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

Trends in the Occurrence of Trends in the Occurrence of Extreme Events:Extreme Events:

An Example From the North SeaAn Example From the North Sea

Manfred Mudelsee

Department of Earth Sciences

Boston University, USA

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ResultsResults

• 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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Background—Background—StatisticalStatistical

• Risk = adverse probability

• Occurrence rate = probability per year

• Occurrence rate may be time-dependent

• Statistical model: inhomogeneous Poisson process

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Background—ClimatologicalBackground—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

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Relevance to (re)insurers (1)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

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Relevance to (re)insurers (2)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 TalkThe 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)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+]0 [TS; TE]) = · (t)

- occurrence rate or intensity (t) (unit:1/yr)

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1500 2000

Elbe, winter floods

Occurrence Rate Estimation (2)Occurrence Rate Estimation (2)

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1500 2000

Elbe, winter floods

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Elbe, winter floods1500 2000

0

5

10

15

4 12 2 6 3

12

Elbe, winter floods1500 2000

0

5

10

15

4 12 2 6 3

Steps toward a better method

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Elbe, winter floods1500 2000

0

5

10

15

4 12 2 6 3

Steps toward a better method Advantage

1. continuous shifting more estimation points (kernel estimation) no ambiguity

14

Elbe, winter floods1500 2000

0

5

10

15

4 12 2 6 3

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 floods1500 2000

0

5

10

15

4 12 2 6 3

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

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Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

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Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

OK, how significant is that trend ??

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Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

19

Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

1500 2000

bootstrap resample (with replacement, same size)

20

Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

1500 2000

bootstrap resample (with replacement, same size)

21

Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

1500 2000

bootstrap resample (with replacement, same size)

1500 2000

2nd bootstrap resample

22

Elbe, winter floods1500 2000

00.10.20.30.4

occu

rren

ce r

ate

(yr-1

)

1500 2000

bootstrap resample (with replacement, same size)

1500 2000

2nd bootstrap resample

take 2000 bootstrap resamples

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Elbe, winter floods1500 2000

00.10 .20 .30 .4

occu

rre

nce

rate

(yr

-1)

90% percentile confidence band

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Elbe, winter floods1500 2000

00.10 .20 .30 .4

occu

rre

nce

rate

(yr

-1)

90% percentile confidence band

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]

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Testing for TrendTesting for Trend

• Null hypothesis H0: “(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.

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Winter Floods in ElbeWinter Floods in Elbe

1000 1200 1400 1600 1800 2000Year

0 .00 .10 .20 .30 .4

Occ

urre

nce

rate

(yr

-1)

123

Mag

nitu

de

Mudelsee et al. (2003) Nature 425: 166–169.

test

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WWindstorms in North Sea (RPI)indstorms 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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WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

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WWindstorms in North Sea (RPI)indstorms 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.

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WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

10–12 December 1792Area: 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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WWindstorms in North Sea (RPI)indstorms 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]

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WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

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WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

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WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

1500 1600 1700 1800 1900 2000Year

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Demonstration (XTREND):Demonstration (XTREND):WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

1500 1600 1700 1800 1900 2000Year

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Demonstration (XTREND): Demonstration (XTREND): WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

• All regions, 1500–1990, both magnitudes

1500 1600 1700 1800 1900 2000Year

0

0.2

0.4

0.6

0.8

1 Occurrencerate (1/yr)

90%

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Next Steps: Next Steps: WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)

• Inter-check (Lamb vs. Weikinn)• Homogeneity problem: document loss• Extension 1990–2003 using measurements• Differentiation: region, magnitude