1. 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

2. Overview Regional climate-change experiment Application of extreme-value theory Daily maximum temperature extremes –SeasonalitySeasonality –ClusteringClustering –Apparent temperatureApparent temperature Concluding remarks

3. 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

4. Extreme-value Theory Aimquantify extremal behaviour Problemslimited data, extrapolation Solutionexploit statistical regularities Example

5. Seasonality: London grid box

6. 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

7. Seasonality: London estimates Scale (ese) 1.27 (0.1) 1.44 (0.2) Shape (ese) -0.11 (0.04) -0.01 (0.07)

8. Seasonality: London estimates Scale (ese) 1.27 (0.1) 1.44 (0.2) Shape (ese) -0.11 (0.04) -0.01 (0.07)

9. Times of annual maxima: Europe day of year ControlScenario – Control days

10. Clustering: London grid box

11. 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

12. Mean Cluster Size: Europe ControlScenario / Control days

13. Apparent Temperature: London

14. Apparent Temperature: model Univariate distributions: GEV model for tails Dependence structure: nonparametric estimate de Haan and Sinha (1999) The Annals of Statistics, 27, 732–759 Steadman (1984) J. Climate Applied Met., 23, 1674–1687

15. Apparent Temperature: results

16. 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

17. Further Information PRUDENCE Climate Analysis Group E-mail address prudence.dmi.dk www.met.rdg.ac.uk/cag  /extremes c.a.t.ferro@reading.ac.uk