Skip to main content
Log in

Handling error propagation in sequential data assimilation using an evolutionary strategy

  • Published:
Advances in Atmospheric Sciences Aims and scope Submit manuscript

Abstract

An evolutionary strategy-based error parameterization method that searches for the most ideal error adjustment factors was developed to obtain better assimilation results. Numerical experiments were designed using some classical nonlinear models (i.e., the Lorenz-63 model and the Lorenz-96 model). Crossover and mutation error adjustment factors of evolutionary strategy were investigated in four aspects: the initial conditions of the Lorenz model, ensemble sizes, observation covariance, and the observation intervals. The search for error adjustment factors is usually performed using trial-and-error methods. To solve this difficult problem, a new data assimilation system coupled with genetic algorithms was developed. The method was tested in some simplified model frameworks, and the results are encouraging. The evolutionary strategy-based error handling methods performed robustly under both perfect and imperfect model scenarios in the Lorenz-96 model. However, the application of the methodology to more complex atmospheric or land surface models remains to be tested.

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

Similar content being viewed by others

References

  • Anderson, J. L., 2007: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99–111.

    Article  Google Scholar 

  • Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the non-linear filtering problem to produce ensemble assimilation and forecasts. Mon. Wea. Rev., 127, 2741–2758.

    Article  Google Scholar 

  • Back, T., U. Hammel, and H.-P. Schwefel. 1997: Evolutionary computation: Comments on the history and current state. IEEE Transactions On Evolutionary Computation, 1(1), 3–17.

    Article  Google Scholar 

  • Bai, Y. L, and X. Li, 2011: Evolutionary Algorithm-Based Error Parametrization Methods for Data Assimilation. Mon. Wea. Rev., 139, 2668–2685.

    Article  Google Scholar 

  • Bishop, C. H., B. J. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420–436.

    Article  Google Scholar 

  • Dee, D. P. 1995: On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev., 123, 1128–1145.

    Article  Google Scholar 

  • Dee, D. P., and A. M. da Silva, 1999: Maximumlikelihood estimation of forecast and observation error covariance parameters. Part I: Metholodgy. Mon. Wea. Rev., 127, 1822–1834.

    Article  Google Scholar 

  • Evensen, G., 2007: Data Assimilation: The Ensemble Kalman Filter. Springer-Verlag, Berlin, 279pp.

    Google Scholar 

  • Fogel, D. B., 2006: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (The third edition) John, Whily & Sons, New Jersey, 273pp.

    Google Scholar 

  • Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511–522.

    Article  Google Scholar 

  • Hamill, T. M., J. S. Whitaker, and C. Snyder, 2005: Accounting for the error due to unresolved scales in ensemble data assimilation: A comparison of different approaches. Mon. Wea. Rev., 133, 3132–3147.

    Article  Google Scholar 

  • Houtekamer, P. L., and H. L. Mitchell, 2001: A sequential ensemble Kalman filter for atmospheric data assimilation. Mon.Wea. Rev., 129, 123–137.

    Article  Google Scholar 

  • Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376pp.

    Google Scholar 

  • Kalnay, E., H. Li., T. Miyoshi., S.-C Yang, and J. Ballabrera Poy, 2007: 4D-Var or ensemble Kalman Filter? Tellus A, 59, 758–773.

    Article  Google Scholar 

  • Khare, S. P., J. L. Anderson, T. J. Hour, and D. Nychka, 2008: An investigation into the application of an ensemble Kalman smoother to high-dimensional geophysical systems. Tellus A, 60, 97–112.

    Article  Google Scholar 

  • Lee, Y. H., S. K. Park, and D. E. Chang, 2006: Parameter estimation using the genetic algorithm and its impact on quantitative precipitation forecast. Annales Geophosicae, 24, 3185–3189.

    Article  Google Scholar 

  • Li, H., E. Kalnay, T. Miyoshi, and C. M. Danforth, 2009: Accounting for model errors in ensemble data assimilation. Mon. Wea. Rev., 137, 3407–3419.

    Article  Google Scholar 

  • Li, X., and Coauthors, 2007: Development of a Chinese land data assimilation system: Its progress and prospects. Progress in Nature Science., 17, 881–892.

    Article  Google Scholar 

  • Liang, X., X. G. Zheng, S. P. Zhang, G. C. Wu, Y. J. Dai, and Y. Li, 2011: Maximum likelihood estimation of inflation factors on forecast error covariance matrix for ensemble Kalman filter assimilation. Quart. J. Roy. Meteor. Soc., doi: 10.1002/qj.912.

    Google Scholar 

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J Atmos. Sci., 20, 130–141.

    Article  Google Scholar 

  • Lorenz, E. N., 1996: Predictability: A problem partly solved. Proc. Semi-nar on Predictability, Volume 1, reading, United Kingdom, ECMWF, 1-19.

    Google Scholar 

  • NG, G.-H., D. Mclaughlin, D. Entekhabi, and A. Ahanin. 2011: The role of model dynamic in ensemble Kalman filter performance for chaotic systems. Tellus A, 63, 958–977.

    Article  Google Scholar 

  • Rechenberg, I., 1965: Cybernetic solution path of an experimental problem Tech. Rep. Library translation No. 1122, Royal Aircraft Establishment, Farnborough, Hants., UK.

    Google Scholar 

  • Reichle, R. H., 2008: Data Assimilation methods in the Earth Science. Advances in Water Resources, 31, 1411–1418.

    Article  Google Scholar 

  • Schwefel, H.-P., 1981: Numerical optimization of computer models, Wiley, New York, 389pp.

    Google Scholar 

  • Tian, X., and Z. Xie, 2012: Implementations of a squareroot ensemble analysis and a hybrid localisation into the POD-based ensemble 4dvar. Tellus A, 64, 1–19.

    Article  Google Scholar 

  • Tian, X., Z. Xie, and Q. Sun, 2011: A POD-based ensemble four-dimensional variational assimilation method. Tellus A, 63, 805–816.

    Article  Google Scholar 

  • Wang, B., J. J. Liu, S. D. Wang, W. Cheng, J. Liu, C. S. Liu, Q. N. Xiao, and Y.-H. Kuo, 2010: An economical approach to four-dimensional variational data assimilation. Adv. Atmos. Sci., 27(4), 715–727, doi: 10.1007/s00376-009-9122-3.

    Article  Google Scholar 

  • Whitaker, J. S., T. M. Hamill, X. Wei, Y. Song, and Z. Toth, 2008: Ensemble data assimilation with NCEP global forecast system. Mon. Wea. Rev., 136, 463–482.

    Article  Google Scholar 

  • Whitley, D., 2001: An overview of evolutionary algorithms: Practical issues and common pitfalls. Information and Software Technology, 43, 817–831.

    Article  Google Scholar 

  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convectivescale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 1238–1253.

    Article  Google Scholar 

  • Zheng, X. G., 2009: An adaptive estimation of forecast error covariance parameters for Kalman filtering data assimilation. Adv. Atmos. Sci., 26(1), 154–160, doi: 10.1007/s00376-009-0154-5.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yulong Bai  (摆玉龙).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bai, Y., Li, X. & Huang, C. Handling error propagation in sequential data assimilation using an evolutionary strategy. Adv. Atmos. Sci. 30, 1096–1105 (2013). https://doi.org/10.1007/s00376-012-2115-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00376-012-2115-7

Key words

Navigation