SENSITIVITY METHODS FOR TIME-CONTINUOUS, SPATIALLY DISCRETE GROUNDWATER CONTAMINANT TRANSPORT MODELS

Existing sensitivity methods for spatially discrete groundwater contam inant transport models have been developed for time-stepping numerical algorithms and cannot be readily used with time-continuous approaches to transport simulation, such as the Laplace transform Galerkin techn ique. We develop direct and adjoint sensitivity methods in which sensi tivity coefficients are computed in the Laplace domain and inverted nu merically to the time domain. The methods are computationally efficien t when used in conjunction with time-continuous transport equations. T he relative efficiency of the two methods depends on the number of mod el parameters, number of performance measures, and number of spatial d iscretization nodes. The adjoint method is favored when the number of performance measures is much smaller than the number of model paramete rs. The adjoint method is limited in that performance measures are res tricted to being linear functions of state variables. A two-dimensiona l transport example is developed in detail, and sensitivities with res pect to nodal hydraulic conductivities are computed. In the problems a nalyzed, the direct and adjoint methods are 9 to 156 times faster than the perturbation method, with the computational savings increasing as the size of the problem is increased.