Analysis of Extremes in Climate Science

Francis ZwiersClimate Research Division, Environment Canada.

Photo: F. Zwiers

• Space and time scales • Simple indices• Annual maxima• Multiple maxima per year• Incorporating spatial

information• One-off events

Outline

Photo: F. Zwiers

• 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 and time scales

Local Continental

hours

Space

Time

days

month

season

years

Regional

Few observations per period (seasons to interannual)

A single observation in the period of interest

(multi-annual and longer)

Process studies

Process studies

Many observationsper season, many

seasons

“Extremes” likely to be conditioned by climate state in all cases

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”

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

Christidis, et al 2005

Alexander, Zhang, et al 2005

DJF Cold nights JJA warm days

Some simple indices not so simple …

Number of days per year in Canada with temperature above 99th percentile

Rate at which 90th percentile is exceeded in simulated 60-year records (when threshold is estimated from first 30-years)

11%

10%

Zhang, Hegerl, Zwiers, Kenyon, 2005

• 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?

Annual extremes

• 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

Observational data rather messy

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

• 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

Multiple extremes per year

• 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.

Using spatial information

• 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?

Isolated, very extreme events

Fig 9.13a

Surface temperature extremes

Human influence:• Has likelylikely affected

temperature extremes• May have increased

the risk of extremely warm summer conditions regionally.

Risk of extreme warm European summer in 1990s (1.6°C > 1961-90 mean):

- natural forcing only - “all” forcing

FAQ 9.1, Fig. 1

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?

The End