Groupe d’études et de recherche en analyse des décisions

Modeling non-stationary extremes: The case of heat waves

Debbie J. Dupuis Professeure titulaire, Département de sciences de la décision, HEC Montréal, Canada

Environmental processes are often non-stationary since climate patterns cause systematic seasonal effects and long-term climate changes cause trends. The usual limit models are not applicable for non-stationary processes, but models from standard extreme value theory can be used along with statistical modeling to provide useful inference. Traditional approaches include letting model parameters be a function of covariates or using time-varying thresholds. These approaches are inadequate for the study of heat waves however and we show how a recent pre-processing approach by Eastoe and Tawn (2009) can be used in conjunction with an innovative change-point analysis to model daily maximum temperature. The model is then fitted to data from four U.S. cities and used to estimate the recurrence probabilities of runs over seasonally high temperatures. We show that the probability of long and intense heat waves has increased considerably over 50 years.