Vine-Copula-Based Quantile Regression for Cascade Reservoirs Management

Abstract

This paper features an application of Regular Vine (R-vine) copulas, a recently developed statistical tool to assess composite risk. Copula-based dependence modelling is a popular tool in conditional risk assessment, but is usually applied to pairs of variables. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using a wide variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. This study emphasises the use of R-vine copulas in an analysis of the co-dependencies of five reservoirs in the cascade of the Saint-John River basin in Eastern Canada. The developed R-vine copulas lead to the joint and conditional return periods of maximum volumes, for hydrologic design and cascade reservoir management in the basin. The main attraction of this approach to risk modelling is the flexibility in the choice of distributions used to model heavy-tailed marginals and co-dependencies.

Keywords

• cascade reservoirs
• quantile regression
• vine-copulas
• watershed management