Direct and integration methods of parameter estimation in groundwater transport systems

Two finite element based methods are developed to identify the spatial distribution of parameters that characterize contaminant transport in two-dimensional irrotational potential flow in the regions over which a concentration front has passed. The required input data are observations of the steady head or pressure distribution and the transient mass concentration distribution of the contaminant, together with a few transmissivity observations. To obtain the distribution of velocity, the transmissivity is first determined by inverting the groundwater flow equation. The velocity components are then computed on the basis of Darcy's law, assuming the porosity and thickness of the aquifer are known. The computed velocity components are used for estimating unknown aquifer dispersivities in two-dimensional transient groundwater transport. In order to avoid the difficulty that often occurs in direct solution an integration-based method is presented. This method performs well in both noise free and relatively high noise level environments. In addition, a method to evaluate the additional parameters of dispersivity and velocity components is presented for the cases where the head or pressure distribution is not available. The equations for the methods are derived for cases in which the dispersivity varies with position, although the methods have not been tested for spatially varying dispersivities in the two-dimensional case.