Numerical solution of the problem of variational data assimilation to restore heat fluxes and initial state for the ocean thermodynamics model

References

[1] V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics INM RAS, Moscow, 2003 (in Russian).Search in Google Scholar

[2] V. I. Agoshkov, A. V. Gusev, N. A. Diansky, and R. V. Oleinikov, An algorithm for the solution of the ocean hydrothermo-dynamics problem with variational assimilation of the sea level function data. Russ. J. Numer. Anal. Math. Modelling 22 (2007), No. 2, 1–10.10.1515/RJNAMM.2007.007Search in Google Scholar

[3] V. I. Agoshkov, N. R. Lezina, E. I. Parmuzin, T. O. Sheloput, V. P. Shutyaev, and N. B. Zakharova, Methods of variational data assimilation with application to problems of hydrotermodenamics of marine water areas. Russ. J. Numer. Anal. Math. Modelling 35 (2020), No. 4, 189–202.10.1515/rnam-2020-0016Search in Google Scholar

[4] V. I. Agoshkov, E. I. Parmuzin, and V. P. Shutyaev, Numerical algorithm for variational assimilation of sea surface temperature data. Comput. Maths. Math. Phys. 48 (2008), No. 8, 1293–1312.10.1134/S0965542508080046Search in Google Scholar

[5] V. I. Agoshkov, E. I. Parmuzin, and V. P. Shutyaev, Observational data assimilation in the problem of Black Sea circulation and sensitivity analysis of its solution. Izvestiya, Atmospheric and Oceanic Physics 49 (2013), No. 6, 592–602.10.1134/S0001433813060029Search in Google Scholar

[6] V. V. Alekseev and V. B. Zalesny, Numerical model of large-scale ocean dynamics. In: Vychislitelnye Processy i Sistemy (Computational Processes and Systems), Nauka, Moscow, 1993, pp. 232–253.Search in Google Scholar

[7] M. Asch, M. Bocquet, and M. Nodet, Data Assimilation: Methods, Algorithms, and Applications SIAM, Philadelphia, 2016.10.1137/1.9781611974546Search in Google Scholar

[8] A. Carrassi, M. Bocquet, L. Bertino, and G. Evensen, Data assimilation in the geosciences: An overview of methods, issues, and perspectives. WIREs Clim. Change 9 (2018), No. 5, e535.10.1002/wcc.535Search in Google Scholar

[9] S. J. Fletcher, Data Assimilation for the Geosciences: from Theory to Application Elsevier, Amsterdam, Netherlands, 2017.10.1016/B978-0-12-804444-5.00023-4Search in Google Scholar

[10] F. X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38A (1986), 97–110.10.1111/j.1600-0870.1986.tb00459.xSearch in Google Scholar

[11] J. L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles Dunod, Paris, 1968.Search in Google Scholar

[12] V. I. Lebedev and S. A. Finogenov, The order of choice of iteration parameters in the cyclic Chebyshev iteration method. USSR Comput. Maths. Math. Phys. 11 (1971) No. 2, 155–170.10.1016/0041-5553(71)90169-8Search in Google Scholar

[13] E. A. Lupyan, A. A. Matveev, I. A. Uvarov, T. Yu. Bocharova, O. Yu. Lavrova, and M. I. Mityagina, ‘See the Sea’ satellite service, instrument for studying processes and phenomena on the ocean surface. In: Sovremennye Problemy Distantsionnogo Zondirovaniya Zemli iz KosmosaProblems in Remote Sensing of the Earth from Space 9 (2012), No. 2, 251–261.Search in Google Scholar

[14] G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems Kluwer, Dordrecht, 1995.10.1007/978-94-017-0621-6Search in Google Scholar

[15] G. I. Marchuk, V. P. Dymnikov and V. B. Zalesny, Mathematical Models in Geophysical Hydrodynamics and Numerical Methods of their Implementation Gidrometeoizdat, Leningrad, 1987 (in Russian).Search in Google Scholar

[16] G. I. Marchuk and V. I. Lebedev, Numerical Methods in the Theory of Neutron Transport Harwood Academic Publ., New York, 1986.Search in Google Scholar

[17] V. V. Penenko, Numerical Modelling Methods for Atmospheric Processes Gidrometeoizdat, Leningrad, 1981 (in Russian).Search in Google Scholar

[18] V. Penenko and N. N. Obraztsov, A variational initialization method for the fields of the meteorological elements. Soviet Meteorol. Hydrol. 11 (1976), 1–11.Search in Google Scholar

[19] Y. K. Sasaki, An objective analysis based on the variational method. J. Meteor. Soc. Japan 36 (1958), 77–88.10.2151/jmsj1923.36.3_77Search in Google Scholar

[20] V. P. Shutyaev, Control Operators and Iterative Algorithms in Problems of Variational Data Assimilation Nauka, Moscow, 2001 (in Russian).10.1515/jiip.2001.9.2.177Search in Google Scholar

[21] V. P. Shutyaev, Adjoint equations in variational data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 33 (2018), No. 2, 137–147.10.1515/rnam-2018-0012Search in Google Scholar

[22] V. P. Shutyaev, Methods for observation data assimilation in problems of physics of atmosphere and ocean. Izvestiya, Atmospheric and Oceanic Physics 55 (2019), No. 1, 17–31.10.1134/S0001433819010080Search in Google Scholar

[23] A. N. Tikhonov, On solution of ill-posed problems and regularization method. Doklady Akad. Nauk SSSR 151 (1963), No. 3, 501–504.Search in Google Scholar

[24] V. B. Zalesny, N. F. Diansky, V. V. Fomin, S. N. Moshonkin, and S. G. Demyshev, Numerical model of the circulation of the Black Sea and the Sea of Azov. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 95–112.10.1515/rnam-2012-0006Search in Google Scholar