Analysis of Extremes in Climate Science

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• Analysis of Extremes in Climate Science
• Francis Zwiers
• Climate Research Division, Environment Canada.

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Outline

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

Photo F. Zwiers
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Space and time scales

• 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)

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Space
Local
Continental
Regional
Time
Process studies
hours
Many observations per season, many seasons
days
month
Few observations per period (seasons to
interannual)
season
A single observation in the period of
interest (multi-annual and longer) Process
studies
years
Extremes likely to be conditioned by climate
state in all cases
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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
• resolution of observational data
• adaptation of threshold to base period
• use of simple analysis techniques that implicitly
  assume data are Gaussian

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Indices approach is attractive for practical
reasons - basis for ETCCDI strategy
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Regional workshops 2002-2005
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Indices of temperature extremes
JJA warm days
DJF Cold nights
Alexander, Zhang, et al 2005

• Anthropogenic influence detected in indices of
  cold nights, warm nights, and cold days

Christidis, et al 2005
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Some simple indices not so simple
Rate at which 90th percentile is exceeded in
simulated 60-year records (when threshold is
estimated from first 30-years)
Number of days per year in Canada with
temperature above 99th percentile
Zhang, Hegerl, Zwiers, Kenyon, 2005
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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
• impose a feasibility constraint
• include covariates
• incorporate some spatial information
• Often used to
• compare models and observations
• compare present with future

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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?

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Observational data rather messy

• Uneven availability in space and time
• Weak spatial dependence
• Spatial averages over grid boxes may not be good
  estimates of grid box quantities simulated by
  climate models

Trend 5-day max pcp 1950-99 (data Alexander et
al. 2006)
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20-yr 24-hr PCP extremes current climate
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Projected waiting time for current climate 20-yr
24-hr PCP event
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Multiple extremes per year

• Considering only annual extreme is probably not
  the best use of the available data resource
• r-largest techniques (r gt 1)
• peaks-over-threshold approach (model exceedence
  process and exceedences)
• Some potential issues include
• clustering
• Cyclostationary rather than stationary nature of
  many observed series
• Has implications for both exceedence process and
  representation of exceedences

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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.

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Isolated, very extreme events

• How to deal with outliers?
• 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?

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Surface temperature extremes

• Human influence
• Has likely affected temperature extremes
• May have increased the risk of extremely warm
  summer conditions regionally.

FAQ 9.1, Fig. 1
Fig 9.13a
Risk of extreme warm European summer in 1990s
(1.6C gt 1961-90 mean) - natural forcing
only - all forcing
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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
• Also attempting to estimate FAR (Fraction of
  Attributable Risk) in the case of one-of events
  
• How does one pose the question and avoid
  selection bias?

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The End