The variational identification algorithm of the speed sedimentation of suspended matter in the sea
UDC
519.63DOI:
https://doi.org/10.31429/vestnik-17-4-43-47Abstract
Technical capacity information from satellites about the state of the surface of the ocean and seas, the development of methods and algorithms of information processing and mathematical modelling of water circulation, leads to the creation of algorithms for assimilation of such information in dynamic models. The parameters found in this case make it possible to obtain a model solution that best matches the measurements due to the minimization of the forecast quality functional used. Variational algorithms for solving various problems of identifying certain parameters of numerical simulation of passive impurity transfer are based on solving adjoint problems and implementing iterative procedures for finding optimal parameters from measurement data. Such parameters in the passive impurity transfer problem can be the initial data, the flows of matter at the bottom and surface, the power of point sources, the coefficients of turbulent diffusion, and the velocity fields. In this paper, this parameter is the particle sedimentation rate. they are deposited by gravity, which naturally depends on the particle size. However, the task of estimating some averaged values is possible on the basis of assimilation of operational information obtained from the satellite. The algorithm is based on solving the conjugate problem and the problem in variations. The problem is solved by searching for the minimum of the quadratic functional of the forecast quality, and the model acts as constraints when minimizing it. To construct the functional gradient, the solution of the corresponding adjoint problem is used. Expressions for determining the desired functional gradient in the parameter space are given.
Keywords:
transfer model, data assimilation, sedimentation rate, parameter identification, functional minimizationAcknowledgement
References
- Kremenchuckij ,D.A., Kubryakov, A.A., Zav'yalov, P.O., Konovalov, B.V., Stanichnyj, S.V., Aleskerova A.A. Opredelenie koncentracii vzveshennogo veshchestva v CHernom more po dannym sputnika MODIS [Determination of the concentration of suspended matter in the Black sea according to the data of the MODIS satellite]. Ekologicheskaya bezopasnost' pribrezhnoj i shel'fovoj zon i kompleksnoe ispol'zovanie resursov shel'fa [Environmental safety of coastal and shelf zones and integrated use of shelf resources], 2014, no. 29, pp. 1–9. (In Russian)
- Timchenko, I.E. Dinamiko-stohasticheskie modeli sostoyaniya okeana [Dynamic-stochastic models of the ocean state]. Naukova dumka, Kiev, 1981. (In Russian)
- Marchuk, G.I., Penenko, V.V. Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment. Modelling and Optimization of Complex Systems. Marchuk G.I. (ed.) Proc. of the IFIP-TC7 Working conf. New York: Springer, 1978, pp. 240–252.
- Kochergin, V.S., Kochergin, S.V. Ispol'zovanie variacionnyh principov i resheniya sopryazhennoj zadachi pri identifikacii vhodnyh parametrov modeli perenosa passivnoj primesi [The use of variational principles and the solution of the conjugate problem in identifying the input parameters of the passive impurity transport model]. Ekologicheskaya bezopasnost' pribrezhnoj i shel'fovoj zon i kompleksnoe ispol'zovanie resursov shel'fa [Environmental safety of coastal and shelf zones and integrated use of shelf resources], 2010, iss. 22, pp. 240–244. (In Russian)
- Penenko, V.V. Metody chislennogo modelirovaniya atmosfernyh processov [Methods of numerical modeling of atmospheric processes]. Gidrometeoizdat, Leningrad, 1981. (In Russian)
- Agoshkov, V.I., Parmuzin, E.I., Shutyaev, V.P. Assimilyaciya dannyh nablyudenij v zadache cirkulyacii Chernogo morya i analiz chuvstvitel'nosti ego resheniya [Assimilation of observational data in the Black sea circulation problem and sensitivity analysis of its solution]. Izv. RAN. Fizika atmosfery i okeana [Izvestiya RAS. Physics of the atmosphere and ocean], 2013, vol. 49, no. 6, pp. 643–654. (In Russian)
- Shutyaev, V.P., Le Dime, F., Agoshkov, V.I., Parmuzin, E.I. Chuvstvitel'nost' funkcionalov zadach variacionnogo usvoeniya dannyh nablyudenij [Sensitivity of functional problems of variational assimilation of observational data]. Izv. RAN. Fizika atmosfery i okeana [Izvestiya RAS. Physics of the atmosphere and ocean], 2015, vol. 51, no. 3, pp. 392–400. (In Russian)
- Shutyaev, V.P., Le Dimet, F.–X., Parmuzin, E. Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation. Nonlinear processes in Geophysics, 2018, vol. 25, iss. 2, pp. 429–439.
- Kochergin, V.S., Kochergin, S.V. Indentification of a pollution source power in the Kazantip bay applying the variation algorithm. Physical Oceanography, 2015, no. 2, pp. 69–76.
- Marchuk, G.I. Matematicheskoe modelirovanie v probleme okruzhayushchej sredy [Mathematical modeling in the environmental problem] [Mathematical modeling in the environmental problem]. Nauka, Moscow, 1982. (In Russian)
- Kochergin, V.S., Kochergin, S.V., Stanichnyj, S.V. Variacionnaya assimilyaciya sputnikovyh dannyh poverhnostnoj koncentracii vzveshennogo veshchestva v Azovskom more. Sovremennye problemy distancionnogo zondirovaniya Zemli iz kosmosa, 2020, vol. 17, no. 2, pp. 40–48.
- NASA Worldview. Available at: http://worldview.earthdata.nasa.gov (accessed 12.11.2020).
- Marine Portal. Marine Hydrophysical Institute of RAS. Available at: http://dvs.net.ru/mp/ data/201507vw.shtml (accessed 12.11.2020).
- Ivanov, V.A., Fomin, V.V. Matematicheskoe modelirovanie dinamicheskih processov v zone more – susha [Mathematical modeling of dynamic processes in the sea – land zone]. EKOSI-gidrofizika, Sevastopol', 2008. (In Russian)
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