Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32759
Applying a Noise Reduction Method to Reveal Chaos in the River Flow Time Series

Authors: Mohammad H. Fattahi

Abstract:

Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: Chaotic behavior, wavelet, noise reduction, river flow.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094385

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2040

References:


[1] A. Kawamora, A. McKerchar, R. H. Spigel, & K. Jinno. "Chaotic characteristics of the southern oscillation index time series". Journal of Hydrology, Vol. 204, pp. 168-181. 1998.
[2] U. Lotric & A. Dobnikar. "Predicting time series using neural networks with wavelet based de-noising layers". Neural computations and applications, Vol. 14, pp. 11-17. 2005.
[3] A. Elshorbagy, S. P. Simonovic, & U. S. Panu. "Noise reduction in chaotic hydrologic time series: facts and doubts", Journal of Hydrology, Vol. 256, pp. 147-165. 2002.
[4] P.Grassberger, I. Schreiber, & C. Schaffrath. "Non-linear time sequences analysis". Int. Journal of Bifurc. Chaos, Vol. 1, pp. 521-547. 1991.
[5] B. Siva Kumar. "Chaos theory in hydrology: important issues and interpretations". Journal of Hydrology, Vol. 227, pp. 1-20. 2000.
[6] T.Gerstner, H. P. Helfrich & A. Kunoth, . Wavelet analysis of geoscientific data dynamics of multiscale earth systems. Springer, pp. 70-88. 2003.
[7] B.Cannas, A.Fanni, L. See & G. Sias. "Data preprocessing for river flow forecasting using neural networks: Wavelet transforms and data partitioning". Physics and Chemistry of the Earth, Vol. 31, pp. 1164–1171. 2006.
[8] K. P.Georgakakos, M. B. Sharif & P. L. "Sturdevant. Analysis of high resolution rainfall data. In: Kundzewicz, Z.W". (Ed.). New uncertainty concepts in hydrology and water resources. Cambridge university press, pp. 114-120. 1995.
[9] C. E. Puente & N. Obegon. "Deterministic geometric representation of temporal rainfall: results for a storm in Boston". Water resources research, Vol. 32, No. 9, pp. 2825-2839. 1996.
[10] T. B.Sangoyomi, U. Lall & H. D. I. Abarbanel. "Non-linear dynamics of the great Salt Lake: dimension estimation", Water resources research, Vol. 25, No. 7, pp. 1667-1675. 1996.
[11] H. Waelbroeck, R. Lopez-Pena, T. Morales, & F. Zertuche. "Prediction of tropical rainfall by local phase space reconstruction" J. Atoms. Sci., Vol. 51, No. 22, pp. 3360-3364. 1994.
[12] M. N. Islam & B. Sivakumar. "Characterization and prediction of runoff dynamics: a nonlinear dynamical view". Adv. Water Resources, Vol. 25, pp. 179–190. 2002.
[13] A.W. Jayawardena & F. Lai. "Analysis and prediction of chaos in rainfall and stream flow time series". Journal of Hydrology, Vol. 153, pp. 23–52. 1994.
[14] Q. Liu, S. Islam, I. Rodriguez-lturbe, & Y. Le. "Phase-space analysis of daily stream flow: characterization and prediction", Adv. Water Resources, Vol. 21, pp. 463–475. 1998.
[15] A. Porporato, & L. Ridolfi. "Clues to the existence of deterministic chaos in river flow". Int. J. Mod. Phys. B, Vol. 10, No. 15, pp. 1821–1862. 1996.
[16] A. Porporato, & L. Ridolfi. "Nonlinear analysis of river flow time sequences". Water Resources Research, Vol. 33, No. 6, pp. 1353–1367. 1997.
[17] B. Sivakumar. "Chaos theory in geophysics: past, present and future". Chaos, Soliton & Fractals, Vol. 19, pp. 441-462. 2004.
[18] I. Krasovskaia, L. Gottschalk, & Z. W. Kundzewicz. "Dimensionality of Scandinavian river flow regimes". Hydrol. Sci. J., Vol. 44, No. 5, pp. 705–723. 1999.
[19] J. Stehlik. "Deterministic chaos in runoff series". J. Hydraul. Hydromech, Vol. 47, No. 4, pp. 271–287. 1999.
[20] Q. Wang, & T. Y. Gan. "Biases of correlation dimension estimates of stream flow data in the Canadian prairies". Water Resources Research, Vol. 34, 9, pp. 2329–2339. 1998.
[21] G. R. Rakhshandehroo, & Z. Ghadampour. "A combination of fractal analysis and artificial neural network to forecast groundwater depth". Iranian Journal of Science and Technology, Transaction B: Engineering, Vol. 35, No. C1, pp. 121-130. 2011.
[22] A. W. Jayawardena, & A. B. Gurung. "Noise reduction and prediction of hydrometrological time series: dynamical system approach vs. stochastic approach". Journal of Hydrology, Vol. 228, pp. 242-264. 2000.
[23] F. Lisi, & V. Villi. "Chaotic forecasting of discharge time series: a case study". J. Am. Water Resour. Assoc., Vol. 37, No. 2, pp. 271-279. 2001.
[24] B. Sivakumar. "Forecasting monthly stream flow dynamics in the western United States: a non-linear dynamical approach", Environmental modeling and software, pp. 18721-728. 2003.
[25] G. P. Nason & R. Von Sachs. "Wavelets in time series analysis. Philosophical Transactions of the Royal Society of London". series A, Vol. 357, pp. 2511–2526. 1999.
[26] B. B. Mandelbrot & J. W. Van Ness. "Fractional Brownian motions, fractional noises and applications". SIAM Rev., Vol. 10, pp. 422-437. 1968.
[27] M. H. Fattahi, N.Talebbeydokhti, G. R.Rakhshandehroo, A. Shamsai & E. Nikooee. "The robust fractal analysis of the time series- concerning signal class and data length". Fractals, Vol. 9, pp. 1-21. 2010.
[28] K. C.Jun Zhang, Lam, W. J. Gao Yan Hang, & L. Yuan. "Time series prediction using Lyapunov exponents in embedding phase space". Computers and Electrical Engineering, Vol. 30, pp. 1–15. 2004.
[29] B. Sivakumar. "A phase space reconstruction approach to prediction of suspended sediment concentration in rivers". Journal of Hydrology, Vol. 258, pp. 149-162. 2002.
[30] N. H.Packard, J. P.Crutchfield, J. D. Farmer & R. S. Shaw. "Geometry from a time series". Phys. Rev. Letters, Vol. 45, No. 9, pp. 712-718. 1980.
[31] F. C. Moon. "Chaotic and fractal dynamics: an introduction for applied scientists and engineers". WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, pp. 77-78. 2004.
[32] M. T. Rosenstein, J. J. Collins, & C. J. De Luca. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, Vol. 65, pp. 117-134. 1993.
[33] P. Grassberger & I. Procaccia. "Measuring the strangeness of the strange attractors". Physica D, Vol. 9, pp. 189-208. 1983.
[34] T. Schreiber. "Extremely simple noise reduction method". Phys Rev E, Vol. 47, pp. 2401-2404. 1993.
[35] J. C.Schouton, F. Takens & C. M. van den Bleek,. "Estimating of the dimension of a noisy attractor". Phys Rev E, Vol. 50, pp.1851-1862. 1994.
[36] L. A Smith. "Identification and prediction of low dimensional dynamics". Physica D, Vol. 58, pp. 50-76. 1992.
[37] C. Diks. "Estimating invariance of noisy attractors". Phys Rev E, Vol. 53, No. 5, pp. 4263-4266. 1996.
[38] D.Yu, M. Small, R.G. Harrison, C. Diks. "Efficient implementation in estimating invariance and noise level from time series data". Phys Rev E, Vol. 61, No. 4, pp. 3750-3756. 2000.
[39] M. H. Fattahi, N. Talebbeydokhti, G. R. Rakhshandehroo, H. Moradkhani & E. Nikooee. "Revealing the chaotic nature of river flows". International Journal of Science & Technology, Vol. 37, C+, pp. 437-456. 2013.
[40] M. H. Fattahi, N. Talebbeydokhti, G. R. Rakhshandehroo, A. Shamsai & E. Nikooee.." Fractal assessment of wavelet based techniques for improving the predictions of the artificial neural network". Journal of Food, Agriculture & Environment, Vol. 9, No. 1, pp.719-724. 2011.
[41] M. H. Fattahi, N. Talebbeydokhti, G. R. Rakhshandehroo, A. Shamsai & E. Nikooee. "Fractal assessment of wavelet based pre-processing methods for river flow time series". Journal of Water Resources Engineering (in Farsi), Vol. 5, pp.1-8. 2011.