Optimal Configuration and Scheduling of Ground‐Water Tracer Test

Abstract

A technique for jointly configuring and scheduling a monitoring network for an aquifer tracer test is presented. A dynamic programming (DP) algorithm is used to select among competing designs for a test to provide data for estimating aquifer model parameters. A maximal information criterion is used to evaluate competing designs that satisfy a particular budget constraint. Decision variables in DP formulation are sampling locations (configuration variables) and sampling initiation times (scheduling variables). A forward DP solution method is used; optimal configuration and scheduling are determined by maximizing information without exceeding a budget. Maximization of information is argued to be equivalent to minimizing total cost of installation as well as sampling and analysis subject to an information demand function constructed from the trace of the covariance matrix of the estimated parameters. A tracer test for a confined aquifer is simulated using a finite difference scheme. A short injection period followed by a monitoring period is simulated. The DP algorithm is applied to this model to design a monitoring network and schedule to estimate aquifer characteristics. The sampling network and schedule is designed with estimation of transmissivity, retardation, and dispersivities in mind. Resulting designs are reasonable, and the method can be extended to regional-sized problems with little modification.