On the nonlocality of reversible-time particle tracking methods

This article presents a novel methodology for time reversal in groundwater transport simulations. A variance minimization procedure leads to a stochastic method, analogous to the Random Walk Particle Tracking Method (RWPTM), capable of tracking groundwater solute concentration profiles over time. This method, called the Reversible-Time Particle Tracking Method (RTPTM), can backtrack in time a certain solute plume, of arbitrary shape, and identify the most probable spill location. The correspondence to the "classical" RWPTM is established for forward-time simulations, and the method is applied to one-dimensional transport of both conservative and nonconservative solutes in spatially invariant and variant groundwater flow fields with great success.