Copula‐Based Chance‐Constrained Hydro‐Economic Optimization Model for Optimal Design of Reservoir‐Irrigation District Systems under Multiple Interdependent Sources of Uncertainty

Abstract

AbstractThis paper presents a new explicit stochastic hydro‐economic optimization model for reservoir‐irrigation district systems design affected by multiple interdependent sources of uncertainties. The model solution determines both optimal design and long‐term operation policies of the systems while accounting for uncertainties of reservoir inflow, rainfall, crop yield, crop price, and production costs. The problem is formulated as a chance‐constrained program in which the dependence structure of discrete and continuous random coefficients is accounted for using copula. In addition to design variables such as the sizing of reservoir capacity and the irrigable area, optimal reservoir operation policies and irrigation management strategies are determined. The model performance and significance is tested in the case study of Chamshir hydrosystem in Iran, consisting of Chamshir Dam and downstream irrigation districts. Various scenarios assessing baseline conditions, risk attitude, and the impacts of change in climatic inputs and upstream conditions are also evaluated. The model results are used to quantify the interrelationships and trade‐offs among optimal values of design parameters, optimal irrigation policy, decision‐makers' risk‐attitude, uncertainty levels of agro‐economic factors, and target reliability levels of meeting crop yield and water requirement. The results demonstrate that smaller sizes of the reservoir and the irrigation district and stress‐avoidance irrigation policies, rather than deficit‐irrigation policies, are preferred when the decision maker is risk‐averse and uncertainties in agro‐economic factors and reliability levels are large. Additionally, we show how the optimal cropping pattern and irrigation strategies are affected by climate change‐induced rainfall variations and the alteration of conditions upstream of the project.