Joint return periods of critical thresholds of duration and severity of crop water stress in some areas of central Italy

As many other natural hazards, the crop water stress has a typical multivariate nature, i.e., it is characterized by the contemporary presence of multiple characteristics correlated with each other (e.g., duration, severity, peak, areal extension, etc.). In this situation, a risk analysis based on a traditional univariate approach is inadequate for a complete interpretation of the phenomenon. Copula models can effectively solve the probabilistic joint analysis of two or more random correlated variables. Copulas are functions that join univariate probability distributions to form multivariate probability distributions, modelling the dependence structure among random variables independently of their marginal distributions. This work illustrates how the joint probability and return periods of the Duration (D, days) and Severity (S, mm) of the crop water stress can be used to obtain information useful in defining drought management strategies. The case study refers to some localities of central Italy and olive crops, widely cultivated in the region considered, mainly under rainfed conditions. In the case study, 65 years of daily precipitation and maximum and minimum temperature were used to obtain a rough estimation (following the FAO 56 guidelines) of the daily soil water dynamics (SWt), available for the olive crops at each locality considered. Then, by applying the Theory of Runs to SWt, with a threshold equal to the crop critical point (SWcrit), the water stress events were identified and characterized by their D (days) and S (i.e., the cumulative evapotranspiration deficit, mm) for each locality. A 2-parameter Gamma distribution was fitted to both D and S, whilst a Frank copula modelled their dependence structure. These joint probability models were then used to quantify the return periods associated with specific user-defined critical threshold events; in this work, the critical threshold events were simply defined on the basis of a statistical approach (e.g., combining the values of D and S corresponding to the 90th percentiles). However, in a real case application, the critical thresholds could arise from considerations on the crop impacts deriving from specific D and S values. Despite the modest areal extension of the case study, results show that the climatic conditions significantly affect the bivariate return period of the critical threshold events, which varies between 3 and 15 years in the localities considered. We also evaluated the return time increment due to some drought management strategies, such as the application of rescue irrigation. For example, the application of an irrigation volume of 50 mm in the mid of the growing season is able to produce a relevant change of the return period, thus varies between 5 and 77 years.