Author(s): Giulio Calvani; Paolo Perona
Linked Author(s): Paolo PERONA
Keywords: Return Period analysis Non-stationarity Peak-Over-Threshold Climate Change Trends
Abstract: Climate change is acknowledged to affect the occurrence of extreme events and the time-series characteristics of hydrological variables. Consequently, the average statistical properties may vary through time and, as such, they are considered to be non-stationary. For non-stationary processes, the classical theory of extreme values analysis based on the Peak-Over-Threshold (POT) method cannot be applied. In this work, we extend the POT method and propose a mathematical framework based on the hypothesis of weak non-stationarity, for which the statistical properties may change slower than the future temporal framework. We apply the hypothesis to the process of rainfall modelled by a Poisson Process with constant average frequency and time-varying mean magnitude, due to the presence of trends in the time-series. A closed-form solution for the maximum value of mean magnitude is derived and graphically discussed for several values of the initial conditions, in terms of mean frequency and return period. The results are readily applicable to various applications, particularly to the design of hydraulic structures based on the return period of over-threshold events.
Year: 2025