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In Extremis pp 166–183Cite as

Extreme Value Analysis Considering Trends: Application to Discharge Data of the Danube River Basin

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Abstract

This chapter proposes and applies an extreme value assessment framework, which allows for auto-correlation and non-stationarity in the extremes. This is, e.g., useful to assess the anticipated intensification of the hydrological cycle due to climate change. The costs related to more frequent or more severe floods are enormous. Therefore, an adequate estimation of these hazards and the related uncertainties is of major concern. Exceedances over a threshold are assumed to be distributed according to a generalised Pareto distribution and we use a point process to approximate the data. In order to eliminate auto-correlation, the data are thinned out. Contrary to ordinary extreme value statistics, potential non-stationarity is included by allowing the model parameters to vary with time. By this, changes in frequency and magnitude of the extremes can be tracked. The model which best suits the data is selected out of a set of models which comprises the stationary model and models with a variety of polynomial and exponential trend assumptions. Analysing winter discharge data of about 50 gauges within the Danube River basin, we find trends in the extremes in about one-third of the gauges examined. The spatial pattern of the trends is not immediately interpretable. We observe neighbouring gauges often to display distinct behaviour, possibly due to non-climatic factors such as changes in land use or soil conditions. Importantly, assuming stationary models for non-stationary extremes results in biased assessment measures. The magnitude of the bias depends on the trend strength and we find up to 100% increase for the 100-year return level. The results obtained are a basis for process-oriented, physical interpretation of the trends. Moreover, common practice of water management authorities can be improved by applying the proposed methods, and costs for flood protection buildings can be calculated with higher accuracy.

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References

  1. A. Bárdossy, F. Fili z, Identification of flood producing atmospheric circulation patterns. J. Hydrol. 313 48–57 (2005)

    Article  Google Scholar 

  2. A. Bárdossy, S. Pakosch, Wahrscheinlichkeiten extremer Hochwasser unter sich ändernden Klimaverhältnissen. Wasserwirtschaft, 7–8, 58–62 (2005)

    Google Scholar 

  3. BlfW. Bayrisches Landesamt für Wasserwirtschaft: Klimaänderungsfaktoren bei Planungen für den Hochwasserschutz. Water Management Directive, 2006

    Google Scholar 

  4. R. Brázdil, C. Pfister, H. Wanner, H. von Storch, J. Luterbacher. Historical climatology in Europe – the state of the art. Clim. Change, 70, 363–430 (2005)

    Article  Google Scholar 

  5. H.J. Caspary, A. Bárdossy, Markieren die Winterhochwasser 1990 und 1993 das Ende der Stationarität in der Hochwasserhydrologie infolge von Klimaänderungen? Wasser Boden, 47(3), 18–24 (1995)

    Google Scholar 

  6. S. Coles, An Introduction to Statistical Modeling of Extreme Values. (Springer, Berlin, 2001)

    Google Scholar 

  7. S. Coles, L.R. Pericchi, S. Sisson, A fully probabilistic approach to extreme rainfall modeling. J. Hydrol. 273, 35–50 (2002)

    Article  Google Scholar 

  8. D.R. Cox, V.S. Isham, P.J. Northrop, Floods: Some probabilistic and statistical approaches. Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci., 360, 1389–1408 (2002)

    Article  Google Scholar 

  9. D.R. Cox, P.A.W. Lewis, The Statistical Analysis of Time Series Events (Methuen, London, 1966)

    Google Scholar 

  10. A.C. Davison, D.V. Hinkley, Bootstrap Methods and Their Application (Cambridge University Press, Cambridge, 1997)

    Google Scholar 

  11. DFO. Dartmouth Flood Observatory. Technical report, 2004. Data available at: http://floodobservatory.colorado.edu/, last access: 2010

  12. B. Dietzer, Th. Günther, A. Klämt, H. Matthäus, T. Reich, Langzeitverhalten hydrometeorologischer Größ en. Technical report, DWD, 2001. Klimastatusbericht

    Google Scholar 

  13. P. Embrechts, C. Klüppelberg, T. Mikosch, Modelling Extremal Events (Springer, Berlin, 1997)

    Google Scholar 

  14. K. Engeland, H. Hisdal, A. Frigessi, Practical extreme value modelling of hydrological floods and droughts: A case study. Extremes, 7, 5–30 (2004)

    Article  Google Scholar 

  15. Ch. A.T. Ferro, Statistical Methods for Clusters of Extreme Values. PhD thesis, University of Lancaster, Great Britain, 2003

    Google Scholar 

  16. R.A. Fisher, L.H.C. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Cambridge Phil. Soc., 24, 180–190 (1928)

    Article  Google Scholar 

  17. C. Frei, H.C. Davies, J. Gurtz, C. Schär, Climate dynamics and extreme precipitation and flood events in Central Europe. Integr. Assess., 1, 281–299 (2000)

    Article  Google Scholar 

  18. B.V. Gnedenko, Sur la distribution limite du terme maximum d’une série aléatoire. Ann. Math., 44, 423–453 (1943)

    Article  Google Scholar 

  19. IPCC. Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University Press, Cambridge, 2001)

    Google Scholar 

  20. M. Kallache, Trends and Extreme Values of River Discharge Time Series. PhD thesis, University of Bayreuth, Bayreuth, 2007

    Google Scholar 

  21. R.W. Katz, M.B. Parlange, P. Naveau, Statistics of extremes in hydrology. Adv. Water Resourc., 25, 1287–1304 (2002)

    Article  Google Scholar 

  22. KLIWA, Klimaveränderung und Konsequenzen für die Wasserwirtschaft. 2. Symposium. Technical report (Arbeitskreis KLIWA, München, 2004)

    Google Scholar 

  23. Z.W. Kundzewicz, D. Graczyk, I. Przymusinska, T. Maurer, M. Radziejewski, C. Svensson, and M. Szwed, Detection of change in world-wide hydrological time series of maximum annual flow. Technical report, Global Runoff Data Centre (GRCD) 2004

    Google Scholar 

  24. Z.W. Kundzewicz, S.P. Simonovic, Non-structural flood protection and sustainability. Water Int., 27, 3–13 (2002)

    Article  Google Scholar 

  25. C.J. MacLean, Estimation and testing of exponential polynomial rate function within the nonstationary Poisson process. Biometrika, 61(1), 81–85 (1974)

    Article  Google Scholar 

  26. D.R. Maidment, Handbook of Hydrology (McGraw-Hill, New York, 1993)

    Google Scholar 

  27. M. Mudelsee, M. Börngen, G. Tetzlaff, U. Grünewald. Extreme floods in central Europe over the past 500 years: Role of cyclone pathway “Zugstrasse Vb”. J. Geophy. Res., 109, D23101 (2004)

    Article  Google Scholar 

  28. J.A. Nelder, R.W.M. Wedderburn, Generalized linear models. J. R. Stat. Soc. A, 135: 370–384 (1972)

    Article  Google Scholar 

  29. M. Nogaj, P. Yiou, S. Parey, F. Malek, P. Naveau, Amplitude and frequency of temperature extremes over the North Atlantic region. Geophy. Res. Lett., 33, L10801, (2006)

    Article  Google Scholar 

  30. S. Pakosch, Statistische Methoden zur stationären und instationären Auswertung von gemessenen Maximalabflüssen mit Hilfe theoretischer Verteilungsfunktionen. Master’s thesis, Universität Stuttgart, 2004

    Google Scholar 

  31. C. Pfister, R. Brázdil, R. Glaser, M. Barriendos, D. Camuffo, M. Deutsch, P. Dobrovolný, S. Enzi, E. Guidoboni, O. Kotyza, S. Militzer, L. Raczii, F.S. Rodrigo. Documentary evidence on climate in sixteenth-century Europe. Clim. Change, 43, 55–110 (1999)

    Article  Google Scholar 

  32. L. Pfister, J. Kwadijk, A. Musy, A. Bronstert, and L. Hoffmann. Climate change, land use change and runoff prediction in the Rhine-Meuse basins. River Res. Appl., 20, 229–241 (2004)

    Article  Google Scholar 

  33. A.J. Robson, Evidence for trends in UK flooding. Philos. Trans. R. Soc. A, 360, 1327–1343 (2002)

    Article  Google Scholar 

  34. H.W. Rust, Detection of Long-Range Dependence – Applications in Climatology and Hydrology. PhD thesis, Potsdam University, Potsdam, 2007

    Google Scholar 

  35. D. Schröter, M. Zebisch, T Grothmann, Climate change in Germany – vulnerability and adaptation of climate-sensitive sectors. Technical report, DWD, 2005. Klimastatusbericht.

    Google Scholar 

  36. R.L. Smith, Maximum likelihood estimation in a class of non-regular cases. Biometrika, 72, 67–90 (1985)

    Article  Google Scholar 

  37. T.M.L. Wigley, Climatology: Impact of extreme events. Nature, 316, 106–107 (1985)

    Google Scholar 

  38. X. Zhang, F.W. Zwiers, G. Li, Monte Carlo experiments on the detection of trends in extreme values. J. Clim., 17(10), 1945–1952 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The study presented was partly carried out within the framework of the project Skalenanalyse.We thank the German Federal Ministry of Science for financial support (under grant no. 0330271) and the Bavarian Environmental Protection Agency for discharge data.

Author information

Authors and Affiliations

  1. Climpact, 75009, Paris, France

    Malaak Kallache

  2. Laboratoire des Sciences du Climat et de l’Environnement, 91191, Gif-sur-Yvette, France

    Henning W. Rust

  3. Norsk institutt for skog og landskap, 1431, Ås, Norway

    Holger Lange

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

    Jürgen P. Kropp

Authors
  1. Malaak Kallache
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  2. Henning W. Rust
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  3. Holger Lange
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  4. Jürgen P. Kropp
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Corresponding author

Correspondence to Malaak Kallache .

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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

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Kallache, M., Rust, H.W., Lange, H., Kropp, J.P. (2011). Extreme Value Analysis Considering Trends: Application to Discharge Data of the Danube River Basin. In: Kropp, J., Schellnhuber, HJ. (eds) In Extremis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14863-7_8

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