Inverse Green element evaluation of source strength and concentration in groundwater contaminant transport

Abstract

Evaluating pollution sources from limited concentration data of their contaminant plumes in groundwater systems is an inverse problem that presents computational challenges because of its ill-posedness. In this work, the Green element method (GEM) is used to solve inverse contaminant transport problems in 2-D orthotropic homogeneous aquifers. The GEM discretization of the differential equation produces an over-determined, ill-conditioned global matrix that is decomposed by the singular value decomposition method and solved by the least square method with Tikhonov regularization. Five test cases of pollution sources of unknown strengths are used to evaluate the performance of GEM. The results indicate that the current methodology is capable of correctly predicting the strength of pollution sources and the historical concentration plumes that they produce. However, the computation accuracy is influenced by the location of the observation points in relation to the source, data errors of observed concentrations, the transport mode, and the value of the Courant number used in the simulations. Data errors at observation points influence more significantly the GEM prediction of the pollution source strength than the concentration plume, while numerical artefacts of dispersion and oscillations observed in direct solutions of advection-dominant transport cases are also evident in inverse modelling.