Abstract
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).
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