Analysis of agricultural drought characteristics through a two-dimensional copula

The potential of a copula model for the description of the joint probability distribution of two agricultural drought characteristics, the relative onset RO and the relative severity RS, is investigated in Perugia (Central Italy) in reference to a sunflower crop. The 1924–2009 time series of daily precipitation and maximum and minimum temperature were used to simulate, by means of the AquaCrop model, the root-zone soil water dynamics (SW _t ) and the crop yield under rainfed conditions. The seasonal values of RO and RS were quantified, by applying the theory of runs to SW _t (assumed as the drought reference variable), with a threshold equal to the crop critical point. The analysis shows that the best-fitting marginal distribution for both RO and RS is a truncated Gumbel distribution. The dependence structure of RO and RS, investigated by graphical and analytical techniques, was modeled by a Student copula, which is able to adequately reproduce both the overall and upper tail dependence among variables. Lastly, the Student copula was applied to obtain joint probabilities and bivariate return periods for RO and RS. These results, compared with the expected estimated yields, provide useful information for drought planning and management. For example, for the case study considered, it was found that the condition RO ≥ 0.43 (i.e., onset before the end of June) and RS ≥ 0.22 has a 5-year return period and is frequently associated with critical yields, and that the condition RO ≥ 0.47 (i.e., onset before mid-June) and RS ≥ 0.25 has a 10-year return period and is almost certainly associated with critical yields.