Optimal Control of Nonlinear Groundwater Hydraulics: Theoretical Development and Numerical Experiments

Abstract

Nonlinear optimization models are presented for the optimal operation of an unconfined aquifer system. The aquifer's response equations are developed using finite difference methods, quasilinearization, and matrix calculus. The optimization model, which is structured as a discrete time optimal control problem, identifies the optimal pumping pattern necessary to satisfy an exogenous water demand. A quasilinearization optimization algorithm and projected Lagrangian methods are used for the solution of the planning model. Example problems are presented which demonstrate the viability of the approach for nonlinear, nonconvex groundwater management problems.

Optimal control of nonlinear groundwater hydraulics using differential dynamic programming

“…The first example problem is taken from Willis and Finney [1985]. They solved this optimal groundwater hydraulic management model using the modular in-core nonlinear optimization system (MINOS) and quasi-linearization.…”

Analytical solutions for minimization of energy use for groundwater pumping

“…Maddock [1972] and Willis and Finney [1985] applied a similar formulation to hypothetical aquifers. Loáiciga and Leipnik [2000] and Loáiciga [2004] incorporated energy use into an expression for the net revenue of the sale of groundwater.…”

Reducing the computational cost of unconfined groundwater flow in conjunctive-use models at basin scale assuming linear behaviour: The case of Adra-Campo de Dalías

“…Willis and Finney (1985) compare, in two simple examples, several methods of resolution of transient unconfined-aquifers management problems in which the aquifer response is not given by a linear function. They approach the Boussinesq equation solution using finite difference methods, quasilinearization, and response matrix.…”