Backward Probabilistic Modeling to Identify Contaminant Sources in a Water Distribution System

In this paper, we present an application of backward modeling to identify possible sources of a reactive contaminant in a water distribution system. In backward modeling the sensor location is treated as a source of probability, and the probabilities are propagated upstream and backward through time. The governing equation for the backward model is the adjoint of the forward transport equation. The adjoint state is related to probability density functions (PDFs) of the backward travel time which is the time in the past that contamination that was observed at a sensor could have been at an upstream node. It is possible to characterize prior positions of the contaminant using these PDFs. In this manner it is possible to identify possible release locations and release times upstream of the sensor location. A similar approach was used by Zierolf et al. to determine the point of origin, travel path, and travel time of chlorine arriving at a particular node in a distribution system. This method was expanded upon by Shang et al. to allow for storage tanks and multiple sources of water and chemicals to be taken into account. In this paper, an example water distribution system is analyzed using EPANET to identify sources of contamination.