Water Resources Research

Optimal pumping test design for parameter estimation and prediction in groundwater hydrology


  • James M. McCarthy,

  • William W-G. Yeh


A systematic approach is developed to design a least cost aquifer pumping test. Systematic pumping test design evaluates the acceptability of all potential pumping test data sets, before actually performing the test. In this way, various acceptable pumping test designs can be compared in order to choose the least cost acceptable alternative. This research utilizes δ identifiability as the acceptability criterion, such that, for a pumping test design to be acceptable, the parameters identified from the pumping test data set must predict some overall management objective within a prescribed error. The pumping test design problem is assumed to be a function of the number and location of the pumping and observation wells, as well as the pumping test pump rate, duration and measurement pattern. Using practical considerations and an evaluation of the pumping test design problem's response, the optimization problem is reduced to three decision variables: (1) the number of observation wells; (2) observation well locations, and (3) the pumping test pump rate. Values for the remaining decision variables are chosen and sensitivity analysis is used to evaluate their effects on the pumping test design problem. The pumping test design problem is decomposed into a main optimization problem and one subproblem. The main problem minimizes the number of observation wells by choice of their location, while the subprobiem minimizes the pumping test pump rate subject to (1) a maximum pump rate, and (2) the δ identifiability constraint.