Transcript No Slide Title

Analysis of Extremes in Climate Science
Francis Zwiers
Climate Research Division, Environment Canada.
Photo: F. Zwiers
Outline
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Space and time scales
Simple indices
Annual maxima
Multiple maxima per year
Incorporating spatial
information
• One-off events
Photo: F. Zwiers
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)
Space
Time
hours
days
Local
Regional
Continental
Process
studies
Many observations
per season, many
seasons
month
season
Few observations per period
(seasons to interannual)
A single observation in the period
of interest
(multi-annual and longer)
years
“Extremes” likely to be conditioned
by climate state in all cases
Process studies
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
Indices approach is attractive for practical
reasons - basis for ETCCDI strategy
Regional workshops – 2002-2005
Indices of temperature “extremes”
DJF Cold nights
JJA warm days
Alexander, Zhang, et al 2005
• Anthropogenic influence detected in indices of cold nights, warm
nights, and cold days
Christidis, et al 2005
Some simple indices not so simple …
11%
Rate at which 90th percentile
is exceeded in simulated
60-year records
(when threshold is estimated
from first 30-years)
10%
Number of days per year in
Canada with temperature
above 99th percentile
Zhang, Hegerl, Zwiers, Kenyon, 2005
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
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 “grid
box” quantities simulated by climate models
Trend 5-day max pcp 1950-99 (data: Alexander et al. 2006)
20-yr 24-hr PCP extremes – current climate
Projected waiting
time for current
climate 20-yr
24-hr PCP event
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
– “clustering”
– 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 “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?
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 (1.6°C > 1961-90
mean):
- natural forcing only
- “all” forcing
Summary
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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?
The End