WATER RESOURCES RESEARCH, VOL. 27, NO. 4, PAGES 577-588. APRIL 19•I Optimal Data AcquisitionStrategy for the Development of a Transport Model for Groundwater Remediation TULLIO TUCCIARELLI Facolt•'• di lngegneria,ReggioCalabria. Italy GEORGE PiNDER College of Engineering and Mathematics. University of Vermont, Burlington The reliability of groundwater quality managementalgorithms is limited in large part by the uncertainty present in the model parameters. Because the field parameter measurement costsand the remediation costs must be suppliedby the samefinancial source,the classical optimization procedure does not minimize the real total remediationinvestment. This researchpresents an algorithm able to find the total minimum for the sum of both the measurementand the pumping costs. A chance- constrained technique is used to cast the optimization problem in stochastic !brm, relating the concentration covariance matrix to the 1og-transmissivity covariance matrix by means of the transport equations and a first-order approximation for the uncertainty. The simulation model solves the stead,,,' state flow equations on a finiteelement triangular mesh and the transport equations using the backward methodof characteristics. The resulting nonlinearly constrained optimization problem is solvedusing the quasi-linearity algorithm; this algorithm is designed to find a goodinitial point for the local minimum search when the feasible domain is not convex. INTRODUCTION Significant concerns in solving groundwater qualityman- agement problems arethe uncertainty of the physical param- eters neededto simulatethe water quality behavior and the costs associated with reducing the uncertainty in the con- centration forecaststhrough reduction in the uncertaintyin the field parameters. Much research effort has been ex- pended in the last few years in two research areas that are relevant to thisproblem: experimental design andparametric inversion. In addition, new stochastic approaches havebeen developed to define andsolve the management problem. The present work builds on theseadvances in presenting a new methodology that, using the previous developments, deter- mines the most effective location of new field measurement sites to minimize the total cost of the field measurementsand the reclamationoperations. In thefollowing we shall group the physical variables of theproblem into three different types.The first type is the physical parameters (transmissivity, porosity,adsorption coelticient, boundary conditions, pollutant sinks and sourc- es); in the present workwe consider thetransmissivity asthe only uncertainparameter.The second type is the state variables; they are the variables thatconstitute the solution generated by the simulation model, thatis, hydraulic head, velocity, and concentration. Finally, the third type is the decision variables, the ones that we seek using our manage- ment model. in this work we assumeas decision variables not only thevolume per unittimeextracted or injected at a predetermined set of remediation well locations within an imposed time, but also the number of field parameter mea- surements and their locations. Copyright 1991 by the American Geophysical Union. Paper number 90WR02397. 0043- ! 397/91190WR-02397505.00 LITERATURE REVIEW Groundwater quality management problems are usually solved in three distinct steps. The firststep is the acquisition of existing data aboutthe aquifer structure and utilization history (water table levels, pumpingrates, water quality parameters, transmissivity and porosity estimates}. Part of this step istheacquisition of newmeasurements. The second step is the calibration of the simulation model, which herein is called parametric inversion. The final stepis the develop- ment of the management model, wherein the simulation model is used as a subroutine for the evaluation of the constraint functions. In the first step,geostatistical theoryhasbeenapplied to select the location of new field measurements of the state variables.The objective function is therein related to the variance of the state variable estimations that, according to the weak second-order stationarity assumption, depends onlyon the measurement locations and not on their actual value. Rouhani [1986] selects the locations usingas a crite- rion the sum of the reduced variances of the water table estimates at selected observation points; Carrera et aL [!984]use a branch andbound technique to select locations for fluoride concentration measurements; Loaiciga [1989] uses aninteger program to select potential locations in space and time for measurements of groundwater quality parame- ters. More complex approaches try to optimize the location of several measurements at the same time, according to a given geometry [Christakos and Olea, 19881. Knopman and Voss [1987, 1988]use the simulation model to choosethe frequency and location of water quality measurements. They optimize theaccuracy of theestimation of water velocity and hydrogeological parameters in a monodimensional mcxiel, for single and multiple layer aquifers. The field measurement of the physical parameters is studied by Yeh in several papers [Yeh, 1984; Mt'Carthy and Yeh, 19901 . He selects the number and the location of the 577