Robust contaminant plume estimation for risk assessment

Remediation costs are closely tied to the volume of contaminated soil; therefore, accurate plume estimation is critical for cost-effective risk management. However, most of the contaminated sites yield small-size and zero-inflated datasets, which present unique challenges for statistical analysis and plume estimation. These conditions severely limit the performance of traditional geostatistical approaches such as Kriging, which is highly sensitive to borehole number, spatial placement, and depth-specific replicates and may inadequately characterize plume features under strong heterogeneity and preferential flow. This study adapts the Integrated Nested Laplace Approximation with a Stochastic Partial Differential Equation (INLA-SPDE) framework to estimate PHC plume volume and mass (benzene and the CCME F1 fraction) and incorporates a tracer covariate to represent preferential flow effects. This study extends INLA-SPDE from general soil-property mapping to contaminant plume estimation. Using three synthetic plumes with known geometry and two real remediation sites, we compared the performance of the INLA-SPDE, Hurdle and Kriging models. Across 100 Monte Carlo runs, the INLA-SPDE model produced robust plume estimates with as few as five boreholes under conditions of high vertical resolution (3-4 incremental vertical samples), presence of at least one high-concentration borehole (>100 mg kg^-1), and relatively continuous plume geometry. Moreover, this study found that addressing vertical heterogeneity is more effective for plume estimation than increasing borehole density. The tracer covariate notably improved predictions for the more hydrophobic and strongly sorbing CCME F1 fraction, with limited benefit for the more mobile benzene. Overall, this framework supports cost-effective remediation planning and regulatory decision-making under limited and zero-inflated data conditions.