The reliable assessment of hazards or risks arising from water contamination problems and the design of efficient and effective techniques to mitigate these problems require the capability to predict the behavior of chemical contaminants in flowing water. Most attempts at quantifying contaminant transport have relied on a solution of some form of the advection-dispersion-reaction equation. In this paper, the Backward Beam Equation (BBE) method is studied and enhanced to solve the Advection-Dispersion Equation (ADE) within a contaminant source identification context. Even though the BBE has been applied successfully to parabolic problems before, it has never been applied to solving the ADE with heterogeneous parameters. The BBE employed in this work is capable of recovering the time history and spatial distribution of a groundwater contaminant plume from measurements of its current position. Using examples involving deterministic heterogeneous dispersion coefficients, we show that the method is robust enough to handle heterogeneous parameters. By altering the method, to produce a hybrid between a marching and a jury method called the Marching-Jury Backward Beam Equation (MJBBE), we were also able to make the problem practical to solve. ¿ 2001 American Geophysical Union