Introducing a general framework for pollution source identification in surface water resources (theory and...

Studies on pollution source identification in water resources date back over three decades. These studies use inverse solution of the transport equation for recovering the release history and/or the location of the pollutant sources. Each of these studies has its own advantages and limitations in accordance with the methods employed and the complexity of the solutions. Moreover, conducted studies on pollution source identification in surface water resources (e.g. rivers) are fewer in number compared to those on groundwater resources. In nearly all previous related studies on rivers, researchers have often developed their own numerical forward models, but these models have never taken into account the complexity of the problem in real conditions, such as river topography, real flow conditions, etc. Therefore, compared to commercial models, these models have many drawbacks and limitations. Thus, it would be desirable to provide a framework that can be employed to solve the transport equation in the inverse model using available software packages. In this study, the inverse solution of the transport equation for recovering release histories of multiple pollutant sources in rivers is achieved by the help of ready software packages via a feasible framework. The proposed framework can be readily applied in one-, two-, and three-dimensional problems. The underlying concept of the proposed framework is the linearity of the governing equation, i.e. transport equation. Furthermore, the present study presents the conditions and rules for the arrangement (number and location) of the measurement points of the pollutant concentration under various conditions. The proper arrangement of the measurement points is significant, since it solves the non-uniqueness problem of the inverse model. The most important factor affecting the arrangement of the measurement points is the flow pattern. In this study, it is suggested that the complexity of the flow pattern may lead to practical arrangements for the control points. The proposed procedure was verified by the use of three series of data in one- and two-dimensional domains under real conditions of flow and topography by employing well-known existing software packages. In each test case, a proper and practical arrangement was proposed for the measurement points of the concentration-time curve. The suggested arrangement resulted in the correct operation of the inverse model. The proposed inverse model showed a good capability with a reasonable percentage of errors of the recovering release rate of pollutant sources. Accordingly, it can be conveniently used in cases where forward models are readily available.