Implementation of Chaotic Analysis on River Discharge Time Series


The gauged river data play an important role in modeling, planning and management of the river basins. Among the hydrological data, the daily discharge data seem to be more significant for determining the amount of energy production and the control the risks of floods and drought. Hence, the data need correct measurement, analysis, and reliable estimates. The purpose of the paper is to investigate the question whether all the stations in a river basin exhibit chaotic behavior. For this purpose, the daily discharge data of four gauge stations are examined by using three nonlinear data analysis methods: 1) phase space reconstruction; 2) correlation dimension; and 3) local approximation where all those methods provide identification of chaotic behaviors. The results show that all stations exhibit chaotic character. Taking into account the proven chaotic characteristic of the stations, local approximation method is applied to observe the prediction accuracy. Considering the fact that global warming is a serious threat on natural resources, the prediction accuracy is becoming a key factor to ensure sustainability. Hence, this study is a good example on the implementation of chaotic analysis by means of the obtained results from the methods.

Share and Cite:

Albostan, A. and Önöz, B. (2015) Implementation of Chaotic Analysis on River Discharge Time Series. Energy and Power Engineering, 7, 81-92. doi: 10.4236/epe.2015.73008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Baggaley, N.J., Langan, S.J., Futter, M.N., Potts, J.M. and Dunn, S.M. (2009) Long-Term Trends in Hydro-Climatology of a Major Scottish Mountain River. Science of the Total Environment, 407, 4633-4641.
[2] Kocak, K. (1997) Application of Local Prediction Model to Water Level Data. A Satellite Conference to the 51st ISI Session in Istanbul, Turkey, Water and Statistics, Ankara, 185-193.
[3] Sivakumar, B. (2000) Chaos Theory in Hydrology: Important Issues and Interpretations. Journal of Hydrology, 227, 1-20.
[4] Rodriguez-Iturbe, I., Febres de Power, B., Sharifi, M.B. and Georgakakos, K.P. (1989) Chaos in Rainfall. Water Resources Research, 25, 1667-1675.
[5] Sharifi, M.B., Georgakakos, K.P. and Rodriguez-Iturbe, I. (1990) Evidence of Deterministic Chaos in the Pulse of Storm Rainfall. Journal of the Atmospheric Sciences, 47, 888-893.<0888:EODCIT>2.0.CO;2
[6] Jayawardena, A.W. and Lai, F. (1994) Analysis and Prediction of Chaos in Rainfall and Stream Flow Time Series. Journal of Hydrology, 153, 28-52.
[7] Krasovskaia, I., Gottsehalk, L. and Kundzewicz, Z.W. (1999) Dimensionality of Scandinavian River Flow Regimes. Hydrological Sciences Journal, 44, 705-723.
[8] Porporato, A and Ridolfi, L. (1997) Nonlinear Analysis of River Flow Time Sequences. Water Resources Research, 33, 1353-1367.
[9] Liu, Q., Islam, S., Rodriguez-lturbe, I. and Le, Y. (1998) Phase-Space Analysis of Daily Streamflow: Characterization and Prediction. Advances in Water Resources, 21, 463-475.
[10] Sang, Y.F., Wanf, D., Wu, J.C., Zhu, Q.P. and Wang, L. (2011) Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales. Entropy, 13, 195-210.
[11] Sivakumar, B., Jayawardena, A.W. and Fernando, T.M.K.G. (2002) River Flow Forecasting: Use of Phase-Space Reconstruction and Artificial Neural Networks Approaches. Journal of Hydrology, 265, 225-245.
[12] Sivakumar, B., Persson, M., Berndtsson, R. and Uvo, C.B. (2002) Is Correlation Dimension a Reliable Indicator of Low-Dimensional Chaos in Short Hydrological Time Series? Water Resources Research, 38, 3-1-3-8.
[13] Sivakumar, B. (2005) Correlation Dimension Estimation of Hydrologic Series and Data Size Requirement: Myth and Reality. Hydrological Sciences Journal, 50, 591-604.
[14] Sivakumar, B. (2009) Nonlinear Dynamics and Chaos in Hydrologic Systems: Latest Developments and a Look Forward. Stochastic Environmental Research and Risk Assessment, 23, 1027-1036.
[15] Khatibi, R., BellieSivakumar, B., Mohammad, A., Kisi, O., Kocak, K. and Zadeh, D. (2012) Investigating Chaos in River Stage and Discharge Time Series. Journal of Hydrology, 414-415, 108-117.
[16] Sivakumar, B. and Singh, V.P. (2011) Hydrologic System Complexity and Nonlinear Dynamic Concepts for a Catchment Classification Framework. Hydrology and Earth System Sciences, 8, 4427-4458.
[17] Pasternack, G.B. (1999) Does the River Run Wild? Assessing Chaos in Hydrological Systems. Advances in Water Resources, 23, 253-260.
[18] Liaw, C., Islam, M.N., Phoon, K.K. and Liong, S. (2001) Comment on ‘‘Does the River Run Wild? Assessing Chaos in Hydrological Systems’’ by G.B. Pasternack. Advances in Water Resources, 24, 575-578.
[19] Koutsoyiannis, D. (2006) On the Quest for Chaotic Attractors in Hydrological Processes. Hydrological Sciences Journal, 51, 1065-1091.
[20] Islam, M.N. and Sivakumar, B. (2002) Characterization and Prediction of Runoff Dynamics: A Nonlinear Dynamical View. Advances in Water Resources, 25, 179-190.
[21] Lisi, F. and Villi, V. (2001) Chaotic Forecasting of Discharge Time Series: A Case Study. Journal of the American Water Resources Association, 37, 271-279.
[22] Ghorbani, M.A., Daneshfaraz, R., Arvanagi, H., Pourzangbar, A., Saghebian, S.M. and KavehKar, Sh. (2012) Local Prediction in River Discharge Time Series. Journal of Civil Engineering and Urbanism, 2, 51-55.
[23] Elshorbagy, A., Simonovic, S.P. and Panu, U.S. (2002) Noise Reduction in Chaotic Hydrologic Time Series: Facts and Doubts. Journal of Hydrology, 256, 147-165.
[24] Meng, Q.F. and Peng, Y.H. (2007) A New Local Linear Prediction Model for Chaotic Time Series. Physics Letters A, 370, 465-470.
[25] Takens, F. (1981) Detecting Strange Attractors in Turbulence. In: Rand, D.A. and Young, L.S., Eds., Lectures Notes in Mathematics, Vol. 898, Springer-Verlag, New York, 366-381.
[26] Hegger, R., Kantz, H. and Schreiber, T. (1999) Practical Implementation of Nonlinear Time Series Methods: The TISEAN Package. Chaos, 9, 413-435.
[27] Fraser, A.M. and Swinney, H.L. (1986) Independent Coordinates for Strange Attractors from Mutual Information. Physical Review A, 33, 1134-1140.
[28] Abarbanel, H.D.I. (1996) Analysis of Observed Chaotic Data. Springer-Verlag, New York, 272.
[29] Kennel, M.B., Brown, R. and Abarbanel, H.D.I. (1992) Determining Minimum Embedding Dimension Using a Geometrical Construction. Physical Review A, 45, 3403-3411.
[30] Theiler, J. (1986) Spurious Dimension from Correlation Algorithms Applied to Limited Time-Series Data. Physical Review A, 34, 2427-2432.
[31] Porporato, A. and Ridolfi, L. (1997) Nonlinear Analysis of River Flow Time Sequences. Water Resources Research, 33, 1353-1367.
[32] Jayawardena, A.W. and Gurung, A.B. (2000) Noise Reduction and Prediction of Hydrometeorological Time Series: Dynamical System Approach vs. Stochastic Approach. Journal of Hydrology, 228, 242-264.
[33] Eng, K., Wolock, D.M. and Carlisle, D.M. (2002) River Flow Changes Related to Land and Water Management Practices across the Conterminous United States. Science of the Total Environment, 463-464, 414-422.
[34] Elorza, F.J., Navarro-Ortega, A. and Barceló, D. (2012) Integrated Modelling and Monitoring at Different River Basin Scales under Global Change. Science of the Total Environment, 440, 1-2.
[35] Sivakumar, B., Jayawardena, A.W. and Li, W.K. (2007) Hydrologic Complexity and Classification: A Simple Data Reconstruction Approach. Hydrological Processes, 21, 2713-2728.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.