Modeling the dependence pattern between two precipitation variables using a coupled copula

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.