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.
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.
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.
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.
Bai, Y. L, and X. Li, 2011: Evolutionary Algorithm-Based Error Parametrization Methods for Data Assimilation. Mon. Wea. Rev., 139, 2668–2685.
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.
Dee, D. P. 1995: On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev., 123, 1128–1145.
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.
Evensen, G., 2007: Data Assimilation: The Ensemble Kalman Filter. Springer-Verlag, Berlin, 279pp.
Fogel, D. B., 2006: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (The third edition) John, Whily & Sons, New Jersey, 273pp.
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.
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.
Houtekamer, P. L., and H. L. Mitchell, 2001: A sequential ensemble Kalman filter for atmospheric data assimilation. Mon.Wea. Rev., 129, 123–137.
Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376pp.
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.
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.
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.
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.
Li, X., and Coauthors, 2007: Development of a Chinese land data assimilation system: Its progress and prospects. Progress in Nature Science., 17, 881–892.
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.
Lorenz, E. N., 1963: Deterministic nonperiodic flow. J Atmos. Sci., 20, 130–141.
Lorenz, E. N., 1996: Predictability: A problem partly solved. Proc. Semi-nar on Predictability, Volume 1, reading, United Kingdom, ECMWF, 1-19.
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.
Rechenberg, I., 1965: Cybernetic solution path of an experimental problem Tech. Rep. Library translation No. 1122, Royal Aircraft Establishment, Farnborough, Hants., UK.
Reichle, R. H., 2008: Data Assimilation methods in the Earth Science. Advances in Water Resources, 31, 1411–1418.
Schwefel, H.-P., 1981: Numerical optimization of computer models, Wiley, New York, 389pp.
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.
Tian, X., Z. Xie, and Q. Sun, 2011: A POD-based ensemble four-dimensional variational assimilation method. Tellus A, 63, 805–816.
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.
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.
Whitley, D., 2001: An overview of evolutionary algorithms: Practical issues and common pitfalls. Information and Software Technology, 43, 817–831.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00376-012-2115-7