Statistical modeling of hot spells and heat waves

Heat waves are an extreme meteorological event with substantial societal impact. Consequently, there is much concern about possible changes in their frequency, duration, and intensity as part of global climate change. Yet the statistical theory of extreme values has only rarely been applied to such events, especially not in the context of climate change.

The point process approach is readily applicable to extreme high temperature events which have been de-clustered to eliminate temporal dependence (i.e., modeling only cluster maxima). In such a framework, the incorporation of trends is straightforward. We extend this approach to hot spells (i.e., clusters of high temperatures) through explicit modeling of the temporal dependence of excesses within a cluster. To simplify matters, we fit the point process model to the first excesses of the clusters, not the cluster maxima. A geometric distribution is assumed for the cluster length. Conditional on this length, the individual excesses are modeled as conditional generalized Pareto (GP) distributions, with the scale parameter depending on the previous excess. This model has the advantage of only requiring univariate extreme value theory, being implemented using existing software for fitting the GP distribution with covariates. One alternative, with a firmer theoretical basis but more complex to apply, would be to make use of bivariate extreme value theory and model the temporal dependence of excesses within a cluster as a Markov process.

The proposed statistical model for hot spells is fitted to summer time series of daily maximum temperature at three locations, Phoenix, AZ, Fort Collins, CO, and Paris, France. Possible trends in each component (i.e., frequency, duration, and intensity) of the statistical model for hot spells are considered. To convert the model for hot spells into the corresponding statistical properties of more realistic heat waves (e.g., combining clusters that are close together, using a higher threshold), a "heat wave simulator" is developed.