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A new method to detect transitory signatures and local time/space variability structures in the climate system: the scale-dependent correlation analysis

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Abstract

The study of transitory signals and local variability structures in both/either time and space and their role as sources of climatic memory, is an important but often neglected topic in climate research despite its obvious importance and extensive coverage in the literature. Transitory signals arise either from non-linearities, in the climate system, transitory atmosphere–ocean couplings, and other processes in the climate system evolving after a critical threshold is crossed. These temporary interactions that, though intense, may not last long, can be responsible for a large amount of unexplained variability but are normally considered of limited relevance and often, discarded. With most of the current techniques at hand these typology of signatures are difficult to isolate because the low signal-to-noise ratio in midlatitudes, the limited recurrence of the transitory signals during a customary interval of data considered. Also, there is often a serious problem arising from the smoothing of local or transitory processes if statistical techniques are applied, that consider all the length of data available, rather than taking into account the size of the specific variability structure under investigation. Scale-dependent correlation (SDC) analysis is a new statistical method capable of highlighting the presence of transitory processes, these former being understood as temporary significant lag-dependent autocovariance in a single series, or covariance structures between two series. This approach, therefore, complements other approaches such as those resulting from the families of wavelet analysis, singular-spectrum analysis and recurrence plots. A main feature of SDC is its high-performance for short time series, its ability to characterize phase-relationships and thresholds in the bivariate domain. Ultimately, SDC helps tracking short-lagged relationships among processes that locally or temporarily couple and uncouple. The use of SDC is illustrated in the present paper by means of some synthetic time-series examples of increasing complexity, and it is compared with wavelet analysis in order to provide a well-known reference of its capabilities. A comparison between SDC and companion techniques is also addressed and results are exemplified for the specific case of some relevant El Niño-Southern Oscillation teleconnections.

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References

  • Alexander MA, Bladé I, Newman M, Lanzante JR, Lau N-C, Scott JD (2002) The atmospheric bridge: The influence of ENSO teleconnections on air-sea interaction over the global oceans. J Climate 15:2205–2231

    Article  Google Scholar 

  • Baliunas S, Frick P, Sokoloff D, Soon W (1997) Time scales and trends in the central England temperature data (1659–1990): A wavelet analysis. Geophys Res Lett 24(11):1351–1354

    Article  Google Scholar 

  • Casdagli MC (1997) Recurrence plots revisited. Physica D 108:12–44

    Article  Google Scholar 

  • Childers DL, Sklar FH, Hutchinson SE (1994) Statistical treatment and comparative analysis of scale-dependent aquatic transect data in estuarine landscapes. Landscape Ecology 9:127–141

    Google Scholar 

  • Covey C, Achutarao KM, Gleckler PJ, Phillips TJ, Taylor KE, Wehner MF (2004) Coupled ocean-atmosphere climate simulations compared with simulations using prescribed sea surface temperature: effect of a “perfect ocean”. Glob Planet Change 41(1):1–14

    Article  Google Scholar 

  • Daubechies I (ed) (1993) Different perspectives on Wavelets. American Mathematical Society, Providence

  • Dettinger MD, Ghil M, Strong CM, Weibel W, Yiou P (1995) Software for singular spectrum analysis of noisy time series. EOS Trans AGU 76:12

    Google Scholar 

  • Eckmann JP (1981) Roads to turbulence in dissipative dynamical systems. Rev Mod Phys 53:643–654

    Article  Google Scholar 

  • Eckmann JP, Oliffson Kamphorst S, Ruelle D (1987) Recurrence plots of dynamical systems. Europhys Lett 4(9):973–977

    Article  Google Scholar 

  • Edgington ES (1987) Randomization tests. 2nd edn Marcel Dekker Inc, New York, pp 341

    Google Scholar 

  • Enfield DB, Mayer DA (1997) Tropical Atlantic sea surface temperature variability and its relation to El Niño-Southern Oscillation. J Geophys Res 102:929–945

    Article  Google Scholar 

  • Enfield DB, Mestas Nuñez AM (1999) Multiscale variabilities in global sea surface temperatures and their relationships with tropospheric climate patterns. J Climate 12:2719–2733

    Article  Google Scholar 

  • Farge M (1992) Wavelet transforms and their applications to turbulence. Ann Rev Fluid Mech 24:395–457

    Article  Google Scholar 

  • Farge M, Kevlahan N, Perrier V, Goirand U (1996) Wavelets and turbulence. Proc IEEE 84(4):639–669

    Article  Google Scholar 

  • Gamage N, Blumen W (1993) Comparative analysis of low level cold fronts: wavelet, fourier, and empirical orthogonal function decompositions. Mon Weath Rev 121(10):2867–2878

    Article  Google Scholar 

  • Gates WL, Boyle J, Covey C, Dease C, Doutriaux C, Drach R, Fiorino M, Gleckler P, Hnilo J, Marlais S, Phillips T, Potter G, Santer B, Sperber K, Taylor K, Williams D (1998) An overview of the results of the atmospheric model intercomparison project (AMIP I ). Bull Am Meteor Soc 73:1962–1970

    Article  Google Scholar 

  • Ghil M, Allen MR, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson AW, Saunders A, Tian Y, Varadi F, Yiou P (2002) Advanced spectral methods for climatic time series. Rev Geophys 40(1):1003

    Article  Google Scholar 

  • Glantz M (1998) Currents of change: El Nino’s impact on climate and society. Cambridge University Press, Cambridge, pp 194

  • Grinsted A, Moore JC, Jevrejeva S (2004). Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics 11:561–566

    Google Scholar 

  • Gu D, Philander SGH (1997) Interdecadal climate fluctuations that depend on excjhanges between the tropics and extratropics. Science 275:805–807

    Article  Google Scholar 

  • Hasselmann K (1976) Stochastic climate models, Part I, Theory. Tellus 28:473–485

    Article  Google Scholar 

  • Hoerling MP, Kumar A (1997) Why do North American climate anomalies differ from one El Niño event to another? Geophys Res Let 24(9):1059–1062

    Article  Google Scholar 

  • Hoerling MP, A Kumar M Zhong (1997) El Niño, La Niña, and the nonlinearity of their teleconnections. J Clim 10:1769–1786

    Article  Google Scholar 

  • Hudgins L, Friehe CA, Mayer ME (1993) Wavelet transforms and atmospheric turbulence. Phys Rev Lett 71(20):3279–3282

    Article  Google Scholar 

  • Jin FF, Ann SI, Timmermann A, Zhang X (2003) Strong El Niño events and nonlinear dynamical heating. Geophys Res Lett 30(3):1120

    Article  Google Scholar 

  • Ju J, Slingo J (1995) The Asian summer monsoon and ENSO. Q J R Meteorol Soc 121:1133–1168

    Article  Google Scholar 

  • Kang I-S, Jin K, Wang B, Lau K-M, Shukla J, Krishnamurthy V, Schubert SD, Waliser DE, Stern WF, Kitoh A, Meehl GA, Kanamitsu M, Galin VY, Satyan V, Park CK, Liu Q (2002). Intercomparison of the climatological variations of Asian summer monsoon precipitation simulated by 10 GCMs. Clim Dyn 19:383–395

    Article  Google Scholar 

  • Keppenne CL, Ghil M (1993) Adaptive filtering and prediction of noisy multivariate signals: an application to subannual variability in atmospheric angular momentum. Intl J Bif & Chaos 3:625–634

    Article  Google Scholar 

  • Kestin TS, Karoly DJ, Yang JI, Rayner NA (1998) Time-frequency variability of ENSO and stochastic simulations. J. Climate 11(9):2258–2272

    Article  Google Scholar 

  • Kiladis G, Díaz HF (1989) Global climatic anomalies associated with extremes in the Southern Oscillation. J Climate 2:1069–1090

    Article  Google Scholar 

  • Kimoto M, Ghil M, Mo KC (1991) Spatial structure of the 40-day oscillation in the Northern Hemisphere extratropics. In: Proceedings of the 8th conference atmospheric & oceanic waves & stability. Amer. Met. Soc., Boston, pp 115–116

  • Klein SA, Soden BJ, Lau N-C (1999) Remote sea surface temperature variations during ENSO: Evidence for a tropical atmospheric bridge. J Clim 12:917–932

    Article  Google Scholar 

  • Koelle K, Rodó X, Pascual M, Yunus Md, Mostafa G (2005) Refractory periods and climate forcing in cholera dynamics. Nature 436:696–700

    Article  Google Scholar 

  • Kumar P, Foufoula-Georgiou E (1997) Wavelet analysis for geophysical applications. Rev Geophys 35:385–412

    Article  Google Scholar 

  • Kump LR (2002) Reducing uncertainty about carbon dioxide as a climate driver. Nature 419:188–190

    Article  Google Scholar 

  • Latif M, Barnett TP (1996) Causes of decadal climate variability over the North Pacific and North America. Science 266:634–637

    Article  Google Scholar 

  • Lau NC, Nath MJ (1994) A modeling study of the relative roles of tropical and extratropical SST anomalies in the variability of the global atmosphere-ocean system. J Climate 7:1184–1207

    Article  Google Scholar 

  • Lau NC, Nath MJ (1999) Observed and GCM-simulated westward propagating, planetary-scale fluctuations with approximately three-week periods. J Climate 127:2324–2345

    Google Scholar 

  • Lau NC, Nath MJ (2001) Impact of ENSO on SST variability in the North Pacific and North Atlantic: seasonal dependence and role of extratropical sea-air coupling. J Climate 14:2846–2866

    Article  Google Scholar 

  • Lau NC, Nath MJ (2003) Atmosphere-ocean variations in the Indo-Pacific sector during ENSO episodes. J Climate 16:3–20

    Article  Google Scholar 

  • Lau K-M, Weng H (1995) Climate signal detection using wavelet transform:how to make a time series sing. Bull Am Meteor Soc 76:2391–2402

    Article  Google Scholar 

  • Legendre P, Legendre L (1998) Numerical ecology, 2nd english edition. Developments in ecological modeling, vol 20. Elsevier, Amsterdam

  • Liu ZY (1994) A simple-model of the mass-exchange between the subtropical and tropical ocean. J Phys Ocean 24(6):1153–1165

    Article  Google Scholar 

  • Mak M (1995) Orthogonal wavelet analysis – interannual variability in the sea-surface temperature. Bull Am Meteor Soc 76(11):2179–2186

    Article  Google Scholar 

  • Manuca R , Savit R (1996). Stationarity and nonstationarity in time series analysis. Physica D 99:134–161

    Article  Google Scholar 

  • Meyers SD, Kelly BG, O’Brien JJ (1993) An introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves. Mon Weath Rev 121:2858–2866

    Article  Google Scholar 

  • Mooley DA, Parthasarathy B (1983) Indian summer monsoon and El Niño. Pure Appl Geophys 121:339–352

    Article  Google Scholar 

  • Monahan AH, Timmermann A, Lohman G (2001) Comments on ‘Noise-induced transitions in a simplified model of the thermohaline circulation. J Phys Oceanogr 32:1112–1116

    Article  Google Scholar 

  • Moron V, Vautard R, Ghil M (1998) Trends, interdecadal and interannual oscillations in global sea-surface temperatures. Clim Dyn 14:545–569

    Article  Google Scholar 

  • Moy CM, Seltzer GO, Rodbell DT, Anderson DM (2002) Variability of El Nino/Southern Oscillation activity at millennial timescales during the Holocene epoch. Nature 420(6912):162–165

    Article  Google Scholar 

  • Peixoto JP, Oort AH (1995) Physics of Climate, 4th edn American Institute of Physics, New York, pp 520

  • Plaut G, Vautard R (1994) Spells of low-frequency oscillations and weather regimes in the northern hemisphere. J Atmos Sci 51:210–236

    Article  Google Scholar 

  • Priestley MB (1992) Spectral analysis and time series: vols. 1 and 2. Academic, San Diego, pp 890

  • Pueyo S (1997) The study of chaotic dynamics by means of very short time series. Physica D 106:57–65

    Article  Google Scholar 

  • Rahmstorf S (2002) Ocean circulation and climate during the past 120,000 years. Nature 419:207–214

    Article  Google Scholar 

  • Reynolds RW, Rayner NA, Smith TM, Stokes DC, Wang W (2002) An improved in situ and satellite SST analysis for climate. J Climate 15:1609–1625

    Article  Google Scholar 

  • Rodó X (2001) Reversal of three global atmospheric fields linking changes in SST anomalies in the Pacific, Atlantic and Indian oceans at tropical latitudes and midlatitudes. Clim Dyn 18:203–217

    Article  Google Scholar 

  • Rodó X, Rodríguez-Arias MA (2004) El Niño-Southern Oscillation: absent in the early Holocene? J Climate 17(3):423–426

    Article  Google Scholar 

  • Rodó X, Pascual M, Fuchs G, Faruque ASG (2002) ENSO and cholera: a non-stationary link related to climate change. Proc Natl Acad Sci USA 99:12901–12906

    Article  Google Scholar 

  • Rodríguez-Arias MA, Rodó X (2004) A primer on the study of transitory dynamics in ecological series using the scale dependent correlation analysis. Oecologia 138:485–504

    Article  Google Scholar 

  • Ruiz-Barradas A, Carton JA, Nigam S (2003) Role of the atmosphere in climate variability of the tropical. Atlantic J Clim 16:2052–2065

    Google Scholar 

  • Saji NH, Goswami B, Vinayachandran PN, Yamagata T (1999) A dipole mode in the tropical Indian Ocean. Nature 401:360–363

    Google Scholar 

  • Sokal RR, Rohlf FJ (1995) Biometry: the principles and practice of statistics in biological research, 3rd edn. W.H. Freeman and Co, New York, pp xix+887

  • Soman MK, Slingo J (1997) Sensitivity of the Asian summer monsoon to aspects of sea-surface temperature anomalies in the tropical Pacific Ocean. Q J R Meteorol Soc 123:309–336

    Article  Google Scholar 

  • Strang G (1989) Wavelets and dilation equations: a brief introduction. SIAM Rev 31(4):614–627

    Article  Google Scholar 

  • Timmermann A, Jin FF (2003) A nonlinear theory for El Niño bursting. J Atmos Sci 60:152–165

    Article  Google Scholar 

  • Timmermann A, Schultz M, Gildor H, Tziperman E (2003) Coherent resonant millenial-scale climate transitions triggered by massive meltwater pulses. J Climate 16(15):2569–2585

    Article  Google Scholar 

  • Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteor Soc 79:61–78

    Article  Google Scholar 

  • Tourre YM, White WB (1995) ENSO signals in global upper-ocean temperature. J Phys Oceanogr 25:1317–1332

    Article  Google Scholar 

  • Trenberth KE (1976) Spatial and temporal variations in the Southern Oscillation. Q J R Meteor Soc 102:639–653

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Vautard R, Yiou P, Ghil M (1992) Singular-Spectrum Analysis – A toolkit for short, noisy chaotic signals. Physica D 58(1–4):95–126

    Article  Google Scholar 

  • Wang B (1995) Interdecadal changes in El Niño onset in the last four decades. J Climate 8:267–285

    Article  Google Scholar 

  • Wang B, Wang Y (1996) Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J Climate 9:1586–1598

    Article  Google Scholar 

  • Webster PJ, Moore AM, Loschnigg JP, Leben RR (1999) Coupled ocean-atmosphere dynamics in the Indian Ocean during 1997–98. Nature 401:356–360

    Article  Google Scholar 

  • Weng H-Y, Lau K-M (1994) Wavelets, period-doubling and time-frequency localization with application to satellite data analysis. J Atmos Sci 51:2523–2541

    Article  Google Scholar 

  • Xie S–P, Annamalai H, Schott FA, McCreary JP (2002) Structure and mechanisms of South Indian Ocean climate variability. J Climate 15:864–878

    Article  Google Scholar 

  • Yiou P, Baert E, Loutre MF (1996) Spectral analysis of climate data. Surveys in Geophysics 17(6):619–663

    Article  Google Scholar 

  • Yiou P, Sornette D, Ghil M (2000) Data-adaptative wavelets and multi-scale SSA. Physica D 142:254–290

    Article  Google Scholar 

  • Zhang R, Sumi A, Kimoto M (1996) Impact of El Niño on the east Asian monsoon: A diagnostic study of the ‘86/87’ and ‘91/92’ events. J Meteor Soc Japan 74:49–62

    Google Scholar 

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Acknowledgements

Authors wish to thank P. Yiou for comments on SDC methodology, C. Torrence and G. Compo for wavelet software and the comments of two anonymous referees. This work received partial funding by a NOAA/OGP research grant. X. Rodó was in receipt of a Ramon y Cajal contract of the MCYT and acknowledges support from ICREA institution. M.A. Rodríguez-Arias received funding from the PCB-UB.

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  1. Laboratori de Recerca del Clima, Parc Científic de Barcelona, University of Barcelona, Baldiri i Reixach, 4-6, Torre D, 08028, Barcelona Catalonia, Spain

    Xavier Rodó & Miquel-Àngel Rodríguez-Arias

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Rodó, X., Rodríguez-Arias, MÀ. A new method to detect transitory signatures and local time/space variability structures in the climate system: the scale-dependent correlation analysis. Clim Dyn 27, 441–458 (2006). https://doi.org/10.1007/s00382-005-0106-4

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