Sensitivity of extreme events to climate change: The case of autocorrelated time series

The relative sensitivity of an extreme event is defined as the partial derivative of its probability with respect to the location or scale parameter of the distribution of the variable involved. Of particular interest in climate applications are extreme events of the form, the maximum of a sequence of observations of the variable exceeding a threshold. In this case, the relative sensitivities are directly related to the hazard rate for the distribution of the maximum. By means of simulations, this hazard rate is determined for the maximum of a finite sequence of autocorrelated random variables. For large values, the hazard rate rises more steeply than the asymptotic theory based on the type I extreme value distribution would predict. Unless the degree of autocorrelation is quite high, the hazard rate does not differ much for large values from that for independent time series. The hazard rate for the so-called “penultimate approximation”, based on the type III extreme value distribution, is also compared to the exact hazard rate under dependence. These results imply that the relative sensitivity of extreme events to overall climate change is even greater than the asymptotic theory would predict. Time series of daily maximum temperature, data that possess substantial autocorrelation, are utilized for illustrative purposes.