Skip to main content
SpringerLink
Log in

Spatial Correlations of River Runoffs in a Catchment

  • Chapter
  • First Online:
In Extremis

Abstract

Hydrological processes are characterised by spatio-temporal patterns with certain correlations in both time and space. Thus, time series of related quantities recorded at different locations show relevant correlations if these locations are influenced by the same patterns. The actual strength and temporal as well as spatial extension of these correlations depend crucially on the considered observable (temperature, runoff, precipitation, etc.). We analyse whether the corresponding interrelationships change significantly in the presence of changing environmental conditions. For this purpose, we systematically study a variety of measures which quantify the statistical dependence between the components of bi- and multivariate hydrological records. As a particular example, we consider runoff time series from an ensemble of gauges in the Upper Main catchment area in southern Germany. The qualitative behaviour of spatial correlations and their changes during extreme weather events are intensively discussed.

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

Access this chapter

Log in via an institution
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. W.S. Broecker, Science 278, 1582–1588 (1997)

    Article  Google Scholar 

  2. P.U. Clark, N.G. Pisias, T.F. Stocker, A.J. Weaver, Nature 415, 863–869 (2002)

    Article  Google Scholar 

  3. E. Koscielny-Bunde, A. Bunde, S. Havlin, Y. Goldreich, Physica A 231, 393–396 (1996)

    Article  Google Scholar 

  4. E. Koscielny-Bunde, H.E. Roman, A. Bunde, S. Havlin, H.-J. Schellnhuber, Philos. Mag. B 77, 1331–1340 (1998)

    Article  Google Scholar 

  5. E. Koscielny-Bunde, A. Bunde, S. Havlin, H.E. Roman, Y. Goldreich, H.-J. Schellnhuber, Phys. Rev. Lett. 81, 729–732 (1998)

    Article  Google Scholar 

  6. A.A. Tsonis, P.J. Roebber, J.B. Elsner, Geophys. Res. Lett. 25, 2821–2823 (1998)

    Article  Google Scholar 

  7. A.A. Tsonis, P.J. Roebber, J.B. Elsner, J. Climate 12, 1534–1541 (1999)

    Article  Google Scholar 

  8. J. Pelletier D. Turcotte, Adv. Geophys. 40, 91–166 (1999)

    Google Scholar 

  9. P. Talkner R.O. Weber, Phys. Rev. E 62, 150–160 (2000)

    Article  Google Scholar 

  10. R.B. Govindan, D. Vjushin, S. Brenner, A. Bunde, S. Havlin, H.-J. Schellnhuber, Physica A 294, 239–248 (2001)

    Article  Google Scholar 

  11. A. Bunde, S. Havlin, E. Koscielny-Bunde, H.-J. Schellnhuber, Physica A 302, 255–267 (2001)

    Article  Google Scholar 

  12. A. Király, I.M. Jánosi, Phys. Rev. E 65, 051102 (2002)

    Article  Google Scholar 

  13. R.B. Govindan, D. Vjushin, A. Bunde, S. Brenner, S. Havlin, H.-J. Schellnhuber, Phys. Rev. Lett. 89, 028501 (2002)

    Article  Google Scholar 

  14. D. Vjushin, R.B. Govindan, S. Brenner, A. Bunde, S. Havlin, H.-J. Schellnhuber, J. Phys. Condens. Matt. 14, 2275–2282 (2002)

    Article  Google Scholar 

  15. A. Bunde S. Havlin, Physica A 314, 15–24 (2002)

    Article  Google Scholar 

  16. A. Bunde, J. Eichner, R. Govindan, S. Havlin, E. Koscielny-Bunde, D. Rybski, D. Vjushin, in Nonextensive Entropy - Interdisciplinary Applications, ed. by M. Gell-Mann, C. Tsallis (Oxford University Press, New York, NY, 2003), pp. 207–220

    Google Scholar 

  17. R.A. Monetti, S. Havlin, A. Bunde, Physica A 320, 581–589 (2003)

    Article  Google Scholar 

  18. K. Fraedrich, R. Blender, Phys. Rev. Lett. 90, 108501 (2003)

    Article  Google Scholar 

  19. A. Bunde, J.F. Eichner, S. Havlin, E. Koscielny-Bunde, H.-J. Schellnhuber, D. Vyushin, Phys. Rev. Lett. 92, 039801 (2004)

    Article  Google Scholar 

  20. K. Fraedrich, R. Blender, Phys. Rev. Lett. 92, 039802 (2004)

    Article  Google Scholar 

  21. R. Blender, K. Fraedrich, Geophys. Res. Lett. 30, 1769 (2003)

    Article  Google Scholar 

  22. J.W. Kantelhardt, D. Rybski, S.A. Zschiegner, P. Braun, E. Koscielny-Bunde, V. Livina, S. Havlin, A. Bunde, Physica A 330, 240–245 (2003)

    Article  Google Scholar 

  23. J.F. Eichner, E. Koscielny-Bunde, A. Bunde, S. Havlin, H.-J. Schellnhuber, Phys. Rev. E 68, 046133 (2003)

    Article  Google Scholar 

  24. M. Pattantyús-Ábrahám, A. Király, I.M. Jánosi, Phys. Rev. E 69, 021110 (2004)

    Article  Google Scholar 

  25. A. Bunde, J.F. Eichner, S. Havlin, J.W. Kantelhardt, Physica A 342, 308–314 (2004)

    Article  Google Scholar 

  26. M.L. Kurnaz, Fractals 12, 365–373 (2004)

    Article  Google Scholar 

  27. D. Maraun, H.W. Rust, J. Timmer, Nonlin. Proc. Geophys. 11, 495–503 (2004)

    Article  Google Scholar 

  28. D. Vyushin, I. Zhidkov, S. Havlin, A. Bunde, S. Brenner, Geophys. Res. Lett. 31, L10206 (2004)

    Article  Google Scholar 

  29. R. Blender, K. Fraedrich, Geophys. Res. Lett. 31, L22213 (2004)

    Article  Google Scholar 

  30. A. Bunde, J.F. Eichner, J.W. Kantelhardt, S. Havlin, Phys. Rev. Lett. 94, 048701 (2005)

    Article  Google Scholar 

  31. A. Beretta, H.E. Roman, F. Raicich, F. Crisciani, Physica A 347, 695–703 (2005)

    Article  Google Scholar 

  32. E. Koscielny-Bunde, J.W. Kantelhardt, P. Braun, A. Bunde, S. Havlin, J. Hydrol. 322, 120–137 (2006)

    Article  Google Scholar 

  33. J.W. Kantelhardt, E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, S. Havlin, J. Geophys. Res. D 111, 01106 (2006)

    Article  Google Scholar 

  34. A.A. Tsonis, P.J. Roebber, Physica A 333, 497–504 (2004)

    Article  Google Scholar 

  35. W. von Bloh, M.C. Romano, M. Thiel, Nonlin. Proc. Geophys. 12, 471–479 (2005)

    Article  Google Scholar 

  36. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization - A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  37. D. Rybski, S. Havlin, A. Bunde, Geophys. Res. Abstr. 8, 04918 (2006)

    Google Scholar 

  38. D. Rybski, S. Havlin, A. Bunde, Physica A 320, 601–610 (2003)

    Article  Google Scholar 

  39. R. Donner, Proc. NDES 2006, 26–29 (2006)

    Google Scholar 

  40. D. Maraun, J. Kurths, Geophys. Res. Lett. 32, L15709 (2005)

    Article  Google Scholar 

  41. P.J. Webster, S. Yang, Q. J. R. Meteorol. Soc. 118, 887–926 (1992)

    Article  Google Scholar 

  42. C. Torrence, P.J. Webster, J. Climate 12, 2679–2690 (1999)

    Google Scholar 

  43. K.K. Kumar, B. Rajagopalan, M.A. Cane, Science 284, 2156–2159 (1999)

    Article  Google Scholar 

  44. S. Sarkar, R.P. Singh, M. Kafatos, Geophys. Res. Lett. 31, L13209 (2004)

    Article  Google Scholar 

  45. F.A. Huff, W.L. Shipp, J. Appl. Meteorol. 8, 542–550 (1969)

    Article  Google Scholar 

  46. F.A. Huff, Wat. Resour. Res. 6, 254–260 (1970)

    Article  Google Scholar 

  47. I. Zawadzki, J. Appl. Meteorol. 12, 459–472 (1973)

    Article  Google Scholar 

  48. R. Berndtsson, Water Res. Res. 24, 1511–1517 (1988)

    Article  Google Scholar 

  49. G. Sumner, C. Ramis, J.A. Guijarro, Theor. Appl. Climatol. 51, 199–221 (1995)

    Article  Google Scholar 

  50. M.F. Hutchinson, Agric. Forest Meteor. 73, 237–264 (1995)

    Article  Google Scholar 

  51. C. Uvo, R. Berndtsson, J. Geophys. Res. D 101, 4221–4233 (1996)

    Article  Google Scholar 

  52. E. Habib, W.F. Krajewski, G.J. Ciach, J. Hydromet. 2, 621–629 (2001)

    Article  Google Scholar 

  53. M. Mohapatra, U.C. Mohanty, S. Behera, Int. J. Climatol. 23, 1867–1887 (2003)

    Article  Google Scholar 

  54. A. Gaume, B. Sivakumar, M. Kolasinski, L. Hazoumé, J. Hydrol. 328, 56–64 (2006)

    Article  Google Scholar 

  55. M. Gebremichael, W. Krajewski, J. Appl. Meteor. 43, 1180–1199 (2004)

    Article  Google Scholar 

  56. A. Molini, P. La Barbera, L.G. Lanza, J. Hydrol. 322, 89–104 (2006)

    Article  Google Scholar 

  57. B. Sivakumar, J. Hydroinf. 7, 175–184 (2005)

    Google Scholar 

  58. B.M. Troutman, M.R. Karlinger, Water Resour. Res. 39, 1095 (2003)

    Article  Google Scholar 

  59. M.C. Romano, M. Thiel, U. Schwarz, J. Kurths, H. Lange, M. Hauhs, Int. J. Bifurcation Chaos 11, 2567–2578 (2001)

    Article  Google Scholar 

  60. J.O. Skøien, G. Blöschl, Hydrol. Earth Syst. Sci. 10, 645–662 (2006)

    Article  Google Scholar 

  61. M.S. Santhanam, P.K. Patra, Phys. Rev. E 64, 016102 (2001)

    Article  Google Scholar 

  62. P. Termonia, Meteor. Atmos. Phys. 78, 143–156 (2001)

    Article  Google Scholar 

  63. R. Donner, A. Witt, Int. J. Bifurcation Chaos. 17, 3685–3689 (2007)

    Article  Google Scholar 

  64. R. Donner, A. Witt, Nonlin. Proc. Geophys. 13, 485–497 (2006)

    Article  Google Scholar 

  65. R. Donner, PhD thesis, University of Potsdam (2007)

    Google Scholar 

  66. D. Schwandt, PhD thesis, University of Potsdam (2003) (in german).

    Google Scholar 

  67. E. Barth, T. Molnar, H. Overland, KLIWA-Berichte 4, 103–120 (2004) (in german).

    Google Scholar 

  68. K. Pearson, Phil. Trans. R. Soc. A 187, 253–318 (1896)

    Article  Google Scholar 

  69. W.C. Conover, Practical Nonparametric Statistics, 2nd ed. (Wiley, New York, NY, 1980)

    Google Scholar 

  70. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C - The Art of Scientific Computing 2nd ed. (Cambridge University Press, Cambridge, 1992)

    Google Scholar 

  71. C. Spearman, Am. J. Psychol. 15, 72–101 (1904)

    Article  Google Scholar 

  72. M.G. Kendall, Biometrika 30, 81–93 (1938)

    Google Scholar 

  73. D. Christensen, Comp. Stat. 20, 51–62 (2005)

    Article  Google Scholar 

  74. A.M. Fraser, H.L. Swinney, Phys. Rev. A 33, 1134–1140 (1986)

    Article  Google Scholar 

  75. I. Kojadinovic, Proc. ASMDA 2005, VII.16 (2005)

    Google Scholar 

  76. B. Pompe, J. Stat. Phys. 73, 587–610 (1993)

    Article  Google Scholar 

  77. J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, D., Europhys. Lett. 4, 973–977 (1987)

    Google Scholar 

  78. M. Thiel, M.C. Romano, J. Kurths, Phys. Lett. A 330, 343–349 (2004)

    Article  Google Scholar 

  79. J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 171, 199–203 (1992)

    Article  Google Scholar 

  80. C.L. Webber Jr., J.P. Zbilut, J. Appl. Physiol. 76, 965–973 (1994)

    Google Scholar 

  81. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Phys. Rev. E 66, 026702 (2002)

    Article  Google Scholar 

  82. M. Thiel, M.C. Romano, P.L. Read, J. Kurths, Chaos 14, 234–243 (2004)

    Article  Google Scholar 

  83. J.P. Zbilut, A. Giuliani, C.L. Webber Jr., C.L., Phys. Lett. A 246, 122–128 (1998)

    Google Scholar 

  84. M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214–223 (2004)

    Article  Google Scholar 

  85. M. Holschneider, Wavelets - An Analysis Tool (Oxford University Press, Oxford, 1995).

    Google Scholar 

  86. E.N. Lorenz, The Nature and Theory of the General Circulation of the Atmosphere (World Meteorological Organization, Geneva, 1967)

    Google Scholar 

  87. K. Hasselmann, in The Science of Disasters - Climate Disruptions, Heart Attacks, and Market Crashes, edited by A. Bunde, J. Kropp, H.-J. Schellnhuber (Springer, Berlin, 2002), pp. 141–169

    Google Scholar 

  88. R. Kleeman, Physica D. 230, 65–71 (2007)

    Article  Google Scholar 

  89. A. Piotrowski, J.J. Napiórkowski, P.M. Rowiński, Nonlin. Proc. Geophys. 13, 443–448 (2006)

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  92. G. Plaut, R. Vautard, J. Atmos. Sc. 51, 210–236 (1994)

    Article  Google Scholar 

  93. D.S. Broomhead, G.P. King, Physica D 20, 217–236 (1986)

    Article  Google Scholar 

  94. J. Tenenbaum, V. de Silva, J.C. Langford, Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  95. S. Roweis, L. Saul, Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  96. M.A. Kramer, Amer. Inst. Chem. Engin. Journal 37, 233–243 (1991)

    Google Scholar 

  97. A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis (Wiley, New York, NY, 2001)

    Book  Google Scholar 

  98. S.M. Zoldi, H.M. Greenside, Phys. Rev. Lett. 78, 1687–1690 (1997)

    Article  Google Scholar 

  99. S.M. Zoldi, J. Liu, K.M.S. Bajaj, H.S. Greenside, G. Ahlers, Phys. Rev. E 58, 6903–6906 (1998)

    Article  Google Scholar 

  100. M. Meixner, S.M. Zoldi, S. Bose, E. Schöll, Phys. Rev. E 61, 1382–1385 (2000)

    Article  Google Scholar 

  101. H. Varela, C. Beta, A. Bonnefort, K. Krischer, Phys. Rev. Lett. 94, 174104 (2005)

    Article  Google Scholar 

  102. S. Ciliberto, B. Nicolaenko, Europhys. Lett. 14, 303–308 (1991)

    Article  Google Scholar 

Download references

Acknowledgments

This work has been financially supported by the Volkswagen foundation (project no. I/78218) and the project “Extreme Events - Causes and Consequences (E2C2)” granted by the European Community (NEST contract no. 012975-E2C2). The data used in this study have been collected by the Bavarian Landesamt für Umwelt and provided by the Potsdam Institute for Climate Impact Research. Discussions with J. Kropp, M. Kallache, H. Rust, A. Witt, and J. Kurths are gratefully acknowledged. For the calculation of the cross-mutual information, we made use of an implementation based on the TISEAN package.

Author information

Authors and Affiliations

  1. Potsdam Institut für Klimafolgenforschung, 14412, Potsdam, Germany

    Reik Donner

Authors
  1. Reik Donner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reik Donner .

Editor information

Editors and Affiliations

  1. Klimafolgenforschung (PIK), Abt. Integrierte Systemanalyse, Potsdam Institut für, Telegraphenberg A31, Potsdam, 14412, Brandenburg, Germany

    Jürgen Kropp

  2. Klimafolgenforschung (PIK), Potsdam Institut für, Telegrafenberg 31 A, Potsdam, 14473, Brandenburg, Germany

    Hans-Joachim Schellnhuber

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Donner, R. (2011). Spatial Correlations of River Runoffs in a Catchment. In: Kropp, J., Schellnhuber, HJ. (eds) In Extremis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14863-7_14

Download citation

Publish with us

Policies and ethics

Search

Navigation