1. 19. September 2003 Int.Conference Earth Systems Modelling1 Climatic Extremes and Rare Events: Statistics and Modelling Andreas Hense, Meteorologisches Institut Universität Bonn

2. 19. September 2003 Int.Conference Earth Systems Modelling2 Overview Definition References/Literature/Ongoing work Precipitation data Theory GEV/GPD Comparison between observations and simulation Conclusion

3. 19. September 2003 Int.Conference Earth Systems Modelling3 Definition acc. to IPCC TAR WGI Rare events: occurences of weather or climate states of high/low quantiles of the underlying probability distribution e.g. less than 10% / 1% ; higher then 90% / 99% weather state: temperature, precipitation, wind –timescale O(1day) or less –univariate: one point, one variable –multivariate: field of one variable –multivariate: one point several variables

4. 19. September 2003 Int.Conference Earth Systems Modelling4 Definition acc. to IPCC TAR WGI Climate states: aggregated state variables –time scale O(1m) and larger –heat waves, cold spells –stormy seasons –droughts and floods (2003 and 2002)

5. 19. September 2003 Int.Conference Earth Systems Modelling5 Definition acc. To IPCC TAR WGI Extreme events depend –costs or losses –see Extreme weather sourcebook by Pielke and Klein (http://sciencepolicy.colorado.edu/sourcebook) –personal perception

6. 19. September 2003 Int.Conference Earth Systems Modelling6 References/Literature/Ongoing Work without claiming completeness BAMS: 2000, Vol. 81, p.413 ff MICE Project funded by EU Commission (J. Palutikof, CRU) http://www.cru.uea.ac.uk/cru/projects/mice/html/extremes.html NCAR: Weather and Climate Impact Assessment Science Initiative http://www.esig.ucar.edu/extremevalues/extreme.html KNMI: Buishand Precipitation and hydrology EVIM: Matlab package by Faruk Selcuk, Bilkent University Ankara, Financial Mathematics

7. 19. September 2003 Int.Conference Earth Systems Modelling7 Precipitation data for illustration Daily sums of precipitation in Europe –74 Stations 1903-1994 A-GCM simulations ECHAM4 - T42 –GISST forced 40°-60°,0°-60°E daily sums annual mean precipitation ECHAM3 and HadCM2 ensembles of GHG szenario simulations

8. 19. September 2003 Int.Conference Earth Systems Modelling8 Theory for rare events Frechet,Fisher,Tippet: generalized extreme value (GEV) distribution summarizes Gumbel, Frechet and Weibull,provides information on maximum or minimum only Peak-over-threshold: generalized Pareto distribution GPD Rate of occurence of exceedance: Poisson process last two provide informations about the tail of the distribution of weather or climate state variables

9. 19. September 2003 Int.Conference Earth Systems Modelling9 Generalized Pareto Distribution

10. 19. September 2003 Int.Conference Earth Systems Modelling10 1/q-return value u = 20 mm/day for the observations = 10 mm/day for simulations

11. 19. September 2003 Int.Conference Earth Systems Modelling11 Maximum likelihood estimation

12. 19. September 2003 Int.Conference Earth Systems Modelling12 Comparing observations with simulations Scale difference between point values and GCM grid scale variables two standard approaches –statistical downscaling, MOS: loss of variance through regression –dynamical downscaling using a RCM upscaling of observations –fit e.g. q-return values with low order polynomials in latitude,longitude,height

13. 19. September 2003 Int.Conference Earth Systems Modelling13

14. 19. September 2003 Int.Conference Earth Systems Modelling14

15. 19. September 2003 Int.Conference Earth Systems Modelling15 Comparing observations with simulations ECHAM4-T42 simulates a 20 year return value of daily precipitation similar to the 10 year return values of observations 10 year return values in ECHAM4-T42 are ~ 20% smaller

16. 19. September 2003 Int.Conference Earth Systems Modelling16 Uncertainty Large confidence intervals for estimated parameters (shape, return values) for models reduction through ensemble simulations model error estimation through multimodel analysis necessary for analysis of changes

17. 19. September 2003 Int.Conference Earth Systems Modelling17 Uncertainty of annual mean precipitation changes

18. 19. September 2003 Int.Conference Earth Systems Modelling18 Conclusion Generalized Pareto distribution approach appears fruitful for model as well as observation analysis Systematic differences in the tail distributions of precipitation between model and observations despite upscaling (projection on large scale structures in observations and simulations) result of coarse model scales? requires an analysis of the spatial covariance structure of the observations Ensemble simulations allow for an adjustment Multivariate methods are necessary