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Synchronous Motions Across the Instrumental Climate Record

  • Peter Carl
Part of the Understanding Complex Systems book series (UCS)

Abstract

The Earth’s climate system bears a rich variety of feedback mechanisms that may give rise to complex, evolving modal structures under internal and external control. Various types of synchronization may be identified in the system’s motion when looking at representative time series of the instrumental period through the glasses of an advanced technique of sparse data approximation, the Matching Pursuit (MP) approach. To disentangle the emerging network of oscillatory modes to the degree that climate dynamics turns out to be separable, a large dictionary of “Gaussian logons,” i.e. frequency modulated (FM) Gabor atoms, is applied. Though the extracted modes make up linear decompositions, this flexible analyzing signal matches highly nonlinear waveforms. Univariate analyses over the period 1870–1997 are presented of a set of customary time series in annual resolution, comprising global and regional climate, central European synoptic systems, German precipitation, and runoff of the Elbe river near Dresden. All the evidence from this first-generation MP-FM study, obtained in subsequent multivariate syntheses, points to dynamically excited regimes of an organized yet complex climate system under permanent change—perhaps a (pre)chaotic one at centennial timescales, suggesting a “chaos control” perspective on global climate dynamics and change. Findings and conclusions include, among others, internal structure of reconstructed insolation, the episodic nature of global warming as reflected in multidecadal temperature modes, their swarm of “interdomain” companions across the whole system that unveils an unknown regime character of interannual climate dynamics, and the apparent onset early in the 1990s of the present thermal stagnation.

Notes

Acknowledgements

Thanks are due to Fred Hattermann of the Potsdam Institute for Climate Impact Research (PIK) who provided the Elbe runoff data. Generally, the success of the study hinges on the quality of data, and the author hopes to have expressed his respect to this community in spending substantial effort and using advanced techniques in order to make the best of the data. MP-FM is an own product, but its coding has much profited from the detailed MP description given in [73]. Further sources which helped in own software developments over the years have been acknowledged in [21]. Last but not least, however, graphics solutions as provided by the freely available GrADS [33] and Xvgr packages [99] are explicitly referred to here with due gratitude.

References

  1. 1.
    Abraham, R.H., Shaw, C.D.: Dynamics. The Geometry of Behavior, 2nd edn. Addison-Wesley, Redwood City (1992)Google Scholar
  2. 2.
    Allan, R.J., Nicholls, N., Jones, P.D., Butterworth, I.J.: A further extension of the Tahiti–Darwin SOI, early SOI results and Darwin pressure. J. Climate 4(7), 743–749 (1991)CrossRefADSGoogle Scholar
  3. 3.
    Allen, J.B.: Short term spectral analysis, synthesis, and modification by discrete Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 25(3), 235–238; corrigendum 25(6), 589 (1977)Google Scholar
  4. 4.
    Ananthakrishnan, R., Soman, M.K.: The onset of the southwest monsoon over Kerala, 1901–1980. J. Climatol. 8(3), 283–296 (1988)CrossRefGoogle Scholar
  5. 5.
    Ananthakrishnan, R., Soman, M.K.: Onset dates of the south–west monsoon over Kerala for the period 1870–1900. Int. J. Climatol. 9(3), 321–322 (1989)CrossRefGoogle Scholar
  6. 6.
    Balmaseda, M.A., Trenberth, K.E., Källèn, E.: Distinctive climate signals in reanalysis of global ocean heat content. Geophys. Res. Lett. 40, 1754–1759 (2013). doi:10.1002/grl.50382CrossRefADSGoogle Scholar
  7. 7.
    Baur, F., Bartels, J., Bider, M., Sestoft, I.: Langjährige Beobachtungsreihen. In: Baur, F. (ed.) Meteorologisches Taschenbuch, vol. 1, Chap. 11, Tables 2 and 3, pp. 740–748. Geest & Portig, Leipzig (1962)Google Scholar
  8. 8.
    Bedrosian, E.: The analytic signal representation of modulated waveforms. Proc. IRE 50(10), 2071–2076 (1962)CrossRefGoogle Scholar
  9. 9.
    Bedrosian, E.: A product theorem for Hilbert transforms. Proc. IEEE 51(5), 868–869 (1963)CrossRefGoogle Scholar
  10. 10.
    Brönnimann, S., Luterbacher, J., Staehelin, J., Svendby, T.M.: An extreme anomaly in stratospheric ozone over Europe in 1940–1942. Geophys. Res. Lett. 31(8), L08101 (2004). doi:10.1029/2004GL019611CrossRefADSGoogle Scholar
  11. 11.
    Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)CrossRefADSzbMATHMathSciNetGoogle Scholar
  12. 12.
    Cane, M.A., Zebiak, S.E.: A theory for El Niño and the southern oscillation. Science 228(4703), 1085–1087 (1985)CrossRefADSGoogle Scholar
  13. 13.
    Carl, P.: Monsoon dynamics in a low–dimensional GCM. WCRP-84, WMO/TD-No. 619(II), 773–780. WMO, Geneva (1994)Google Scholar
  14. 14.
    Carl, P.: Growth of thermal signal energy, phase coincidence with insolation—and cooling ahead? Geophys. Res. Abstr. CD-ROM 3(OA25), 5267 (2001)Google Scholar
  15. 15.
    Carl, P.: Solar vs. thermal signal separation in the global surface air temperature series. In: International Conference on Earth System Modelling, Proceedings on CD-ROM, Hamburg, 15 pp. (2003)Google Scholar
  16. 16.
    Carl, P.: Synchronized motions within the instrumental climate record, 1870–1997. Terra Nostra Schr. Alfred-Wegener-Stiftung 6, 89–95 (2003)Google Scholar
  17. 17.
    Carl, P.: MP based detection of synchronized motions across the instrumental climate record. In: Proceedings on IEEE Statistical Signal Processing Workshop, pp. 557–560. IEEE, Nice (2011). 978-1-4577-0568-7/11Google Scholar
  18. 18.
    Carl, P.: On the dynamical status of the climate system – II: synchronous motions galore across the records. In: Stavrinides, S.G., Banerjee, S., Caglar, H., Ozer, M. (eds.) Proceedings on Chaos and Complex Systems, pp. 529–539. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-33914-1_74
  19. 19.
    Carl, P.: A general circulation model en route to intraseasonal monsoon chaos. In: Banerjee, S., Rondoni, L. (eds.) Applications of Chaos and Nonlinear Dynamics in Science and Engineering. Understanding Complex Systems, vol. 3, Chap. 3, pp. 63–99. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-34017-8_3
  20. 20.
    Carl, P.: Atmospheric tracers and the monsoon system: lessons learnt from the 1991 Kuait oil well fires. In: Banerjee, S., Ercetin, S.S. (eds.) Chaos, Complexity and Leadership 2012. Springer Proceedings in Complexity, Chap. 47, pp. 371–410. Springer, Dordrecht (2014). doi: 10.1007/978-94-007-7362-2_47
  21. 21.
    Carl, P., Behrendt, H.: Regularity based functional streamflow disaggregation: 1. Comprehensive foundation. Water Resour. Res. 44(W02420) (2008). doi: 10.1029/2004WR003724
  22. 22.
    Carl, P., Gerlinger, K., Hattermann, F.F., Krysanova, V., Schilling, C., Behrendt, H.: Regularity based functional streamflow disaggregation: 2. Extended demonstration. Water Resour. Res. 44(W03426) (2008). doi: 10.1029/2006WR005056; and corrigendum: Water Resour. Res. 44(W06701) (2008). doi: 10.1029/2008WR007105
  23. 23.
    Charney, J.G., DeVore, J.G.: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36(7), 1205–1216 (1979)CrossRefADSGoogle Scholar
  24. 24.
    Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by Basis Pursuit. SIAM Rev. 43(1), 129–159 (2001)CrossRefADSzbMATHMathSciNetGoogle Scholar
  25. 25.
    Christiansen, B.: On the nature of the arctic oscillation. Geophys. Res. Lett. 29(16), 1805 (2002). doi: 10.1029/2001GL014130 CrossRefADSGoogle Scholar
  26. 26.
    Christensen, J.H., Christensen, O.B.: Severe summertime flooding in Europe. Nature 421(6925), 805–806 (2003)CrossRefADSGoogle Scholar
  27. 27.
    Claasen, T.A.C.M., Mecklenbräuker, W.F.G.: The Wigner distribution—a tool for time–frequency analysis. Part 2: discrete–time signals. Philips J. Res. 35(4/5), 276–300 (1980)Google Scholar
  28. 28.
    Coumou, D., Petoukhov, V., Rahmstorf, S., Petri, S., Schellnhuber, J.: Quasi-resonant circulation regimes and hemispheric synchronization of extreme weather in boreal summer. Proc. Natl. Acad. Sci. 111(34), 12331–12336 (2014)CrossRefADSGoogle Scholar
  29. 29.
    Crowley, T.J.: Causes of climate change over the past 1000 years. Science 289(5477), 270–277 (2000)CrossRefADSGoogle Scholar
  30. 30.
    Daubechies, I.: The wavelet transform, time–frequency localization and signal analysis. IEEE Trans. Inf. Theory 36(5), 961–1005 (1990)CrossRefADSzbMATHMathSciNetGoogle Scholar
  31. 31.
    Daubechies, I., Grossmann, A., Meyer, Y.: Painless nonorthogonal expansions. J. Math. Phys. 27(5), 1271–1283 (1986)CrossRefADSzbMATHMathSciNetGoogle Scholar
  32. 32.
    Donoho, D.L., Elad, M., Temlyakov, V.N.: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52(1), 6–18 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Doty, B.E.: Using the Grid Analysis and Display System (GrADS). Manual, Version 1.3.1. University of Maryland, College Park (1992)Google Scholar
  34. 34.
    Duane, G.S., Tribbia, J.J.: Weak Atlantic–Pacific teleconnections as synchronized chaos. J. Atmos. Sci. 61(17), 2149–2168 (2004)CrossRefADSGoogle Scholar
  35. 35.
    Emresoy, M.K., El-Jaroudi, A.: Evolutionary Burg spectral estimation. IEEE Signal Process. Lett. 4(6), 173–175 (1997)CrossRefADSGoogle Scholar
  36. 36.
    England, M.H., McGregor, S., Spence, P., Meehl, G.A., Timmermann, A., Cai, W., Gupta, A.S., McPhaden, M.J., Purich, A., Santoso, A: Recent intensification of wind-driven circulation in the Pacific and the ongoing warming hiatus. Nat. Clim. Change 4, 222–227 (2014). doi: 10.1083/NCLIMATE2106 Google Scholar
  37. 37.
    Faybishenko, B.: Nonlinear dynamics in flow through unsaturated fractured porous media: status and perspectives. Rev. Geophys. 42(2), RG2003 (2004)CrossRefADSGoogle Scholar
  38. 38.
    Foukal, P., Fröhlich, C., Spruit, H., Wigley, T.M.L.: Variations in solar luminosity and their effect on the Earth’s climate, Nature 443(7108), 161–166 (2006)CrossRefADSGoogle Scholar
  39. 39.
    Fraedrich, K.: An ENSO impact on Europe? A review. Tellus 46A(4), 541–552 (1994)CrossRefADSGoogle Scholar
  40. 40.
    Friis-Christensen, E., Lassen, K.: Length of the solar cycle: an indicator of solar activity closely associated with climate. Science 254(5032), 698–700 (1991)CrossRefADSGoogle Scholar
  41. 41.
    Fyfe, J.C., Gillett, N.P., Zwiers, F.W.: Overestimated global warming over the past 20 years. Nat. Clim. Change 3, 767–769 (2013)CrossRefADSGoogle Scholar
  42. 42.
    Gabor, D.: Theory of communication. J. Inst Electr. Eng. III 93, 429–457 (1946)Google Scholar
  43. 43.
    Gerstengarbe, F.-W., Werner, P.C.: Katalog der Großwetterlagen Europas nach Paul Hess und Helmuth Brezowsky, 1881–1998, 5th revised and extended edition. Ber. Dt. Wetterd., 113, Offenbach (1999)Google Scholar
  44. 44.
    Ghil, M., Kimoto, M., Neelin, J.D.: Nonlinear dynamics and predictability in the atmospheric sciences. Rev. Geophys. 29(Suppl.), 46–55 (1991)Google Scholar
  45. 45.
    Graf, H.-F.: On El Niño/Southern Oscillation and Northern Hemispheric temperature. Gerlands Beitr. Geophys. 95(1), 63–75 (1986)ADSGoogle Scholar
  46. 46.
    Graf, H.-F., Zanchettin, D.: Central Pacific El Niño, the “subtropical bridge,” and Eurasian climate. J. Geophys. Res. 117(D01102) (2012). doi: 10.1029/2011JD016493
  47. 47.
    Graham, N.E., White, W.B.: The El Niño cycle: a natural oscillator of the Pacific ocean–atmosphere system. Science 240(4857), 1293–1302 (1988)CrossRefADSGoogle Scholar
  48. 48.
    Gribonval, R., Vandergheynst, P.: On the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries. IEEE Trans. Inf. Theory 52(1), 255–261 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  49. 49.
    Hahn, S.L.: Hilbert Transforms in Signal Processing. Artech House, Boston (1996)zbMATHGoogle Scholar
  50. 50.
    Hess, P., Brezowsky, H.: Katalog der Großwetterlagen Europas, 1881–1976, 3rd revised and extended edition, Ber. Dt. Wetterd., 15, Offenbach (1977)Google Scholar
  51. 51.
    Houghton, J.T., Ding, Y., Griggs, D.J., Noguer, M., van der Linden, P. J., Dai, X., Maskell, K., Johnson, C.A. (eds.) IPCC: Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel of Climate Change. Cambridge University Press, Cambridge (2001)Google Scholar
  52. 52.
    Hoyt, D.V., Schatten, K.H.: The Role of the Sun in Climate Change. Oxford University Press, Oxford (1997)Google Scholar
  53. 53.
    Huang, J., Higuchi, K., Shabbar, A.: The relationship between the North Atlantic oscillation and El Niño–southern oscillation. Geophys. Res. Lett. 25(14), 2707–2710 (1998)CrossRefADSGoogle Scholar
  54. 54.
    Huang, N.E., Shen, Z., Long, S.R., Wu. M.C., Shi, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. 454, 903–995 (1998)Google Scholar
  55. 55.
    Huber, P.J.: Projection Pursuit. Ann. Stat. 13(2), 435–475; incl. discussion, 475–525 (1985)Google Scholar
  56. 56.
    Hurrel, J.W.: Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science 269(5224), 676–679 (1995)CrossRefADSGoogle Scholar
  57. 57.
    Jin, F.-F., Ghil, M.: Intraseasonal oscillations in the extratropics: Hopf bifurcation and topographic instabilities. J. Atmos. Sci. 47(24), 3007–3022 (1990)CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    Jin, F.-F., Neelin, J.D., Ghil, M.: El Niño on the devil’s staircase: annual subharmonic steps to chaos. Science 264(5155), 70–72 (1994)CrossRefADSGoogle Scholar
  59. 59.
    Jones, P.D.: Hemispheric surface air temperature variations: a reanalysis and an update to 1993. J. Clim. 7(11), 1794–1802 (1994)CrossRefADSGoogle Scholar
  60. 60.
    Jones, P.D., Jonsson, T., Wheeler, D.: Extension to the North Atlantic Oscillation using early instrumental pressure observations from Gibraltar and South–West Iceland. Int. J. Climatol. 17(13), 1433–1450 (1997)CrossRefGoogle Scholar
  61. 61.
    Kapala, A., Mächel, H., Flohn, H.: Behaviour of the centres of action above the Atlantic since 1881. Part II: Associations with regional climate anomalies. Int. J. Climatol. 18(1), 23–36 (1998)ADSGoogle Scholar
  62. 62.
    Krishnamurti, T.N., Bhalme, H.N.: Oscillations of a monsoon system. Part I. Observational aspects. J. Atmos. Sci. 33(10), 1937–1954 (1976)Google Scholar
  63. 63.
    Lagarias, J.C.: Number theory and dynamical systems. Proc. Symp. Appl. Math. 46, 35–72 (1992)CrossRefMathSciNetGoogle Scholar
  64. 64.
    Lamb, H.H.: Re: the onset of the southwest monsoon over Kerala. Int. J. Climatol. 9(3), 323 (1989)CrossRefGoogle Scholar
  65. 65.
    Lau, K.-M., Peng, L., Sui, C.H., Nakazawa, T.: Dynamics of super cloud clusters, westerly wind bursts, 30–60 day oscillations and ENSO: an unified view. J. Meteorol. Soc. Jpn. 67(2), 205–219 (1989)Google Scholar
  66. 66.
    Lean, J., Beer, J., Bradley, R.: Reconstruction of solar irradiance since 1610: implications for climate change. Geophys. Res. Lett. 22(23), 3195–3198 (1995)CrossRefADSGoogle Scholar
  67. 67.
    Lean, J., Wang, Y.-M., Sheeley, N.R., Jr.: The effect of increasing solar activity on the Sun’s total and open magnetic flux during multiple cycles: implications for solar forcing of climate. Geophys. Res. Lett. 29(24), 2224 (2002). doi: 10.1029/2002GL015880 CrossRefADSGoogle Scholar
  68. 68.
    Lewis, N., Curry., J.A.: The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dyn. (2014). doi: 10.1007/s00382-014-2342-y
  69. 69.
    Lorenz, E.N.: Can chaos and intransitivity lead to interannual variability? Tellus 42A(3), 378–389 (1990)CrossRefADSGoogle Scholar
  70. 70.
    Mächel, H., Kapala, A., Flohn, H.: Behaviour of the centres of action above the Atlantic since 1881. Part I: Characteristics of seasonal and interannual variability. Int. J. Climatol. 18(1), 1–22 (1989)Google Scholar
  71. 71.
    Madden, R.A., Julian, P.R.: Observations of the 40–50-day tropical oscillation—a review. Mon. Weather Rev. 122(5), 814–837 (1994)CrossRefADSGoogle Scholar
  72. 72.
    Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic, San Diego (1999)zbMATHGoogle Scholar
  73. 73.
    Mallat, S.G., Zhang, Z.: Matching Pursuits with time–frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)CrossRefADSzbMATHGoogle Scholar
  74. 74.
    Maragos, P.: Differential morphology. In: Mitra, S.K., Sicuranza, G.L. (eds.) Nonlinear Image Processing, chap. 10, pp. 289–329. Academic, San Diego (2001)CrossRefGoogle Scholar
  75. 75.
    McKinnon, J.: Sunspot numbers: 1610-1985. Report UAG-95, WDC-A for Solar-Terrestrial Physics (1987)Google Scholar
  76. 76.
    Meyboom, P.: Estimating groundwater recharge from stream hydrographs. J. Geophys. Res. 66(4), 1203–1214 (1961)CrossRefADSGoogle Scholar
  77. 77.
    Mudelsee, M., Börngen, M., Tetzlaff, G., Grünewald, U.: No upward trend in the occurrence of extreme floods in central Europe. Nature 425(6954), 166–169 (2003)CrossRefADSGoogle Scholar
  78. 78.
    Normand, C.: Monsoon seasonal forecasting. Q. J. R. Meteorol. Soc. 79(342), 463–473 (1953)CrossRefADSGoogle Scholar
  79. 79.
    Parker, D.E., Legg, M., Folland, C.K.: A new daily central England temperature series, 1772–1991. Int. J. Climatol. 12(4), 317–342 (1992)CrossRefGoogle Scholar
  80. 80.
    Parker, D.E., Jones, P.D., Folland, C.K., Bevan, A.: Interdecadal changes of surface temperature since the late nineteeth century. J. Geophys. Res. 99(D7), 14373–14399 (1994)CrossRefADSGoogle Scholar
  81. 81.
    Parthasarathy, B., Munot, A.A., Kothawale, D.R.: Monthly and seasonal rainfall series for All-India homogeneous regions and meteorological subdivisions: 1871–1994. RR–065, Indian Institute of Tropical Meteorology, Pune (1995)Google Scholar
  82. 82.
    Raj, Y.E.A.: Objective determination of northeast monsoon onset dates over coastal Tamil Nadu for the period 1901–90. Mausam 43(3), 273–282 (1992)Google Scholar
  83. 83.
    Raj, Y.E.A.: A statistical technique for determination of withdrawal of northeast monsoon over coastal Tamil Nadu. Mausam 49(3), 309–320 (1998)MathSciNetGoogle Scholar
  84. 84.
    Rasmusson, E.M., Wallace, J.M.: Meteorological aspects of the El Niño/Southern Oscillation. Science 222(4629), 1195–1202 (1983)CrossRefADSGoogle Scholar
  85. 85.
    Rodwell, M.J., Hoskins, B.J.: Monsoons and the dynamics of deserts. Q. J. R. Meteorol. Soc. 122(534), 1385–1404 (1996)CrossRefADSGoogle Scholar
  86. 86.
    Rogers, J.C.: The association between the North Atlantic Oscillation and the Southern Oscillation in the northern hemisphere. Mon. Weather Rev. 112(10), 1999–2015 (1984)CrossRefADSGoogle Scholar
  87. 87.
    Selten, F.M., Branstator, G.W., Dijkstra, H.A., Kliphuis, M.: Tropical origins for recent and future Northern Hemisphere climate change. Geophys. Res. Lett. 31, L21205 (2004). doi: 10.1029/2004GL020739 CrossRefADSGoogle Scholar
  88. 88.
    Sirocko, F., Sarntheim, M., Erlenkeuser, H., Lange, H., Arnold, M., Duplessy, J.C.: Century-scale events in monsoonal climate over the past 24,000 years. Nature 364(6435), 322–324 (1993)CrossRefADSGoogle Scholar
  89. 89.
    Sirocko, F., Garbe–Schönberg, D., McIntyre, A., Molfino, B.: Teleconnections between the subtropical monsoons and high-latitude climates during the last deglaciation. Science 272(5261), 526–529 (1996)Google Scholar
  90. 90.
    Sivakumar, B.: Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward. Stoch. Environ. Res. Risk Assess. 23, 1027–1036 (2009). doi: 10.1007/s00477-008-0265-z CrossRefGoogle Scholar
  91. 91.
    So, P.: Unstable periodic orbits. Scholarpedia 2(2), 1353 (2007). doi: 10.4249/scholarpedia.1353 CrossRefADSMathSciNetGoogle Scholar
  92. 92.
    Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tigmor, M., Miller, H.L. (eds.) IPCC: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel of Climate Change. Cambridge University Press, Cambridge (2007)Google Scholar
  93. 93.
    Soman, M.K., Krishna Kumar, K.: Space–time evolution of meteorological features associated with the onset of Indian summer monsoon. Mon. Weather Rev. 121(4), 1177–1194 (1993)CrossRefADSGoogle Scholar
  94. 94.
    Sontakke, N.A., Pant, G.B., Singh, N.: Construction of All-India summer monsoon rainfall series for the period 1844–1991. J. Clim. 6(9), 1807–1811 (1993)CrossRefADSGoogle Scholar
  95. 95.
    Suarez, M.J., Schopf, P.S.: A delayed action oscillator for ENSO. J. Atmos. Sci. 45(21), 3283–3287 (1988)CrossRefADSGoogle Scholar
  96. 96.
    Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79(1), 61–78 (1998)CrossRefADSGoogle Scholar
  97. 97.
    Tropp, I.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2241 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  98. 98.
    Tropp, I.: Just relax: convex programming methods for identifying sparse signals in noise. IEEE Trans. Inf. Theory 52(3), 1030–1051 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  99. 99.
    Turner, P.J.: ACE/gr user’s manual. Graphics for exploratory data analysis. Software Documentation Series, SDS3, 91-11, Oregon Graduate Institute of Science and Technology (1992)Google Scholar
  100. 100.
    Tziperman, E., Stone, L., Cane, M.A., Jarosh, H.: El Niño chaos: overlapping of resonances between the seasonal cycle and the Pacific ocean–atmosphere oscillator. Science 264(5155), 72–74 (1994)CrossRefADSGoogle Scholar
  101. 101.
    van der Pol, B.: The fundamentals of frequency modulation. J. Inst. Electr. Eng. III 93, 153–158 (1946)Google Scholar
  102. 102.
    Vautard, R., Yiou, P., Ghil, M.: Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Physica D 58(1–4), 95–126 (1992)CrossRefADSGoogle Scholar
  103. 103.
    Visser, R., Molenaar, J.: Trend estimation analysis in climatological time series: an application of structural time series models and the Kalman filter. J. Clim. 8(5), 969–979 (1995)CrossRefADSGoogle Scholar
  104. 104.
    von Storch, H., Barkhordarian, A., Hasselmann, K., Zorita, E.: Can climate models explain the recent stagnation in global warming? (2013). http://www.academia.edu/4210419
  105. 105.
    Wallace, J.M.: North Atlantic Oscillation/annular mode: two paradigms – one phenomenon. Q. J. R. Meteorol. Soc. 126(564), 791–805 (2000)CrossRefADSGoogle Scholar
  106. 106.
    Wallace, J.M., Thompson, D.W.J.: The Pacific center of action of the Northern Hemisphere annular mode: real or artifact? J. Clim. 15(14), 1987–1991 (2002)CrossRefADSGoogle Scholar
  107. 107.
    Walter, K., Graf, H.-F.: Life cycles of the North Atlantic teleconnections under strong and weak polar vortex conditions. Q. J. R. Meteorol. Soc. 132(615), 467–483 (2006)CrossRefADSGoogle Scholar
  108. 108.
    Wang, B., Wang, Y.: Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J. Clim. 9(7), 1586–1598 (1996)CrossRefADSGoogle Scholar
  109. 109.
    Webster, P.J., Yang, S.: Monsoon and ENSO: selectively interactive systems. Q. J. R. Meteorol. Soc. 118(507), 877–926 (1992)CrossRefADSGoogle Scholar
  110. 110.
    Webster, P.J., Magaña, V.O., Palmer, T.N., Shukla, J., Tomas, R.A., Yanai, M., Yasunari, T.: Monsoons: processes, predictability, and the prospects for prediction. J. Geophys. Res. 103(C7), 14451–14510 (1998)CrossRefADSGoogle Scholar
  111. 111.
    Yasunari, T., Seki, Y.: Role of the Asian monsoon on the interannual variability of the global climate system. J. Meteorol. Soc. Jpn. 70(1B), 177–189 (1992)Google Scholar
  112. 112.
    Young, P.C.: Parallel processes in hydrology and water quality: a unified time series approach. J. Inst. Water Environ. Manag. 6(5), 598–612 (1992)CrossRefGoogle Scholar
  113. 113.
    Zakharov, V.E., Ostrovsky, L.A.: Modulation instability: the beginning. Physica D 238, 540–548 (2009)CrossRefADSzbMATHMathSciNetGoogle Scholar
  114. 114.
    Zhao, J.-X., Ghil, M.: Nonlinear symmetric instability and intraseasonal oscillations in the tropical atmosphere. J. Atmos. Sci. 48(24), 2552–2568 (1991)CrossRefADSGoogle Scholar

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Authors and Affiliations

  1. 1.ASWEX – Applied Water ResearchClimate Dynamics & Signal Analysis ProjectBerlinGermany

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