results and Discussion
In determining the delay time using the autocorrelation function (ACF( curve, the appropriate lag is where the graph reaches a value close to zero or about 0.1 to 0.2. An appropriate embedding dimension is an embedded dimension in which the number of false neighbors has reached to about zero. For a lag of 1-month, the delay vectors are concentrated around the diagonal axis of space. Therefore, X(t) and X(t +1) are very close and continuous. Therefore, they will cause the characteristics of the adsorbent structure to be lost. Also in the state (phase) space for the delay time of 100 months, the density of lag vectors is close to the horizontal and vertical axes of the graph and indicates the incoherence and complexity of successive components in the lag vectors and its inadequacy to achieve system dynamics. However, due to the 5 months delay state space obtained from the average actual information (AMI) method, the delay vectors have a better distribution and the state space is well filled with points. The correlation dimension of the monthly time series is 3.37.
Conclusion
The presence of stochastic behavior in the river flow was determined using the correlation dimension test and Hurst exponent. The correlation exponent was saturated after increasing the embedded dimension in an incorrect value equal to 3.37. In addition, the closest correct value to the correlation dimension indicates the minimum variables required to describe the system, which is a value of 4. The obtained Hurst exponent is opposite to 0.5 and according to Hurst studies, it indicates the non-randomness and the presence of chaos in the river. The Hurst exponent obtained in daily scales is between 0.5 and 1 and indicates the existence of long-term memory in this series.

Keywords

References

ABarbanel, H.D., Brown, R., Sidorowich, J.J., & Tsimring, L.S. (1993). The analysis of observed chaotic data in physical systems. Reviews of Modern Physics, 65(4), 1331.
Adab, F., Karami, H., Mousavi, S., & Farzin, S. (2018). Application of Chaos theory in modeling and analysis of river discharge under different time scales (Case Study: Karun River). Physical Geography Research Quarterly, 50(3), 443-457 (in Persian).
Alami, M., & Malekani, L. (2013). Phase space reconstruction and fractal dimension using of lag time and embedding dimension. Journal of Civil and Environmental Engineering, 43.1(70), 15-21 (in Persian).
Anishosseini, M., & Zakermoshfegh, M. (2015). Comparison between phase space-based local chaotic models for river flow forecasting. IQBQ; 15(3), 13-24 (in Persian).
Anishosseini, M., & Zakermoshfegh, M. (2013). Analysis and prediction of the Kashkan river flow using chaos theory. Journal of Hydraulics, 8(3), 45-61 (in Persian).
Boustani, M., Karami, H., Mousavi, S., & Farzin, S. (2019). Relationship between chaos theory indicators in monitoring of river flow at short-term time scales. Irrigation and Water Engineering, 9(4), 98-116 (in Persian).
Damle, C., & Yalcin, A. (2007). Flood prediction using time series data mining. Journal of Hydrology, 333, 305-316.
Elshorbagy, A., Simonovic, S.P., & Panu, U.S. (2002). Estimation of missing streamflow data using principles of chaos theory. Journal of Hydrology, 255(1-4), 123-133.
Embrechts, M. (1994). Basic concepts of nonlinear dynamics and chaos theory. Trading on the Edge: Neural, Genetic, and Fuzzy Systems for Chaotic Financial Markets, Wiley, New York, 265-279.
Eslami, A., Ghahraman, B., Ziaee, A., & Eslami, P. (2016). Effect of Noise reduction in nonlinear dynamic analysis of maximum daily temperature series in Kerman station. Iran-Water Resources Research, 12(1), 171-185 (in Persian).
Farzin, S., Hajiabadi, R., & Ahmadi, M. (2017). Application of chaos theory and artificial neural networks to evaluate evaporation from lake's water surface. Water and Soil, 31(1), 61-74 (in Persian).
Farzin, S., Hosseini, Kh., Karami, H., & Mousavi S. (2017). Analysis of time series in hydrological processes using chaos theory (Case study: Monthly rainfall of Urmia lake). Civil Engineering Journal, 17(2), 213-223 (in Persian).
Ghaheri, A., Ghorbani, M.A., Delafrouz, H., & Malekani, L. (2012). Evaluation of river flow using turbulence theory, Iranian Journal of Water Research, 6(10), 177-186 (in Persian).
Ghorbani, M.A., Kisi, O., & Aalinezhad, M., (2010). A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods. Applied Mathematical Modelling, 34(12), 4050-4057.
Hassanzadeh, Y., Aalami, M., Farzin, S., Sheikholeslami, S., & Hassanzadeh, E. (2012). Study of Chaotic Nature of daily water level fluctuations in Urmia lake. Journal of Civil and Environmental Engineering, 42.1(66), 9-20 (in Persian).
Hurst, H.E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-808.
Jabbari Gharabgh, S., Rezaie, H., & Mohammadnezhad, B. (2016). Comparison of reconstructed phase space and chaotic behavior of Nazloochay river flow at different temporal scales. Journal of Water and Soil Conservation, 22(5), 135-151 (in Persian).
Janbozorgi, M., Hanifepour, M., & Khosravi, H. (2021). Temporal changes in meteorological-hydrological drought (Case study: Guilan Province). Water and Soil Management and Modelling, 1(2), 1-14 (in Persian).
Jones, C.L., Lonergan, G.T., & Mainwaring, D.E. (1996). Wavelet packet computation of the Hurst exponent. Journal of Physics A: Mathematical and General, 29(10), 2509.
Kantz, H., & Schreiber, T. (1997). Nonlinear Time Series Analysis. Cambridge University Press, 369 pages.
Kennel, N., & Brown, R. (1992). Determining embedding dimension for phase space reconstruction using a geometrical construction. Physica Review A, 45(6), 3403-3411.
Khan, S., Ganguly, A.R., & Saigal, S. (2005). Detection and predictive modeling of chaos in finite hydrological time series. Nonlinear Processes in Geophysics, 12(1), 41-53.
Kocak, K., Bali, A., & Bektasoglu, B. (2007). Prediction of monthly flows by using chaotic approach. International Congress on river Basin Management. Antalya, Turkey. Pp. 553-559.
Lange, H. (1999). Time series analysis of ecosystem variables with complexity measures. Interantional Journal of Complex Systems, 250, 1-9.
Moradizadeh Kermani, F., Ghorbani, M. A., Dinpashoh, Y., & Farsadizadeh, D. (2013). Predicting model of river Stream flow based on chaotic phase space reconstruction. Water and Soil Science, 22(4), 1-16 (in Persian).
Moshiri, S. (2002). A review on chaos and its applications in economic. Iranian Journal of Economic Research, 4(12), 29-68 (in Persian).
Mousavi, S., Boustani, M., Karami, H., & Farzin, S. (2018). Analysis of river parameters using chaos-theory based indices (Case study: Zayandehrud river flow). Iran-Water Resources Research, 14(4), 253-256 (in Persian).
Ng, W.W., Panu, U.S., & Lennox, W.C. (2007). Chaos based analytical techniques for daily extreme hydrological observations. Journal of Hydrology, 342(1-2), 17-41.
Pari Zanganeh, M., Ataee, M., & Moalam, P. (2009). Reconstruct the chaotic time series space using an intelligent method. Electronic Journal and Power, 1(2), 3-10 (in Persian).
Regonda, S.K., Sivakumar, B., & Jain A. (2004). Temporal scaling in river flow: can it be chaotic? Hydrological Sciences Journal- des Sciences Hydrologiques, 49(3), 373-385.
Rezaei, H., & Jabbari Gharabagh, S. (2017). Noise reduction effect on chaotic analysis of Nazluchay river flow. Water and Soil Science, 27(3), 239-250 (in Persian).
Rosenstein, M.T., Collins, J.J., & De Luca, C.J. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 65(1-2), 117-134.
Scott, D.W. (1992). Multivariable density estimation: Theory, practice, and visualization. Wiley, New York, 336 pages.
Shannon, C.E. (1948). A Mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.
Sivakumar, B., & Berndtsson, R. (2010). Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific, Singapore, 441 pages.
Sivakumar, B. (2001). Rainfall dynamics at different temporal scales: A chaotic perspective. Hydrology and Earth System Sciences, 5(4), 645-652.
Takens, F. (1981). Detecting strange attractors in turbulence. Pp. 366-381, In: Rand D., Young LS. (eds), Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics, vol 898. Springer, Berlin, Heidelberg.
Thomas, M. Cover., J., & Thomas, A. (1991). Elements of Information Theory. John Wiley & Sons, Inc, New York, 776 pages.
Wolf, A., Swift, J.B., Swinney, H.L., & Vastano, J.A. (1985). Determining Lyapunov exponents from a time series. Physica D: nonlinear phenomena, 16(3), 285-317.
Zounemat Kermani, M., & Amirkhani, K. (2015). Determining of dynamic parameters of strong breeze and significant wave using chaos theory , (Case study: Asaluyeh port). Iranian Journal of Marine Science and Technology, 19(73), 37-45 (in Persian).
Water and Soil Management and Modelling
Volume 2, Issue 1
2022
Pages 27-41

Files

History

  • Receive Date: 22 August 2021
  • Revise Date: 03 October 2021
  • Accept Date: 04 October 2021

Share

How to cite

Statistics