An analytical solution for the advection-dispersion equation inversely in time for pollution source identification

• Published in: Physics and chemistry of the earth. Parts A/B/C 2022-12, Vol.128, p.103255, Article 103255
• Main Authors: Permanoon, Erfan, Mazaheri, Mehdi, Amiri, Siamak
• Format: Article
• Language: English
• Subjects: Advection-dispersion equation (ADE); Analytical solution; Fourier transform (FT); Pollutant source identification; Quasi-reversibility (QR) method; River
• ISSN: 1474-7065; 1873-5193
• DOI: 10.1016/j.pce.2022.103255

Researchers have long explored inverse solution methods for identifying unknown pollutant sources in water resources. More often than rivers, these methods are used to study groundwater; therefore, employing efficient and up-to-date methods to determine the characteristics of unknown pollutants in rivers has been the cause for concern to water and environmental researchers. This study was thus designed to solve the pollutant transport equation in rivers as an inverse problem to reconstruct pollutant source intensity functions. A unique analytical method, based on the quasi-reversibility (QR) method and the Fourier transform tool, was developed to solve the advection-dispersion equation (ADE) in rivers inversely in time and a one-dimensional domain for various pollutant loading patterns. In this method, a stability term is incorporated into the original transport equation to prevent the problem from becoming ill-posed during the inverse solution process. The analytical solution results demonstrate its computational cost-effectiveness, high accuracy and potential capability for practical modes (particularly when applied to observational concentration data with errors). •An analytical method for the pollutant transport equation in rivers is presented.•This unique method, solves the advection-dispersion equation inversely in time.•The proposed solution is a useful tool to reconstruct pollutant loadings.•The method can be accurately applied to any pattern of pollutant sources.•The solution results demonstrate its computational cost-effectiveness and accuracy.