Conditioned Backward Probability Modeling to Identify Contamination Sources in a Water Distribution System

If a chemical or biological agent is released into a water distribution system, sensors that are installed in the pipe network may detect the contamination as it travels through the system. To minimize the adverse impact of the contaminant release, the source must be characterized to determine the extent of the contamination and to remediate the contaminated area. We develop an adjoint-based backward modeling approach that uses the collected sensor data to identify the location and timing of the release. In the adjoint model, the sensor location is treated as a source of probability, and the probability is transported upgradient and backward in time to obtain probability density functions (PDFs) that describe the random time in the past that the observed contamination was at a particular upgradient position. These PDFs can be used to identify the source location and release time. Conditioning these PDFs on the measured concentrations improves their accuracy and decreases their uncertainty. We demonstrate the effectiveness of this method by using it to characterize a contaminant source in a hypothetical water distribution system.