A semi-probabilistic Bayesian method to identify the number and location of potential sources in 3D unconfined aquifer using limited observed concentration

Source identification of a contaminant has always been challenging for accurately modeling groundwater transport. Source identification problems are classified into several parts, such as identifying the location of contamination, the strength of contamination, the time the contaminant is introduced into the groundwater, and the duration of its activity. Identifying the sources considering all the parts as variables increases the computational complexity. Reducing the number of variables in source identification problems is necessary for a swift solution through optimization approaches. The most challenging variable in source identification modeling is the location of contamination, as it is a discrete variable for almost all the numerical solutions of groundwater models. In this research study, we have created a methodology to narrow the location of contamination from a random distribution throughout the aquifer to a reasonable number of probable locations. Although methods to identify the location of contamination were devised earlier, we have attempted an approach of combining a particle tracking approach with Bayesian method of updating the probabilities as a novel approach, where the observation data is limited. We have considered the aquifer parameters and observation well data and devised a method with a Lagrangian approach to particle movement to identify the potential source locations. We have refined the source locations to a narrower probability distribution using the Bayesian method of updating the probability through new information of refined grid space. We have tested the models to identify the potential sources with different hypothetical problems and identified the sources in advective dominant transport with an average probability of 0.53, diffusion dominant transport with an average probability of 0.62, heterogenous soils with an average probability of 0.99, anisotropic aquifer with an average probability of 0.91, and aquifer with irregular boundary with an average probability of 0.96 to identify the location nearest to the actual contaminant source. The results are satisfactory in identifying the number of potential sources with an accuracy of 88 % (15 identified out of 17 sources with a probability greater than 0.4) and their locations in the aquifer with a probability of 0.223 for exact location identification. The probability of finding a source nearest to the actual location is 0.745 at an average distance of 11.6 m from the actual source location.