Estimation of multivariate design quantiles for drought characteristics using joint return period analysis, Vine copulas, and the systematic sampling method

Abstract

Abstract The Wei River Basin has suffered from severe droughts. It is essential to build drought relief projects to cope with drought disasters. Traditionally, design quantiles have been estimated using univariate analysis, in which multiple characteristics of hydrological events are not considered. To design the more appropriate hydrological projects for the case study area, the Wei River Basin, it is essential to conduct research on multivariate analysis allowing multiple characteristics to be considered simultaneously. Here, the authors focus on hydrological drought (the basis for designing a hydrological project), and a framework to calculate the joint design quantiles of three drought characteristics is proposed. The most likely design quantiles relating to a specific return period, reflecting the highest occurrence probabilities among multiple combinations of variables, are derived by the maximum joint probability density function. Results show that compared to univariate analysis, design quantiles calculated via joint return period yield infrastructure with a smaller total storage capacity in the study area relating to a specific return period, i.e., reduces the economic input while maintaining the project safety. Proposed methods bring new sights to the design project. However, multi-method comparisons considering more uncertainties, inherent laws, investment, and other limited factors are still vital.