are easily adapted to nonstationary time series by allowing the three GEV parameters to be time varying.

An extension of classical extreme value theory is to use threshold methods. Rather than characterize extreme events solely in terms of the distribution of annual maxima, threshold methods take account of all events beyond a given high threshold, also known as exceedances. A common probability distribution for events beyond a threshold is the Generalized Pareto distribution, which has properties very similar to those of the GEV distribution. In this case, also, one can take account of time dependence by allowing the parameters of the model to vary with time, thus creating a theoretical framework for calculating the probabilities of extreme events in the presence of a changing climate.

Kharin and Zwiers (2000) were possibly the first to use these methods to explore the effect of climate change on extremes. Recent contributions include assessing the role of anthropogenic influence on extremes of temperature (Zwiers et al., 2011) and precipitation (Min et al., 2011). Wehner et al. (2010) used the GEV distribution to compare observational and model-based calculations of precipitation extremes, showing that the agreement is highly dependent on the resolution of the climate model.

For all of these methods, the emphasis in most climate studies has been on relatively long time horizons (e.g., 40 years), but the same statistical models can be used (via simulation) to estimate probabilities over shorter time horizons, such as 10 years.

ATTRIBUTION OF INDIVIDUAL EXTREME EVENTS

As noted elsewhere in this report, our primary focus has not been on the question of attribution, that is, on whether observed climate change is due to anthropogenic factors as opposed to natural forcing or internal variability. Nevertheless, some of the analytic methods developed in that context are relevant to understanding how extreme event probabilities might change over a time span of 10 years or less.

In a paper motivated by the 2003 heat wave in Europe, Stott et al. (2004) calculated summer (June, July, August) annual temperature averages over a large area of western Europe and used climate models both with and without anthropogenic forcing to estimate the probability of an extreme event under either scenario. Their statistical methodology used a conventional detection and attribution approach to decompose the observational time series into components due to anthropogenic forcing, natural forcing, and internal variability, combined with the Generalized Pareto distribution, fitted to events beyond a high threshold, to estimate probabilities of extreme events. More recently, Pall et al. (2011) showed how to extend the methodology to much smaller temporal and spatial scales using large



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