Theoretical and Practical Issues of Ensemble Data Assimilation in Weather and Climate

  • Milija Zupanski


Practical and theoretical issues of ensemble data assimilation are presented and discussed. In presenting the issues, the dynamical view, rather than a typical statistical view, is emphasized. From this point of view, most problems in ensemble data assimilation, and in data assimilation in general, are seen as means of producing an optimal state that is in dynamical balance, rather than producing a state that is optimal in a statistical sense. Although in some instances these two approaches may produce the same results, in general they are different. Details of this difference are discussed.

An overview of several fundamental issues in ensemble data assimilation is presented in more detail: dynamical balance of analysis/forecast, inclusion of nonlinear operators, and handling of reduced number of degrees of freedom in realistic high-dimensional applications.

An ensemble data assimilation algorithm named the Maximum Likelihood Ensemble Filter (MLEF) is described as a prototype method that addresses the above-mentioned issues. Some results with the MLEF are shown to illustrate its performance, including the assimilation of real observations with the Weather Research and Forecasting (WRF) model.


Data Assimilation Ensemble Forecast Variational Data Assimilation Data Assimilation Method Iterative Solution Method 
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.


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  1. Anderson JL (2001) An ensemble adjustment Kalman filter data assimilation. Mon Wea Rev 129: 2884–2903CrossRefGoogle Scholar
  2. Arulampalam S, Maskell S, Gordon SN, Clapp T (2001) Tutorial on particle filters for on-line nonlinear/non-gaussian Bayesian tracking. IEEE Trans Signal Proc 50:174–188CrossRefGoogle Scholar
  3. Bishop CH, Etherton BJ, Majumdar SJ (2001) Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon Wea Rev 129:420–436CrossRefGoogle Scholar
  4. Bishop CH, Hodyss D (2007) Flow-adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation. Quart J Roy Meteor Soc 133:2029–2044CrossRefGoogle Scholar
  5. Brasseur P, Ballabrera-Poy J, Verron J (1999) Assimilation of altimetric data in the mid-latitude oceans using the Singular evolutive Extended Kalman filter with an eddy-resolving, primitive equation model. J Marine Syst 22:269–294CrossRefGoogle Scholar
  6. Cohn SE (1997) Estimation theory for data assimilation problems: Basic conceptual framework and some open questions. J Meteor Soc Japan 75: 257–288Google Scholar
  7. Courtier P et al (1998) The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation. Quart J Roy Meteor Soc 124:1783–1808Google Scholar
  8. Crisan D, Doucet A (2002) A survey of convergence results on particle filtering for practitioners. IEEE Trans Signal Proc 50:736–746CrossRefGoogle Scholar
  9. Doucet A, de Freitas N, Gordon N (2001) Sequential Monte Carlo methods in practice. Statistics for engineering and information science, Springer-Verlag, New York, 622ppGoogle Scholar
  10. Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics. J Geophys Res 99:10143–10162CrossRefGoogle Scholar
  11. Evensen G, van Leeuwen PJ (2000) An ensemble Kalman smoother for nonlinear dynamics. Mon Wea Rev 128:1852–1867Google Scholar
  12. Fletcher SJ, Zupanski M (2006a) A data assimilation method for lognormally distributed observation errors. Quart J Roy Meteor Soc 132:2505–2520CrossRefGoogle Scholar
  13. Fletcher SJ, Zupanski M (2006b) A hybrid multivariate normal and lognormal distribution for data assimilation. Atmos Sci Let 7:43–46CrossRefGoogle Scholar
  14. Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-gaussian Bayesian state estimation. Radar and Signal Process IEE-F 140:107–113CrossRefGoogle Scholar
  15. Hamill TM, Snyder C (2000) A hybrid ensemble Kalman filter – 3D variational analysis scheme. Mon Wea Rev 128:2905–2919CrossRefGoogle Scholar
  16. Hamill TM, Whitaker JS, Snyder C (2001) Distance-dependent filtering of background error covariance estimates in an ensemble Kalamn filter. Mon Wea Rev 129:2776–2790CrossRefGoogle Scholar
  17. Hamill, TM (2006) Ensemble-based atmospheric data assimilation. Predictability of weather and climate. In: Palmer T, Hagedorn R (eds) Cambridge University Press, Cambridge, 718ppGoogle Scholar
  18. Houtekamer PL, Mitchell HL (1998) Data assimilation using ensemble Kalman filter technique. Mon Wea Rev 126:796–811CrossRefGoogle Scholar
  19. Houtekamer PL, Mitchell HL (2001) A sequential ensemble Kalman filter for atmospheric data assimilation. Mon Wea Rev 129:123–137CrossRefGoogle Scholar
  20. Hunt BR, Kostelich EJ, Szunyogh I (2007) Efficient datra assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D 230: 112–126CrossRefGoogle Scholar
  21. Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New York.Google Scholar
  22. Liu JS, Chen R (1998) Sequential Monte Carlo methods for dynamic systems. J. Amer. Stat. Soc. 93:1032–1044Google Scholar
  23. Lorenc AC (1986) Analysis methods for numerical weather prediction. Quart J Roy Meteor Soc 112:1177–1194CrossRefGoogle Scholar
  24. Mandel J (2006) Efficient implementation of the ensemble Kalman filter. CCM Report 231, University of Colorado at Denver and Health Sciences Center, June 2006Google Scholar
  25. Mandel J (2007) A brief tutorial on the ensemble Kalman filter. CCM Report 242, University of Colorado at Denver and Health Sciences Center, February 2007Google Scholar
  26. Mihailovic DT, Kallaos G, Arsenic ID, Lalic B, Rajkovic B, Papadopoulos A (1999) Sensitivity of soil surface temperature in a force-restore equation to heat fluxes and deep soil temperature. Int J Climatol 19:1617–1632CrossRefGoogle Scholar
  27. Ott E, Hunt BR, Szunyogh I, Zimin AV, Kostelich EJ, Corazza M, Kalnay E, Patil DJ, Yorke JA (2004) A local ensemble Kalman filter for atmospheric data assimilation. Tellus 56A:273–277Google Scholar
  28. Parrish DF, Derber JC (1992) The National Meteorological Center’s spectral statistical interpolation analysis system. Mon Wea Rev 120:1747–1763CrossRefGoogle Scholar
  29. Pikovsky A, Politi A (1998) Dynamic localization of Lyapunov vectors in spacetime chaos. Nonlinearity 11:1049–1062CrossRefGoogle Scholar
  30. Pham DT, Verron J, Roubaud MC (1998) A singular evolutive extended Kalman filter for data assimilation in oceanography. J Marine Sys 16:323–340CrossRefGoogle Scholar
  31. Rabier F, Jarvinen H, Klinker E, Mahfouf J-F, Simmons A (2000) The ECMWF operational implementation of four-dimensional variational data assimilation. I: Experimental results with simplified physics. Quart J Roy Meteor Soc 126A:1143–1170Google Scholar
  32. Randall D, Khairoutdinov M, Arakawa A, Grabowski W (2003) Breaking the cloud parameterization deadlock. Bull Amer Meteorol Soc 82: 2357–2376Google Scholar
  33. Rozier D, Birol F, Cosme E, Brasseur P, Brankart JM, Verron J (2007) A reduced-order Kalman filter for data assimilation in physical oceanography. SIAM Rev 49:449–465CrossRefGoogle Scholar
  34. Tao W-K, Simpson J (1993) The Goddard cumulus ensemble model. Part I: model description. Terr Atmos Oceanic Sci 4:19–54Google Scholar
  35. Tao W-K, Simpson J, Baker D, Braun S, Johnson D, Ferrier B, Khain A, Lang S, Shie C-L, Starr D, Sui C-H, Wang Y, Wetzel P (2003) Microphysics, radiation and surface processes in a non-hydrostatic model. Meteorol Atmos Phys 82:97–137CrossRefGoogle Scholar
  36. Tippett MK, Anderson JL, Bishop CH, Hamill TM, Whitaker JS (2003) Ensemble square-root filters. Mon Wea Rev 131:1485–1490CrossRefGoogle Scholar
  37. van Leeuwen PJ (2003) A variance-minimizing filter for large-scale applications. Mon Wea Rev 131:2071–2084CrossRefGoogle Scholar
  38. Xiong X, Navon IM, Uzunoglu B (2006) A note on the particle filter with posterior Gaussian resampling. Tellus 58A:456–460Google Scholar
  39. Wang X, Hamill TM, Whitaker JS, Bishop CH (2006) A comparison of hybrid ensemble transform Kalman filter-optimum interpolation and ensemble square root filter analysis schemes. Mon Wea Rev 135:1055–1076CrossRefGoogle Scholar
  40. Whitaker JS, Hamill TM (2002) Ensemble data assimilation without perturbed observations. Mon Wea Rev 130:1913–1924CrossRefGoogle Scholar
  41. Zupanski D, Zupanski M (2006) Model error estimation employing ensemble data assimilation approach. Mon Wea Rev 134:1337–1354CrossRefGoogle Scholar
  42. Zupanski M (2005) Maximum likelihood ensemble filter: Theoretical aspects. Mon Wea Rev 133:1710–1726CrossRefGoogle Scholar
  43. Zupanski M, Navon IM, Zupanski D (2008) The maximum likelihood ensemble filter as a non-differentiable minimization algorithm. Quart J Roy Meteor Soc 134:1039–1050CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Milija Zupanski
    • 1
  1. 1.Cooperative Institute for Research in the AtmosphereColorado State UniversityFort CollinsUSA

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