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

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Trends in the Occurrence of Extreme EventsAn
Example From the North Sea

• Manfred Mudelsee
• Department of Earth Sciences
• Boston University, USA

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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

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BackgroundStatistical

• Risk adverse probability
• Occurrence rate probability per year
• Occurrence rate may be time-dependent
• Statistical model inhomogeneous Poisson process

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BackgroundClimatological

• 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

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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 gt430 30 billion
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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 !?

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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

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Occurrence Rate Estimation (1)

• Dates of extreme eventsT1, T2,,TN
• Observation interval TS TE
• Inhomogeneous Poisson process
• independent events
• no simultaneous events
• Prob(event in t tdd?0 ? TS TE) d l(t)
• occurrence rate or intensity l(t) (unit1/yr)

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Occurrence Rate Estimation (2)
Elbe, winter floods
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Elbe, winter floods
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Elbe, winter floods
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Elbe, winter floods
Steps toward a better method
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Elbe, winter floods
Steps toward a better method
Advantage 1. continuous shifting more estimation
points (kernel estimation) no ambiguity
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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
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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
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Elbe, winter floods
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OK, how significant is that trend ??
Elbe, winter floods
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Elbe, winter floods
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Elbe, winter floods
bootstrap resample (with replacement, same size)
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Elbe, winter floods
bootstrap resample (with replacement, same size)
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Elbe, winter floods
bootstrap resample (with replacement, same size)
2nd bootstrap resample
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Elbe, winter floods
bootstrap resample (with replacement, same size)
2nd bootstrap resample
take 2000 bootstrap resamples
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90 percentile confidence band
Elbe, winter floods
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90 percentile confidence band
Elbe, winter floods
Method Cowling et al. (1996) Journal of the
American Statistical Association 91
15161524. Mudelsee M (2002) Sci. Rep. Inst.
Meteorol. Univ. Leipzig 26 149195. available
online
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Testing for Trend

• Null hypothesis H0 l(t) is constant
• Test statistic u ?i Ti /N-(TSTE)/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.

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Winter Floods in Elbe
test
Mudelsee et al. (2003) Nature 425 166169.
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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

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Windstorms in North Sea (RPI)
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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 (19582002) Quellentexte zur
  Witterungsgeschichte Europas von der Zeitwende
  bis zum Jahre 1850 Hydrographie. Vols. 14,
  Akademie-Verlag, Berlin, Vols. 56, Gebrüder
  Borntraeger, Berlin.

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Windstorms in North Sea (RPI)
1012 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
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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 19582002
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Windstorms in North Sea (RPI)
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Windstorms in North Sea (RPI)
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Windstorms in North Sea (RPI)
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Demonstration (XTREND)Windstorms in North Sea
(RPI)
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Demonstration (XTREND) Windstorms in North Sea
(RPI)

• All regions, 15001990, both magnitudes

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Next Steps Windstorms in North Sea (RPI)

• Inter-check (Lamb vs. Weikinn)
• Homogeneity problem document loss
• Extension 19902003 using measurements
• Differentiation region, magnitude