Analyzing the conditional behavior of rainfall deficiency and groundwater level deficiency signatures by using copula functions

TLDR

The complex hydrological events such as storms, floods, and droughts are characterized by correlated random variables, and copulas can model their dependence structure independently of marginal distributions. The study investigates the conditional relationship between rainfall deficiency and groundwater level deficiency in Naqadeh sub‑basin using copula functions, proposing a conditional density approach as an alternative to conditional return periods. The authors model the joint distribution of rainfall and groundwater level deficiencies with copulas, computing the dependence structure to estimate groundwater level deficiency values from rainfall changes. Results show that a 90–135 mm rainfall reduction raises groundwater levels by 1.2–1.7 m, and the copula‑based conditional density produces probability curves linking rainfall deficiency to groundwater level deficiency.

Abstract

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.