Quantification of contaminant mass discharge and uncertainties: Method and challenges in application at contaminated sites

Contaminant mass discharge (CMD) estimation involves combining multilevel concentration and flow measurements to quantify the contaminant mass passing through a control plane downgradient of a point source. However, geological heterogeneities and limited data introduce uncertainties that complicate CMD estimation and risk assessment. Although CMD is increasingly used in groundwater management, methods for quantifying and handling these uncertainties are still needed. This study develops and tests a CMD estimation method based on Bayesian geostatistics to quantify CMD uncertainties using data from a control plane perpendicular to the contaminant plume. By combining geostatistical conditional simulations of the spatial concentration distribution with the flow, an ensemble of CMD realizations is generated, from which a cumulative distribution function is derived. A key element of this approach is the use of a macrodispersive transport model to simulate the spatial concentration trend. This ensures that the estimated concentration reflects the expected physical behavior of the contaminant plume while also allowing the integration of site-specific conceptual information. The method is applicable to plumes with dissolved contaminants, such as chlorinated solvents, petroleum hydrocarbons, Per- and polyfluoroalkyl substances (PFAS) and pesticides. Site-specific conceptual understanding is used to inform the prior probability density functions of the structural model parameters and to define acceptable simulated concentration limits. We applied the method at three sites contaminated with chlorinated ethenes, demonstrating its robustness across varying information levels and data availability. Our results shows that strong site-specific conceptual knowledge and high sampling density constrain the CMD uncertainty (CV = 21 %) and results in estimated model parameters and a spatial concentration distribution that agrees well with the conceptual model. For a site with less data and limited conceptual knowledge, CMD and concentration distribution estimates are still feasible, though with higher uncertainty (CV = 41 %). Extending the method to account for multiple source zones and complex plume migration improved parameter identification and reduced the 95 % CMD confidence interval by 11 % ([4950-8750] to [5090-8480] g yr^-1), while also providing a spatial concentration distribution in better agreement with the plume conceptualization. This study highlights the importance of integrating site-specific conceptual knowledge in CMD estimation, particularly for less-sampled sites. The method can furthermore assist in identifying remediation targets, evaluating remedial effectiveness, and optimizing sampling strategies.