Analysis of Extremes in Climate Science Francis Zwiers Climate 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., 90 th 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

LocalContinental 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 Many observations per 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 90 th percentile Some studies use thresholds as high as 99.7 th 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 –

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 99 th percentile Rate at which 90 th percentile is exceeded in simulated 60-year records (when threshold is estimated from first 30-years) 11% 10% Zhang, Hegerl, Zwiers, Kenyon, 2005

T max, T min, P 24-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 (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: likelyHas likely 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 > 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?

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