1. Manfred Mudelsee Department of Earth Sciences Boston University, USA
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:
Event
Deaths
Damages ($)
Oder flood 1997
114
4.4 billion
Elbe flood 2002 36
13.2 billion
Windstorms
>430
30 billion

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 estimate kernel

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 estimate kernel
3. cross-validated minimal estimation bandwidth error

16. Elbe, winter floods

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

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 “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