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<p>Over the past three decades, one challenge researchers have faced is obtaining reliable information about unknown pollutant sources in aquatic environments. Among these challenges, the contribution of studies conducted in rivers is significantly lower than in groundwater. Therefore, developing a method that, in addition to being practical, can accurately identify information about unknown pollutant sources in rivers would be valuable. This study aims to present a method based on the inverse problem solution to simultaneously identify the location and intensity function of point pollutant sources in rivers without requiring any prior information, within a mathematical framework. The presented inverse model can calculate the unknowns of the problem with acceptable accuracy, requiring very low computational cost and only the concentration-time curve at two points upstream and downstream of the pollutant source. In this study, the complete problem-solving process is based on solving both forward and inverse models. The results of the forward model are the pollutant concentration as a function of time at different points in the river, which are used as input to the inverse model. The results of the inverse model include the location and intensity function of the pollutant source, determined using methods such as the Tikhonov regularization method. The accuracy of the presented inverse model was verified using a hypothetical test case. To ensure the capability of the presented model, a range of error values was applied to certain parameters, such as flow velocity and dispersion coefficient, to evaluate the model's robustness in identifying the location and retrieving the intensity function of the pollutant source. The results demonstrate that the proposed model has minimal sensitivity to errors in the mentioned parameters. Furthermore, even when a 10% measurement error was applied to the concentration values at the measurement station, the location of the pollutant source could be identified with an <i>R</i><sup><i>2</i></sup> value of 99.32%, illustrating the acceptable accuracy of the inverse model.</p>

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Theoretical Basis for Designing a Mathematical Sensor for Pollution Source Identification in Rivers

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Akram Dahmardan,
  • Siamak Amiri,
  • Mehdi Mazaheri

摘要

Over the past three decades, one challenge researchers have faced is obtaining reliable information about unknown pollutant sources in aquatic environments. Among these challenges, the contribution of studies conducted in rivers is significantly lower than in groundwater. Therefore, developing a method that, in addition to being practical, can accurately identify information about unknown pollutant sources in rivers would be valuable. This study aims to present a method based on the inverse problem solution to simultaneously identify the location and intensity function of point pollutant sources in rivers without requiring any prior information, within a mathematical framework. The presented inverse model can calculate the unknowns of the problem with acceptable accuracy, requiring very low computational cost and only the concentration-time curve at two points upstream and downstream of the pollutant source. In this study, the complete problem-solving process is based on solving both forward and inverse models. The results of the forward model are the pollutant concentration as a function of time at different points in the river, which are used as input to the inverse model. The results of the inverse model include the location and intensity function of the pollutant source, determined using methods such as the Tikhonov regularization method. The accuracy of the presented inverse model was verified using a hypothetical test case. To ensure the capability of the presented model, a range of error values was applied to certain parameters, such as flow velocity and dispersion coefficient, to evaluate the model's robustness in identifying the location and retrieving the intensity function of the pollutant source. The results demonstrate that the proposed model has minimal sensitivity to errors in the mentioned parameters. Furthermore, even when a 10% measurement error was applied to the concentration values at the measurement station, the location of the pollutant source could be identified with an R2 value of 99.32%, illustrating the acceptable accuracy of the inverse model.