Application of the Quasi-Reversibility Method in Inverse Computation of Temporal and Spatial Pollutant Concentration in Time

Pollutants are usually drained off imperceptibly and suddenly in the rivers, which can be of human or natural origin, thus finding information from contaminant source as quickly as possible is important to reduce damage. The pollutant is released by the Advection-Dispersion processes in the river. Therefore, information on contaminant release site and release time can be obtained using inverse solution of the Advection-Dispersion equation. The purpose of this study is to solve Advection-Dispersion Equation (ADE) reversely and to obtain information on the release time and time series data of pollutant concentration discharged into the studied rivers. In this research, the quasi-reversibility method is used to reverse the ADE. In this method, by adding the stability term (fourth derivative term) to ADE, the mentioned relationship can be solved reversely without the instability of the answers. A hypothetical example and a case study of Karun River have been used for model validation. The aforementioned method determines the concentration experienced at different points and intervals of the river by reversing the ADE. The highest contaminant intake in each interval, maximum and average intake time are the obtained results by this method. The results show that the quasi-reversibility method has been performed with high accuracy and the proposed method has been satisfied in stability of solving ADE.