Optimization Model for Ground‐Water Planning

Abstract

A planning model is presented for the optimal management of groundwater systems. The model, which is formulated as a bi‐objective optimization problem, allocates over a series of planning periods, groundwater to competing water (irrigation) demands in a river basin. The model is predicated on the response equations of the ground‐water system. The equations are developed for an inhomogeneous, isotropic aquifer system with the Galerkin finite element method. The matrix calculus is used to obtain a continuous solution in time relating the hydraulic head and the initial state of the system, the system's time dependent boundary conditions, and the planning or management policies. The planning model is applied to the Yun Lin groundwater basin in southwestern Taiwan. Parametric linear programming is used to generate optimal planning policies, the set of non‐inferior solutions, and the relationship between the total water deficit and: (1) The maximum pumping rate; and (2) the minimum permissible head values in the aquifer system.