A Non-Stationary Analytical Framework for the Probabilistic Characterization of Drought Events

Probabilistic characterization of droughts is an essential step for designing and implementing appropriate mitigation strategies. Traditionally, it has been carried out by assuming stationarity for the underlying hydrological series (i.e., probability distributions and moments of hydrological processes invariant with time). However many studies in the past decades have highlighted the presence of non-stationary patterns (such as trends or shifts) in hydrological records, leading to question the stationarity paradigm. Regardless of the causes, the need arises to develop new statistical concepts and tools able to deal with such non-stationarity. In the present work, an analytical framework for deriving probabilities of drought length, assuming non-stationarity in the underlying hydrological series, is developed. In particular, analytical expressions for the probability distribution and expected value of drought length are derived as a function of the non-stationary probability distribution of the hydrologic process under investigation, as well as of the threshold level. The derived expressions are applied to four precipitation series in Sicily (Italy), exhibiting different degrees of trend. Results indicate the feasibility of the proposed methodology to compute probabilities of drought length in a non-stationary context.