trends in the occurrence of extreme events: an example from the north sea manfred mudelsee...
TRANSCRIPT
![Page 1: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/1.jpg)
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
![Page 2: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/2.jpg)
2
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
![Page 3: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/3.jpg)
3
Background—Background—StatisticalStatistical
• Risk = adverse probability
• Occurrence rate = probability per year
• Occurrence rate may be time-dependent
• Statistical model: inhomogeneous Poisson process
![Page 4: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/4.jpg)
4
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
![Page 5: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/5.jpg)
5
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
![Page 6: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/6.jpg)
6
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 !?
![Page 7: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/7.jpg)
7
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
![Page 8: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/8.jpg)
8
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)
![Page 9: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/9.jpg)
9
1500 2000
Elbe, winter floods
Occurrence Rate Estimation (2)Occurrence Rate Estimation (2)
![Page 10: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/10.jpg)
10
1500 2000
Elbe, winter floods
![Page 11: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/11.jpg)
11
Elbe, winter floods1500 2000
0
5
10
15
4 12 2 6 3
![Page 12: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/12.jpg)
12
Elbe, winter floods1500 2000
0
5
10
15
4 12 2 6 3
Steps toward a better method
![Page 13: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/13.jpg)
13
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
![Page 14: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/14.jpg)
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
![Page 15: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/15.jpg)
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
![Page 16: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/16.jpg)
16
Elbe, winter floods1500 2000
00.10.20.30.4
occu
rren
ce r
ate
(yr-1
)
![Page 17: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/17.jpg)
17
Elbe, winter floods1500 2000
00.10.20.30.4
occu
rren
ce r
ate
(yr-1
)
OK, how significant is that trend ??
![Page 18: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/18.jpg)
18
Elbe, winter floods1500 2000
00.10.20.30.4
occu
rren
ce r
ate
(yr-1
)
![Page 19: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/19.jpg)
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)
![Page 20: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/20.jpg)
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)
![Page 21: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/21.jpg)
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
![Page 22: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/22.jpg)
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
![Page 23: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/23.jpg)
23
Elbe, winter floods1500 2000
00.10 .20 .30 .4
occu
rre
nce
rate
(yr
-1)
90% percentile confidence band
![Page 24: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/24.jpg)
24
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]
![Page 25: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/25.jpg)
25
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.
![Page 26: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/26.jpg)
26
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
![Page 27: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/27.jpg)
27
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
![Page 28: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/28.jpg)
28
WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)
![Page 29: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/29.jpg)
29
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.
![Page 30: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/30.jpg)
30
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]
![Page 31: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/31.jpg)
31
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]
![Page 32: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/32.jpg)
32
WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)
![Page 33: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/33.jpg)
33
WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)
![Page 34: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/34.jpg)
34
WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)
1500 1600 1700 1800 1900 2000Year
![Page 35: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/35.jpg)
35
Demonstration (XTREND):Demonstration (XTREND):WWindstorms in North Sea (RPI)indstorms in North Sea (RPI)
1500 1600 1700 1800 1900 2000Year
![Page 36: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/36.jpg)
36
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%
![Page 37: Trends in the Occurrence of Extreme Events: An Example From the North Sea Manfred Mudelsee Department of Earth Sciences Boston University, USA](https://reader036.vdocuments.site/reader036/viewer/2022062511/5513c5285503463a298b4b76/html5/thumbnails/37.jpg)
37
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