Trends in the Occurrence of Extreme Events: An Example From the North Sea

1. Trends in the Occurrence of Extreme Events:An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA

2. Results • Computer program XTREND estimates trends in occurrence rate (risk) • Can be applied to occurrence of extreme climate events (floods, storms, etc.) • Example: major windstorms in North Sea region over past 500 years • Preliminary result, occurrence rate: (1) low at 1800, (2) recent upward trend

3. Background—Statistical • Risk = adverse probability • Occurrence rate = probability per year • Occurrence rate may be time-dependent • Statistical model: inhomogeneous Poisson process

4. Background—Climatological • Climate system is complex (atmosphere, ocean, surface; nonlinear interactions) • Intergovernmental Panel on Climate Change (IPCC) (Houghton et al. 2001): • changed atmosphere (greenhouse gases) • radiative effects • concern: increased risk of extreme climate

5. Relevance to (re)insurers (1) • Losses in Europe caused by extreme climate events:

6. Relevance to (re)insurers (2) • Trends in the occurrence rate of extreme climate events should be estimated and tested before an extreme value analysis. nonstationarity • Extrapolation of trends: risk prediction !?

7. The Rest of This Talk • Method: occurrence rate estimation • Method: testing for trend • Example: winter floods in Elbe • Example: windstorms in North Sea (RPI) • Demonstration (XTREND): estimating/testing occurrences of major windstorms in North Sea

8. Occurrence Rate Estimation (1) • Dates of extreme events:T1, T2,…,TN • Observation interval [TS; TE] • Inhomogeneous Poisson process: • independent events • no simultaneous events • Prob(event in [t; t+d]d0[TS; TE]) = d · l(t) • occurrence rate or intensity l(t) (unit:1/yr)

9. Occurrence Rate Estimation (2) Elbe, winter floods

10. Elbe, winter floods

11. Elbe, winter floods

12. Elbe, winter floods Steps toward a better method

13. Elbe, winter floods Steps toward a better method Advantage 1. continuous shifting more estimation points (kernel estimation) no ambiguity

14. Elbe, winter floods Steps toward a better method Advantage 1. continuous shifting more estimation points (kernel estimation) no ambiguity 2. Gaussian (not uniform) smooth estimatekernel

15. Elbe, winter floods Steps toward a better method Advantage 1. continuous shifting more estimation points (kernel estimation) no ambiguity 2. Gaussian (not uniform) smooth estimatekernel 3. cross-validated minimal estimation bandwidth error

16. Elbe, winter floods

17. OK, how significant is that trend ?? Elbe, winter floods

18. Elbe, winter floods

19. Elbe, winter floods bootstrap resample (with replacement, same size)

20. Elbe, winter floods bootstrap resample (with replacement, same size)

21. Elbe, winter floods bootstrap resample (with replacement, same size) 2nd bootstrap resample

22. Elbe, winter floods bootstrap resample (with replacement, same size) 2nd bootstrap resample take 2000 bootstrap resamples

23. 90% percentile confidence band Elbe, winter floods

24. 90% percentile confidence band Elbe, winter floods Method: Cowling et al. (1996) Journal of the American Statistical Association 91: 1516–1524. Mudelsee M (2002) Sci. Rep. Inst. Meteorol. Univ. Leipzig 26: 149–195. [available online]

25. Testing for Trend • Null hypothesis H0: “l(t) is constant” • Test statistic: u= [∑i Ti /N−(TS+TE)/2] / [(TS−TE)/(12 N)1/2] • Under H0: u ~ N(0; 1) • Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen, London.

26. Winter Floods in Elbe test Mudelsee et al. (2003) Nature 425: 166–169.

27. Windstorms in North Sea (RPI) • Acknowledgments: • RPI • Jens Neubauer, Institute of Meteorology, University of Leipzig, Germany • Frank Rohrbeck, Institute of Meteorology, Free University Berlin, Germany

28. Windstorms in North Sea (RPI)

29. Windstorms in North Sea (RPI) • Long-term perspective (last 500 yr) • Information: historical documents • Lamb H (1991) Historic Storms of the North Sea. Cambridge University Press, Cambridge. • Weikinn C (1958–2002) Quellentexte zur Witterungsgeschichte Europas von der Zeitwende bis zum Jahre 1850: Hydrographie. Vols. 1–4, Akademie-Verlag, Berlin, Vols. 5–6, Gebrüder Borntraeger, Berlin.

30. Windstorms in North Sea (RPI) 10–12 December 1792 Area: Whole North Sea [...] Maximum wind strength: The strongest gusts of the surface wind probably exceeded 100 knots over both these regions [southern North Sea near Dutch and German coast]. Minimal pressure estimate: 945 mbar. [From Lamb 1991]

31. Windstorms in North Sea (RPI) 1792 & 10. Dez. & Gegend von Hamburg & Sturmflut & & 1 & I, 5: 539 (4260) 10. Dez. Der Sturm trieb das Wasser zu Hamburg 20 F 6 Z über die ordin. Ebbe, eine Höhe, wie sie daselbst, soweit die Nachrichten reichen, noch nie gehabt, zu Cuxhafen 20 F 3 Z. Sie richtete in [...] (Fr. Arends 1833 “Physische Geschichte d. Nordsee-Küste etc.” II. S. 305.) [From Weikinn 1958–2002]

32. Windstorms in North Sea (RPI)

33. Windstorms in North Sea (RPI)

34. Windstorms in North Sea (RPI)

35. Demonstration (XTREND):Windstorms in North Sea (RPI)

36. Demonstration (XTREND): Windstorms in North Sea (RPI) • All regions, 1500–1990, both magnitudes

37. Next Steps: Windstorms in North Sea (RPI) • Inter-check (Lamb vs. Weikinn) • Homogeneity problem: document loss • Extension 1990–2003 using measurements • Differentiation: region, magnitude