Evaluating backward probability model under various hydrogeologic and hydrologic conditions.

Contaminant source identification improves the understanding of contaminant source characteristics including location and release time, which can lead to more effective remediation and water resources management plans. The backward probability model can provide probabilities of source locations and release times under various contaminant properties and hydrogeologic conditions. The backward probability model has been applied to numerous synthetic and real contamination sites for locating possible contaminant sources, but it is also important to evaluate the reliability of the backward probability model through rigorous verification analyses. Here, we present a model verification framework for the backward probability model using a stepwise approach from simple to complex model settings: comparison with previous studies, transient saturated flow under various hydrogeologic conditions, and transient variably-saturated flow conditions. As a simple condition, one-dimensional homogeneous problems under steady-state and transient flow conditions were verified by comparing with previous studies. Model verifications with complex conditions were conducted by comparing forward and backward probability simulation results. The verification results demonstrate that the backward probability model performs well for homogeneous problems. For heterogeneous problems, the backward probability model results in slightly different backward travel times due to differences in solute decay and boundary conditions assigned for both forward and backward probability simulations, but the backward travel time at the maximum probability can be reproduced well.