Statistical modeling of hot spells and heat waves

Although hot spells and heat waves are considered extreme meteorological phenomena, the statistical theory of extreme values has only rarely, if ever, been applied. To address this shortcoming, we extend the point process approach to extreme value analysis to model the frequency, duration, and intensity of hot spells. The annual frequency of hot spells is modeled by a Poisson distribution, their length by a geometric distribution. To account for the temporal dependence of daily maximum temperatures within a hot spell, the excesses over a high threshold are modeled by a conditional generalized Pareto distribution, whose scale parameter depends on the excess on the previous day. Requiring only univariate extreme value theory, our proposed approach is simple enough to be readily generalized to incorporate trends in hot spell characteristics. Through a heat wave simulator, the statistical modeling of hots spells can be extended to apply to more full-fledged heat waves, which are difficult to be modeled directly. Our statistical model for hot spells is fitted to time series of daily maximum temperature during the summer heat wave season at Phoenix, AZ, USA, Fort Collins, CO, USA, and Paris, France. Trends in the frequency, duration, and intensity of hot spells are fitted as well. The heat wave simulator is used to convert any such trends into the corresponding changes in the characteristics of heat waves. By being based at least in part on extreme value theory, our proposed approach is demonstrated to be both more realistic and more flexible than techniques heretofore applied to model hot spells and heat waves.