| "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 |