Statistical Analyses of Extremes from a Regional Climate Model Chris Ferro Climate Analysis Group Department of Meteorology University of Reading Royal.

Statistical Analyses of Extremes from a Regional Climate Model

Chris Ferro

Climate Analysis Group

Department of Meteorology

University of Reading

Royal Meteorological Society, London, 21 January 2004

Overview

• Regional climate-change experiment

• Application of extreme-value theory

• Daily maximum temperature extremes– Seasonality– Clustering– Apparent temperature

• Concluding remarks

Regional Modelling Experiment

• PRUDENCE• 10 high-res. RCMs

nested in global GCM• 30-year control

simulation, 1961-1990• 30-year A2 scenario

simulation, 2071-2100

Extreme-value Theory

Aim quantify extremal behaviour

Problems limited data, extrapolation

Solution exploit statistical regularities

Example

ondistributi GEV),,max(

ondistributi Normal

1

1

n

n

XX

XX

Seasonality: London grid box

Seasonality: statistical model

Estimate threshold: quantile regression

Excess distribution: generalised Pareto

Estimate parameters: maximum likelihood

Davison and Smith (1990) J. Royal Statistical Soc. B, 52, 393–442

Seasonality: London estimates

Scale (ese)1.27 (0.1)1.44 (0.2)

Shape (ese)-0.11 (0.04)-0.01 (0.07)

/1/1

ExcessPr

x

x

Seasonality: London estimates

Scale (ese)1.27 (0.1)1.44 (0.2)

Shape (ese)-0.11 (0.04)-0.01 (0.07)

/1/1

ExcessPr

x

x

Times of annual maxima: Europe

day of year

Control Scenario – Control

days

Clustering: London grid box

Clustering: London results

Mean cluster size (days)

90% confidence interval (days)

Control 3.2 (2.4, 3.9)

Scenario 4.0 (3.3, 4.7)

Ferro and Segers (2003) J. Royal Statistical Soc. B, 65, 545–556

Mean Cluster Size: EuropeControl Scenario / Control

days

Apparent Temperature: London

1984) (Steadman,e2.2T92.03.1Tapp

Apparent Temperature: model

Univariate distributions: GEV model for tails

Dependence structure: nonparametric estimate

cAXcAX PrPr

de Haan and Sinha (1999) The Annals of Statistics, 27, 732–759

Steadman (1984) J. Climate Applied Met., 23, 1674–1687

year) ain C35(TPrp Estimate app (scenario) 0.70(control), 0p̂:Empirical

Apparent Temperature: results

04.0,0017.0p̂ 89.0,50.061.0p̂

Review

• Many applications of extreme-value theory– Individual values (e.g. seasonality)– Clusters (e.g. warm spells)– Combinations (e.g. temp. and humidity)

• Preliminary Tmax analysis (London)– Shifted annual cycle– Longer warm spells– Greater heat stress

Further Information

PRUDENCE

Climate Analysis

Group

E-mail address

prudence.dmi.dk

www.met.rdg.ac.uk/cag /extremes

[email protected]