Trivariate joint frequency analysis of water resources deficiency signatures using vine copulas

Abstract

Investigating the interaction of water resources such as rainfall, river flow and groundwater level can be useful to know the behavior of water balance in a basin. In this study, using the rainfall, river flow and groundwater level deficiency signatures for a 60-day duration, accuracy of vine copulas was investigated by joint frequency analysis. First, while investigating correlation of pair-variables, tree sequences of C-, D- and R-vine copulas were investigated. The results were evaluated using AIC, Log likelihood and BIC statistics. Finally, according to the physics of the problem and evaluation criteria, D-vine copula was selected as the best copula and the relevant tree sequence was introduced. Kendall’s tau test was used to evaluate the correlation of pair-signatures. The results of the Kendall’s tau test showed that pair-signatures studied have a good correlation. Using D-vine copula and its conditional structure, the joint return period of groundwater deficiency signature affected by rainfall and river flow deficiency signatures was investigated. The results showed that the main changes in the groundwater level deficiency is between 0.3 and 2 m, which due to the rainfall and the corresponding river flow deficiency, return periods will be less than 5 years. Copula-based simulations were used to investigate the best copula accuracy in joint frequency analysis of the studied signatures. Using copula data of the studied signatures, the groundwater deficiency signature was simulated using D-vine copula and a selected tree sequence. The results showed acceptable accuracy of D-vine copula in simulating the copula values of the groundwater deficiency signature. After confirming the accuracy of D-vine copula, the probability of occurrence of groundwater deficiency signature was obtained from the joint probability of occurrence of other signatures. This method can be used as a general drought monitoring system for better water resources management in the basin.