I. A. Shnaider¹, A. S. Bogomolov^{1, 2}, V. A. Kushnikov^{1, 2}

¹Institute of Precision Mechanics and Control, Saratov Scientific Center of the Russian Academy of Sciences (Saratov, Russian Federation)

²Saratov State University (Saratov, Russian Federation)

Abstract. The problem of localizing unauthorized sources of atmospheric pollution in an industrial area under varying meteorological conditions is considered. A mathematical model of pollutant dispersion is proposed, based on the solution of the transport equation. The model extends the classical Gaussian plume model by incorporating dry deposition and wet scavenging processes. Also the model takes into account the effect of relative humidity on the variation of pollutant particle mass. The source identification problem is formulated as an ill-posed inverse problem and reduced to minimization of a root-mean-square deviation between predicted and observed concentrations. The particle swarm optimization method is applied to solve this problem, providing global optimization of source parameters under limited input data. A software implementing the proposed models and algorithms is developed, providing integration with environmental monitoring systems. Computational experiments demonstrate improved accuracy of modelling and confirm the effectiveness of the proposed approach for source localization in comparison with existing methods.

Key Words: environmental monitoring, pollutants, a pollutant dispersion, Gaussian plume, source localization, simulation

For citation: I. A. Shnaider, A. S. Bogomolov, V. A. Kushnikov. Solution of a problem on localizing unauthorized sources of atmospheric pollution by means of mathematical modelling. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:3(2026), 308–320. DOI: https://doi.org/10.15507/2079-6900.28.202603.308-320

Information about the authors:

Ilya A. Shnaider, Junior Researcher, Institute of Precision Mechanics and Control -- Subdivision of the Federal State Budgetary Research Institution Saratov Federal Scientific Centre of the Russian Academy of Sciences (24 Rabochaya St., Saratov 410028, Russia), ORCID: https://orcid.org/0009-0003-4739-0130, e-mail: es1098@mail.ru

Aleksey S. Bogomolov, D.Sc. (Engineering), Leading Researcher, Head of the Laboratory of System Analysis and Management, Institute of Precision Mechanics and Control -- Subdivision of the Federal State Budgetary Research Institution Saratov Federal Scientific Centre of the Russian Academy of Sciences (24 Rabochaya St., Saratov 410028, Russia); Professor, Saratov State University (83 Astrakhanskaya St., Saratov 410012, Russia), ORCID: https://orcid.org/0000-0002-6972-3181, e-mail: alexbogomolov@ya.ru

Vadim A. Kushnikov, D.Sc. (Engineering), Chief Researcher, Head of the Laboratory for Integrated Scientific Research, Institute of Precision Mechanics and Control -- Subdivision of the Federal State Budgetary Research Institution Saratov Federal Scientific Centre of the Russian Academy of Sciences (24 Rabochaya St., Saratov 410028, Russia); Professor, Saratov State University (83 Astrakhanskaya St., Saratov 410012, Russia), ORCID: https://orcid.org/0000-0002-9195-2546, e-mail: kushnikoff@yandex.ru