"Extremes"
Extremes
Francis Zwiers
Climate Research Division, Environment Canada.

Outline
Space and time scales
Simple indices
Annual maxima
Multiple maxima per year
Incorporating spatial information
One-off events

"Very wide range of space..."
Very wide range of space and time scales
Language used in climate circles not very precise
High impact (but not really extreme)
Exceedence of a relatively low threshold (e.g., 90th percentile of daily precipitation amounts)
Rare events (long return period)
Unprecedented events (in the available record)
Range from very small scale (tornadoes) to large scale (eg drought)

Slide 4
Simple indices
Time series of annual counts or exceedences
E.g., number of exceedence above 90th percentile
Some studies use thresholds as high as 99.7th percentile
Coupled with simple trend analysis techniques or standard detection and attribution methods
Detected anthropogenic influence in observed surface temperature indices
Perfect and imperfect model studies of potential to detect anthropogenic influence in temperature and precipitation extremes
Statistical issues include
ÒresolutionÓ of observational data
adaptation of threshold to base period
use of simple analysis techniques that implicitly assume data are Gaussian

Indices approach is attractive for practical reasons - basis for ETCCDI strategy
Regional workshops – 2002-2005
Slide 8
Some simple indices not so simple É
Annual extremes
Tmax, Tmin, P24-hour, etc
Analyzed by fitting an extreme value distribution
Typically use the GEV distribution
Fitted by MLE or L-moments
Analyses sometimes É
impose a ÒfeasibilityÓ constraint
include covariates
incorporate some spatial information
Often used to
compare models and observations
compare present with future

Annual extremes
Detection and attribution is an emerging application
include expected responses to external forcing as covariates
one approach is via Bayes Factors
Main Assumptions
Observed process is weakly stationary
Annual sample large enough to justify use of EV distribution
Some challenges
Data coverage
Scaling issue
How best to use spatial information
What to compare model output against
Are data being used efficiently?

Observational data rather messy
Uneven availability in space and time
Weak spatial dependence
Spatial averages over grid boxes may not be good estimates of Ògrid boxÓ quantities simulated by climate models

Slide 13
20-yr 24-hr PCP extremes – current climate
Projected waiting time for current climate 20-yr
24-hr PCP event
Slide 16
Multiple extremes per year
Considering only annual extreme is probably not the best use of the available data resource
r-largest techniques (r > 1)
peaks-over-threshold approach (model exceedence process and exceedences)
Some potential issues include
ÒclusteringÓ
Cyclostationary rather than stationary nature of many observed series
Has implications for both exceedence process and representation of exceedences

Using spatial information
Practice varies from
crude (e.g., simple averaging of GEV parameters over adjacent points)
to more sophisticated (e.g., Kriging of parameters or estimated quantiles)
Fully generalized model would require simplifying assumptions about spatial dependence structure
Precipitation has rather complex spatial structure because it is conditioned by surface topography, atmospheric circulation, strength of moisture sources, etc.

Isolated, very extreme events
How to deal with ÒoutliersÓ?
Annual max daily pcp amount that is much larger than others, and occurs in 1885
Recently observed value that lies well beyond range of previously observed values
Both would heavily leverage extreme-value distributions (raising questions about the suitability of the statistical model)
Recent events also beg the question – was this due to human interference in the climate system?

Surface temperature extremes
Slide 21
Summary
Several methods available
Annual (or seasonal extremes), r-largest, POT, simple indices
EV distributions can be fitted by moments, l-moments, mle
Latter also allows inclusion of covariates (e.g., time)
Should evaluate
Feasibility
Stationarity assumption
Goodness-of-fit, etc
Data limitations
quality, availability, continuity, etc
suitability for climate model assessment
R-largest and POT methods use data more efficiently
Do need to be more careful about assumptions
Data may not be readily available for widespread use
Formal climate change detection studies on extremes beginning to appear despite challenges É
Also attempting to estimate FAR (Fraction of Attributable Risk) in the case of Òone-ofÓ events
How does one pose the question and avoid selection bias?

The End