Long-term correlations in earth sciences

Czasopismo : Acta Geophysica
Tytuł artykułu : Long-term correlations in earth sciences

Autorzy :
Vallianatos, F.
Technological Educational Institute of Crete, Laboratory of Geophysics and Seismology, Crete, Greece, fvallian@chania.teicrete.gr,
Tsallis, C.
Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil, tsallis@cbpf.br,
Sotolongo-Costa, O.
Catedra de Sistemas Complejos “Henri Poincare”, Universidad de La Habana, osotolongo@fisica.uh.cu,
Celikoglu, A.
Department of Physics, Faculty of Science, Ege University, Izmir, Turkey, ahmet.celikoglu@ege.edu.tr,
Abe, S.
Department of Physical Engineering, Mie University, Mie, Japan, suabe@sf6.so-net.ne.jp,
Bunde, A.
Institut fur Theoretische Physik, Giessen, Germany, Armin.Bunde@uni-giessen.de,
Abstrakty : In this article we review the occurrence and consequences of longterm memory in geophysical records like climate and seismic records, and describe similarities with financial data sets. We review several methods to detect linear and nonlinear long-term correlations, also in the presence of external trends, and show how external trends can be detected in data with long-term memory. We show as well that long-term correlations lead to a natural clustering of extreme events and discuss the implications for several geophysical data sets.

Słowa kluczowe : long-term correlations, extreme values, multi-fractality, trend detection,
Wydawnictwo : Instytut Geofizyki PAN
Rocznik : 2012
Numer : Vol. 60, no. 3
Strony : 562 – 588
Bibliografia : Bogachev, M.I., and A. Bunde (2008), Memory effects in the statistics of interoccurence times between large events in financial markets, Phys. Rev. E 78, 036114, DOI: 10.1103/PhysRevE.78.036114.
Bogachev, M.I., J.F. Eichner, and A. Bunde (2007), The effect of nonlinear correlations on the statistics of return intervals in multifractal data sets, Phys. Rev. Lett. 99, 240601, DOI: 10.1103/PhysRevLett.99.240601.
Bogachev, M.I., I.S. Kireenkov, E.M. Nifontov, and A. Bunde (2009), Statistics of return intervals between large heartbeat intervals and their usability for online prediction of disorders, New J. Phys. 11, 063036, DOI: 10.1088/1367-2630/11/6/063036.
Brohan, P., J.J. Kennedy, I. Harris, S.F.B. Tett, and P.D. Jones (2006), Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850, J. Geophys. Res. 111, D12106, DOI: 10.1029/2005JD006548.
Bunde, A., S. Havlin, J.W. Kantelhardt, T. Penzel, J.-H. Peter, and K. Voigt (2000), Correlated and uncorrelated regions in heart-rate fluctuations during sleep, Phys. Rev. Lett. 85, 3736, DOI: 10.1103/PhysRevLett.85.3736.
Bunde, A., J. Kropp, and H.-J. Schellnhuber (eds.) (2002), The Science of Disasters-Climate Disruptions, Heart Attacks, and Market Crashes, Springer, Berlin.
Bunde, A., J. Eichner, S. Havlin, and J.W. Kantelhardt (2003), The effect of longterm correlations on the return periods of rare events, Physica A 330, 1, DOI: 10.1016/j.physa.2003.08.004.
Bunde, A., J. Eichner, S. Havlin, and J.W. Kantelhardt (2005), Long-term memory: A natural mechanism for the clustering of extreme events and anomal residual times in climate records, Phys. Rev. Lett. 94, 048701, DOI: 10.1103/Phys-RevLett.94.048701.
Corral, A. (2004), Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes, Phys. Rev. Lett. 92, 108501, DOI: 10.1103/Phys-RevLett.92.108501.
Eichner, J.F., E. Koscielny-Bunde, A. Bunde, S. Havlin, and H.-J. Schellnhuber (2003), Power-law persistence and trends in the atmosphere: A detailed study of long temperature records, Phys. Rev. E 68, 046133, DOI: 10.1103/Phys-RevE.68.046133.
Eichner, J.F., J. W. Kantelhardt, A. Bunde, and S. Havlin (2006), Extreme value statistics in records with long-term persistence, Phys. Rev. E 73, 016130, DOI: 10.1103/PhysRevE.73.016130.
Feder, J. (1988), Fractals, Plenum, New York.
Giese, E., I. Mossig, D. Rybski, and A. Bunde (2007), Long-term analysis of air temperature trends in Central Asia, Erdkunde 61, 186-202.
Glaser, R. (2001), Klimageschichte Mitteleuropas,Wissenschaftliche Buchgesellschaft, Darmstadt.
Govindan, R.B., D. Vjushin, S. Brenner, A. Bunde, S. Havlin, and H.-J. Schellnhuber (2002), Global climate models violate scaling of the observed atmospheric variability, Phys. Rev. Lett. 89, 028501, DOI: 10.1103/Phys-RevLett.89.028501.
Hurst, H.E., R.P. Black, and Y.M. Simaika (1965), Long-term Storage: An Experimental study, Constable & Co. Ltd., London.
Ivanov, P.Ch., A.L. Goldberger, S. Havlin, M.G. Rosenblum, Z. Struzik, and H.E. Stanley (1999), Multifractality in human heartbeat dynamics, Nature 399, 461-465, DOI: 10.1038/20924.
Kantelhardt, J.W., E. Koscielny-Bunde, H.H.A. Rego, A. Bunde, and S. Havlin (2001), Detecting long-range correlations with detrended fluctuation analysis, Physica A 295, 441-454, DOI: 10.1016/S0378-4371(01)00144-3.
Kantelhardt, J.W., E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Havlin (2006), Long-term persistence and multifractality of precipitation and river runoff records, J. Geophys. Res. 111, D01106, DOI: 10.1029/2005JD005881.
Király, A., I. Bartos, and I.M. Jánosi (2006), Correlation properties of daily temperature anomalies over land, Tellus, 58A, 5, 593-600, DOI: 10.1111/j.1600-0870.2006.00195.x.
Koscielny-Bunde, E., A. Bunde, S. Havlin, H.E. Roman, Y. Goldreich, and H.-J. Schellnhuber (1998), Indication of a universal persistence law governing atmospheric variability, Phys. Rev. Lett. 81, 3, 729-732, DOI: 10.1103/Phys-RevLett.81.729.
Koscielny-Bunde, E., J.W. Kantelhardt, P. Braun, A. Bunde, and S. Havlin (2006), Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies, J. Hydrol. 322, 120-137, DOI: 10.1016/j.jhydrol.2005.03.004.
Leland, W.E., M.S. Taqqu, W. Willinger, and D.V. Wilson (1994), On the self-similar nature of ethernet traffic (extended version), IEEE ACM Trans. Network. 2, 1-15, DOI: 10.1109/90.282603.
Lennartz, S., and A. Bunde (2009a), Trend evaluation in records with long-term memory; Application to global warming, Geophys. Res. Lett. 36, L16706, DOI: 10.1029/2009GL039516.
Lennartz, S., and A. Bunde (2009b), Eliminating finite-size effects and detecting the amount of white noise in short records with long-term memory, Phys. Rev. E 79, 066101, DOI: 10.1103/PhysRevE.79.066101.
Lennartz, S., and A. Bunde (2011), Distribution of natural trends in long-term correlated records: A scaling approach, Phys. Rev. E 84, 021129, DOI: 10.1103/PhysRevE.84.021129.
Lennartz, S., V.N. Livina, A. Bunde, and S. Havlin (2008), Long-term memory in earthquakes and the distribution of interoccurrence times, Europhys. Lett. 81, 69001, DOI: 10.1209/0295-5075/81/69001.
Lennartz, S., A. Bunde, and D.L. Turcotte (2011), Modelling seismic catalogues by cascade models: Do we need long-term magnitude correlations?, Geophys. J. Int. 184, 1214-1222, DOI: 10.1111/j.1365-246X.2010.04902.x.
Liu, Y.H., P. Cizeau, M. Meyer, C.-K. Peng, and H.E. Stanley (1997), Correlations in economic time series, Physica A 245, 437-440, DOI: 10.1016/S0378-4371(97)00368-3;
Liu, Y.H., P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, and H.E. Stanley (1999), Statistical properties of the volatility of price fluctuations, Phys. Rev. E 60, 1390-1400, DOI: 10.1103/PhysRevE.60.1390.
Livina, V.N., Y. Ashkenazy, P. Braun, A. Monetti, A. Bunde, S. Havlin (2003), Nonlinear volatility of river flux fluctuations, Phys. Rev. E 67, 042101, DOI: 10.1103/PhysRevE.67.042101.
Livina, V.N., S. Havlin, and A. Bunde (2005), Memory in the occurence of earthquakes, Phys. Rev. Lett. 95, 208501, DOI: 10.1103/PhysRevLett.95.208501.
Ludescher, J., C. Tsallis, and A. Bunde (2011), Universal behaviour of interoccurrence times between losses in financial markets: An analytical description, Europhys. Lett. 95, 68002, DOI: 10.1209/0295-5075/95/68002.
Malamud, B.D., and D.L. Turcotte (1999), Self-affine time series: I. Generation and Analyses, Adv. Geophys. 40, 1-90.
Mandelbrot, B.B. (1977), Fractals: Form, Chance and Dimension, Freeman, San Francisco.
Mandelbrot, B.B. (1982), The Fractal Geometry of Nature, Freeman, San Francisco.
Mandelbrot, B.B., and J. van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAM Review 10, 422-437.
Mandelbrot, B.B., and J.R. Wallis (1969), Some long-run properties of geophysical records, Water. Resour. Res. 5, 321-340, DOI: 10.1029/WR005i002p00321.
Monetti, A., S. Havlin, and A. Bunde (2003), Long-term persistence in the sea surface temperature fluctuations, Physica A 320, 581-589, DOI: 10.1016/S0378-4371(02)01662-X.
Mudelsee, M. (2007), Long memory of rivers from spatial aggregation, Water. Resour. Res. 43, W01202, DOI: 10.1029/2006WR005721.
Mudelsee, M., M. Börngen, G. Tetzlaff, and U. Grünwald (2003), No upward trends in the occurrence of extreme floods in central Europe, Nature, 425, 166-169, DOI: 10.1038/nature01928.
Peitgen, H.-O., H. Jürgens, and D. Saupe (1991), Chaos and Fractals, Springer Verlag, Heidelberg.
Peitgen, H.-O., H. Jürgens, and D. Saupe (1992), Chaos and Fractals, Springer Verlag, New York.
Pelletier, J.D., and D.L. Turcotte (1999), Self-affine time series: II. Applications and models, Adv. Geophys. 40, 91, DOI: 10.1016/S0065-2687(08)60294-0.
Peng, C.-K., J. Mietus, J.M. Hausdorff, S. Havlin, H.E. Stanley, and A.L. Goldberger (1993), Long-range anticorrelations and non-Gaussian behavior of the heartbeat, Phys. Rev. Lett. 70, 1343-1346, DOI: 10.1103/PhysRevLett.70.1343.
Pfisterer, C. (1998), Wetternachhersage. 500 Jahre Klimavariationen und Naturkatastrophen 1496-1995, Verlag Paul Haupt, Bern.
Rybski, D., and A. Bunde (2009), On the detection of trends in long-term correlated records, Physica A 388, 1687-1695, DOI: 10.1016/j.physa.2008.12.026.
Rybski, D., A. Bunde, S. Havlin, and H. von Storch (2006), Long-term persistence in climate and the detection problem, Geophys. Res. Lett. 33, 6, L06718, DOI: 10.1029/2005GL025591.
Santhanam, M.S., and H. Kantz (2005), Long-range correlations and rare events in boundary layer wind fields, Physica A 345, 713-721, DOI: 10.1016/j.physa.2004.07.012.
Schertzer, D., and S. Lovejoy (1991), Nonlinear Variability in Geophysics: Scaling and Fractals, Springer, New York.
Schertzer, D., S. Lovejoy, F. Schmitt, Y. Chigirinskaya, and D. Marsan (1997), Multifractal cascade dynamics and turbulent intermittency, Fractals 5, 3, 427-471, DOI: 10.1142/S0218348X97000371.
Schreiber, T., and A. Schmitz (1996), Improved Surrogate Data for Nonlinearity Tests, Phys. Rev. Lett. 77, 635-638, DOI: 10.1103/PhysRevLett.77.635.
Stanley, H.E., and P. Meakin (1988), Multifractal Phenomena in Physics and Chemistry, Nature 355, 405-409, DOI: 10.1038/335405a0.
Talkner, P., and R.O. Weber (2000), Power spectrum and detrended fluctuation analysis: application to daily temperatures, Phys. Rev. E 62, 150-160, DOI: 10.1103/PhysRevE.62.150.
Turcotte, D.L. (1997), Fractals and Chaos in Geology and Geophysics, 2nd edn., Cambridge Univ. Press, Cambridge.
Vjushin, D., I. Zhidkov, S. Brenner, S. Havlin, and A. Bunde (2004), Volcanic forcing improves atmosphere-ocean coupled general circulation model scaling performance, Geophys. Res. Lett. 31, L10206, DOI: 10.1029/2004GL019499.
Yamasaki, K., L. Muchnik, S. Havlin, A. Bunde, and H.E. Stanley (2005), Scaling and memory in volatility return intervals in financial markets, PNAS 102, 26, 9424-9428, DOI: 10.1073/pnas.0502613102.
Cytuj : Vallianatos, F. ,Tsallis, C. ,Sotolongo-Costa, O. ,Celikoglu, A. ,Abe, S. ,Bunde, A. , Long-term correlations in earth sciences. Acta Geophysica Vol. 60, no. 3/2012