Pure and Applied Geophysics

, Volume 176, Issue 8, pp 3769–3786 | Cite as

Application of Singular Spectrum Analysis for Investigating Chaos in Sea Surface Temperature

  • Swarnali MajumderEmail author
  • Partha Pratim Kanjilal


The goal of this study is to explore the chaotic behavior of sea surface temperature (SST) in the Indian Ocean and in the equatorial Pacific Ocean. The SST time series is analyzed for Bay of Bengal, Arabian Sea and South Indian Ocean as well as for two extreme phenomena: El Niño and Indian Ocean Dipole (IOD). The analysis is based on Singular spectrum analysis, and singular value decomposition (SVD). Our analysis reveals that the dynamics of SST is chaotic in varying degrees in all the studied cases, since Lyapunov exponent, an indicator of chaoticity, is positive in each case. To study the degree of predictability of these SST series, we search for embedded periodic component(s) using two different approaches: Orthogonal functions extracted from the Singular spectrum analysis and Periodicity spectrum analysis based on SVD. Both the methods reveal presence of a strong periodic component(s) for the SST signals in the Arabian Sea, Bay of Bengal and South Indian Ocean, whereas no periodicity is found for El Niño and IOD. Therefore, it can be concluded that the dynamics of SST is more complex in the El Niño and IOD region compared to Bay of Bengal, Arabian Sea and South Indian Ocean; hence it is much more difficult to predict El Niño and IOD.


Sea surface temperature chaos singular spectrum analysis singular value decomposition El Niño Indian Ocean Dipole 



Swarnali Majumder would like to thank Director of INCOIS for supporting this work and Department of Science and Technology, Government of India for financial support vide reference no. SR/WOS-A/EA3/2016 under Women Scientist Scheme to carry out this work. The authors thank Mr. N. Kiran Kumar for the graphics. The valuable comments and suggestions by the anonymous reviewers are thankfully acknowledged.

Supplementary material

24_2019_2140_MOESM1_ESM.doc (20 kb)
Supplementary material 1 (DOC 20 kb)


  1. Alexander, M. A., & Scott, J. D. (2008). The role of Ekman ocean heat transport in the Northern Hemisphere response to ENSO. Journal of Climate, 21(21), 5688–5707.CrossRefGoogle Scholar
  2. Anderson, D. (1999). Extremes in the Indian Ocean. Nature, 401(6751), 337–338.CrossRefGoogle Scholar
  3. Behera, S. K., & Yamagata, T. (2001). Subtropical SST dipole events in the southern Indian Ocean. Geophysical Research Letters, 28(2), 327–330.CrossRefGoogle Scholar
  4. Broomhead, D. S., & King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena, 20(2–3), 217–236.CrossRefGoogle Scholar
  5. Casdagli, M., Eubank, S., Farmer, J. D., & Gibson, J. (1991). State space reconstruction in the presence of noise. Physica D: Nonlinear Phenomena, 51(1–3), 52–98.CrossRefGoogle Scholar
  6. Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276.CrossRefGoogle Scholar
  7. Chen, C., Cane, M. A., Henderson, N., Lee, D. E., Chapman, D., Kondrashov, D., et al. (2016). Diversity, nonlinearity, seasonality, and memory effect in ENSO simulation and prediction using empirical model reduction. Journal of Climate, 29, 1809–1830.CrossRefGoogle Scholar
  8. Clarke, A. J. (2008). An introduction to the dynamics of El Nino and the Southern Oscillation. London: Elsevier Academic Press.Google Scholar
  9. Dammig, M., & Mitschke, F. (1993). Estimation of Lyapunov exponents from time series: The stochastic case. Physics Letters A, 178(5–6), 385–394.CrossRefGoogle Scholar
  10. Deser, C., Alexander, M. A., Xie, S. P., & Phillips, A. S. (2010). Sea surface temperature variability: Patterns and mechanisms. Annual Review of Marine Science, 2(1), 115–143.CrossRefGoogle Scholar
  11. Dommenget, D. (2007). Evaluating EOF modes against a stochastic null hypothesis. Climate Dynamics, 28(5), 517–531.CrossRefGoogle Scholar
  12. Dommenget, D., & Latif, M. (2002). A cautionary note on the interpretation of EOFs. Journal of Climate, 15(2), 216–225.CrossRefGoogle Scholar
  13. Eckmann, J.-P., & Ruelle, D. (1992). Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D: Nonlinear Phenomena, 56(2–3), 185–187.CrossRefGoogle Scholar
  14. Golyandina, N., Nekrutkin, V., & Zhigljavsky, A. (2001). Analysis of time series structure: SSA and related techniques. Boca Raton: Chapman & Hall/CRC.CrossRefGoogle Scholar
  15. Hannachi, A., Jolliffe, I. T., & Stephenson, D. B. (2007). Empirical orthogonal functions and related techniques in atmospheric science: A review. International Journal of Climatology, 27(9), 1119–1152.CrossRefGoogle Scholar
  16. Hannachi, A., Stephenson, D. B., & Sperber, K. R. (2003). Probablity based method for quantifying nonlinearity in the ENSO. Climate Dynamics, 20(2–3), 241–256.CrossRefGoogle Scholar
  17. Hegger, R., & Kantz, H. (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos, 9(2), 413–435.CrossRefGoogle Scholar
  18. Huang, B., Banzon, V. F., Freeman, E., Lawrimore, J., Liu, W., Peterson, T. C., et al. (2014). Extended reconstructed sea surface temperature version 4 (ERSST.v4): Part I. Upgrades and intercomparisons. Journal of Climate, 28(3), 911–930.CrossRefGoogle Scholar
  19. Jin, E. K., KinterIII, J. L., Wang, B., Park, C. K., Kang, I. S., Kirtman, B. P., et al. (2008). Current status of ENSO prediction skill in coupled ocean–atmosphere models. Climate Dynamics, 31(6), 647–664.CrossRefGoogle Scholar
  20. Jochum, M., & Murtugudde, R. (2005). Internal variability of Indian Ocean SST. Journal of Climate, 18(18), 3726–3738.CrossRefGoogle Scholar
  21. Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). New York: Springer.Google Scholar
  22. Kanjilal, P. P. (1995). Adaptive prediction and predictive control. London: Peter Peregrinus.CrossRefGoogle Scholar
  23. Kanjila, P. P., Palit, S., & Saha, G. (1997). Fetal ECG extraction from single-channel maternal ECG using singular value decomposition. IEEE Transactions on Biomedical Engineering, 44(1), 51–59.CrossRefGoogle Scholar
  24. Kanjilal, P. P., Bhattacharya, J., & Saha, G. (1999). Robust method for periodicity detection and characterization of irregular cyclical series in terms of embedded periodic components. Physical Review E, 59(4), 4013–4025.CrossRefGoogle Scholar
  25. Kleeman, R., & Moore, A. M. (1997). A theory for the limitation of ENSO predictability due to stochastic atmospheric transients. Journal of Atmospheric Science, 54, 753–767.CrossRefGoogle Scholar
  26. Kondragunta, C. R., & Gruber, A. (1997). Intercomparison of spatial and temporal variability of various precipitation estimates. Advances in Space Research, 19(3), 457–460.CrossRefGoogle Scholar
  27. Li, G., & Xie, S. P. (2012). Origins of tropical-wide SST biases in CMIP multi-model ensembles. Geophysical Research Letter, 39(22), L22703.CrossRefGoogle Scholar
  28. Majumder, S., Balakrishnan, T. M. N., & Kiran Kumar, N. (2019). Reconstruction of state space figure of Indian Ocean Dipole. In J. Bansal, K. Das, A. Nagar, K. Deep, & A. Ojha (Eds.), Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing (Vol. 816, pp. 471–482). Singapore: Springer.CrossRefGoogle Scholar
  29. Martinez-Villalobos, C., Vimont, D. J., Penland, C., Newman, M., & Neelin, J. D. (2018). Calculating state-dependent noise in a linear inverse model framework. Journal of Atmospheric Science, 75, 479–496.CrossRefGoogle Scholar
  30. Munnich, M., Cane, M. A., & Zebiak, S. E. (1991). A study of self-excited oscillations of the tropical ocean–atmosphere system. Journal of Atmospheric Sciences. Part II: Nonlinear cases, 48(10), 1238–1248.CrossRefGoogle Scholar
  31. Neelin, J. D., Battisti, D. S., Hirst, A. C., Jin, F. F., Wakata, Y., Yamagata, T., et al. (1998). ENSO theory. Journal of Geophysical Research, 103(C7), 14261–14290.CrossRefGoogle Scholar
  32. Newman, M., & Sardeshmukh, P. D. (2017). Are we near the predictability limit of tropical Indo-Pacific sea surface temperatures? Geophysical Research Letters, 44, 8520–8529.CrossRefGoogle Scholar
  33. Penland, C. (1996). A stochastic model of IndoPacific sea surface temperature anomalies. Physica D: Nonlinear Phenomena, 98(2), 534–558.CrossRefGoogle Scholar
  34. Penland, C., & Sardeshmukh, P. D. (1995). The optimal growth of tropical sea surface temperature anomalies. Journal of Climate, 8, 1999–2024.CrossRefGoogle Scholar
  35. Plaut, G., & Vautard, R. (1994). Spells of low-frequency oscillations and weather regimes in the northern hemisphere. Journal of the Atmospheric Sciences, 51(2), 210–236.CrossRefGoogle Scholar
  36. Rao, R. R., & Sivakumar, R. (2000). Seasonal variability of near-surface thermal structure and heat budget of the mixed layer of the tropical Indian Ocean from a new global ocean temperature climatology. Journal of Geophysical Research, 105(C1), 995–1015.CrossRefGoogle Scholar
  37. Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L. V., Rowell, D. P., et al. (2003). Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. Journal of Geophysical Research, 108(D14), 4407.CrossRefGoogle Scholar
  38. 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.CrossRefGoogle Scholar
  39. Saji, N. H., Goswami, B. N., Vinaychandran, P. N., & Yamagata, T. (1999). A dipole mode in the tropical Indian Ocean. Nature, 401(6751), 360–363.Google Scholar
  40. Sarachik, E. S., & Cane, M. A. (2010). The El Niño–southern oscillation phenomenon. Cambridge, London: Cambridge University Press.CrossRefGoogle Scholar
  41. Shi, L., Hendon, H. H., Alves, O., Luo, J. J., Balmaseda, M., & Anderson, D. (2012). How Predictable is Indian Ocean Dipole? Monthly Weather Review, 140(12), 3867–3884.CrossRefGoogle Scholar
  42. Stein, K., Timmermann, A., Schneider, N., Jin, F., & Stuecker, M. F. (2014). ENSO seasonal synchronization theory. Journal of Climate, 27, 5285–5310.CrossRefGoogle Scholar
  43. Stone, L., Saparin, P. I., Huppert, A., & Price, C. (1998). El Nino Chaos: the role of stochastic resonance on the ENSO Cycle. Geophysical Research Letters, 25(2), 175–178.CrossRefGoogle Scholar
  44. Sura, P., Newman, M., Penland, C., & Sardeshmukh, P. (2005). Multiplicative noise and non-gaussianity: a paradigm for atmospheric regimes? Journal of Atmospheric Science, 62, 1391–1409.CrossRefGoogle Scholar
  45. Takens, F. (1981). Detecting strange attractors in turbulence. In D. A. Rand & L. S. Young (Eds.), Lecture notes in mathematics (Vol. 898, pp. 366–381). Berlin: Springer.Google Scholar
  46. Thompson, C. J., & Battisti, D. S. (2000). A linear stochastic dynamical model of ENSO. Journal of Climate. Part I: model development, 13(15), 2818–2832.CrossRefGoogle Scholar
  47. Tourre, Y. M., & White, W. B. (1995). ENSO signals in global upper-ocean temperature. Journal of Physical Oceanography, 25(6), 1317–1332.CrossRefGoogle Scholar
  48. Trenberth, K. E. (1997). The definition of El Nino. Bulletin of American Meteorological Society, 78(12), 2771–2777.CrossRefGoogle Scholar
  49. Tziperman, E., Stone, L., Cane, M. A., & Carosh, H. (1994). El Nino chaos: overlapping of resonances between the seasonal cycle and the Pacific ocean–atmosphere oscillator. Science, 264(5155), 72–74.CrossRefGoogle Scholar
  50. Waliser, D. E., Murtugudde, R., & Lucas, L. E. (2003). Indo-Pacific Ocean response to atmospheric intraseasonal variability: 1. Austral summer and the Madden–Julian oscillation. Journal of Geophysical Research, 108(C5), 3160.CrossRefGoogle Scholar
  51. Yamagata, T., Behera, S. K., Luo, J. J., Masson, S., Jury, M., & Rao, S. A. (2004). Coupled ocean–atmosphere variability in the tropical Indian Ocean. In C. Wang, S. P. Xie, & J. A. Carton (Eds.), Earth climate: the ocean–atmosphere interaction, geophysical monograph series (Vol. 147, pp. 189–212). Washington: American Geophysical Union.Google Scholar
  52. Yiou, P., Baert, E., & Loutre, M. F. (1996). Spectral analysis of climate data. Surveys in Geophysics, 17(6), 619–663.CrossRefGoogle Scholar
  53. Yu, Y., Mu, M., Duan, W., & Gong, T. (2012). Contribution of the location and spatial pattern of initial error to uncertainties in El Niño predictions. Journal of Geophysical Research, 117(C6), C06018.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Indian National Centre for Ocean Information ServicesHyderabadIndia
  2. 2.FINRANew YorkUSA

Personalised recommendations