Optimum experimental design for parameter identification in groundwater hydrology

Abstract

The experimental design for parameter identification of a confined groundwater system is formulated as a nonlinear mixed integer programming problem. The decision variables considered are the number and locations of the pumping and observation wells, and the pumping rates. The constraints include the allowable drawdown, the restricted locations of pumping wells and observation wells, the permissible pumping rates, and the required information. The amount of the required information is determined by the prescribed reliability of the response for the future operation of the groundwater system. The Galerkin finite element‐Crank Nicolson approach is used to develop the simulation models for solving the groundwater governing equation for the system responses. The sensitivity coefficients are computed by the influence coefficient method. The principle of superposition is used to combine the simulation models with the optimization model. The characteristics of the optimization problem have been investigated and are clarified, and its difficulties are pointed out. An efficient heuristic solution approach is proposed for solving this problem. A test problem is constructed to demonstrate the usefulness of the proposed methodology. Observations generated from the optimal design are used to identify the parameters. A covariance analysis is then carried out to verify the validity of the assumptions made in the formulation of the optimization problem. The results obtained indicate that the proposed methodology is feasible and can be used to solve complicated experimental design problems associated with a confined groundwater system.