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эксперимента путем включения большого числа наблюдений на коротком интервале значений аргумента. По аналогии с линейным регрессионным анализом оцениваются значения функций в правой части системы и значения производных по неточным наблюдениям. Используя систему дифференциальных уравнений, по полученным оценкам методом моментов определяются неизвестные параметры. Доказывается сходимость полученных оценок по вероятности к точным значениям при устремлении к бесконечности числа наблюдений.
Список литературы
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Variational data assimilation applied for sea dynamics problems
V. Shutyaev1,2, V. Agoshkov1,3, V. Zalesny1, E. Parmuzin1,2, N. Zakharova1
1Marchuk Institute of Numerical Mathematics, RAS
2Moscow Institute of Physics and Technology
3Lomonosov Moscow State University
Email: victor.shutyaev@mail.ru
DOI: 10.24412/cl-35065-2022-1-01-25
The 4D variational data assimilation technique is presented for modeling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations and observation and background error covariances. Efficient algorithms for solving the variational data assimilation problems based on iterative processes with a special choice of iterative parameters are presented. The technique is illustrated for sea dynamics problems with variational data assimilation to restore the initial states and the heat fluxes on the sea surface
This work was supported by the Russian Science Foundation (project 20-11-20057). References
1. Marchuk G. I. Adjoint equations and analysis of complex systems. Dordrecht: Kluwer, 1995.
2. Zalesny V. B., Agoshkov V. I., Shutyaev V. P., Le Dimet F.-X., Ivchenko B. O. Numerical modeling of ocean hydrodynamics with variational assimilation of observational data // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 431-442.
3. Shutyaev V. P. Methods for observation data assimilation in problems of physics of atmosphere and ocean // Izv. Atmos. Ocean. Phys. 2019. V. 55. P. 17-31.
4. Zalesny V., Agoshkov V., Shutyaev V., Parmuzin E., Zakharova N. Numerical modeling of marine circulation with 4D variational data assimilation // J. Mar. Sci. Eng. 2020. V. 8 (503). P. 1-19.
5. Shutyaev V. P., Parmuzin E. I. Numerical solution of the problem of variational data assimilation to restore heat fluxes and initial state for the ocean thermodynamics model // RJNAMM. 2021. V. 36, N. 1. P. 43-53.
