Combining Markov-Chain Monte Carlo Sampling and Geostatistics to Quantify Contaminant Mass Discharge and Uncertainty

Contaminated legacy sites pose a risk to the environment and human health worldwide. The accurate characterization and monitoring of subsurface contamination is crucial for effective risk assessment, management and prioritization of contaminated sites and ultimately ensures a more efficient and sustainable use of the allocated resources.

Contaminant mass discharge (CMD) integrates two important features of contaminant risk: concentration and mobility. CMD is increasingly being incorporated into risk assessments of contaminated sites as an alternative to point-value concentration-based risk assessment. The CMD is estimated by interpolating and integrating multilevel point measurements of concentration and flow across a control plane of interest. However, the geological settings at contaminated sites are typically subject to large heterogeneities resulting in complex hydrogeological conditions and significant spatial variability in the CMD, which combined with limited data availability renders it impossible to determine exact or error-free estimates.

We present a geostatistical method for quantification of CMD uncertainties in a multilevel control plane downstream a contaminated site aimed at practical implementation, with focus on the interpolation and associated uncertainty related to the concentration measurements.

The method uses geostatistical conditional simulation and applies an analytical solution of a macro-dispersive transport equation to simulate the spatially varying global mean. A Box-cox transformation is employed to ensure non-negative concentration values and account for skewness. The method is a development of that presented by Troldborg et al. (2012). We have refined the parameter identification by applying a Markov-Chain Monte Carlo (MCMC) algorithm for parameter sampling and furthermore constrained the prior sampling distributions to ensure the posterior is linked to conceptual site-specific knowledge. This links the CMD estimation to the conceptual site model and allows for source-zone data and geologic knowledge to be incorporated into the CMD estimate, which increases credibility, especially for low sampling density transects. The MCMC algorithm efficiently explores the high-dimensional parameter space, generating a statistically representative sample of geostatistical, transformation and transport-model parameters, thereby characterizing the uncertainty associated with model parameter identification in heterogeneous geologic settings. The result of the conditional simulations is an ensemble of concentration realizations that all honor the measured concentration data and capture the spatial variability of the contaminant plume.

The method has successfully been applied to determine the CMD uncertainty at multiple contaminated sites. It is firstly demonstrated at a site with substantial data and prior knowledge, and secondly at two sites to assess the challenges related to prior knowledge, sampling density and different hydrogeological conditions.

The proposed method represents a practical solution for quantifying CMD uncertainty at contaminated sites. By combining MCMC sampling and geostatistics, it overcomes the limitations of traditional deterministic methods and provides involved stakeholders with probabilistic estimates for better informed remediation and risk assessment practice when managing contaminated soil- and groundwater. 

References
Troldborg, M., Nowak, W., Lange, I. V., Pompeia Ramos dos Santos, M. C., Binning, P. J., and Bjerg, P.L. (2012). Application of bayesian geostatistics for evaluation of mass discharge uncertainty at contaminated sites. Water Resources Research, 48(9):W09535. DOI: 10.1029/2011WR011785