Identification of contaminant point source in surface waters based on backward location probability density function method

A backward location probability density function (BL-PDF) method capable of identifying location of point sources in surface waters is presented in this paper. The relation of forward location probability density function (FL-PDF) and backward location probability density, based on adjoint analysis, is validated using depth-averaged free-surface flow and mass transport models and several surface water test cases. The solutions of the backward location PDF transport equation agreed well to the forward location PDF computed using the pollutant concentration at the monitoring points. Using this relation and the distribution of the concentration detected at the monitoring points, an effective point source identification method is established. The numerical error of the backward location PDF simulation is found to be sensitive to the irregularity of the computational meshes, diffusivity, and velocity gradients. The performance of identification method is evaluated regarding the random error and number of observed values. In addition to hypothetical cases, a real case was studied to identify the source location where a dye tracer was instantaneously injected into a stream. The study indicated the proposed source identification method is effective, robust, and quite efficient in surface waters; the number of advection–diffusion equations needed to solve is equal to the number of observations.