19. September 2003 Int.Conference Earth Systems Modelling 1

Climatic Extremes and Rare Events: Statistics and Modelling

Andreas Hense, Meteorologisches Institut

Universität Bonn

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Overview

• Definition• References/Literature/Ongoing work• Precipitation data• Theory GEV/GPD• Comparison between observations and simulation• Conclusion

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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

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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)

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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

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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

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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

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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

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Generalized Pareto Distribution

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1/q-return value

u = 20 mm/day for the observations = 10 mm/day for simulations

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Maximum likelihood estimation

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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

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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

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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

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Uncertainty of annual mean precipitation changes

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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