Two-stage non-linear approach in the analysis of precipitation time series

An increasing perception of climate change both on a global and local scale, accompanied by the increase in observed average surface temperature of the oceans, and by the increased frequency of extreme events in different territories, creates the necessity of developing hydrological tools and models within the framework of non-stationarity. This study analyses the daily and hourly rainfalls recorded in Puglia (Southern Italy). In scientific literature the widely used non-parametric Mann-Kendall (MK) test is suggested 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 (co-variant) t in the probability distribution. In this framework the Two-Stage (TS) method allows to tackle this problem by associating the linear or non-linear temporal dependence to both mean and standard deviation of time series (Kochanek et al., 2013). In this field, we propose an advancement of the TS methodology by introducing a polynomial function in the mean trend, leaving the variance trend linear. The obtained results represent the first non-linear application of the TS method in a non-stationary approach to extreme events. With such application of the TS method, we show how to update the evaluation of quantiles with 5 or 10 years return time, in the aim of a technical application to hydraulic risk management and urban planning.