Probabilistic Analysis of Extreme Discharges and Precipitations with a Nonparametric Copula Model

Yan Liu,Youcun Liu,Qiaozhen Zhang,Tongke Wang,Yonghong Hao,Tian-Chyi Yeh,Yonghui Fan

doi:10.3390/w10070823

Abstract

Urumqi River is an important river in the Xinjiang autonomous region, China, where floods or droughts are the major concerns of the local communities. This river’s discharge is mainly influenced by the natural factors such as precipitation and climates, rather than human activities. This paper quantifies the interdependent structure between Urumqi River’s discharge and precipitation using a nonparametric Copula method. It then analyzes the relationship between the extreme discharges of this river and extreme precipitation of the region. Comparison between simulation result and real data is conducted to verify the rationality of the model. Furthermore, the conditional probabilities of maximum and minimum discharge at different precipitation levels are also investigated using the Copula distribution functions. The results show a strong relationship between large discharge and heavy precipitation in this region. The upper dependence coefficient is nearly 0.6 and the probability of large discharge reaches 0.64 when the rainfall is greater than 159.56 mm. The relationship between small discharge and rainfall is insignificant. The lower dependence coefficient is zero, suggesting that the base flow and snowmelt from Tianshan likely contribute to Urumqi River’s discharge during the dry season.

Highlights

Water resources are one of the most important natural resources for the sustainable development of society [1], especially in the arid and semi-arid areas [2,3]
The stationarity and homogeneity of precipitation and discharge series are tested through Augmented Dickey-Fuller (ADF) [47] and Levene’s [48] test, respectively
The results show that both the p values of ADF test for precipitation and discharge are far less than

Summary

Introduction

Water resources are one of the most important natural resources for the sustainable development of society [1], especially in the arid and semi-arid areas [2,3]. As one of the world’s extreme arid inland areas with the highest water scarcity index, water resources of the Xinjiang autonomous region have been a great concern to China, and many studies have focused on this issue [4,5,6,7,8,9,10]. River, located on the northern slope of Tianshan Mountain, is one of the most important inland rivers in the region. It is the major water resource for Urumqi City, which has a population of more than 3.5 million [6]. The hydrology process in this area, as well as its response to the climate change, has drawn great attention in recent decades, especially the dependence between climate

Methods

Results

Conclusion