Space-Time Distribution of Trichloroethylene Groundwater Concentrations: Geostatistical Modeling and Visualization

This paper describes a geostatistical approach to model and visualize the space-time distribution of groundwater contaminants. It is illustrated using data from one of the world's largest plume of trichloroethylene (TCE) contamination, extending over 23 km², which has polluted drinking water wells in northern Michigan. A total of 613 TCE concentrations were recorded at 36 wells between May 2003 and October 2018. To account for the non-stationarity of the spatial covariance, the data were first projected in a new space using multidimensional scaling. During this spatial deformation the domain is stretched in regions of relatively lower spatial correlation (i.e., higher spatial dispersion), while being contracted in regions of higher spatial correlation. The range of temporal autocorrelation is 43 months, while the spatial range is 11 km. The sample semivariogram was fitted using three different types of non-separable space-time models, and their prediction performance was compared using cross-validation. The sum-metric and product-sum semivariogram models performed equally well, with a mean absolute error of prediction corresponding to 23% of the mean TCE concentration. The observations were then interpolated every 6 months to the nodes of a 150 m spacing grid covering the study area and results were visualized using a three-dimensional space-time cube. This display highlights how TCE concentrations increased over time in the northern part of the study area, as the plume is flowing to the so-called Chain of Lakes.