Skip to main content

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

  • 1579 Accesses

Part of the Understanding Complex Systems book series (UCS)

Abstract

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.

Keywords

  • Mixed Layer
  • Kalman Filter
  • Data Assimilation
  • Ocean General Circulation Model
  • Assimilation Experiment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Kalnay, E., et al.: The NCEP/NCAR reanalysis project. Bull. Am. Meteor. Soc. 77, 437–472 (1996)

    CrossRef  Google Scholar 

  2. Hamill, T.M., Snyder, C.: A hybrid ensemble Kalman Filter-3D variational analysis scheme. Mon. Wea. Rev. 128, 2906–2919 (2000).

    ADS  Google Scholar 

  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. Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic, New York (1970)

    MATH  Google Scholar 

  5. Ghil, M., Malanotte-Rizzoli, P.: Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141–266 (1991)

    CrossRef  ADS  Google Scholar 

  6. Cohn, S.: An introduction to estimation theory. J. Meteor. Soc. Jpn. 75(1B), 257–288 (1997)

    Google Scholar 

  7. Evensen, G.: The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)

    CrossRef  ADS  Google Scholar 

  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. Derber, J., Rosati, A.: A global data assimilation system. J. Phys. Oceanogr. 19, 1333–1347 (1989)

    CrossRef  ADS  Google Scholar 

  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)

    CrossRef  ADS  Google Scholar 

  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)

    CrossRef  MATH  Google Scholar 

  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)

    CrossRef  ADS  Google Scholar 

  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)

    CrossRef  MathSciNet  Google Scholar 

  14. Servain, J., et al.: A pilot research moored array in the tropical Atlantic (PIRATA). Bull. Am. Meteor. Soc. 29, 2019–2031 (1998)

    CrossRef  Google Scholar 

  15. Bryan, K.: A numerical method for the study of the World. Ocean. J. Comp. Phys. 4, 347–376 (1969)

    CrossRef  ADS  MATH  Google Scholar 

  16. Pacanowski, R.C., Griffies, S.M.: The MOM3 manual, NOAA/Geophysical Fluid Dynamics Laboratory (1999)

    Google Scholar 

  17. Conkright, M.E., et al.: World ocean database: documentation and quality control. NOAA/NODC Inter. Rep. 14 (1998)

    Google Scholar 

  18. Gikhman, I.I., Skorokhod, A.V.: Introduction to the Theory of Random Processes. Dover, New York (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. P. Belyaev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Belyaev, K.P., Tanajura, C.A.S. (2013). A Time-Space Description of the Analysis Produced by a Data Assimilation Method. In: Rubio, R., et al. Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34070-3_52

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34070-3_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34069-7

  • Online ISBN: 978-3-642-34070-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)