Inexact Copula-Based Stochastic Programming Method for Water Resources Management under Multiple Uncertainties

Extensive uncertainties exist in many resources and environmental management problems, which can be interrelated and thus amplify the complexity and nonlinearity of study systems. The interactions from dependent random variables pose significant impacts on the potential management strategies. In this study, an inexact copula-based stochastic programming (ICSP) method was developed to deal with interactive uncertainties with interval and stochastic characteristics as well as to address nonlinear dependence among multiple random variables. Specifically, the impacts of their interactions among random variables were revealed based on the concept of copula. ICSP can also reflect the risk of violating system constraints with linear and nonlinear dependences. The developed ICSP method was then applied to planning water resources management problems; results (i.e., system benefit, economic penalty, water allocation, and flood diversion) under a variety of risk levels have been generated. Results are useful for generating desired strategies for water allocation and flood diversion under various individual and joint probabilities. Compared with the conventional joint-probabilistic chance-constrained programming (JCCP) approach, ICSP can better reveal multiple uncertainties and their interrelationships under nonlinear conditions and generate more robust solutions.