Non-stationary approach in the spatio-temporal analysis of precipitation time series

An increasing perception of climate change both on a global and local scale, on the one hand confirmed by the increase in average surface temperature of the oceans, and on the other one by the random extreme events occurring in different territories, creates the necessity of developing and use of hydrological tools and models in the framework of non-stationarity. In most official national guidelines for risk assessment the traditional stationary approach to hydrological modelling is still widely recommended. This thesis aims to strengthen the change of this paradigm in the statistical treatment of hydrological data, by enhancing methods for detection of non-stationarity in hydrological processes. In these analyses I focus on the extreme hydrological events, especially on floods, mainly triggered by rainfall. In particular, my research concentrates on the analysis of the daily and hourly rainfalls recorded in Puglia (Southern Italy). These datasets are published in the Annals part I by Puglia Region Civil Protection Section. The thesis begins with a qualitative analysis, focused on identifying the number of consecutive missing data, to select the annual maxima precipitation time series that guarantee good quality, necessary to provide best interpretation of the results of the statistical tools used. The non-stationarity in hydrology takes different forms, including abrupt change in datasets, trends, cyclicality, seasonality or combination of all or some of them. In accordance with the Italian Institute for Environmental Protection and Research (ISPRA), the search for change points for the time series is recom-mended to be conducted by the non-parametric Pettitt test which allows to identify abrupt and sudden changes in the series considered. Furthermore, in scientific literature the widely used non-parametric test, Mann-Kendall (MK) test is sug-gested to identify monotonic trends, then followed by the application of a further non-parametric measure of trend, the Sen's Slope. Indeed, in parametric methods the non-stationary character is exercised with the addition of the temporal variable t in the probability distribution, thus increasing the number of parameters and mak-ing the process of estimating more onerous. In this framework the Two-Stage (TS) method allows to tackle this prob-lem by associating the temporal dependence directly to the mean and standard deviation of the observed data. Usually, the non-stationary character of the process is introduced by the addition of the temporal dependence of the probability distri-bution’s parameters, thus increasing the total number of distribution parameters and thus making the computational process of inference more demanding. The TS incorporates time covariate directly to the first two moments, namely: mean and standard deviation, usually in the form of a linear trend in both the mean and vari-ance, or just in the first or the latter. Such an incorporation of the time in the moments tends to model the processes that concern the Earth sciences in a linear way, which is commonly accepted by the hydrological scientists and practitioners as a simple and parsimo-nious choice. However, in this work, I exploit the versatility and adaptability of the TS method, to investigate also non-linear trends, suggested by the temporal vari-ability of datasets whose behavior resamples oscillations. The aim of this thesis is to contribute to the complex interpretation of the hydrological processes that are nowadays in the center of the scientific debate. The acceptance of a more general approach, including feasibility and testing of non-stationarity of the extreme events, is undoubtedly the first step to enhance the design practice and, consequently, the natural hazards management, such as flood risk.