Extreme Value Theory

Extreme Value Theory is the branch of statistics that is used to model extreme events. The topic is of interest to meteorologists because much of the recent literature on climate change has focussed on the possibility that extreme events (very high or low temperatures, high precipitation events, droughts, hurricanes etc.) may be changing in parallel with global warming. As a specific example, the paper by Stott, Stone and Allen (2004) used the generalized Pareto distribution (see Section 2) to estimate the probability of the European heatwave event of 2003 under two conditions, (a) based on climate model data without an anthropogenic signal, (b) including anthropogenic effects (greenhouse gases etc.). They estimated a probability of about 1/1000 under (a) but about 1/250 under (b). Although even the probability under (b) is low, the increase in probability compared with (a) led them to conclude that the fraction of attributable risk due to the anthropogenic influence is about 75%. Another example of the use of statistics to examine trends in probabilities of extreme events is the recent paper by Elsner et al. (2008), which is highly relevant to the question of whether there is an increasing trend in severe hurricanes that may possibly be associated with anthropogenic global warming.