Climate Dynamics

, Volume 49, Issue 1–2, pp 131–141 | Cite as

Long-term potential nonlinear predictability of El Niño–La Niña events

  • H. F. Astudillo
  • R. Abarca-del-Río
  • F. A. Borotto
Article

Abstract

We show that the monthly recorded history (1866–2014) of the Southern Oscillation Index (SOI), a descriptor of the El Niño Southern Oscillation (ENSO) phenomenon, can be correctly described as a dynamic system supporting a potential nonlinear predictability well beyond the spring barrier. Long-term predictability is strongly connected to a detailed knowledge about the topology of the attractor obtained by embedding the SOI index in a wavelet base state space. By utilizing the state orbits on the attractor, we show that the information contained in the SOI is sufficient to provide nonlinear attractor information, allowing the detection of predictability for longer than a year: 2, 3, and 4 years in advance throughout the record with an acceptable error. This is possible due to the fact that the lower-frequency variability of the SOI presents long-term positive autocorrelation. Thus, by using complementary methods, we confirm that the reconstructed attractor of the low-frequency part (lower than 1/year) of SOI time series cannot be attributed to stochastic influences. Furthermore, we establish its multifractality. As an example of the capabilities of the methodology, we investigate a few specific El Niño (1972–1973, 1982–1983, 1997–1998) and La Niña (1973–1973, 1988–1989 and 2010–2011) events. Our results indicate that each of these present several equivalent temporal structures over other eras of these 149 years (1866–2014). Accordingly, none of these cases, including extreme events, presents temporal singularity. We conclude that the methodology’s simplicity of implementation and ease of use makes it suitable for studying nonlinear predictability in any area where observations are similar to those describing the ENSO phenomenon.

Keywords

ENSO SOI Nonlinear predictability Determinism Multifractal 

References

  1. Abarbanel HD, Brown R, Sidorowich JJ, Tsimring LS (1993) The analysis of observed chaotic data in physical systems. Rev Mod Phys 65(4):1331CrossRefGoogle Scholar
  2. Ahmed I (2010) Detection of nonlinearity and stochastic nature in time series by delay vector variance method. Int J Eng Technol 10(2):22–27Google Scholar
  3. Astudillo H, Borotto F, Abarca-del Rio R (2010) Embedding reconstruction methodology for short time series-application to large El Nino events. Nonlinear Process Geophys 17(6):753–764CrossRefGoogle Scholar
  4. Bjerknes J (1969) Atmospheric teleconnections from the equatorial pacific 1. Mon Weather Rev 97(3):163–172CrossRefGoogle Scholar
  5. Brunner AD (2002) El Nino and world primary commodity prices: warm water or hot air? Rev Econ Stat 84(1):176–183CrossRefGoogle Scholar
  6. Burn MJ, Palmer SE (2014) Solar forcing of caribbean drought events during the last millennium. J Quat Sci 29(8):827–836CrossRefGoogle Scholar
  7. Capotondi A, Sardeshmukh PD (2015) Optimal precursors of different types of ENSO events. Geophys Res Lett 42(22):9952–9960. doi:10.1002/2015GL066171 CrossRefGoogle Scholar
  8. Capotondi A et al (2015) Understanding ENSO diversity. Bull Am Meteorol Soc 96:921–938. doi:10.1175/BAMS-D-13-00117.1 CrossRefGoogle Scholar
  9. Cazenave A, Henry O, Munier S, Delcroix T, Gordon A, Meyssignac B, Llovel W, Palanisamy H, Becker M (2012) Estimating ENSO influence on the global mean sea level, 1993–2010. Mar Geod 35(sup1):82–97CrossRefGoogle Scholar
  10. Chen D, Cane MA (2008) El Niño prediction and predictability. J Comput Phys 227(7):3625–3640CrossRefGoogle Scholar
  11. Chen D, Lian T, Fu C, Cane MA, Tang Y, Murtugudde R, Song X, Wu Q, Zhou L (2015) Strong influence of westerly wind bursts on El Niño diversity. Nat Geosci 8(5):339–345. doi:10.1038/ngeo2399 CrossRefGoogle Scholar
  12. Craigmile PF, Percival DB (2002) Wavelet-based trend detection and estimation. In: El-Shaarawi A, Piegorsch WW (eds) Encyclopedia of environmetrics, vol 4. Wiley, Hoboken, NJ, pp 2334–2338Google Scholar
  13. Ding R, Li J (2007) Nonlinear finite-time Lyapunov exponent and predictability. Phys Lett A 364(5):396–400CrossRefGoogle Scholar
  14. Ding R, Li J, Ha K (2008) Nonlinear local Lyapunov exponent and quantification of local predictability. Chin Phys Lett 25(5):1919CrossRefGoogle Scholar
  15. Ding R, Li J, Zheng F et al (2016) Estimating the limit of decadal-scale climate predictability using observational data. Clim Dyn 46:1563–1588. doi:10.1007/s00382-015-2662-6 CrossRefGoogle Scholar
  16. Farmer JD, Sidorowich JJ (1987) Predicting chaotic time series. Phys Rev Lett 59(8):845CrossRefGoogle Scholar
  17. Feder J (2013) Fractals. Physics of solids and liquids. Springer, BerlinGoogle Scholar
  18. Fedorov A, Harper S, Philander S, Winter B, Wittenberg A (2003) How predictable is El Niño? Bull Am Meteorol Soc 84(7):911–919CrossRefGoogle Scholar
  19. Gautama T, Mandic DP, Van Hulle MM (2004) The delay vector variance method for detecting determinism and nonlinearity in time series. Phys D 190(3):167–176CrossRefGoogle Scholar
  20. Golyandina N, Zhigljavsky A (2013) Singular spectrum analysis for time series. Springer, BerlinCrossRefGoogle Scholar
  21. Guillas S, Day SJ, McGuire B (2010) Statistical analysis of the El Niño-southern oscillation and sea-floor seismicity in the eastern tropical pacific. Philos Trans R Soc Lond A Math Phys Eng Sci 368(1919):2481–2500CrossRefGoogle Scholar
  22. Hsiang SM, Meng KC, Cane MA (2011) Civil conflicts are associated with the global climate. Nature 476(7361):438–441CrossRefGoogle Scholar
  23. Huang NE, Shen SS (2005) Hilbert–Huang transform and its applications, vol 5. World Scientific, SingaporeCrossRefGoogle Scholar
  24. Ihlen EAF (2012) Introduction to multifractal detrended fluctuation analysis in matlab. Front Physiol 3:141. doi:10.3389/fphys.2012.00141 CrossRefGoogle Scholar
  25. Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A 316(1):87–114CrossRefGoogle Scholar
  26. Kaplan DT, Glass L (1992) Direct test for determinism in a time series. Phys Rev Lett 68(4):427CrossRefGoogle Scholar
  27. Kodba S, Perc M, Marhl M (2005) Detecting chaos from a time series. Eur J Phys 26(1):205–215CrossRefGoogle Scholar
  28. Komm R (1995) Hurst analysis of Mt. Wilson rotation measurements. Sol Phys 156(1):17–28CrossRefGoogle Scholar
  29. Können G, Jones P, Kaltofen M, Allan R (1998) Pre-1866 extensions of the southern oscillation index using early Indonesian and Tahitian meteorological readings. J Clim 11(9):2325–2339CrossRefGoogle Scholar
  30. Kovats RS, Bouma MJ, Hajat S, Worrall E, Haines A (2003) El Niño and health. Lancet 362(9394):1481–1489CrossRefGoogle Scholar
  31. Landsea CW, Knaff JA (2000) How much skill was there in forecasting the very strong 1997–98 El Niño? Bull Am Meteorol Soc 81(9):2107–2119CrossRefGoogle Scholar
  32. Li J, Ding R (2011) Temporal-spatial distribution of atmospheric predictability limit by local dynamical analogs. Mon Weather Rev 139(10):3265–3283CrossRefGoogle Scholar
  33. Li J, Ding R (2013) Temporal-spatial distribution of the predictability limit of monthly sea surface temperature in the global oceans. Int J Climatol 33(8):1936–1947CrossRefGoogle Scholar
  34. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141CrossRefGoogle Scholar
  35. Lorenz EN, Kerry AE (1998) Optimal sites for supplementary weather observations: simulation with a small model. J Atmos Sci 55(3):399–414CrossRefGoogle Scholar
  36. Ludescher J, Gozolchiani A, Bogachev MI, Bunde A, Havlin S, Schellnhuber HJ (2014) Very early warning of next El Niño. Proc Nat Acad Sci 111(6):2064–2066Google Scholar
  37. McPhaden MJ, Zebiak SE, Glantz MH (2006) ENSO as an integrating concept in earth science. Science 314(5806):1740–1745CrossRefGoogle Scholar
  38. Murguía JS, Rosu HC (2011) Discrete wavelet analyses for time series. In: Olkkonen JT (ed) Discrete wavelet transforms-theory and applications. InTech, Vukovar. doi:10.5772/16016 Google Scholar
  39. Neelin JD, Battisti DS, Hirst AC, Jin FF, Wakata Y, Yamagata T, Zebiak SE (1998) ENSO theory. J Geophys Res Oceans (1978–2012) 103(C7):14,261–14,290CrossRefGoogle Scholar
  40. Niedzielski T (2014) Chapter two-El Niño/southern oscillation andselected environmental consequences. Adv Geophys 55:77–122. doi:10.1016/bs.agph.2014.08.002 CrossRefGoogle Scholar
  41. Packard NH, Crutchfield JP, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45(9):712CrossRefGoogle Scholar
  42. Peng C, Buldyrev S, Goldberger A, Havlin S, Sciortino F, Simons M, Stanley H et al (1992) Long-range correlations in nucleotide sequences. Nature 356(6365):168–170CrossRefGoogle Scholar
  43. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49(2):1685CrossRefGoogle Scholar
  44. Phillips T, Nerem RS, Fox-Kemper B, Famiglietti JS, Rajagopalan B (2012) The influence of ENSO on global terrestrial water storage using GRACE. Geophys Res Lett 39:L16705. doi:10.1029/2012GL052495 Google Scholar
  45. Rong-Yi Y, Xiao-Jing H (2011) Phase space reconstruction of chaotic dynamical system based on wavelet decomposition. Chin Phys B 20(2):020,505CrossRefGoogle Scholar
  46. Shao YH, Gu GF, Jiang ZQ, Zhou WX, Sornette D (2012) Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series. Sci Rep 2:835. doi:10.1038/srep00835
  47. Takens F (1981) Detecting strange attractors in turbulence. In: Rand D, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. Lecture notes in mathematics, vol 898. Springer, Berlin, pp 366–381. doi:10.1007/BFb0091924 CrossRefGoogle Scholar
  48. Tsonis AA (2009) Dynamical changes in the ENSO system in the last 11,000 years. Clim Dyn 33(7–8):1069–1074CrossRefGoogle Scholar
  49. Viron O, Dickey JO (2014) The two types of El-Niño and their impacts on the length of day. Geophys Res Lett 41(10):3407–3412CrossRefGoogle Scholar
  50. Wang C, Deser C, Yu J-Y, DiNezio P, Clement A (2012a) El Niño-Southern Oscillation (ENSO): a review. In: Glymn P, Manzello D, Enochs I (eds) Coral reefs of the Eastern Pacific. Springer, pp 3–19Google Scholar
  51. Wang S-Y, L’Heureux M, Chia H-H (2012b) ENSO prediction one year in advance using western North Pacific sea surface temperatures. Geophys Res Lett 39:L05702. doi:10.1029/2012GL050909
  52. Wang SY, Jiang X, Fosu B (2015) Global eastward propagation signals associated with the 4–5-year ENSO cycle. Clim Dyn 44(9):2825–2837. doi:10.1007/s00382-014-2422-z CrossRefGoogle Scholar
  53. Zebiak SE, Cane MA (1987) A model El Niño-southern oscillation. Mon Weather Rev 115(10):2262–2278CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • H. F. Astudillo
    • 1
  • R. Abarca-del-Río
    • 2
  • F. A. Borotto
    • 1
  1. 1.Departamento de FisícaUniversidad de ConcepciónConcepciónChile
  2. 2.Departamento de GeofísicaUniversidad de ConcepciónConcepciónChile

Personalised recommendations