Analysis of Hydrologic Drought Frequency Using Multivariate Copulas in Shaying River Basin

Abstract

Droughts, considered one of the most dangerous and costly water cycle expressions, always occurs over a certain region, lasting several weeks or months, and involving multiple variables. In this work, a multivariate approach was used for the statistical characterization of hydrological droughts in Shaying River Basin with data from 1959–2008. The standard runoff index (SRI) and the run theory were employed to defined hydrological drought character variables (duration, severity, and intensity peak). Then, a multivariate joint probability analysis with four symmetric and corresponding asymmetric Archimedean Copulas was presented; and the multivariate frequency analysis with the joint return periods (Tand and Tor) were estimated. The results showed that the hydrological droughts have a severity of 4.79 and 5.09, and the drought intensity peak is of 1.35 and 1.50 in Zhoukou station and Luohe station, respectively; the rank correlation coefficients τ are more than 0.5, which means multivariate copulas can effectively describe the joint frequency distributions among multivariate variables. Drought risk shows a spatial variation: the downstream observed at Zhoukou station is characterized by a higher multivariate drought risk. In general, multivariate copulas provide a reliable method when constructing a comprehensive drought index and evaluating multivariate drought characteristics. Thus, this paper can provide useful indications for the multi-dimensional droughts’ risks assessment in Shaying River Basin.

Keywords

• hydrologic droughts
• standardized runoff index (<i>SRI</i>)
• runs theory
• copulas function
• Shaying River Basin