Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

Highlights

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking.

● Model is not stuck in local optimal solutions for high-dimensional problem.

● Model can estimate source parameters accurately with known river water levels.

● Both sudden spill incident and normal sewage inputs into the river can be tracked.

● Model is superior to the traditional approaches based on the test cases.

Abstract

Water quality restoration in rivers requires identification of the locations and discharges of pollution sources, and a reliable mathematical model to accomplish this identification is essential. In this paper, an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge. The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method (MCMC). The methodological framework is tested using a designed case of a sudden wastewater spill incident (i.e., source location, flow rate, and starting and ending times of the discharge) and a real case of multiple sewage inputs into a river (i.e., locations and daily flows of sewage sources). The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites. It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space. In comparison, the inverse models based on the popular random walk Metropolis (RWM) algorithm and microbial genetic algorithm (MGA) do not produce reliable estimates for the two scenarios even after multiple simulation runs, and they fall into locally optimal solutions. Since much more water level data are available than water quality data, the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data, especially for rivers receiving significant sewage discharges.

Graphical abstract

Keywords

Identification of pollution sources / Water quality restoration / Bayesian inference / Hydrodynamic model / Inverse problem

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Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (Grant No. 51979195) and the National Key R&D Program of China (No. 2021YFC3200703).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11783-023-1685-1 and is accessible for authorized users.

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