Identifying sources of sorbing solutes in groundwater using backward location probabilities conditioned on measured concentrations

Abstract

If contamination is observed in an aquifer, a backward probability model can be used to obtain information about the prior position of the observed contamination or the source location. Backward location probability describes the possible prior positions of the observed contaminant particle at a specified time in the past. If the source release time is known or can be estimated, the backward location probability can be used to identify possible source locations. For sorbing solutes, the location probability depends on the phase (aqueous or sorbed) of the observed contamination and on the phase of the contamination at the source. We present a two-step approach for obtaining backward location probabilities that are conditioned on the observed concentrations. In the first step, a backward location probability distribution is obtained that depends only on the observation locations, on the phase of the observed contamination, and on the transport properties of the aquifer and solute. This unconditioned backward location probability distribution is obtained by solving the adjoint of a forward contaminant transport equation. The second step is to condition this backward location probability distribution on the measured concentrations using an equation based on Bayes' theorem. The conditioned probability distribution has a smaller variance than the unconditioned distribution, and it is more accurate.