Modelling Climate Changes with Stationary Models. Is It Possible or Is It a Paradox?

Climate is changing; many studies of time series confirm this sentence, but this does not imply that the past is no more representative of the future, and then that “stationarity is dead”. In fact, “stationarity” and “change” are not mutually exclusive. As examples: (1) according to Newton’s first law, without an external force, the position of a body in motion changes in time but the velocity is unchanged; (2) according to Newton’s second law, a constant force implies a constant acceleration and a changing velocity. Consequently, “non-stationarity” is not synonymous with change; change is a general notion applicable everywhere, including the real (material) world, while stationarity and non-stationarity only regard the adopted models. Thus, stationary models can be also adopted for environmental changes. With this aim, in this work Authors show some numerical experiments concerning rainfall processes. In detail, a Neymann Scott Rectangular Pulse model (NRSP), with some changing temporal scenarios for its parameters, is adopted, and the derived Annual Maximum Rainfall (AMR) time series are investigated for several temporal resolutions (sub-hourly and hourly scales). The goal is to analyze if there are some particular scales in which the assumed temporal changes in parameters could be “hidden” when AMR series (which are nowadays more available and longer than high-resolution continuous time series for many sites in the world) are studied, and then stationary models for Extreme Value distributions could be adopted. The results confirm what is obtained from analysis of AMR series in some parts of Italy, for which it is not essential to remove the hypothesis of stationary parameters: significant trends could not appear only from the observed AMR data, as a relevant rate of outlier events also occurred in the central part of the last century.