"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 |