Hydrology Research (Dec 2020)
Analyzing the conditional behavior of rainfall deficiency and groundwater level deficiency signatures by using copula functions
Abstract
The complex hydrological events such as storm, flood and drought are often characterized by a number of correlated random variables. Copulas can model the dependence structure independently of the marginal distribution functions and provide multivariate distributions with different margins and the dependence structure. In this study, the conditional behavior of two signatures was investigated by analyzing the joint signatures of groundwater level deficiency and rainfall deficiency in Naqadeh sub-basin in Lake Urmia Basin using copula functions. The study results of joint changes in the two signatures showed that a 90–135 mm reduction in rainfall in the area increased groundwater level between 1.2 and 1.7 m. The study results of the conditional density of bivariate copulas in the estimation of groundwater level deficiency values by reducing rainfall showed that changes in values of rainfall deficiency signature in the sub-basin led to the generation of probability curves of groundwater level deficiency signature. Regarding the maximum groundwater level deficiency produced, the relationship between changes in rainfall deficiency and groundwater level deficiency was calculated in order to estimate the groundwater level deficiency signature values. The conditional density function presented will be an alternative method to the conditional return period. HIGHLIGHTS The purpose of the present study is to investigate the conditional density analysis of bivariate copulas to estimate the groundwater level deficiency using the rainfall deficiency.; In this regard, the diagonal section of the copulas was used to reduce the complexity of the conditional density of the pairwise variables.; By using conditional density and combining it with copula simulation, the dependent values can be simulated and predicted.; Due to the lack of application of the conditional return period, the best alternative method is to use the proposed method based on conditional density.; The presented equation can be used as an alarm and monitoring system.;
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