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.
Highlights
Drought in various fields, both directly and indirectly, will have adverse effects on different parts of the community and environment
The purpose of the present study is to investigate the conditional density analysis of bivariate copulas to estimate the groundwater level deficiency using rainfall deficiency in Naqadeh sub-basin (NSB) located in Lake Urmia Basin (LUB)
Regarding the effective parameter involvement in the studied signatures, the results showed that the use of conditional density in joint analyses and presentation of bivariate returns period provides useful information on water resources management as well as the designs
Summary
Both directly and indirectly, will have adverse effects on different parts of the community and environment. The most important direct effect of drought is its negative impact on the quantity and quality of water resources. As the global climate changes, natural disasters caused by extreme weather events are becoming more frequent and leading to increasingly serious consequences around the world (Duan et al ). It is important to understand the relative contributions of rainfall and its changes in runoff to sustainable water resources management (Lyu et al ). Using a univariate hydrological frequency analysis, the probability of an event can be calculated. The univariate hydrological frequency analysis plays an important role in estimating the return period of flood or rainfall that are used to design structures such as dams, bridges, roads, highways, wastewater treatment facilities and industrial buildings
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