A robust formulation of the ensemble Kalman filter

Quarterly Journal of the Royal Meteorological Society

Volumn 135, Issue 639, 2009, Pages 507-521

  Thomas, Stephe J ^a   Hacker, J P ^a   Anderson, J L ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

EnKF; Numerical algorithms

Indexed keywords

CHAOTIC DYNAMICS; CORRELATED OBSERVATIONS; EFFICIENT ALGORITHM; EIGEN-VALUE; ENKF; ENSEMBLE ADJUSTMENT KALMAN FILTER; ENSEMBLE KALMAN FILTER; ILL-CONDITIONED; MODEL ERRORS; NORMAL EQUATIONS; NUMERICAL ALGORITHMS; NUMERICAL RESULTS; QUADRATIC FUNCTIONAL; RECURSIVE FILTERS; ROBUST FORMULATIONS; SAMPLING ERRORS; WEIGHTED LEAST SQUARES;

CHANNEL CAPACITY; CONTROL THEORY; ERRORS; KALMAN FILTERS; LARGE SCALE SYSTEMS; SINGULAR VALUE DECOMPOSITION;

ALGORITHMS;

ALGORITHM; DECOMPOSITION ANALYSIS; EIGENVALUE; ENSEMBLE FORECASTING; ERROR ANALYSIS; KALMAN FILTER; LEAST SQUARES METHOD; REGRESSION ANALYSIS;

EID: 67649442685     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1002/qj.372     Document Type: Article

References (36)

1. Anderson JL. 2001. An ensemble adjustment filter for data assimilation Mon. Weather Rev. 129: 2884-2903.
2. Anderson JL. 2003. A local least squares framework for ensemble filtering. Mon. Weather Rev. 131: 634-642.
3. Anderson JL. 2006. Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D: Nonlinear Phenomena 230: 99-111.
4. Anderson JL, Anderson SL. 1999. A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Weather Rev. 127: 2741-2758.
5. Andrews A. 1968. A square root formulation of the Kalman covariance equations. AIAA Journal 6: 1165-1166.
6. Bishop CH, Etherton B, Majumdar SJ. 2001. Adaptive sampling with the ensemble transform Kalman filter: Part I: Theoretical aspects. Mon. Weather Rev. 129: 420-436.
7. Burgers G, van Leeuwen PJ, Evensen G. 1998. Analysis scheme in the ensemble Kalman filter. Mon. Weather Rev. 126: 1719-1724.
8. Courtier P, Andersson E, Heckley W, Pailleux J, Vasiljevic D, Hamrud M, Hollingsworth A, Rabier F, Fisher M. 1998. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation. Q. J. R. Meteorol. Soc. 124: 1783-1807.
9. Duncan DB, Horn SD. 1972. Linear dynamic recursive estimation from the viewpoint of regression analysis. J. Amer. Statist. Assoc. 67: 815-821.
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: 10143-10162.
11. Evensen G. 2003. The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn. 53: 343-367.
12. Evensen G. 2004. Sampling strategies and square root analysis schemes for the EnKF. Ocean Dyn. 54: 539-560.
13. Gaspari G, Cohn SE. 1999. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125: 723-757.
14. Golub GH, Van Loan CF. 1996. Matrix Computations. Third edition. Johns Hopkins University Press: Baltimore, USA.
15. Hamill TM. 2006. Ensemble-based atmospheric data assimilation. Pp. 124-156 in Predictability of Weather and Climate. Palmer TN, Hagedorn R. (eds.) Cambridge University Press: Cambridge, UK.
16. Hamill TM, Whitaker J. 2005. Accounting for the error due to unresolved scales in ensemble data assimilation: A comparison of different approaches. Mon. Weather Rev. 133: 3132-3147.
17. Hamill TM, Whitaker J, Snyder C. 2001. Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Weather Rev. 129: 2776-2790.
18. Houtekamer PL, Mitchell HL. 1998. Data assimilation using an ensemble Kalman filter technique. Mon.Weather Rev. 126: 796-811.
19. Houtekamer PL, Mitchell HL. 2001. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Weather Rev. 129: 123-136.
20. Ide K, Courtier P, Ghil M, Lorenc AC. 1997. Unified notation for data assimilation: Operational, sequential and variational. J. Meteorol. Soc. Japan 75: 181-189.
21. Jazwinski AH. 1970. Stochastic Processes and Filtering Theory. Academic Press: New York.
22. Kalman RE. 1960. A new approach to linear filtering and prediction problems. J. Basic Eng. Trans. ASME 82: 35-45.
23. Kalman RE, Bucy R. 1961. New results in linear filtering and prediction theory. J. Basic Eng. Trans. ASME 83: 95-108.
24. Kourouklis S, Paige CC. 1981. A constrained least squares approach to the general Gauss-Markov linear model. J. Amer. Statist. Assoc. 76: 620-625.
25. Lorenc AC. 2003. The potential of the ensemble Kalman filter for NWP - A comparison with 4D-Var. Q. J. R. Meteorol. Soc. 129: 3183-3203.
26. Lorenc AC, Ballard SP, Bell RS, Ingleby NB, Andrews PLF, Barker DM, Bray JR, Clayton AM, Dalby T, Li D, Payne TJ, Saunders FW. 2000. The Met Office global three-dimensional variational data assimilation scheme. Q. J. R. Meteorol. Soc. 126: 2991-3012.
27. Lorenz EN. 1995. Predictability - A problem partly solved. Pp. 1-18 of Proceedings of Seminar on Predictability, Vol. 1. ECMWF: Reading, UK.
28. Lorenz EN. 2005. Designing chaotic models. J. Atmos. Sci. 62: 1574-1587.
29. Maybeck PS. 1979. Stochastic Models, Estimation, and Control. Vol. 1. Academic Press: New York.
30. Mitchell HL, Houtekamer PL, Pellerin G. 2002. Ensemble size, balance, and model-error representation in an ensemble Kalman filter. Mon. Weather Rev. 130: 2791-2808.
31. 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 A 56: 415-428.
32. Parrish DF, Derber JC. 1992. The National Meteorological Center's spectral statistical-interpolation analysis system. Mon. Weather Rev. 120: 1747-1763.
33. Potter JE. 1964. W matrix augmentation. MIT Instrumentation Laboratory Memo SGA 5-64. Massachusetts Institute of Technology: Cambridge, Massachusetts.
34. Sorenson HW, Sacks JE. 1971. Recursive fading memory filtering. Inform. Sciences 3: 101-119.
35. Tippett MK, Anderson JL, Bishop CH, Hamill TH, Whitaker JS. 2003. Ensemble square root filters. Mon. Weather Rev. 131: 1485-1490.
36. Whitaker JS, Hamill TM. 2002. Ensemble data assimilation without perturbed observations. Mon. Weather Rev. 130: 1913-1924.