Modeling the dependence pattern between two precipitation variables using a coupled copula
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ORIGINAL ARTICLE
Modeling the dependence pattern between two precipitation variables using a coupled copula Longxia Qian1 · Xiaojun Wang2,3 · Zhengxin Wang1 Received: 23 May 2019 / Accepted: 1 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Hydrological process is very complex, so it is difficult for one copula to describe dependence patterns between two hydrological variables comprehensively (dependence pattern refers to the correlation and tail dependence between two random variables). This paper applied a linear weighted function of Gumbel copula, Clayton copula and Frank copula (coupled copula) to study dependence patterns between two hydrological variables and take precipitation as an example. Two experiments to study the joint probabilistic characteristics of the daily precipitation sequences in summer at two pairs of stations on the tributaries of Jinghe are performed to test our new method and compared with Gumbel copula, Clayton copula and Frank copula. Both experiments indicate that the coupled copula is superior to study the upper tail dependence, lower tail dependence and symmetric tail dependence between two precipitation sequences simultaneously. Moreover, the coupled copula is applied to estimate the joint return periods and conditional probabilities, and the joint return periods are 57.5 and 59.6 when the designed return period is 100. The result shows that there is a high probability of occurrence of precipitation extremes at the Huanxian and Xifeng stations when once in a 1000 or 100 years daily precipitation occur at the Guyuan and Pingliang stations. The coupled copula can also be applied in flood and drought frequency analysis. Keywords Dependence pattern · Coupled copula · Upper tail dependence · Lower tail dependence · Precipitation
Introduction Heavy precipitation has the potential to trigger floods, rainfall-induced soil erosion and landslides. Extreme precipitation events are characterized by multidimensional variables. Describing joint probability behaviours of precipitation extremes has been important for disaster mitigation and water resources management (Xiao et al. 2009; Zhao et al. * Xiaojun Wang [email protected] Longxia Qian [email protected] Zhengxin Wang [email protected] 1
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
2
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China
3
Research Centre for Climate Change, Ministry of Water Resources, Nanjing 210029, China
2012; Kavianpour et al. 2018; Jhong and Tung 2018; Kang et al. 2019; Kong et al. 2019). Copulas have been applied to drought, precipitation and flood frequency analysis during the past years. For example, Saghafian and Mehdikhani (2014) selected Frank copula to study two meteorological drought characteristics. Fan et al. (2016) used Frank copula to study the joint distribution of peak and volume. Shiau et al. (2010) applied Plackett co
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