We are very grateful for the insights provided by Anna Trevisan, Arlindo da Silva, and Fuqing Zhang. Takemasa Miyoshi and Kayo Ide and other members of the University of Maryland Weather and Chaos Group, Ross Hoffman (AER), and Xiang-Yu Huang (NCAR Data Assimilation Test Center) made very helpful suggestions. We also appreciate the comments and suggestions of the three reviewers and of the editor, Herschel Mitchell, and Adrienne Norwood’s English proofreading. Shu-Chih Yang is sponsored by Taiwan National Science Council Grants 97-2111-m-008-25 and 98-2111-m-008-014, and the NCU Development Program for the Top-Ranked University sponsored by the Ministry of Education. Eugenia Kalnay acknowledges support from NASA Grants NNX08AD40G and NN07AM97G and DOE Grant DEFG0207ER64437.
Andersson, E., , M. Fisher, , E. Hólm, , L. Isaksen, , G. Radnóti, , and Y. Trémolet, 2005: Will the 4D-Var approach be defeated by nonlinearity? ECMWF Tech. Memo. 479, 26 pp.
Bell, B. M., , and F. W. Cathey, 1993: The iterated Kalman filter update as a Gauss-Newton method. IEEE Trans. Autom. Control, 38, 294–297.
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.
Burgers, G., , P. J. van Leeuwen, , and G. Evensen, 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126, 1719–1724.
Corazza, M., and Coauthors, 2003: Use of the breeding technique to estimate the structure of the analysis “errors of the day.” Nonlinear Processes Geophys., 10, 233–243.
Courtier, P., , J.-N. Thépaut, , and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-VAR, using an incremental approach. Quart. J. Roy. Meteor. Soc., 120, 1367–1387.
Evans, E., , N. Bhatti, , L. Pann, , J. Kinney, , M. Peña, , S.-C. Yang, , E. Kalnay, , and J. Hansen, 2004: RISE: Undergraduates find that regime changes in Lorenz’s Model are predictable. Bull. Amer. Meteor. Soc., 85, 520–524.
Evensen, G., 1992: Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. J. Geophys. Res., 97 (C11), 17 905–17 924.
Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 (C5), 10 143–10 162.
Fertig, E. J., , J. Harlim, , and B. R. Hunt, 2007: A comparative study of 4D-VAR and a 4D Ensemble Kalman Filter: Perfect model simulations with Lorenz-96. Tellus, 59A, 96–100.
Gu, Y., , and D. S. Oliver, 2007: An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. Soc. Pet. Eng. J., 12, 438–446.
Houtekamer, P. L., , and H. L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126, 796–811.
Hunt, B. R., , E. J. Kostelich, , and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112–126.
Ide, K., , P. Courtier, , M. Ghil, , and A. C. Lorenc, 1997: Unified notation for data assimilation: Operational, sequential and variational. J. Meteor. Soc. Japan, 75, 181–189.
Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376 pp.
Kalnay, E., , and S.-C. Yang, 2008: Accelerating the spin-up of Ensemble Kalman Filtering. Arxiv: physics:Nonlinear/0806.0180v1.
Kalnay, E., , and S.-C. Yang, 2010: Accelerating the spin-up of Ensemble Kalman Filtering. Quart. J. Roy. Meteor. Soc., 136, 1644–1651.
Kalnay, E., , H. Li, , T. Miyoshi, , S.-C. Yang, , and J. Ballabrera-Poy, 2007a: 4D-Var or Ensemble Kalman Filter? Tellus, 59A, 758–773.
Kalnay, E., , H. Li, , T. Miyoshi, , S.-C. Yang, , and J. Ballabrera-Poy, 2007b: Response to the discussion on “4D-Var or EnKF?” by Nils Gustaffson. Tellus, 59A, 778–780.
Krymskaya, M. V., , R. G. Hanea, , and M. Verlaan, 2009: An iterative ensemble Kalman filter for reservoir engineering applications. Comput. Geosci., 13, 235–244.
Lawson, W. G., , and J. A. Hansen, 2004: Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth. Mon. Wea. Rev., 132, 1966–1981.
Leeuwenburgh, O., , G. Evensen, , and L. Bertino, 2005: The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific. Quart. J. Roy. Meteor. Soc., 131, 3291–3300.
Lorenz, E. N., 1996: Predictability—A problem partly solved. Proc. Conf. on Predictability, Reading, United Kingdom, ECMWF.
Miller, R. N., , M. Ghil, , and F. Gauthiez, 1994: Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci., 51, 1037–1056.
Penny, S., 2011: Data assimilation of the global ocean using the 4D local ensemble transform Kalman Filter (4D-LETKF) and the Modular Ocean Model (MOM2). Ph.D. thesis, University of Maryland. [Available online at http://hdl.handle.net/1903/11716.]
Pires, C., , R. Vautard, , and O. Talagrand, 1996: On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus, 48A, 96–121.
Rabier, F., , H. Järvinen, , E. Klinker, , J.-F. Mahfouf, , and A. Simmons, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 126, 1143–1170.
Sakov, P., , and P. R. Oke, 2008: A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters. Tellus, 60A, 361–371.
Tippett, M. K., , J. L. Anderson, , C. H. Bishop, , T. M. Hamill, , and J. S. Whitaker, 2003: Ensemble square root filters. Mon. Wea. Rev., 131, 1485–1490.
Verlaan, M., , and A. W. Heemink, 2001: Nonlinearity in data assimilation applications: A practical method for analysis. Mon. Wea. Rev., 129, 1578–1589.
Wang, X., , C. H. Bishop, , and S. J. Julier, 2004: Which is better, an ensemble of positive–negative pairs or a centered spherical simplex ensemble? Mon. Wea. Rev., 132, 1590–1605.
Wang, Y., , G. Li, , and A. C. Reynolds, 2010: Estimation of depths of fluid contacts by history matching using iterative Ensemble-Kalman smoothers. Soc. Pet. Eng. J., 15, 509–525.
Whitaker, J. S., , and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 1913–1924.
Yang, S.-C., and Coauthors, 2006: Data assimilation as synchronization of truth and model: Experiments with the three-variable Lorenz system. J. Atmos. Sci., 63, 2340–2354.
Yang, S.-C., , M. Corazza, , A. Carrassi, , E. Kalnay, , and T. Miyoshi, 2009a: Comparison of local ensemble transform Kalman filter, 3DVAR, and 4DVAR in a quasigeostrophic model. Mon. Wea. Rev., 137, 693–709.
Yang, S.-C., , E. Kalnay, , B. Hunt, , and N. E. Bowler, 2009b: Weight interpolation for efficient data assimilation with the local ensemble transform Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 251–262.
Yang, S.-C., , E. Kalnay, , and T. Miyoshi, 2012: Accelerating the EnKF spinup for typhoon assimilation and prediction. Wea. Forecasting, in press.