A Time-Space Description of the Analysis Produced by a Data Assimilation Method

  • K. P. BelyaevEmail author
  • C. A. S. Tanajura
Part of the Understanding Complex Systems book series (UCS)


The objective analysis of the upper ocean temperature field and its error covariance structure are discussed. The assimilation technique used to produce the analysis is based on the application of the Fokker-Planck equation. In the present study, the ocean general circulation model MOM3 from GFDL/NOAA and vertical profiles of temperature from the PIRATA observational array in the tropical Atlantic Ocean are utilised in conjunction with a data assimilation scheme. The results show that the analysis has warmer mixed layer than the model, and cooler temperatures immediately below the mixed layer. The analysis was compared with independent data. The structure of the analysis is assessed by an eigenvector expansion of the error covariance matrix. It is shown that the largest covariance is in the mixed layer, with maxima located around the observational points. Also, the covariance is relevant in a large area in the tropical Atlantic, showing the basin is dynamically linked.


Mixed Layer Kalman Filter Data Assimilation Ocean General Circulation Model Assimilation Experiment 
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  1. 1.
    Kalnay, E., et al.: The NCEP/NCAR reanalysis project. Bull. Am. Meteor. Soc. 77, 437–472 (1996)CrossRefGoogle Scholar
  2. 2.
    Hamill, T.M., Snyder, C.: A hybrid ensemble Kalman Filter-3D variational analysis scheme. Mon. Wea. Rev. 128, 2906–2919 (2000).ADSGoogle Scholar
  3. 3.
    Kalman, R.: A new approach to linear filtering and prediction problems. Trans. ASME, Ser. D, J. Basic Eng. 82, 35–45 (1960)Google Scholar
  4. 4.
    Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic, New York (1970)zbMATHGoogle Scholar
  5. 5.
    Ghil, M., Malanotte-Rizzoli, P.: Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141–266 (1991)ADSCrossRefGoogle Scholar
  6. 6.
    Cohn, S.: An introduction to estimation theory. J. Meteor. Soc. Jpn. 75(1B), 257–288 (1997)Google Scholar
  7. 7.
    Evensen, G.: The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Ott, E., Hunt, B.R., Szunyogh, I., Zimin, A.V., Kostelich, E.J., Corazza, M., Kalnay, E., Patil, D.J., Yorke, J.A.: A local ensemble Kalman Filter for atmospheric data assimilation. Tellus 56(A), 415–428 (2004)Google Scholar
  9. 9.
    Derber, J., Rosati, A.: A global data assimilation system. J. Phys. Oceanogr. 19, 1333–1347 (1989)ADSCrossRefGoogle Scholar
  10. 10.
    Barker, D.M., Huang, W., Guo, Y.-R., Bourgeois, A., Xiao, X.N.: A three-dimensional variational data assimilation system for MM5: implementation and initial results. Mon. Wea. Rev. 132, 897–914 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Belyaev, K.P., Tanajura, C.A.S., O’Brien, J.J.: A data assimilation method with an ocean circulation model and its application to the tropical Atlantic. Appl. Math. Modell. 25, 655–670 (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Tanajura, C.A.S., Belyaev, K.: On the oceanic impact of the data assimilation method in coupled-ocean-land atmosphere model. Ocean Dyn. 52, 123–132 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Tanajura, C.A.S., Belyaev, K.: A sequential data assimilation method based on the properties of a diffusion-type process. Appl. Math. Modell. 33, 115–135 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Servain, J., et al.: A pilot research moored array in the tropical Atlantic (PIRATA). Bull. Am. Meteor. Soc. 29, 2019–2031 (1998)CrossRefGoogle Scholar
  15. 15.
    Bryan, K.: A numerical method for the study of the World. Ocean. J. Comp. Phys. 4, 347–376 (1969)ADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Pacanowski, R.C., Griffies, S.M.: The MOM3 manual, NOAA/Geophysical Fluid Dynamics Laboratory (1999)Google Scholar
  17. 17.
    Conkright, M.E., et al.: World ocean database: documentation and quality control. NOAA/NODC Inter. Rep. 14 (1998)Google Scholar
  18. 18.
    Gikhman, I.I., Skorokhod, A.V.: Introduction to the Theory of Random Processes. Dover, New York (1996)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Shirshov Institute of Oceanology (SIORAS)Russian Academy of ScienceMoscowRussia
  2. 2.Dept. Geophysics and GeologyFederal University of Bahia, CPGGSalvadorBrazil

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