Transcript No Slide Title

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
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Background—Statistical
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Risk = adverse probability
Occurrence rate = probability per year
Occurrence rate may be time-dependent
Statistical model: inhomogeneous
Poisson process
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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
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Relevance to (re)insurers (1)
• Losses in Europe caused by extreme
climate events:
Event
Deaths
Damages ($)
Oder flood 1997
Elbe flood 2002
Windstorms
1990-2001
114
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>430
4.4 billion
13.2 billion
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
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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 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)
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Occurrence Rate Estimation (2)
1500
2000
Elbe, winter
floods
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1500
2000
Elbe, winter
floods
10
15
10
5
0
4 12 2
1500
6
3
2000
Elbe, winter
floods
11
15
10
5
0
4 12 2
6
3
1500
2000
Elbe, winter
floods
Steps toward a better method
12
15
10
5
0
4 12 2
6
3
1500
Steps toward a better method
1.
continuous shifting
(kernel estimation)
2000
Elbe, winter
floods
Advantage
more estimation points
no ambiguity
13
15
10
5
0
4 12 2
6
3
1500
Steps toward a better method
2000
Elbe, winter
floods
Advantage
1.
continuous shifting
(kernel estimation)
more estimation points
no ambiguity
2.
Gaussian (not uniform)
kernel
smooth estimate
14
15
10
5
0
4 12 2
6
3
1500
Steps toward a better method
2000
Elbe, winter
floods
Advantage
1.
continuous shifting
(kernel estimation)
more estimation points
no ambiguity
2.
Gaussian (not uniform)
kernel
smooth estimate
3.
cross-validated
bandwidth
minimal estimation
error
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
2000
Elbe, winter
floods
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
2000
Elbe, winter
floods
OK, how significant is that trend ??
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
2000
Elbe, winter
floods
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
1500
2000
Elbe, winter
floods
bootstrap resample
(with replacement,
2000
same size)
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
1500
2000
Elbe, winter
floods
bootstrap resample
(with replacement,
2000
same size)
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
1500
1500
2000
Elbe, winter
floods
bootstrap resample
(with replacement,
2000
same size)
2nd
bootstrap resample
2000
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
1500
1500
1500
2000
Elbe, winter
floods
bootstrap resample
(with replacement,
2000
same size)
2nd
bootstrap resample
2000
take 2000 bootstrap
resamples
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
90% percentile
confidence band
1500
2000
Elbe, winter
floods
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occurrence rate (yr-1)
0.4
0.3
0.2
0.1
0
90% percentile
confidence band
1500
2000
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]
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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.
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Winter Floods in Elbe
Occurrence rate (yr -1)
Magnitude
Year
1000
1200
1400
1600
1800
0.4
0.3
0.2
0.1
0.0
3
2
1
2000
test
Mudelsee et al. (2003) Nature 425: 166–169.
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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 (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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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]
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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 1958–2002]
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Windstorms in North Sea (RPI)
Year
Region
Month
1509
1530
1532
1552
1570
1588
1588
1592
2
2+3
2
1,2,3
1+2+3
3
October
November
November
January
November
August
September
November
1
Start
Day
6
14
12
18
11
14
21
2
End
Day
6
15
12
25
12
18
21
2
Magnitude
gale
storm
x
x
x
x
x
x
x
x
x
Wind
direction
NW,W,E
N
N,NW
NW
NW, SW
SW,W
NE,NW,
SW,W ,NW
...
Region 1= Denmark/Norway
Region 2= Germany/Holland
Region 3= Great Britain
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Windstorms in North Sea (RPI)
Wind direction Number of storms (all regions, 1500 to 1990)
N
NW
W
SW
S
SE
E
NE
13
23
39
25
11
4
4
3
Sum
122
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Windstorms in North Sea (RPI)
1500
1600
1700
1800
1900
2000
Year
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Demonstration (XTREND):
Windstorms in North Sea (RPI)
1500
1600
1700
1800
1900
2000
Year
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Demonstration (XTREND):
Windstorms in North Sea (RPI)
• All regions, 1500–1990, both magnitudes
1
0.8
Occurrence
rate (1/yr)
0.6
90%
0.4
0.2
0
1500
1600
1700
1800
1900
2000
Year
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Next Steps:
Windstorms in North Sea (RPI)
• Inter-check (Lamb vs. Weikinn)
• Homogeneity problem: document loss
• Extension 1990–2003 using
measurements
• Differentiation: region, magnitude
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