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Russian Journal of Numerical Analysis and Mathematical Modelling

Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri

Managing Editor: Vassilevski, Yuri V.

Editorial Board: Agoshkov, Valeri I. / Amosov, Andrey A. / Kaporin, Igor E. / Kobelkov, Georgy M. / Mikhailov, Gennady A. / Repin, Sergey I. / Shaidurov, Vladimir V. / Shokin, Yuri I. / Tyrtyshnikov, Eugene E.

IMPACT FACTOR 2018: 0.779

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Volume 31, Issue 3


An application of a data assimilation method based on the diffusion stochastic process theory using altimetry data in Atlantic

Konstantin P. Belyaev
  • Shirshov Institute of Oceanology, Moscow, Russia. Oceanographic Modelling and Observational Network (REMO), Federal University of Bahia (UFBA), Salvador, Brazil
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Andrey A. Kuleshov / Clemente A. S. Tanajura
  • Corresponding author
  • Oceanographic Modelling and Observational Network (REMO), Federal University of Bahia (UFBA), Salvador, Brazil. Department of Earth and Environmental Physics, Physics Institute, Federal University of Bahia (UFBA), Salvador, Brazil. Department of Ocean Sciences, University of California, Santa Cruz (UCSC), USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-05-28 | DOI: https://doi.org/10.1515/rnam-2016-0014


A data assimilation (DA) method based on the application of the diffusion stochastic process theory, particularly, of the Fokker-Planck equation, is considered. The method was introduced in the previous works; however, it is substantially modified and extended to the multivariate case in the current study. For the first time, the method is here applied to the assimilation of sea surface height anomalies (SSHA) into the Hybrid Coordinate Ocean Model (HYCOM) over the Atlantic Ocean. The impact of assimilation of SSHA is investigated and compared with the assimilation by an Ensemble Optimal Interpolation method (EnOI). The time series of the analyses produced by both assimilation methods are evaluated against the results from a free model run without assimilation. This study shows that the proposed assimilation technique has some advantages in comparison with EnOI analysis. Particularly, it is shown that it provides slightly smaller error and is computationally efficient. The method may be applied to assimilate other data such as observed sea surface temperature and vertical profiles of temperature and salinity.

Keywords: Ocean data assimilation; Fokker-Planck equation; ensemble optimal interpolation; HYCOM; sea level anomaly data; Atlantic Ocean

MSC 2010: 65C20


  • [1]

    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. Izv. Atmos. Ocean. Phys. 49 (2013), No. 6, 592-602.Web of ScienceGoogle Scholar

  • [2]

    K. Belyaev, C. A. S.Tanajura, and J. J. O’Brien, A data assimilation method used with ocean circulation model and its application to the tropical Atlantic. Appl Math. Modelling25 (2001), 655-670.Google Scholar

  • [3]

    K. Belyaev, D. Mueller, and C. A. S. Tanajura, A data assimilation method and its application to analysis of the ocean state in the tropical Pacific. Oceanology 45 (2005), 26-36.Google Scholar

  • [4]

    K. Belyaev, C. A. S. Tanajura, and N. Tuchkova, Comparison of Argo drifter data assimilation methods for hydrodynamic models. Oceanology 52 (2012), 523-615.Google Scholar

  • [5]

    L. Bengtsson, On the use of a time sequence of surface pressures in four-dimensional data assimilation. Tellus 32 (1980), 189-197.Google Scholar

  • [6]

    R. Bleck, An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. OceanModell. 4(2002), 55-88.Google Scholar

  • [7]

    R. Bleck and D. B. Boudra, Initial testing of a numerical ocean circulation model using a hybrid quasi isopycnal vertical coordinate. J. Phys. Oceanogr. 11 (1981), 755-770.Google Scholar

  • [8]

    R. Bleck and S. G. Benjamin, Regional weather prediction with a model combining terrain-following and isentropic coordinates. Part I: Model description. Mon. Wea.Rev. 121 (1993), 1770-1785.Google Scholar

  • [9]

    E. P. Chassignet, H. E. Hurlburt, E. J. Metzger, O. M. Smedstad, J. Cummings, G. R. Halliwell, R. Bleck, R. Baraille, A. J. Wall-craft, C. Lozano et al., US GODAE: Global Ocean Prediction with the HYbrid Coordinate Ocean Model (HYCOM). Oceanography22 (2009), 64-75.Google Scholar

  • [10]

    S. E. Cohn, An introduction to estimation theory.J.Meteorol.Soc.Japan 75 (1997), 257-288.Google Scholar

  • [11]

    F. Counillon and L. Bertino, High-resolution ensemble forecasting for the Gulf of Mexico eddies and fronts. OceanDyn.59 (2009), 83-95.Google Scholar

  • [12]

    R. Daley, Atmospheric Data Analysis. Cambridge University Press, Cambridge, 1991.Google Scholar

  • [13]

    N. A. Diansky, Modellingofthe Ocean Circulation and the Investigation of its Reaction on Short-and-Long Term Atmosphere Impact. Moscow, Fizmatlit, 2013 (in Russian).Google Scholar

  • [14]

    G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn. 53 (2003), 343-367.Google Scholar

  • [15]

    M. Ghill and P. Malanotte-Rizzoli, Data assimilation in meteorology and oceanography. Adv. Geophys. 33 (1991), 141-266.Google Scholar

  • [16]

    R. Kalman, A new approach to linear filtering and prediction problem. Trans. AMSE, J. BasicEngrg. 82 (1960), 35-45.Google Scholar

  • [17]

    E. Kalnay, Atmospheric Modelling, Data Assimilation and Predictability. Cambridge University Press, Cambridge, 2003.Google Scholar

  • [18]

    G. I. Marchukand V. B. Zalesny, A numerical technique for geophysical data assimilation problems using Pontryagin’s principle and splitting-up method. Russ. J. Numer Anal. Math. Modelling8 (1993), No. 4, 311-326.Google Scholar

  • [19]

    P. R. Oke and P. Sakov, Representation error of oceanic observations for data assimilation.J. Atmos. Oceanic Technol. 25 (2007), 1004-1017.Google Scholar

  • [20]

    P. R. Oke, G. B. Brassington, D. A. Griffin, and A. Schiller, The BLUElink ocean data assimilation system. OceanModell. 21(2008), 46-70.Web of ScienceGoogle Scholar

  • [21]

    V. V. Penenko and N. N. Obraztsov, A variational method for the adaptation of the fields of Meteorological variables. Meteorol. Hydrol. (1976), No. 11, 3-16.Google Scholar

  • [22]

    P. Sakov, F. Counillon, L. Bertino, K. A. Lisaeter, P. R. Oke, and A. Korablev, TOPAZ4: An ocean sea-ice data assimilation system for the North Atlantic and Arctic. Ocean Sci. 8 (2012), 633-656.Web of ScienceGoogle Scholar

  • [23]

    A. A. Samarsky, The Theory of Difference Schemes. CRC Press, 2001.Google Scholar

  • [24]

    A. Schiller and G. Brassington (Eds.), Operational Oceanography in the 21st Century. Springer, NewYork, 2011.Google Scholar

  • [25]

    N. Smith, Perspectives from the Global Ocean Data Assimilation Experiment (Eds. E. Chassignet and J. Verron). Ocean Weather Forecasting, Springer, 2006, pp. 1-17.Google Scholar

  • [26]

    O. Talagrand and P. Courtier, Variational assimilation of meteorological observations with the adjoint vorticity equation I: Theory. Quart. J. Roy. Meteor Soc. 113 (1987), 1311-1328.Google Scholar

  • [27]

    C. A. S. Tanajura and L. N. Lima, Assimilation of sea surface height anomalies into HYCOM with an optimal interpolation scheme over the Atlantic ocean Metarea V. Geophys. Bras. J. 31 (2013), 257-270.Google Scholar

  • [28]

    C. A. S. Tanajura and K. Belyaev, A sequential data assimilation method based on the properties of diffusion-type process. Appl. Math. Modelling33 (2009), 2165-2174.Web of ScienceGoogle Scholar

  • [29]

    C. A. S. Tanajura and K. Belyaev, On the oceanic impact of data assimilation method in a coupled ocean-land-atmosphere model. Ocean Dyn. 52 (2002), 123-132.Google Scholar

  • [30]

    W. M.Wonham, Stochastic Problems in optimal control. IEEEConv. Record, Part 11 (1963), 114-124.Google Scholar

  • [31]

    J.Xie, F. Counillon, J. Zhu, and L. Bertino, An eddy-resolving tidal-driven model in China South Sea assimilation along track satellite data using EnOI. Ocean Sci. 7 (2011), 609-627.Google Scholar

  • [32]

    V. B. Zalesny and A. S. Rusakov, Numerical algorithm of data assimilation based on splitting and adjoint equation methods. Russ. J. Numer. Anal. Math. Modelling22 (2007), No. 2,199-219.Google Scholar

About the article

Received: 2015-09-28

Accepted: 2016-03-10

Published Online: 2016-05-28

Published in Print: 2016-06-01

Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 31, Issue 3, Pages 137–147, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam-2016-0014.

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