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Climate Risk and Climate Change. Manfred Mudelsee Climate Risk Analysis, Hannover, Germany Alfred Wegener Institute, Bremerhaven, Germany. Potsdam, September 2010 Millennium Flood, July 1342 (Stadtarchiv Nürnberg). Climate.

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slide1

Climate Risk

and

Climate Change

Manfred Mudelsee

Climate Risk Analysis, Hannover, Germany

Alfred Wegener Institute, Bremerhaven, Germany

Potsdam, September 2010 Millennium Flood, July 1342 (Stadtarchiv Nürnberg)

slide2

Climate

Solomon et al. (Eds.) (2007) Climate Change 2007: The Physical Science Basis. Cambridge Univ. Press

slide3

Climate

Dresden, river Elbe

 long-term

 mean and variability

Brückner (1890) Geographische Abhandlungen 4:153

Hann (1901) Lehrbuch der Meteorologie, Tauchnitz

Köppen (1923) Die Klimate der Erde: Grundriss der Klimakunde, de Gruyter

Global Runoff Data Centre, Koblenz

slide4

Climate Risk

Dresden, river Elbe

 mean and variability risk

and extremes

Gardenier & Gardenier (1988) In: Encyclopedia of statistical sciences 8:141, Wiley

Mudelsee (2006) DKKV/ARL Workshop

slide5

Climate Change

Dresden, river Elbe

 climate risk change?

Solomon et al. (Eds.) (2007) Climate Change 2007: The Physical Science Basis. Cambridge Univ. Press

slide6

Estimation

Climate Risk Estimation

 risk changes

Climate Risk Test

Examples

slide7

Estimation

{t(i), x(i)} sample (time series)

n sample size

q parameter

q estimator

CIq,12 = [ql; qu] confidence interval

12 confidence level

seq standard error

E[q ],biasq expectation, bias

n

i=1

^

^

^

^

^

^

^

slide8

Estimation

PDF

“Estimates without error bars are useless.”

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide9

Estimation

Simple problem

 derive CI analytically

(e.g., mean estimation, t distribution of q)

Advanced problem

 resample data: bootstrap,

Bayesian

^

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide10

Estimation: Bootstrap

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide11

Estimation: Bootstrap

resample data  shape

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide12

Estimation: Bootstrap

resample data  shape

resample data blocks  shape, persistence

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide13

Climate Risk Estimation I

Data type Parametric model

 Block maxima  Generalized Extreme

Value distribution (GEV)

 Peaks over  Generalized Pareto

threshold (POT) distribution (GP)

p tail probability, risk

1/p return period (time units)

xp return level

u threshold

slide14

Climate Risk Estimation I

GEV distribution

GEV distribution, time-dependent

Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide15

Climate Risk Estimation I

GEV distribution

GEV distribution, time-dependent

“Recent achievements ...”

 use of covariates

 multivariate: difficult

Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide16

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

slide17

Climate Risk Estimation II

nonparametric:

kernel estimation

l occurrence rate, risk per time unit (Poisson process) h bandwidth

T time K kernel function

Tout extreme event date m number of extremes

Elbe, winter, class 2–3

m = 64, h = 35 yr

Diggle (1985) Applied Statistics 34:138

slide18

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

Bootstrap resample

(with replacement, same size)

slide19

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

Bootstrap resample

(with replacement, same size)

slide20

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

Bootstrap resample

(with replacement, same size)

2nd

Bootstrap resample

slide21

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

Bootstrap resample

(with replacement, same size)

2nd

Bootstrap resample

10 000

Bootstrap resamples

slide22

Climate Risk Estimation II

Elbe, winter, class 2–3

m = 64, h = 35 yr

Bootstrap resample

(with replacement, same size)

2nd

Bootstrap resample

10 000

Bootstrap resamples

slide23

Climate Risk Estimation II

90% confidence band

Elbe, winter, class 2–3

m = 64, h = 35 yr

Cowling et al. (1996) Journal of the American Statistical Association 91:1516

slide24

Climate Risk Estimation II

more maths

 CI construction

 bandwidth selection

 boundary bias correction

90% confidence band

Elbe, winter, class 2–3

m = 64, h = 35 yr

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide25

Climate Risk Estimation II

“Recent achievements ...”

 uncertain timescales (Tout*), paleoclimate

 hybrid model

90% confidence band

Elbe, winter, class 2–3

m = 64, h = 35 yr

Smith (1989) Statistical Science 4:367

slide26

Climate Risk Test: Cox–Lewis

H0: “Constant occurrence rate, l(T).”

H1: “Increasing occurrence rate.”

U test statistic Under H0, statistic U

Tout extreme event date (“POT data”) is standard normally distributed.

m number of extremes

[T(1); T(n)] observation interval

n sample size

Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

slide27

Climate Risk Test: Cox–Lewis

H0: “Constant occurrence rate, l(T).”

H1: “Increasing occurrence rate.”

U test statistic Under H0, statistic U

Tout extreme event date (“POT data”) is standard normally distributed.

m number of extremes

[T(1); T(n)] observation interval

n sample size

Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

slide28

Climate Risk Test: Cox–Lewis

H0: “Constant occurrence rate, l(T).”

H1: “Increasing occurrence rate.”

U test statistic Under H0, statistic U

Tout extreme event date (“POT data”) is standard normally distributed.

m number of extremes

[T(1); T(n)] observation interval

n sample size

Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

slide29

Climate Risk Test: Mann–Kendall

H0: “Constant trend (mean).”

H1: “Increasing trend.”

Kendall (1938) Biometrika 30:81 Mann (1945) Econometrica 13:245

slide30

Climate Risk Test: Mann–Kendall

Zhang et al. (2004) Journal of Climate 17:1945

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide31

Climate Risk Test: Monte Carlo

start

simulation

prescribed prescribed

l(T) PDFs

end

simulation

empirical power = #(H1) / nsim

generate time series

test H0 vs. H1

slide32

Climate Risk Test: Monte Carlo

nsim = 90000 n sample size

significance level = 0.10 mtrue prescribed number of extremes

sepower = 0.001 k scaling parameter l(T) ~ T1/k–1

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide33

Climate Risk Test

“Recent achievements ...”

 use Cox–Lewis, not Mann–Kendall

Zhang et al. (2004) Journal of Climate 17:1945

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide34

Examples

Floods: Elbe, Oder

Mudelsee et al. (2003) Nature 425:166

slide35

Examples

Wildfires,

Canada

Girardin & Mudelsee (2008) Ecological Applications 18:391

Girardin et al. (2009) Global Change Biology 15:2751 Canadian Forest Service

slide36

Examples

Hurricanes,

Boston

Besonen et al. (2008) Geophysical Research Letters 35:L14705

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide37

Examples

Myth “Extremes are by definition rare.”

 Consider a

two-state system

slide38

Climate change  Climate risk change?

1. Estimates: give error bars

2. Tests: use Cox–Lewis,

not Mann–Kendall

3. Future achievements:

 better estimators

 systematic application,

data/models, small scale

• floods

• hurricanes

slide39

Climate change  Climate risk change?

1. Estimates: give error bars

2. Tests: use Cox–Lewis,

not Mann–Kendall

3. Future achievements:

 better estimators

 systematic application,

data/models, small scale

• floods

• hurricanes

Thank you!

slide41

Climate Risk Test: Mann–Kendall

Appendix

H0: “Constant trend (mean).”

H1: “Increasing trend.”

x(3) x(1)

x(2) x(2)

x(4) x(3)

x(1) x(4)

U test statistic

U’ #(interchanges) Under H0, statistic U

n sample size is normally distributed.

Kendall (1938) Biometrika 30:81 Mann (1945) Econometrica 13:245

slide42

Climate Risk Test: Monte Carlo

Appendix

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide43

Climate Risk Test: Monte Carlo

Appendix

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

slide44

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

slide45

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

slide46

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

slide47

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

slide48

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

slide49

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

slide50

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

slide51

Climate Risk Test: Monte Carlo

Appendix

n sample size

mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise

k scaling parameter for upwards trend, l(T) ~ T1/k–1

Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards

trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

slide52

Examples

Appendix

m

Floods: Werra

Mudelsee et al. (2006) Hydrological Sciences Journal 51:818

slide53

Examples

Appendix

Heatwaves

index variable = intensity x number of days

Kürbis et al. (2009) Theoretical and Applied Climatology 98:187

slide54

Examples

Myth 2 “Extremes changed in magnitude,

not in risk.”

 Consider PDF, threshold u,

risk p

slide55

Internet Links

Book

 http://www.manfredmudelsee.com/book

Climate Risk and Time Series Analysis

 http://www.climate-risk-analysis.com

 http://www.mudelsee.com

Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer