Skip to main content

Complexity of Spatio-Temporal Correlations in Japanese Air Temperature Records

  • Chapter
Nonlinear Time Series Analysis in the Geosciences

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 112))

The variability of meteorological observables is known to crucially depend on the geographical conditions and the considered spatial as well as temporal scales. In this contribution, we explicitly take the spatial dimension into account. Recent studies on this aspect have considered individual investigations of spatially distributed records from different stations, which form network structures with interesting statistical properties. However, the results of such studies are strongly influenced by the preprocessing of the time series, in the case of temperature records particularly by the applied deseasonalisation strategy. As a complementary approach, we investigate whether the interdependences between pairs of meteorological records can be used to extract additional information about the regularity of temporal variations of the regional climate and its potential change with time. As an alternative to the consideration of univariate estimates of fractal dimensions, the concept of multivariate dimension estimates is introduced. Different quantitative measures for the complexity of linear correlations are introduced and thoroughly compared. After studying the results for stationary model systems, our approach is used to characterise the variability of temperature records from 13 Japanese meteorological stations. The complexity of the complete record varies on an annual period with a larger complexity during the summer season, which is possibly related to the action of the East Asian monsoonal circulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Nicolis, G. Nicolis, Is there a climatic attractor? Nature 311, 529–532 (1984)

    Article  Google Scholar 

  2. K. Fraedrich, Estimating the Dimensions of Weather and Climate Attractors. J. Atmos. Sci 3, 419–432 (1986)

    Article  Google Scholar 

  3. C. Essex, T. Lookman, M.A.H. Nerenberg, The climate attractor over short timescales. Nature 326, 64–66 (1987)

    Article  Google Scholar 

  4. A.A. Tsonis, J.B. Elsner, Chaos, strange attractors, and weather. Bull. Amer. Meteor. Soc 70, 16–23 (1989)

    Google Scholar 

  5. X. Zeng, R.A. Pielke, R. Eykholt, Estimating the fractal dimension and the predictability of the atmosphere. J. Atmos. Sci 49, 649–659 (1992)

    Article  Google Scholar 

  6. R. Kleeman, Statistical predictability in the atmosphere and other dynamical systems. Physica D 230, 65–71 (2007)

    Article  Google Scholar 

  7. W.S. Broecker, Thermohaline circulation, the Achilles heel of our climate system: will man-made CO_2 upset the current balance? Science278, 1582–1588 (1997)

    Article  Google Scholar 

  8. P.U. Clark, N.G. Pisias, T.F. Stocker, A.J. Weaver, The role of the thermohaline circulation in abrupt climate change. Nature415, 863–869 (2002)

    Article  Google Scholar 

  9. A.A. Tsonis, P.J. Roebber, The architecture of the climate network. Physica A333, 497–504 (2004)

    Article  Google Scholar 

  10. W. von Bloh, M.C. Romano, M. Thiel, Long-term predictability of mean daily temperature data. Nonlin. Proc. Geophys 12, 471–479 (2005)

    Google Scholar 

  11. R.B. Govindan, J. Raethjen, F. Kopper, J.C. Claussen, G. Deuschl, Estimation of time delay by coherence analysis. Physica A 350, 277–295 (2005)

    Article  Google Scholar 

  12. D. Rybski, S. Havlin, A. Bunde, Phase synchronization in temperature and precipitation records. Physica A 320, 601–610 (2003)

    Article  Google Scholar 

  13. A. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization – A Universal Concept in Nonlinear SciencesCambridge University Press, Cambridge (2003)

    Google Scholar 

  14. L. Cimponeriu, M. Rosenblum, A. Pikovsky, Estimation of delay in coupling from time series. Phys. Rev. E 70, 046213 (2004)

    Article  Google Scholar 

  15. R. Donner, Interdependences between daily European temperature records: Correlation or phase synchronization? In: P. Marquié (ed.), Nonlinear Dynamics of Electronic Systems (NDES 2006), Université de Bourgogne, Dijon, 26–29 (2006)

    Google Scholar 

  16. R. Donner, Advanced Methods for Analysing and Modelling Multivariate Palaeoclimatic Time SeriesPhD thesis, University of Potsdam (2007)

    Google Scholar 

  17. R. Donner, M. Thiel, Scale-resolved phase coherence analysis of hemispheric sunspot activity: a new look onto the north-south asymmetry. Astron. Astrophys 475, L33–L36 (2007)

    Article  Google Scholar 

  18. V. Lucarini, T. Nanni, A. Speranza, Statistics of the seasonal cycle of the 1951–2000 surface temperature records in Italy. Il Nuovo Cimento C 27, 285–298 (2004)

    Google Scholar 

  19. K. Edel, K.A. Schäffer, W. Stier, Analyse Saisonaler ZeitreihenPhysica, Heidelberg (1997)

    Google Scholar 

  20. S. Pezzulli, D.B. Stephenson, A. Hannachi, The variability of seasonality. J. Clim 18, 71–88 (2005)

    Article  Google Scholar 

  21. W.M. Persons, Indices of business conditions. Rev. Econom. Stat 1, 5–107 (1919)

    Article  Google Scholar 

  22. A. Wald, Berechnung und Ausschaltung von Saisonschwankungen Springer, Vienna (1936)

    Google Scholar 

  23. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. London A 454, 903–995 (1998)

    Article  Google Scholar 

  24. D.G. Duffy, The application of Hilbert-Huang transforms to meteorological datasets. J. Atmos. Ocean. Technol 21, 599–611 (2004)

    Article  Google Scholar 

  25. H. El-Askary, S. Sarkar, L. Chiu, M. Kafatos, T. El-Ghazawi, Rain gauge derived precipitation variability over Virginia and its relation with the El Nino southern oscillation. Adv. Space Res 33, 338–342 (2004)

    Article  Google Scholar 

  26. K. Coughlin, K.K. Tung, Empirical mode decomposition of climate variability. In: N. Huang, S. Shen (eds.), Hilbert-Huang Transform and Its Applications World Scientific, Singapore, 149–166 (2005)

    Google Scholar 

  27. M.K.I. Molla, M.S. Rahman, A. Sumi, P. Banik, Empirical mode decomposition analysis of climate changes with special reference to rainfall data. Discr. Dyn. Nature Soc 2006, 45348 (2006)

    Google Scholar 

  28. I.M. Jánosi, R. Müller, Empirical mode decomposition and correlation properties of long daily ozone records. Phys. Rev. E 71, 056126 (2005)

    Article  Google Scholar 

  29. V.N. Livina, Y. Ashkenazy, A. Bunde, S. Havlin, Seasonality effects on nonlinear properties of hydrometeorological records. In: J. Kropp, H.J. Schellnhuber (eds.), In Extremis: Extremes, Trends and Correlations in Hydrology and ClimateSpringer, Berlin, 2008, (in revision)

    Google Scholar 

  30. J.C. Sprott, Chaos and Time Series Analysis Oxford University Press, Oxford (2003)

    Google Scholar 

  31. M. Bauer, H. Heng, W. Martienssen, Characterization of spatiotemporal chaos from time series. Phys. Rev. Lett 71, 521–524 (1993)

    Article  Google Scholar 

  32. E. Olbrich, R. Hegger, H. Kantz, Analysing local observations of weakly coupled maps. Phys. Lett. A 244, 538–544 (1998)

    Article  Google Scholar 

  33. C. Raab, J. Kurths, Estimation of large-scale dimension densities. Phys. Rev. E 64, 016216 (2001)

    Article  Google Scholar 

  34. C. Raab, N. Wessel, A. Schirdewan, J. Kurths, Large-scale dimension densities for heart rate variability analysis. Comput. Cardiol 32, 985–988 (2005)

    Article  Google Scholar 

  35. D.S. Broomhead, G.P. King, Extracting qualitative dynamics from experimental data. Physica D 20, 217–236 (1986)

    Article  Google Scholar 

  36. R. Vautard, M. Ghil, Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D 35, 395–424 (1989)

    Article  Google Scholar 

  37. R. Vautard, P. Yiou, M. Ghil, Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Physica D 58, 95–126 (1992)

    Article  Google Scholar 

  38. J.B. Elsner, A.A. Tsonis, Singular Spectrum Analysis: A New Tool in Time Series Analysis Springer, New York (1996)

    Google Scholar 

  39. A.I. Mees, P.E. Rapp, L.S. Jennings, Singular-value decomposition and embedding dimension. Phys. Rev. A 36, 340–346 (1987)

    Article  Google Scholar 

  40. A.M. Albano, J. Muench, C. Schwartz, A.I. Mees, P.E. Rapp, Singular-value decomposition and the Grassberger-Procaccia algorithm. Phys. Rev. A 38, 3017–3026 (1988)

    Article  Google Scholar 

  41. M. Paluš, I. Dvořák, Singular-value decomposition in attractor reconstruction: pitfalls and precautions. Physica D221–234 (1992)

    Google Scholar 

  42. J.T. Joliffe, Principal Component Analysis Springer, New York (1986)

    Google Scholar 

  43. R.W. Preisendorfer, Principal Component Analysis in Meteorology and Oceanography Elsevier, Amsterdam (1988)

    Google Scholar 

  44. T.F. Cox, M.A.A. Cox, Multidimensional Scaling 2nd ed., Chapman and Hall, London (2000)

    Google Scholar 

  45. G. Plaut, R. Vautard, Spells of low-frequency oscillations and weather regimes in the Northern Hemisphere. J. Atmos. Sci 51, 210–236 (1994)

    Article  Google Scholar 

  46. J. Tenenbaum, V. de Silva, J.C. Langford, A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  47. S. Roweis, L. Saul, Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  48. M.A. Kramer, Nonlinear principal component analysis using autoassociative neural networks. Am. Inst. Chem. Engin. J. 37, 233–243 (1991)

    Google Scholar 

  49. A. Hyvärinen, J. Karhunen, E. Oja, Independent Component AnalysisWiley, New York (2001)

    Google Scholar 

  50. S. Ciliberto, B. Nicolaenko, Estimating the number of degrees of freedom in spatially extended systems. Europhys. Lett 14, 303–308 (1991)

    Article  Google Scholar 

  51. Y. Pomeau, Measurement of the information density in turbulence. Compt. Rend. Acad. Sci. Ser. II 300, 239–241 (1985)

    Google Scholar 

  52. K. Kaneko, Spatiotemporal chaos in one-dimensional and two-dimensional coupled map lattices. Physica D 37, 60–82 (1989)

    Article  Google Scholar 

  53. G. Mayer-Kress, K. Kaneko, Spatiotemporal chaos and noise. J. Stat. Phys54, 1489–1508 (1989)

    Article  Google Scholar 

  54. S.M. Zoldi, H.M. Greenside, Karhunen-Loève decomposition of extensive chaos. Phys. Rev. Lett78, 1687–1690 (1997)

    Article  Google Scholar 

  55. S.M. Zoldi, J. Liu, K.M.S. Bajaj, H.S. Greenside, G. Ahlers, Extensive scaling and nonuniformity of the Karhunen-Loève decomposition for the spiral-defect chaos state. Phys. Rev. E58, 6903–6906 (1998)

    Article  Google Scholar 

  56. M. Meixner, S.M. Zoldi, S. Bose, E. Schöll, Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system. Phys. Rev. E61, 1382–1385 (2000)

    Article  Google Scholar 

  57. H. Varela, C. Beta, A. Bonnefort, K. Krischer, Transitions to electrochemical turbulence. Phys. Rev. Lett94, 174104 (2005)

    Article  Google Scholar 

  58. M. Thiel, Recurrences: Exploiting Naturally Occurring AnaloguesPhD thesis, University of Potsdam (2004)

    Google Scholar 

  59. H.B. Wilson, M.J. Keeling, Spatial scales and low-dimensional deterministic dynamics. In: U. Dieckmann, R. Law, J.A.J. Metz (eds.), The Geometry of Ecological Interactions: Simplifying Spatial ComplexityCambridge University Press, Cambridge, 209–226 (2000)

    Google Scholar 

  60. R. Proulx, P. Coté, L. Parrott, Multivariate recurrence plots for visualizing and quantifying the dynamics of spatially extended natural systems. In revision.

    Google Scholar 

  61. S.A. Farmer, An investigation into the results of principal component analysis of data derived from random numbers. The Statistician20, 63–72 (1971)

    Article  Google Scholar 

  62. J.R. Probert-Jones, Orthogonal pattern (Eigenvector) analysis of random and partly random fields. Conf. Prob. Stat. Atmos. Sci3, 187–192 (1973)

    Google Scholar 

  63. J.M. Craddock, C.R. Flood, Eigenvectors for representing the 500 mb geopotential surface over the Northern Hemisphere. Quart. J. Roy. Meteor. Soc95, 576–593 (1969)

    Article  Google Scholar 

  64. P.V. Baily, B.H. KenKnight, J.M. Rogers, E.E. Johnson, R.E. Ideker, W.M. Smith, Spatial organization, predictability, and determinism in ventricular fibrillation. Chaos8, 103–115 (1998)

    Article  Google Scholar 

  65. R. Donner, A. Witt, Temporary dimensions of multivariate data from paleoclimate records – A novel measure for dynamic characterization of long-term climate change. Int. J. Bifurcation Chaos17, 3685–3689 (2007)

    Article  Google Scholar 

  66. R. Donner, A. Witt, Characterisation of long-term climate change by dimension estimates of multivariate palaeoclimatic proxy data. Nonlin. Proc. Geophys13, 485–497 (2006)

    Google Scholar 

  67. R. Donner, Spatial correlations of hydro-meteorological records in a river catchment. In: J. Kropp, H.J. Schellnhuber (eds.), In Extremis: Extremes, Trends and Correlations in Hydrology and ClimateSpringer, Berlin, 2008, (in revision)

    Google Scholar 

  68. C. Spearman, The proof and measurement of association between two things. Amer. J. Psychol15, 72–101 (1904)

    Article  Google Scholar 

  69. M.G. Kendall, A new measure of rank correlation. Biometrika 30, 81–93 (1938)

    Google Scholar 

  70. B. Pompe, Measuring statistical dependences in a time series. J. Stat. Phys73, 587–610 (1993)

    Article  Google Scholar 

  71. R. Donner, A. Hofleitner, J. Höfener, S. Lämmer, D. Helbing, Dynamic stabilization and control of material flows in networks and its relationship to phase synchronization. Proc. PhysCon2007, 1188 (2007).

    Google Scholar 

  72. R. Donner, Multivariate analysis of spatially heterogeneous phase synchronisation in complex systems: application to self-organised control of material flows in networks. Eur. Phys. J. B(in press), doi:10.1140/epjb/e2008–00151–8 (2008)

    Google Scholar 

  73. S.M. Barbosa, M.E. Silva, M.J. Fernandes, Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry. Nonlin. Proc. Geophys13, 177–184 (2006)

    Article  Google Scholar 

  74. A. Politi, A. Witt, Fractal dimension of space-time chaos. Phys. Rev. Lett82, 3034–3037 (1999)

    Google Scholar 

  75. A.A. Tsonis, K.L. Swanson, P.J. Roebber, What do networks have to do with climate? Bull. Amer. Meteorol. Soc87, 585–595 (2006)

    Article  Google Scholar 

  76. A.A. Tsonis, K. Swanson, S. Kravtsov, A new dynamical mechanism for major climate shifts. Geophys. Res. Lett34, L13705 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Donner, R., Sakamoto, T., Tanizuka, N. (2008). Complexity of Spatio-Temporal Correlations in Japanese Air Temperature Records. In: Donner, R.V., Barbosa, S.M. (eds) Nonlinear Time Series Analysis in the Geosciences. Lecture Notes in Earth Sciences, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78938-3_7

Download citation

Publish with us

Policies and ethics