Variational methods for identifying the power of an instantaneous point source on the sea surface

Authors

UDC

51.37

EDN

OIUOBV

DOI:

10.31429/vestnik-23-1-56-62

Abstract

Using the example of a passive impurity transfer model, variation algorithms for identifying the power of an instantaneous source of pollution on the sea surface are considered. The solution to this problem is possible with several variation approaches. One of them is an algorithm based on variation principles and solving related problems, and in the case of a point instantaneous source, a simplified algorithm based on the linearization method can be used. It should be noted that the properties of the algorithms used in this case can be significantly improved by choosing the optimal measurement scheme, i.e. optimal plans. From a mathematical point of view, an optimal plan is understood as a set of measurement points distributed over space and time, which gives the best conditionality of the problem being solved. The Jacobi information matrix is constructed using solutions to a series of related problems. It is known that measurements of the concentration field, which are performed at the points of maximum values, lead to increased conditionality of the problem being solved and faster convergence of the iterative process. The algorithm for constructing the Fischer information matrix is presented for the case of a three-dimensional model of passive impurity transport in the Sea of Azov. The effect of an instantaneous and permanent point source of pollution is considered. The results can be used to solve various environmental problems in studying the effects of anthropogenic pollution sources in the waters of the Azov and Black Seas.

Keywords:

experimental design, transport model, passive admixture, identification, adjoint problem, minimization, Sea of Azov

Funding information

The work was carried out within the framework of the state assignment on topic No. FNNN-2024-0016 "Study of the spatio-temporal variability of oceanographic processes in the coastal, coastal and shelf zones of the Black Sea under the influence of natural and anthropogenic factors based on contact measurements and mathematical modeling" (code "Coastal research").

Authors info

  • Vladimir S. Kochergin

    младший научный сотрудник отдела теории волн Федерального исследовательского центра «Морской гидрофизический институт РАН»

  • Sergei V. Kochergin

    старший научный сотрудник отдела вычислительных технологий и математического моделирования Федерального исследовательского центра «Морской гидрофизический институт РАН»

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Issue

Vol. 23 (2026) No. 1

Pages

56-62

Section

Mechanics

Dates

Submitted

January 26, 2026

Accepted

March 17, 2026

Published

March 24, 2026

How to Cite

[1]
Kochergin, V.S., Kochergin, S.V., Variational methods for identifying the power of an instantaneous point source on the sea surface. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2026, т. 23, № 1, pp. 56–62. DOI: 10.31429/vestnik-23-1-56-62

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Copyright (c) 2026 Кочергин В.С., Кочергин С.В.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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