Skip to main content
Log in

Variational Data Assimilation in Problems of Modeling Hydrophysical Fields in Open Water Areas

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

The formulation of boundary conditions at liquid (open) boundaries is a topical problem in mathematically modeling the hydrothermodynamics of open water areas. Variational data assimilation is one method allowing one to take into account liquid boundaries in models. According to the approach considered in this paper, observational data at a certain time are given and the problem is treated as an inverse one with open boundary flows as additional unknowns. This paper presents a formulation of the general problem of the variational assimilation of observational data for a model of the hydrothermodynamics of open water areas based on the splitting method. Algorithms for the variational assimilation of temperature and sea-level data at the liquid boundary are formulated and the results of numerical experiments on the use of the algorithms in the Baltic Sea circulation model are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. A. I. Kubryakov, “The use of overset grid technology for the construction of a system for hydrophysical field moitoring in the coastal areas of the Black Sea, in Ecological Safety of Coastal and Shelf Zones and Integrated Exploitation of the Shelf Resources (EKOSI-Gidrofizika, Sevastopol, 2004), no. 11, pp. 31–50.

  2. I. A. Chernov and A. V. Tolstikov, “Numerical modeling of large-scale dynamics of the White Sea,” Trudy Karel. Nauch. Tsentra RAN, No. 4, 137–142 (2014).

    Google Scholar 

  3. S. A. Myslenkov, “The use of satellite altimetry for the numerical simulation of water transfer in the Northern Atlantic Ocean,” Tr. GU Gidromettsentr Rossii 345, 119–125 (2011).

    Google Scholar 

  4. I. Orlanski, “A simple boundary condition for unbounded hyperbolic flows,” J. Comput. Phys. 21 (3), 251–269 (1976).

    Article  Google Scholar 

  5. P. Marchesiello, J. C. McWilliams, and A. Shchepetkin, “Open boundary conditions for long-term integration of regional oceanic models,” Ocean Model. 3, 1–20 (2001).

    Article  Google Scholar 

  6. C. A. Edwards, A. M. Moore, I. Hoteit, and B. D. Cornuelle, “Regional ocean data assimilation,” Annu. Rev. Mar. Sci. 7, 6:1–6:22 (2015).

  7. G. I. Marchuk and V. B. Zalesny, “Modeling of the world ocean circulation with the four-dimensional assimilation of temperature and salinity fields,” Izv., Atmos. Ocean. Phys. 48 (1), 15–29 (2012).

    Article  Google Scholar 

  8. V. B. Zalesny, V. I. Agoshkov, V. P. Shutyaev, F. Le Dimet, and B. O. Ivchenko, “Numerical modeling of ocean hydrodynamics with variational assimilation of observational data,” Izv., Atmos. Ocean. Phys. 52, 431–442 (2016).

    Article  Google Scholar 

  9. H. Ngodock and M. Carrier, “A weak constraint 4D-Var assimilation system for the navy coastal ocean model using the representer method,” in Data Assimilation for At-mospheric, Oceanic and Hydrologic Applications (Springer, Berlin, Heidelberg, 2013), Vol. II.

    Google Scholar 

  10. V. I. Agoshkov, V. P. Shutyaev, E. I. Parmuzin, N. B. Zakharova, T. O. Sheloput, and N. R. Lezina, “Variational Data Assimilation in the Mathematical Model of the Black Sea Dynamics,” Physical Oceanography. 26 (6), 515–527 (2019).

    Article  Google Scholar 

  11. H. S. Tang, K. Qu, and X. G. Wu, “An overset grid method for integration of fully 3D fluid dynamics and geophysics fluid dynamics models to simulate multiphysics coastal ocean flows,” J. Comput. Phys. 273, 548–571 (2014).

    Article  Google Scholar 

  12. A. F. Bennett and P. C. McIntosh, “Open ocean modeling as an inverse problem: tidal theory,” J. Phys. Oceanogr. 12 (10), 1004–1018 (1982).

    Article  Google Scholar 

  13. V. I. Agoshkov, “Application of mathematical methods for solving the problem of liquid boundary conditions in hydrodynamics,” Z. Angew. Math. Mech. 76 (S1), 337–338 (1995)

    Google Scholar 

  14. V. I. Agoshkov, “Inverse problems of the mathematical theory of tides: boundary-function problem,” Russ. J. Numer. Anal. Math. Model. 20 (1), 1–18 (2005).

    Article  Google Scholar 

  15. V. I. Agoshkov, “Statement and study of some inverse problems in modelling of hydrophysical fields for water areas with ‘liquid’ boundaries,” Russ. J. Numer. Anal. Math. Model. 32 (2), 73–90 (2017).

    Google Scholar 

  16. V. I. Agoshkov, Methods of Solving Inverse Problems and the Problems of Variational Assimilation of Observation DataInStudies of Large-Scale Dynamics of Oceans and Seas (IVM RAN, Moscow, 2016) [in Russian].

    Google Scholar 

  17. V. I. Agoshkov, N. R. Lezina, and T. O. Sheloput, “Domain decomposition method for the variational assimilation of the sea level in a model of open water areas hydrodynamics,” J. Mar. Sci. Eng. 7 (6), 195 (2019).

    Article  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. Model. 28 (1), 85–100 (2013).

    Article  Google Scholar 

  19. V. B. Zalesnyi, A. V. Gusev, and V. I. Agoshkov, “Modeling Black Sea circulation with high resolution in the coastal zone,” Izv., Atmos. Ocean. Phys. 52, 277–293 (2016).

    Article  Google Scholar 

  20. E. V. Dement’eva, E. D. Karepova, and V. V. Shaidurov, “Recovery of a boundary function from observation data for the surface wave propagation problem in an open basin,” Sib. Zh. Industr. Matem. 16 (1), 10–20 (2013).

    Google Scholar 

  21. V. I. Agoshkov and T. O. Sheloput, “The study and numerical solution of some inverse problems in simulation of hydrophysical fields in water areas with ‘liquid’ boundaries,” Russ. J. Numer. Anal. Math. Model. 32 (3), 147–164 (2017).

    Google Scholar 

  22. G. I. Marchuk, V. P. Dymnikov, and V. B. Zalesnyi, Mathematical Models in Geophysical Fluid Dynamics and Numerical Methods of Their Implementation (Gidrometeoizdat, Leningrad, 1987) [in Russian].

    Google Scholar 

  23. V. I. Agoshkov and M. V. Assovskii, Mathematical Modelling of the Dynamics of the World’s Oceans with Tide-Forming Forces Taken Into Account (IVM RAN, Moscow, 2016) [in Russian].

    Google Scholar 

  24. V. I. Agoshkov, Optimal Control Methods and Adjoint Equations in Mathematical Physics Problems (IVM RAN, Moscow, 2016) [in Russian].

    Google Scholar 

  25. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  26. V. I. Agoshkov and T. O. Sheloput, “The study and numerical solution of the problem of heat and salinity transfer assuming ‘liquid’ boundaries,” Russ. J. Numer. Anal. Math. Model. 31 (2), 71–80 (2016).

    Article  Google Scholar 

  27. Copernicus. Marine Environment Monitoring Service. http://marine.copernicus.eu/

  28. J. L. Hoyer and J. She, “Optimal interpolation of sea surface temperature for the North Sea and Baltic Sea,” J. Mar. Syst. 65 (1–4), 176–189 (2007).

    Article  Google Scholar 

  29. J. L. Høyer, P. Le Borgne, and S. Eastwood, “A bias correction method for Arctic satellite sea surface temperature observations,” Remote Sens. Environ. 146, 201–213 (2014).

    Article  Google Scholar 

  30. R. Hordoir et al., “Influence of sea level rise on the dynamics of salt inflows in the Baltic Sea,” J. Geophys. Res.: Oceans 120 (10), 6653–6668 (2015).

    Article  Google Scholar 

  31. M. I. Pujol et al., “DUACS DT2014: the new multi-mission altimeter data set reprocessed over 20 years,” Ocean Sci. 12, 1067–1090 (2016).

    Article  Google Scholar 

  32. V. B. Zalesnyi, S. N. Moshonkin, V. L. Perov, and A. V. Gusev, “Ocean Circulation Modeling with K-Omega and K-Epsilon Parameterizations of Vertical Turbulent Exchange,” Physical Oceanography. 26 (6), 455–466 (2019).

    Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00595 (investigation into the formulated problems), as well as by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2019-1624.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. O. Sheloput.

Additional information

Translated by A. Nikol’skii

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agoshkov, V.I., Zalesny, V.B. & Sheloput, T.O. Variational Data Assimilation in Problems of Modeling Hydrophysical Fields in Open Water Areas. Izv. Atmos. Ocean. Phys. 56, 253–267 (2020). https://doi.org/10.1134/S0001433820030020

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433820030020

Keywords:

Navigation