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.

诸如风暴，洪水和干旱等复杂的水文事件通常以许多相关的随机变量为特征。Copulas可以独立于边际分布函数对依存关系模型进行建模，并提供具有不同边距和依存关系结构的多元分布。在这项研究中，通过使用copula函数分析了Urmia湖盆地纳卡德次流域地下水位缺乏和降雨缺乏的联合特征，研究了两个特征的条件行为。两个特征共同变化的研究结果表明，该地区降雨减少90-135毫米，使地下水位增加了1.2至1.7 m。通过减少降雨估算地下水位不足值的二元copulas的条件密度的研究结果表明，该子流域降雨不足特征值的变化导致了地下水位缺乏特征的概率曲线的产生。关于产生的最大地下水位不足，计算降雨不足和地下水位不足之间的关系，以估计地下水位不足特征值。提出的条件密度函数将是条件返回期的替代方法。关于产生的最大地下水位不足，计算降雨不足和地下水位不足之间的关系，以估计地下水位不足特征值。提出的条件密度函数将是条件返回期的替代方法。关于产生的最大地下水位不足，计算降雨不足和地下水位不足之间的关系，以估计地下水位不足特征值。提出的条件密度函数将是条件返回期的替代方法。