Runs of Extremes of Observables on Dynamical Systems and Applications

Abstract

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed) or Weibull (bounded) distribution. The motivation for this work was to give estimates of the probabilities of sustained periods of weather anomalies such as heat-waves, cold spells or prolonged periods of rainfall in climate models. Our predictions are borne out by numerical simulations and also analysis of rainfall and temperature data.