In this study, a new method was proposed to model the occurrence of related variables based on the conditional density of copula functions. The proposed method was adopted to investigate the dynamics of meteorological and hydrological droughts in the Zarinehroud basin, southeast of Lake Urmia, during the period 1994–2015. For this purpose, the modified precipitation anomaly percentage and streamflow drought indices were extracted. Finally, the joint frequency analysis of duration-duration and severity-severity characteristics of meteorological and hydrological droughts was analyzed. Analysis of 7 different copulas used to create the joint distribution in the Zarinehroud basin indicated that the Frank copula had the best performance in describing the relationship between the meteorological and hydrological drought severities and durations. By examining the results of the bivariate analysis of duration-duration of meteorological and hydrological droughts at different stations, the expected meteorological and hydrological drought durations were estimated in the years ahead. For example, at Chalkhmaz station, 4- to 7-month duration for the hydrological drought and 9- to 12-month duration for the meteorological drought is expected in the years ahead. The joint frequency analysis of drought characteristics allows to determine the meteorological and hydrological drought characteristics at a single station at the same time using joint probabilities. Also, the results indicated that by knowing the conditional density, the hydrological drought characteristics can be easily estimated for the given meteorological drought characteristics. This could provide users and researchers useful information about the probabilistic behavior of drought characteristics for optimal operation of surface water.

在这项研究中，提出了一种新方法，以基于copula函数的条件密度来建模相关变量的出现。1994-2015年期间，采用拟议的方法调查了Urmia湖东南部Zarinehroud盆地的气象和水文干旱动态。为此，提取了修正的降水异常百分比和径流干旱指数。最后，对气象和水文干旱的持续时间和严重性-严重性特征进行联合频率分析。对Zarinehroud盆地用于建立联合分布的7种不同系动词的分析表明，Frank系动词在描述气象和水文干旱严重程度与持续时间之间的关系方面表现最佳。通过检查不同站点的气象和水文干旱持续时间的二元分析结果，可以估算未来几年的预期气象和水文干旱持续时间。例如，在查尔克马兹（Chalkhmaz）站，预计未来几年水文干旱将持续4至7个月，气象干旱将持续9至12个月。干旱特征的联合频率分析允许使用联合概率同时确定单个站点的气象和水文干旱特征。此外，结果表明，通过了解条件密度，可以轻松地估算给定气象干旱特征的水文干旱特征。