Inverse solution of transport equation for pollution source identification in rivers under realistic conditions using the geostatistical method

The inverse transport problem is very difficult and challenging to solve due to some special characteristics, including the lack of solution, non-uniqueness and instability. Regarding to these complexities, usually some simplifications are made in solution process, which ultimately leads to identification methods that cannot be extended for real-world applications. This study aims to develop a practical method for pollution source identification in rivers under realistic conditions, which considers irregular cross-sections, unsteady flow and both physical and chemical transport processes. The stochastic framework of proposed method provides the possibility of estimation of source characteristics in greater time instances than available observation data as well as consideration of uncertainty due to error in those data. Considering that direct solution is also required in the solution of inverse transport problem, at first flow and transport equations is solved by finite difference numerical scheme. Then, inverse transport equation is solved to identify active pollution sources using the geostatistical method. Results of application of the method to three hypothetical examples and two sets of real data indicated the great accuracy and numerical stability of proposed method in reconstruction of source characteristics even in complicated real-world condition and using sparse and erroneous observation data. Furthermore, the identification uncertainty was considered through 95 percent confidence interval.