Variational assimilation with covariance matrices of observation data errors for the model of the Baltic Sea dynamics
Abstract
The mathematical model of the Baltic Sea dynamics developed at the Institute of Numerical Mathematics of RAS is considered. The problem of variational assimilation of average daily data for the sea surface temperature (SST) is formulated and studied with the use of covariance matrices of observation data errors. Based on variational assimilation of satellite observation data, we propose an algorithm for solving the inverse problem of the heat flux reconstruction on the sea surface. The results of numerical experiments on reconstruction of the heat flux function are presented for the problem of variational assimilation of observation SST data.
Funding: The work was supported by the Russian Science Foundation (project 14–11–00609, the studies of Sections 1, 1), the Russian Foundation for Basic Research (project 18–01–00267, the studies of Section 3), and the Grant of the President of the Russian Federation (project MK-3228.2016.5, processing of the observation data).
References
[1] V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian).Suche in Google Scholar
[2] V. I. Agoshkov, A. V. Gusev, N. A. Dianskii, and R. V. Oleinikov, An algorithm for the solution of the ocean hydrothermodynamics problem with variational assimilation of the sea level function data. Russ. J. Numer. Anal. Math. Modelling22 (2007), No. 2, 1–10.10.1515/RJNAMM.2007.007Suche in Google Scholar
[3] V. I. Agoshkov, E. I. Parmuzin, and V. P. Shutyaev, Numerical algorithm for variational assimilation of sea surface temperature data. Comp. Math. Math. Phys. 48 (2008), No. 8, 1293–1312.10.1134/S0965542508080046Suche in Google Scholar
[4] V. I. Agoshkov, E. I. Parmuzin, V. B. Zalesny, V. P. Shutyaev, N. B. Zakharova, and A. V. Gusev, Variational assimilation of observation data in the mathematical model of the Baltic Sea dynamics. Russ. J. Numer. Anal. Math. Modelling30 (2015), No. 4, 203–212.10.1515/rnam-2015-0018Suche in Google Scholar
[5] 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 (in Russian).Suche in Google Scholar
[6] I. Karagali, J. Hoyer, and C. B. Hasager, SST diurnal variability in the North Sea and the Baltic Sea. Remote Sensing of Environment121 (2012), 159–170. 10.1016/j.rse.2012.01.016.Suche in Google Scholar
[7] F. X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus38A (1986), 97–110.10.1111/j.1600-0870.1986.tb00459.xSuche in Google Scholar
[8] J. L. Lions, Contrôle Optimal des Systèmes Gouvernés par des Équations aux Dérivées Partielles. Dunod, Paris, 1968.Suche in Google Scholar
[9] G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems. Kluwer, Dordrecht, 1995.10.1007/978-94-017-0621-6Suche in Google Scholar
[10] G. I. Marchuk, V. P. Dymnikov, and V. B. Zalesny, Mathematical Models in Geophysical Fluid Dynamics and Numerical Methods for Their Implementation. Gidrometeoizdat, Leningrad, 1987 (in Russian).Suche in Google Scholar
[11] G. I. Marchuk, Splitting and alternative direction methods. In: Handbook of Numerical Analysis (Eds. P. G. Ciarlet and J. L. Lions). North-Holland, Amsterdam, 1990, Vol. 1, pp. 197–462.10.1016/S1570-8659(05)80035-3Suche in Google Scholar
[12] G. I. Marchuk, A. S. Rusakov, V. B. Zalesny, and N. A. Dianskii, Splitting numerical technique with application to the high resolution simulation of the Indian ocean circulation. Pure and Applied Geophysics162 (2005), 1407–1429.10.1007/3-7643-7376-8_3Suche in Google Scholar
[13] K. Mogensen, M. A. Balmaseda, A. T. Weaver, M. Martin, and A. Vidard, NEMOVAR: A Variational Data Assimilation System for the NEMO Ocean Model. ECMWF Technical Memorandum No. 120, 2009.Suche in Google Scholar
[14] H. U. Roll, Physics of the Marine Atmosphere. Academic Press, New York, 1965.Suche in Google Scholar
[15] N. B. Zakharova, Verification of the sea surface temperature observation data. Current Problems of Remote Sensing of the Earth from Space13 (2016), No. 3. 106–113.10.21046/2070-7401-2016-13-3-106-113Suche in Google Scholar
[16] N. B. Zakharova, V. I. Agoshkov, and E. I. Parmuzin, The new method of ARGO buoys system observation data interpolation. Russ. J. Numer. Anal. Math. Modelling28 (2013), No. 1, 67–84.10.1515/rnam-2013-0005Suche in Google Scholar
[17] V. B. Zalesny, G. I. Marchuk, V. I. Agoshkov, A. V. Bagno, A. V. Gusev, N. A. Dianskii, S. N. Moshonkin, R. Tamsalu, and E. M. Volodin, Numerical simulation of large-scale ocean circulation based on multicomponent splitting method. Russ. J. Numer. Anal. Math. Modelling25 (2010), No. 6, 581–609.10.1515/rjnamm.2010.036Suche in Google Scholar
[18] V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling28 (2013), No. 1, 85–100.10.1515/rnam-2013-0006Suche in Google Scholar
[19] V. B. Zalesny, A. V. Gusev, S. Yu. Chernobai, R. Aps, R. Tamsalu, P. Kujala, and J. Rytkönen, The Baltic Sea circulation modelling and assessment of marine pollution. Russ. J. Numer. Anal. Math. Modelling29 (2014), No. 2, 129–138.10.1515/rnam-2014-0010Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Variational assimilation with covariance matrices of observation data errors for the model of the Baltic Sea dynamics
- Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium
- Modelling the Azov Sea circulation and extreme surges in 2013-2014 using the regularized shallow water equations
- Two-dimensional projection Monte Carlo estimators for the study of angular characteristics of polarized radiation
- On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates
Artikel in diesem Heft
- Frontmatter
- Variational assimilation with covariance matrices of observation data errors for the model of the Baltic Sea dynamics
- Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium
- Modelling the Azov Sea circulation and extreme surges in 2013-2014 using the regularized shallow water equations
- Two-dimensional projection Monte Carlo estimators for the study of angular characteristics of polarized radiation
- On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates