Numerical Experiments to Identify Suspended Matter Flow Rate over the Seabed in a Model of Impurity Transport

V. S. Kochergin*, S. V. Kochergin

Marine Hydrophysical Institute of RAS, Sevastopol, Russia

* e-mail: vskocher@gmail.com

Abstract

The paper deals with variation assimilation of model data on the concentration of suspended matter in the upper layer of the Sea of Azov. Such information is used during practical evaluation of identification algorithms to test the assimilation of concentration values derived from satellite information. Combined use of surface concentration estimates and modeling results based on the transport model is of interest for determining the strength of sources of suspended matter inflow. The test problem has been solved of determination of the required parameter in the sea bottom boundary condition when parameterizing the sediment inflow (agitation) from bottom sediments due to dynamic processes in the sea bottom layer. Two approaches to search for the required constant for the parameterization used in the calculations are implemented. A variational identification algorithm based on adjoint problem solving is used in determining the spatially variable flow of suspended matter on the seabed. The assimilation of measurement data into a model of passive admixture transport allows to determine the spatial structure of such flows at a given time interval. When implementing the variational identification algorithm, gradient methods are used to find optimal estimates by minimizing the quadratic functional of the prognosis quality. The solution of the adjoint problem is used to construct the gradient of the prognosis quality functional. Descent is performed in the direction of this gradient. During realization of variational procedure the main problem, the adjoint problem and the problem in variations, which is necessary to determine an iteration parameter, are solved. The flow fields and turbulent diffusion coefficients used in the calculations were obtained using a dynamic model of the Sea of Azov in sigma coordinates under exposure to intense easterly wind.

Keywords

suspended matter concentration, variational identification algorithm, assimilation, adjoint problem, Sea of Azov, assimilation of measurement data, flow of matter.

Acknowledgments

The research is performed under state order on topic No. 0555-2021-0005 “Complex interdisciplinary research of oceanologic processes, which determine functioning and evolution of the Black and Azov Sea coastal ecosystems” (“Coastal studies” code name).

For citation

Kochergin, V.S. and Kochergin, S.V., 2021. Numerical Experiments to Identify Suspended Matter Flow Rate on the Sea Bottom in the Impurity Transport Model. Ecological Safety of Coastal and Shelf Zones of Sea, (1), pp. 23–33. doi:10.22449/2413-5577-2021-1-23-33 (in Russian).

DOI

10.22449/2413-5577-2021-1-23-33

References

  1. Blumberg, A.F. and Mellor, G.L., 1987. A Description of a Three-Dimensional Coastal Ocean Circulation Model. In: N.S. Heaps, ed., 1987. Three-Dimensional Coastal Ocean Models. Washington, DC: American Geophysical Union, pp. 1–16. https://doi.org/10.1029/CO004p0001
  2. Fomin, V.V., 2002. Numerical Model of the Circulation of Waters in the Sea of Azov. In: UHMI, 2002. Trudy UkrNIGMI [Proceedings of UHMI]. Kiev: UHMI. Iss. 249, pp. 246–255 (in Russian).
  3. Ivanov, V.A. and Fomin, V.V., 2010. Mathematical Modeling of Dynamical Processes in the Sea–Land Area. Kyiv: Akademperiodyka, 286 p. https://doi.org/10.15407/akademperiodyka.158.286
  4. Kremenchutskiy, D.A., Kubryakov, A.A., Zav’yalov, P.O., Konovalov, B.V., Stanichniy, S.V. and Aleskerova, A.A., 2014. Determination of the Suspended Matter Concentration in the Black Sea Using to the Satellite MODIS Data. In: MHI, 2014. Ekologicheskaya Bezopasnost' Pribrezhnykh i Shel'fovykh Zon i Kompleksnoe Ispol'zovanie Resursov Shel'fa [Ecological Safety of Coastal and Shelf Zones and Comprehensive Use of Shelf Resources]. Sevastopol: ECOSI-Gidrofizika. Iss. 29, pp. 5–9 (in Russian).
  5. Marchuk, G.I., 1986. Mathematical Models in Environmental Problems. Amsterdam: Elsevier Science Publishers B.V., 216 p.
  6. Marchuk, G.I. and Penenko, V.V., 1979. Application of Optimization Methods to the Problem of Mathematical Simulation of Atmospheric Processes and Environment. In: G.I. Marchuk, ed., 1979. Modelling and Optimization of Complex System. Berlin: Springer, pp. 240–252. https://doi.org/10.1007/BFb0004167
  7. Shutyaev, V.P., 2019. Methods for Observation Data Assimilation in Problems of Physics of Atmosphere and Ocean. Izvestiya, Atmospheric and Oceanic Physics, 55(1), pp. 17–31. doi:10.1134/S0001433819010080
  8. Shutyaev, V.P., Le Dimet, F.-X. and Parmuzin, E., 2018. Sensitivity Analysis with Respect to Observations in Variational Data Assimilation for Parameter Estimation. Nonlinear Processes in Geophysics, 25(2), pp. 429–439. https://doi.org/10.5194/npg-25-429-2018
  9. Zalesny, V.B., Agoshkov, V.I., Shutyaev, V.P., Le Dimet, F. and Ivchenko, B.O., 2016. Numerical Modeling of Ocean Hydrodynamics with Variational Assimilation of Observational Data. Izvestiya, Atmospheric and Oceanic Physics, 52(4), pp. 431–442. https://doi.org/10.1134/S0001433816040137
  10. Shutyaev, V.P. and Parmuzin, E.I., 2019. Sensitivity of Functionals to Observation Data in a Variational Assimilation Problem for a Sea Thermodynamics Model. Numerical Analysis and Applications, 12(2), pp. 191–201. https://doi.org/10.1134/S1995423919020083
  11. Kochergin, V.S. and Kochergin, S.V., 2015. Identification of a Pollution Source Power in the Kazantip Bay Applying the Variation Algorithm. Physical Oceanography, (2), pp. 69–76. doi:10.22449/1573-160X-2015-2-69-76
  12. Harten, A., 1984. On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes. SIAM Journal on Numerical Analysis, 21(1, pp. 1–23. https://doi.org/10.1137/0721001
  13. Kochergin, S.V. and Kochergin, V.S., 2010. Using of Variational Principles and Adjoint Problem Decision During Identification of Input Parameters of Passive Impurity Transport Model. In: MHI, 2010. Ekologicheskaya Bezopasnost' Pribrezhnykh i Shel'fovykh Zon i Kompleksnoe Ispol'zovanie Resursov Shel'fa [Ecological Safety of Coastal and Shelf Zones and Comprehensive Use of Shelf Resources]. Sevastopol: ECOSI-Gidrofizika. Iss. 22, pp. 240–244 (in Russian).
  14. Gorsky, V.G., 1984. [Planning of Kinetic Experiments]. Moscow: Nauka, 241 p. (in Russian).

Download the article (PDF, in Russian)