Abstract
State space reconstruction is an important index for describing nonlinear time series. However, reconstruction of state space figure is difficult if the data is noisy. Hence, noise reduction is an important step for reconstructing state space figure. In this study, we propose a method which can reconstruct state space picture from a noisy time series. This method is used for reconstructing state space figure from the data of Indian Ocean Dipole. Dimension of the reconstructed attractor is measured by computing correlation dimension. The dynamics of Indian Ocean Dipole is not well understood. The reconstruction of state space figure indicates that there is chaos in Indian Ocean Dipole. Positive Lyapunov exponent reconfirms that the dynamics of Indian Ocean Dipole is chaotic.
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Shin, L., Hendon, H.H., Alves, O., Luo, J.J., Balmaseda, M., Anderson, D.: How Predictable is Indian Ocean Dipole? Mon. Weather Rev. 140(12), 3867–3884 (2012)
Dommenget, D.: Evaluating EOF modes against a stochastic null hypothesis. Clim. Dyn. 28, 517–531 (2007)
Penland, C.: A stochastic model of IndoPacific sea surface temperature anomalies. Phys. D 98, 534–558 (1996)
Saji, N.H., Goswami, B.N., Vinaychandran, P.N., Yamagata, T.: A dipole mode in the tropical Indian Ocean. Nature 401, 360–363 (1999)
Yamagata, T., Behera, S.K., Luo, J-J., Masson, S., Jury, M., Rao, S.A.: Coupled ocean- atmosphere variability in the tropical Indian Ocean. In: Wang, C., Xie, S.P., Carton, J.A. (eds.) Earth climate: the Ocean–Atmosphere Interaction. Geophs. Monogr. vol. 147, pp. 189–212. AGU, Washington (2004)
Packard, N.H., Crutchfield, J.P., Farmer, J.D., Shaw, R.S.: Geometry from a time series. Phys. Rev. Lett. 45, 712–716 (1980)
Takens, F.: Detecting strange attractors in turbulence. In: Rand, D.A., Young, L.S. (eds.) Lecture Notes in Mathematics, vol. 898, pp. 366–381. Springer, Berlin (1981)
Casdagli, M., Eubank, S., Farmer, J.D., Gibson, J.: State space reconstruction in the presence of noise. Phys. D 51, 52–98 (1991)
Hu, B., Li, Q., Smith, A.: Noise reduction of hyperspectral data using singular spectral analysis. Int. J. Remote Sens. 30, 2277–2296 (2009)
Tan, J.P.L.: Simple noise-reduction method based on nonlinear forecasting. Phys. Rev. E 95, 032218 (2017)
http://www.jamstec.go.jp/frsgc/research/d1/iod/iod/dipole_mode_index.html
Golyandina, N., Nekrutkin, V., Zhigljavsky, A.: Analysis of time series structure: ssa and related techniques. Chapman & Hall/CRC, USA (2001)
Vautard, R., Yiou, P., Ghil, M.: Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Phys. D 58, 95–126 (1992)
Yiou, P., Sornette, D., Ghil, M.: Data Adaptive wavelets and multi-scale singular-spectrum analysis. Phys. D 142, 254–290 (2000)
Majumder, S.: Application of Topology in Inverse Problem: Getting Equations from data. Ph.D. Thesis. Manipal University, India (2013)
Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983)
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D 65(1–2), 117–134 (1993)
Dammig, M., Mitschke, F.: Estimation of Lyapunov exponents from time series: the stochastic case. Phys. Lett. A 178, 385–394 (1993)
Eckmann, J.-P., Ruelle, D.: Fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems. Phys. D 56, 185–187 (1992)
Vaidya, P.G., Majumder, S.: Embedding in higher dimension causes ambiguity for the problem of determining equation from data. Eur. Phys. J. Spec. Top. 165, 15–24 (2008)
Broomhead, D.S., King, G.P.: Extracting qualitative dynamics from experimental data. Phys. D 20, 217–236 (1986)
Palus, M., Dvorak, I.: Singular-value decomposition in attractor reconstruction: pitfalls and precautions. Phys. D 55, 221–234 (1992)
Acknowledgements
One of the authors acknowledge Department of Science & Technology, Government of India, for financial support vide reference no. SR/WOS-A/EA3/2016 under Women Scientist Scheme to carry out this work. We thank Director, INCOIS for supporting this work. This is ESSO-INCOIS contribution No. 325.
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Majumder, S., Balakrishnan Nair, T.M., Kiran Kumar, N. (2019). Reconstruction of the State Space Figure of Indian Ocean Dipole. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 816. Springer, Singapore. https://doi.org/10.1007/978-981-13-1592-3_37
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DOI: https://doi.org/10.1007/978-981-13-1592-3_37
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