Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities. iNTRODUCTiON Adjoint sensitivity theory is currently being considered as a potential method to aid in calculating the uncertainty of performance measures for proposed nuclear waste repositories [Ronen et al., 1980; Thomas, 1982]. While the method is well known in electrical engineering [Director and Rohrer, 1969], nuclear reactor assessments [Lewins, 1964; Oblow, 1978], and in history matching of petroleum reservoirs [Dogru and $einfeld, 1981; Chavent et al., 1975], it has received little application to groundwater flow and contaminant transport problems. Vemuri and Karplus [1969] and Neuman [1980a, b] used an adjoint methodology as part of parameter estimation routines for the inverse problem of aquifer hydrology. In their inverse applications the adjoint method is used to determine the derivatives of a function that relates predicted and measured piezometric heads with respect to aquifer hydraulic conductivity. The solution of the primary flow problem and the adjoint problem enables the calculation of the required derivatives for use in a nonlinear search algorithm. Thus the time consuming and costly process bf trial and error or direct parameter sampling is avoided. Currently, most groundwater characterization studies rely upon direct sampling, wherein the primary problem is repeatedly solved for selected parameter combinations for '•' "'• : "':"--'''' t,• ue,•rm.n.,.,,. of system sensitivities. McElwee and Yukler [1978] and McElwee [1982] discuss sensitivity analysis of groundwater models.In th...
