Distribution of natural trends in long-term correlated records: A scaling approach

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 2, 2011, Pages

  Lennartz, Sabine ^a,b   Bunde, Armin ^a  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; CONFIDENCE INTERVAL; CONFIDENCE PROBABILITY; EXCEEDANCE PROBABILITY; GLOBAL TEMPERATURES; LENGTH SCALE; LOCAL CLIMATE; REGRESSION LINES; SCALING THEORIES; STANDARD DEVIATION;

PROBABILITY DISTRIBUTIONS;

EID: 80052222741     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.021129     Document Type: Article

References (60)

1. B. B. Mandelbrot, Gaussian Self-Affinity and Fractals (Springer, New York, Berlin, Heidelberg, 2001).
2. E. Koscielny-Bunde, A. Bunde, S. Havlin, and Y. Goldreich, Physica A PHYADX 0378-4371 10.1016/0378-4371(96)00187-2 231, 393 (1996). (Pubitemid 126385650)
3. E. Koscielny-Bunde, A. Bunde, S. Havlin, H. E. Roman, Y. Goldreich, and H. J. Schellnhuber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.729 81, 729 (1998).
4. J. D. Pelletier and D. L. Turcotte, Adv. Geophys. PRLTAO 0065-2687 10.1016/S0065-2687(08)60294-0 40, 91 (1999).
5. R. O. Weber and P. Talkner, J. Geophys. Res. 0148-0227 10.1029/2001JD000548 106, 20131 (2001).
6. J. F. Eichner, E. Koscielny-Bunde, A. Bunde, S. Havlin, and H.-J. Schellnhuber, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.046133 68, 046133 (2003).
7. K. Fraedrich and R. Blender, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.108501 90, 108501 (2003).
8. R. A. Monetti, S. Havlin, and A. Bunde, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01662-X 320, 581 (2003).
9. D. Rybski, A. Bunde, and H. von Storch, J. Geophys. Res. JGREA2 0148-0227 10.1029/2007JD008568 113, D02106 (2008).
10. H. E. Hurst, Trans. Am. Soc. Civil Eng. 116, 770 (1951).
11. B. B. Mandelbrot and J. R. Wallis, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR005i002p00321 5, 321 (1969).
12. J. D. Pelletier and D. L. Turcotte, J. Hydrology. JHYDA7 0022-1694 10.1016/S0022-1694(97)00102-9 203, 198 (1997). (Pubitemid 28118239)
13. J. W. Kantelhardt, D. Rybski, S. A. Zschiegner, P. Braun, E. Koscielny-Bunde, V. Livina, S. Havlin, and A. Bunde, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.08.019 330, 240 (2003).
14. D. Koutsoyiannis, Hydrological Sciences J. HSJODN 0262-6667 10.1623/hysj.48.1.3.43481 48, 3 (2003). (Pubitemid 36242577)
15. J. W. Kantelhardt, E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Havlin, J. Geophys. Res. Atmos. JGREA2 0148-0227 10.1029/2005JD005881 111, D01106 (2006). (Pubitemid 43263779)
16. D. Koutsoyiannis, J. Hydrology JHYDA7 0022-1694 10.1016/j.jhydrol.2005. 02.030 322, 25 (2006). (Pubitemid 44294323)
17. C. K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1343 70, 1343 (1993).
18. C. Schäfer, M. G. Rosenblum, J. Kurths, and H. H. Abel, Nature (London) NATUAS 0028-0836 10.1038/32567 392, 239 (1998). (Pubitemid 28155089)
19. A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J. H. Peter, and K. Voigt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3736 85, 3736 (2000).
20. Y. Ashkenazy, P. Ch, S. Havlin, K. Peng, A. L. Goldberger, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1900 86, 1900 (2001). (Pubitemid 32252805)
21. J. W. Kantelhardt, Y. Ashkenazy, P. C. Ivanov, A. Bunde, S. Havlin, T. Penzel, J. H. Peter, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.051908 65, 051908 (2002). (Pubitemid 40606798)
22. J. W. Kantelhardt, T. Penzel, S. Rostig, H. F. Becker, S. Havlin, and A. Bunde, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01502-9 319, 447 (2003).
23. Z. Ding, C. W. J. Granger, and R. F. Engle, J. Empirical Finance PHYADX 0927-5398 10.1016/0927-5398(93)90006-D 1, 83 (1983).
24. Y. Liu, P. Cizeau, M. Meyer, C. K. Peng, and H. E. Stanley, Physica A PHYADX 0378-4371 10.1016/S0378-4371(97)00368-3 245, 437 (1997).
25. Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C. K. Peng, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.1390 60, 1390 (1999).
26. K. Yamasaki, L. Muchnik, S. Havlin, A. Bunde, and H. E. Stanley, Proc. Natl. Acad. Sci. PNASA6 0027-8424 10.1073/pnas.0502613102 102, 9424 (2005). (Pubitemid 40923579)
27. B. D. Malamud and D. L. Turcotte, Advances in Geophysics PNASA6 0065-2687 10.1016/S0065-2687(08)60293-9 40, 1 (1999).
28. S. Lennartz and A. Bunde, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.066101 79, 066101 (2009).
29. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.49.1685 49, 1685 (1994).
30. J. W. Kantelhardt, E. Koscielny-Bunde, H. H. A. Rego, S. Havlin, and A. Bunde, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00144-3 295, 441 (2001). (Pubitemid 32495759)
31. H. E. Hurst, R. Black, and Y. M. Sinaika, Long-Term Storage in Reservoirs: An Experimental Study (Constable & Co. Ltd., London, 1965).
32. J. Feder, Fractals (Plenum Press, New York, 1988).
33. T. A. Cohn and H. F. Lins, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2005GL024476 32, L23402 (2005). (Pubitemid 43159349)
34. D. Rybski, A. Bunde, S. Havlin, and H. von Storch, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2005GL025591 33, L06718 (2006).
35. E. Zorita, T. F. Stocker, and H. von Storch, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2008GL036228 35, L24706 (2008).
36. J. M. Halley, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.02.027 388, 2492 (2009).
37. S. Lennartz and A. Bunde, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2009GL039516 36, L16706 (2009).
38. D. Rybski and A. Bunde, Physica A PHYADX 0378-4371 10.1016/j.physa.2008. 12.026 388, 1687 (2009).
39. P. Bloomfield and D. Nychka, Climatic Change PHYADX 0165-0009 10.1007/BF00139727 21, 275 (1992).
40. K. Hasselmann, J. Clim. JLCLEL 0894-8755 10.1175/1520-0442(1993) 006<1957:OFFTDO>2.0.CO;2 6, 1957 (1993).
41. G. C. Hegerl, H. von Storch, K. Hasselmann, B. D. Santer, U. Cubasch, and P. D. Jones, J. Clim. 0894-8755 10.1175/1520-0442(1996)009<2281:DGGICC>2. 0.CO;2 9, 2281 (1996).
42. F. W. Zwiers, in Anthropogenic Climate Change (Springer, New York, 1999), pp. 163-209.
43. T. Barnett, J. Clim. JLCLEL 0894-8755 10.1175/JCLI3329.1 18, 1291 (2005). (Pubitemid 40815457)
44. E. Giese, I. Mossig, D. Rybski, and A. Bunde, Erdkunde JLCLEL 0014-0015 10.3112/erdkunde.2007.02.05 61, 186 (2007). (Pubitemid 47079298)
45. S. Lovejoy and D. Schertzer (private communication).
46. E. Koscielny-Bunde, J. W. Kantelhardt, P. Braun, A. Bunde, and S. Havlin, J. Hydrology JHYDA7 0022-1694 10.1016/j.jhydrol.2005.03.004 322, 120 (2006).
47. D. Schertzer and S. Lovejoy, Nonlinear Variability in Geophysics: Scaling and Fractals (Springer, New York, 1991).
48. D. Schertzer, S. Lovejoy, F. Schmitt, Y. Chigirinskaya, and D. Marsan, Fractals FRACEG 0218-348X 10.1142/S0218348X97000371 5, 427 (1997).
49. Z. Chen, P. Ch, K. Hu, and H. E. Stanley, Phys. Rev. E FRACEG 1539-3755 10.1103/PhysRevE.65.041107 65, 041107 (2002). (Pubitemid 40618803)
50. K. Hu, P. Ch, Z. Chen, P. Carpena, and H. E. Stanley, Phys. Rev. E FRACEG 1539-3755 10.1103/PhysRevE.64.011114 64, 011114 (2001).
51. J. Ludescher, M. I. Bogachev, J. W. Kantelhardt, A. Y. Schumann, and A. Bunde, Physica A PHYADX 0378-4371 10.1016/j.physa.2011.03.008 390, 2480 (2011).
52. L. Xu, P. Ch, K. Hu, Z. Chen, A. Carbone, and H. E. Stanley, Phys. Rev. E PHYADX 1539-3755 10.1103/PhysRevE.71.051101 71, 051101 (2005). (Pubitemid 41480917)
53. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics, 2nd ed. (Cambridge University Press, Cambridge, 1997).
54. T. Schreiber and A. Schmitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.635 77, 635 (1996).
55. [http://www.cru.uea.ac.uk/cru/data/temperature/]
56. P. Brohan, J. J. Kennedy, I. Harris, S. F. B. Tett, and P. D. Jones, J. Geophys. Res. JGREA2 0148-0227 10.1029/2005JD006548 111, D12106 (2006). (Pubitemid 44687620)
57. P. D. Jones, D. H. Lister, and Q. Li, J. Geophys. Res. Atmos. JGREA2 0148-0227 10.1029/2008JD009916 113, D16122 (2008).
58. J. Hansen, R. Ruedy, M. Sato, and K. Lo, Rev. Geophys. REGEEP 8755-1209 10.1029/2010RG000345 48, RG4004 (2010).
59. D. E. Parker, Nature (London) NATUAS 0028-0836 10.1038/432290a 432, 290 (2004).
60. T. C. Peterson, J. Clim. JLCLEL 0894-8755 10.1175/1520-0442(2003) 016<2941:AOUVRI>2.0.CO;2 16, 2941 (2003) (Pubitemid 37358613)