Climatic Extremes and Rare Events: Statistics and Modelling

1
Climatic Extremes and Rare Events Statistics and
Modelling

• Andreas Hense, Meteorologisches Institut
• Universität Bonn

2
Overview

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

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

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)

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/sourceboo
  k)
• personal perception

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/proje
  cts/mice/html/extremes.html
• NCAR Weather and Climate Impact Assessment
  Science Initiative http//www.esig.ucar.edu/extrem
  evalues/extreme.html
• KNMI Buishand Precipitation and hydrology
• EVIM Matlab package by Faruk Selcuk, Bilkent
  University Ankara, Financial Mathematics

7
Precipitation data for illustration

• Daily sums of precipitation in Europe
• 74 Stations 1903-1994
• A-GCM simulations ECHAM4 - T42
• GISST forced 40-60,0-60E daily sums
• annual mean precipitation ECHAM3 and HadCM2
  ensembles of GHG szenario simulations

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

9
Generalized Pareto Distribution
10
1/q-return value
u 20 mm/day for the observations 10
mm/day for simulations
11
Maximum likelihood estimation
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

13
(No Transcript)
14
(No Transcript)
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

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

17
Uncertainty of annual mean precipitation changes
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