Backward probability model using multiple observations of contamination to identify groundwater contamination sources at the Massachusetts Military Reservation

Abstract

Backward location and travel time probability density functions characterize the possible former locations (or the source location) of contamination that is observed in an aquifer. For an observed contaminant particle the backward location probability density function (PDF) describes its position at a fixed time prior to sampling, and the backward travel time probability density function describes the amount of time required for the particle to travel to the sampling location from a fixed upgradient position. The backward probability model has been developed for a single observation of contamination (e.g., Neupauer and Wilson, 1999). In practical situations, contamination is sampled at multiple locations and times, and these additional data provide information that can be used to better characterize the former position of contamination. Through Bayes' theorem we combine the individual PDFs for each observation to obtain a PDF for multiple observations that describes the possible source locations or release times of all observed contaminant particles, assuming they originated from the same instantaneous point source. We show that the multiple‐observation probability density function is the normalized product of the single‐observation PDFs. The additional information available from multiple observations reduces the variances of the source location and travel time probability density functions and improves the characterization of the contamination source. We apply the backward probability model to a trichloroethylene (TCE) plume at the Massachusetts Military Reservation (MMR). We use four TCE samples distributed throughout the plume to obtain single‐observation and multiple‐observation location and travel time PDFs in three dimensions. These PDFs provide information about the possible sources of contamination. Under assumptions that the existing MMR model is properly calibrated and the conceptual model is correct the results confirm the two suspected sources of contamination and reveal that one or more additional sources is likely.