Multivariate analysis of rainfall and its deficiency signatures using vine copulas

In the present study, a method based on the conditional density of vine copulas was used to drought monitoring and predicting the rainfall deficiency signature for a 60‐day duration in Dashband, sub‐basin of Lake Urmia basin. The annual rainfall and rainfall deficiency signatures at 10‐, 30‐ and 60‐day durations were considered as variables. D‐, C‐ and R‐vine copulas were used to represent the dependence among the variables, finding that D‐vine copula results to be more accurate for the case of interest. We found that, if the rainfall is less than the long‐term mean in the region, the rainfall deficiency signature for near future can be estimated by acceptable accuracy. Moreover, the results of the conditional probability analysis of rainfall deficiency signature for a 60‐day duration respect to the other variables showed that, on average, the probability of the occurrence of rainfall deficiency signature of 250 mm compared to the long‐term mean in the study area is more than 50% per year. The results showed that the proposed approach may facilitate the meteorological drought management in the considered sub‐basin. A 4‐D method due to the conditional density of vine copulas was proposed to provide predictive equations and simulate the values of rainfall deficiency signatures for meteorological drought management. The diagonal section of copulas was used to reduce the complexity of the conditional density of pairwise variables. While, examining the accuracy of C‐, D‐, and R‐vine copulas, the proposed method was used to predict short‐term rainfall deficiency signatures in the studied basin.