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
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
Background—Statistical Risk = adverse probability Occurrence rate = probability per year Occurrence rate may be time-dependent Statistical model: inhomogeneous Poisson process
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
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 1990-2001 >430 30 billion
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 !?
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
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]d0 [TS; TE]) = d · l(t) occurrence rate or intensity l(t) (unit:1/yr)
Occurrence Rate Estimation (2) Elbe, winter floods
Elbe, winter floods
Elbe, winter floods
Elbe, winter floods Steps toward a better method
Elbe, winter floods Steps toward a better method Advantage 1. continuous shifting more estimation points (kernel estimation) no ambiguity
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
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
Elbe, winter floods
OK, how significant is that trend ?? Elbe, winter floods OK, how significant is that trend ??
Elbe, winter floods
Elbe, winter floods bootstrap resample (with replacement, same size)
Elbe, winter floods bootstrap resample (with replacement, same size)
Elbe, winter floods bootstrap resample (with replacement, same size) 2nd bootstrap resample
Elbe, winter floods bootstrap resample (with replacement, same size) 2nd bootstrap resample take 2000 bootstrap resamples
90% percentile confidence band Elbe, winter floods
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]
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.
Winter Floods in Elbe test Mudelsee et al. (2003) Nature 425: 166–169.
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
Windstorms in North Sea (RPI)
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.
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]
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]
Windstorms in North Sea (RPI)
Windstorms in North Sea (RPI)
Windstorms in North Sea (RPI)
Demonstration (XTREND): Windstorms in North Sea (RPI)
Demonstration (XTREND): Windstorms in North Sea (RPI) All regions, 1500–1990, both magnitudes
Next Steps: Windstorms in North Sea (RPI) Inter-check (Lamb vs. Weikinn) Homogeneity problem: document loss Extension 1990–2003 using measurements Differentiation: region, magnitude