A comparative study of 4D-VAR and a 4D Ensemble Kalman Filter: perfect model simulations with Lorenz-96

Elana J. Fertig; John Harlim; Brian R. Hunt

doi:10.1111/j.1600-0870.2006.00205.x

A comparative study of 4D-VAR and a 4D Ensemble Kalman Filter: perfect model simulations with Lorenz-96

Tellus

Volume 59 (2007): Issue 1

By: Elana J. Fertig, John Harlim and Brian R. Hunt

Open Access

|Jan 2007

Abstract

We formulate a four-dimensional Ensemble Kalman Filter (4D-LETKF) that minimizes a cost function similar to that in a 4D-VAR method. Using perfect model experiments with the Lorenz-96 model, we compare assimilation of simulated asynchronous observations with 4D-VAR and 4D-LETKF. We find that both schemes have comparable error when 4D-LETKF is performed sufficiently frequently and when 4D-VAR is performed over a sufficiently long analysis time window.We explore how the error depends on the time between analyses for 4D-LETKF and the analysis time window for 4D-VAR.

References

Anderson , J. L. 2001 . An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Re v . 129 , 2884 – 2903 .
Search in Google Scholar Back to article
Bishop , C. H. , Etherton , B. and Majumdar , S. J. 2001 . Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Re v . 129 , 420 – 436 .
Search in Google Scholar Back to article
Burgers , G., van Leeuwen , P. J. and Evensen , G. 1998 . Analysis scheme in the ensemble Kalman filter . Mon. Wea. Rev . 126 , 1719– 1724 .
Search in Google Scholar Back to article
Courtier , P. , Thepaut , J. N. and Hollingsworth , A. 1994 . A strategy for operational implementation of 4D-VAR, using an incremental ap-proach . Quart. J. R. Meteorol. Soc . 120 , 1367 – 1387 .
Search in Google Scholar Back to article
Evensen , G. 1994 . Sequential data assimilation with a non-linear quasi-geostropic model using Monte Carlo Methods to forecast error statistics . J. Geophys. Res . 99 , 10143 – 10162 .
Search in Google Scholar Back to article
Evensen , G. and van Leeuwen, P. J. 2000. An ensemble Kalman smoother for nonlinear dynamics . Mon. Wea. Rev . 128 , 1852– 1867 .
Search in Google Scholar Back to article
Houtekamer , P. L. and Mitchell , H. L. 1998 . Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev. 126 , 796 - 811 .
Search in Google Scholar Back to article
Houtekamer , P. L. , Mitchell , H. L. , Pellerin , G. , Buehner , M. , Charron , M , et al. 2005 . Atmospheric data assimilation with the ensemble Kalman filter: Results with real observations. Mon. Wea. Re v . 133 , 604 – 620 .
Search in Google Scholar Back to article
Houtekamer , P. L. and Mitchell , H. L. 2006 . Ensemble Kalman Filtering . Quart. J. R. Meteorol. Soc ., in press .
Search in Google Scholar Back to article
Hunt , B. R. , Kalnay , E. , Kostelich , E. J. , Ott , E. , Patil , D. J. and co-authors. 2004. Fourdimensional ensemble Kalman filtering. Tellus 56A , 273 - 277 .
Search in Google Scholar Back to article
Lawson , L.M , Spitz , Y. H. , Hofmann , E. E. and Long , R. B. 1995 . A data assimilation technique applied to a predator-prey model . Bull. Math. Biol . 57 ( 4 ), 593 – 617 .
Search in Google Scholar Back to article
Le Dimet , E X. and Talagrand , O. 1986 . Variational algorithm for anal-ysis and assimilation of meteorological observations: Theoretical aspects . Tellus 38A , 97 – 110 .
Search in Google Scholar Back to article
Lorenc , A. C. 2003 . The potential of the ensemble Kalman filter for NWP-a comparison with 4D-VAR. Quart. .1. R . Meteorol. Soc . 129 , 3183 – 3203 .
Search in Google Scholar Back to article
Lorenz , E. N. 1996 . Predictability-a problem partly solved. In Proceedings on predictability, held at ECMWF on 4-8 September 1995.
Search in Google Scholar Back to article
Ott , E. , Hunt , B. R. , Szunoygh , I. , Zimin , A. , Kostelich , E. J. , and co-authors. 2004. A local ensemble Kalman filter for atmospheric data assimilation. Tellus 56A , 415 - 428 .
Search in Google Scholar Back to article
Parrish , D. E and Derber , J. C. 1992 . The National Meteorological Center’s spectral statistical-interpolation analysis system . Mon. Wea. Rev . 120 ( 8 ), 1747 – 1763 .
Search in Google Scholar Back to article
Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. V. 1992 . Numerical Recipes in Fortran . Cambridge University Press , New York .
Search in Google Scholar Back to article
Rabier , E , Thepaut , J. N. and Courtier , P. 1998 . Extended assimilation and forecast experiments with a four-dimensional variational assimilation system . Quart. J. R. Meteorol. Soc . 124 , 1861 – 1887 .
Search in Google Scholar Back to article
Rabier , E , Järvien , H. , Mahfouf , J. E and Simmons , A. 2000. The ECMWF operational implementation of four-dimensional variational assimilation: Experimental results with simplified physics. Quart. J. R. Meteorol. Soc . 126 , 1148-117 0 .
Search in Google Scholar Back to article
Szunoygh , I. , Kostelich , E. J. , Gyarmati , G. , Patil , D. J. , Kalnay , E. , and co-authors. 2005. Assessing a local ensemble Kalman filter: Perfect model experiments with the National Centers for Environmental Prediction global model. Tellus 57A , 528 - 545 .
Search in Google Scholar Back to article
Wang , X. , Bishop , C. H. and Julier , S. J. 2004 . Which is better, an ensemble of positive-negative pairs or a centered spherical simplex ensemble? Mon. Wea. Rev . 132 ( 7 ), 1590 – 1605 .
Search in Google Scholar Back to article
Wang , X. , Hamill , T.M , Whitaker , J. S. and Bishop , C. H. 2006 . A com-parison of hybrid ensemble transform Kalman filter-OI and ensemble square-root filter analysis schemes . Mon. Wea. Rev ., in press .
Search in Google Scholar Back to article
Whitaker , J. S. and Hamill , T. M. 2002 . Ensemble data assimila-tion without perturbed observations. Mon. Wea. Re v . 130 , 1913 – 1924 .
Search in Google Scholar Back to article
Whitaker , J. S. , Compo , G. P. , Wei , X. and Hamill , T. M. 2004 . Reanalysis without radiosondes using ensemble data assimilation. Mon. Wea. Re v . 132 , 1190 – 1200 .
Search in Google Scholar Back to article
Whitaker , J. S. , Hamill , T. M. , Wei , X. , Song , Y. and Toth , Z. 2006 . Ensemble data assimilation with the NCEP global forecast system . Mon. Wea. Rev ., submitted .
Search in Google Scholar Back to article
Zupanski , M. 2005 . Maximum likelihood ensemble filter: Theoretical aspects. Mon. Wea. Re v . 133 , 1710 – 1726 .
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1111/j.1600-0870.2006.00205.x | Journal eISSN: 3035-9554

Journal RSS Feed

Language: English

Page range: 96 - 100

Submitted on: Jun 7, 2006

Accepted on: Aug 22, 2006

Published on: Jan 1, 2007

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 2007 Elana J. Fertig, John Harlim, Brian R. Hunt, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 59 (2007): Issue 1