Methods for diagnosing extreme events in gridded data sets

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Methods for diagnosing extreme events in gridded
data sets

• D. J. Steinskog, D. B. Stephenson, C. A. S.
  Coelho and C. A. T. Ferro

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Outline

• Why look at extremes?
• Short about R and RCLIM
• Standard statistical methods used in climate
• Methods for looking at extremes at gridded
  datasets
• Future development

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What is an extreme in meteorology?

• Large meteorological values
• Maximum value (i.e. a local extremum)
• Exceedance above a high threshold
• Record breaker (thresholdmax of past values)
• Rare event
• (e.g. less than 1 in 100 years p0.01)
• Large losses (severe or high-impact)
• (e.g. 200 billion if hurricane hits Miami)
• risk p(hazard) x vulnerability x exposure

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Future changes in extremes?
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R and RCLIM

• R freely and powerful statistical software
• RCLIM Climate analysis requires increasingly
  good statistical analysis tools
• All the analysis in this presentation is done
  using freely available R software on a laptop

http//www.met.reading.ac.uk/cag/rclim/
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Data used in this presentation

• Monthly mean gridded surface temperature
  (HadCRUT2v)
• 5 degree resolution
• January 1870 to December 2005
• Summer months only June July August
• Grid points with gt50 missing values and SH are
  omitted.
• Special focus on the 2003 summer heat wave in
  Europe

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Mean temperature
Central Europe (12.5ºE, 47.5ºN)
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Standard Deviation
Standard Deviation
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Model for tails peaks-over-threshold
For sufficiently large thresholds, the
distribution of values above a sufficiently large
threshold u approximates the Generalized Pareto
Distribution (GPD)
Shape -0.4 upper cutoff Shape 0.0
exponential tail Shape 10 power law tail
Probability density function
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Example Central England Temperature

• n 3082 values
• Min -3.1C
• Max 19.7C
• 90th quantile 15.6C

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GPD fit to values above 15.6C

• Location parameter u15.6C
• Maximum likelihood estimates
• Scale parameter 1.38 /- 0.09C
• Shape parameter -0.30 /- 0.04C
• ? Upper limit estimate

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1870-2005 time series of summer
(June-July-August) monthly mean temperatures for
a grid point in Central Europe (12.5ºE, 47.5ºN)
2003 exceedance
75th quantile (uy,m 16.2ºC)
Excess (Ty,m uy,m)
15.2ºC
Long term trend (Ly,m)
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Time varying threshold
JJA pts trendseasonal terms
Excesses
? Flexible approach that gives exceedances 25 of
months
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Time mean of 75 threshold
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Mean of the excesses
? Large over extra-tropical land regions
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GPD scale parameter estimate
? Large over extra-tropical land regions
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GPD shape parameter estimate
Generally negative ? finite upper temperature
limit
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Upper limit for excesses
? Largest over high-latitude land regions
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Return periods for August 2003 event
? Central Europe return period of 133 years (c.f.
Schar et al 46000 years!)
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The role of large-scale modes
? ENSO effect on temperature extremes in NH
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Teleconnections between extremes
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1-point association map for extreme events
? association with extremes in subtropical
Atlantic
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Future development of RCLIM

• Methods for data with high temporal correlation
  will be introduced (e.g. daily dataset)
• Improve the plotting procedure filled contours
  and projections
• Feedback on methods that should be included is
  wanted!

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Conclusions

• Huge potential of doing extremes on gridded
  datasets
• Simple extremes can be analysed using
  peaks-over-threshold methods
• Extremes do not have a unique definition
• Future work include testing the methods on daily
  datasets and develop new methods for data with
  high autocorrelation

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Reference

• Coelho, C. A. S., C. A. T. Ferro, D. B.
  Stephenson and D. J. Steinskog Exploratory tools
  for the analysis of extreme weather and climate
  events in gridded datasets, Submitted to Journal
  of Climate
• Contact info
• David Stephenson, d.b.stephenson_at_reading.ac.uk

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Thank you for your attention!
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Info about R and RCLIM
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R Short intro

• RCLIM make use of R, a powerful statistical tool.
• R is freely available, and can be used on most
  computer platforms
• It is a huge community working with and on R.
• R can be downloaded from
• www.r-project.org

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RCLIM-initiative

• Main motivation
• Climate analysis requires increasingly good
  statistical analysis tools.
• Aims
• Develop statistical methods and write user
  friendly functions in the R language for
  describing and exploring weather and climate
  extremes in gridded datasets, making efficient
  use of the already existing packages.
• Webpage
• http//www.met.reading.ac.uk/cag/rclim/

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RCLIM-initiative

• The RCLIM initiative will develop functions for
• Reading and writing netcdf gridded datasets
• Exploratory climate analysis in gridded datasets
• Climate analysis of extremes in gridded datasets
• Animating and plotting climate analysis of
  gridded datasets
• Team
• David Stephenson, Caio Coelho, Chris Ferro and
  Dag Johan Steinskog

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RCLIM-initiative

• Part of Workpackage 4.3 Understanding Extreme
  Weather and Climate Events
• Progress
• Spring 2005 Initiative started
• March 2006 Delivery finished and methods made
  public
• Future More methods to be included, especially
  for daily datasets.