Runs of extremes of observables on dynamical systems and applications

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 Frechet (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. We illustrate that these results can be used to more accurately estimate returns of successive extreme events in climate, such as those characterizing heat -waves or flooding, compared to current statistical methods.