A Geostatistical Framework for Incorporating Transport Information in Estimating the Distribution of a Groundwater Contaminant Plume

The goal of groundwater plume interpolation is to maximize the accuracy in estimating the spatial distribution of a contaminant plume given the data limitations associated with sparse monitoring networks with irregular geometries. To this end, some form of kriging of available concentration measurements is typically used. However, this geostatistical tool cannot take advantage of prior knowledge of flow/transport equations and parameters (e.g. conductivities, dispersion coefficients, porosities), the location of a contaminant source, or the distribution of a historical plume. This study presents a new method for incorporating transport information into the analysis, based on a combination of geostatistical kriging and inverse modeling within a data assimilation framework. The prerequisites are a local groundwater flow/transport model and concentration measurements. The method accounts for the spatial/temporal covariance of the current and/or historical contaminant distribution in a stochastic framework, yielding a best estimate of the plume distribution and its associated uncertainty. The overall objective function has three components, namely reproducing the measurements to within a specified measurement error, requiring the retrieved source to comply with a specified covariance structure, and the resulting plume distribution to comply with the measurements' correlation structure. Simulations with both homogeneous and heterogeneous formations have been carried out and compared to kriging estimates. The new method yields accurate results (even with relatively few observations), which are superior to those obtained by kriging in the sense that the best estimate more closely reproduces the actual plume and the uncertainty is lower. Spatially, the uncertainty is related to the distribution of the sampling wells, and after inverse-modeling it is propagated with the local contaminant mass. For high concentrations, the effects of dispersion are more pronounced, resulting in higher uncertainties. Conversely, there is low uncertainty away from the plume (especially in the transverse direction). In contrast, uncertainty for kriging is lowest at the measurement locations, and increased with distance from them.