Forward and backward location probabilities for sorbing solutes in groundwater

Location probability can be used to describe the likely position of a solute particle as it travels through an aquifer. Forward location probability describes the likely future positions of a particle, and can be used to predict the movement of a contaminant plume. Backward location probability describes the likely prior positions of a solute particle, and can be used to identify sources of contamination. For sorbing solutes, the probability distributions must also account for the phase (aqueous or sorbed) of a solute particle. We present new phase-dependent forward and backward location probabilities to describe transport of a solute undergoing linear non-equilibrium sorption. The effects of sorption are incorporated directly into the governing equations that are used to calculate the probability distributions. The shape and magnitude of the distributions depend on the phase of the contamination at both the source (or prior location) and receptor (or future location). These probabilities are related to adjoint states of concentration. Using adjoint theory, Bayesʹ theorem, and a clever transformation, we develop a model to efficiently calculate backward location probabilities for one or a few receptors. We illustrate important features of backward location probabilities for a sorbing solute with a hypothetical, one-dimensional confined aquifer, and we demonstrate their use in identifying sources of contamination for a trichloroethylene plume at the Massachusetts Military Reservation using a three-dimensional numerical model.