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Climatic Extremes and Rare Events: Statistics and Modelling

Climatic Extremes and Rare Events: Statistics and Modelling. Andreas Hense, Meteorologisches Institut Universität Bonn. Overview. Definition References/Literature/Ongoing work Precipitation data Theory GEV/GPD Comparison between observations and simulation Conclusion.

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Climatic Extremes and Rare Events: Statistics and Modelling

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

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

  3. 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 Int.Conference Earth Systems Modelling

  4. 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) Int.Conference Earth Systems Modelling

  5. 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 Int.Conference Earth Systems Modelling

  6. References/Literature/Ongoing Workwithout 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 Int.Conference Earth Systems Modelling

  7. 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 Int.Conference Earth Systems Modelling

  8. 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 Int.Conference Earth Systems Modelling

  9. Generalized Pareto Distribution Int.Conference Earth Systems Modelling

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

  11. Maximum likelihood estimation Int.Conference Earth Systems Modelling

  12. 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 Int.Conference Earth Systems Modelling

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  15. 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 Int.Conference Earth Systems Modelling

  16. 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 Int.Conference Earth Systems Modelling

  17. Uncertainty of annual mean precipitation changes Int.Conference Earth Systems Modelling

  18. 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 Int.Conference Earth Systems Modelling

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