Time-space weak-constraint data assimilation for nonlinear models

Francesco Uboldi; Masafumi Kamachi

doi:10.3402/tellusa.v52i4.12277

Time-space weak-constraint data assimilation for nonlinear models

Tellus

Volume 52 (2000): Issue 4

By: Francesco Uboldi and Masafumi Kamachi

Open Access

|Jan 2000

Abstract

A general perturbation–linearization scheme is proposed for the problem of data assimilationwith an imperfect and nonlinear model, allowing for the application of the weak constraintrepresenter method. The scheme is shown in discrete formalism for a generic model. An applicationexample is given with computer-generated data in the case of the Burgers equation.Discussion in reference to the assimilation example concerns: the rôle of the model error, seenas a forcing term in the dynamics; the rôle of representers as a posteriori error covariances; acomparison among different choices for a priori dynamic error variance and strong constraintassimilation. Weak and strong constraint methods are also compared in a forecastingexperiment.

References

Bennett , A. F . 1992 . Inverse methods in physical oceano-graphy . Cambridge University Press, 346 pp.
Search in Google Scholar Back to article
Bennett , A. F. , Chua , B. and Leslie , L . 1996 . Generalized inversion of a global numerical weather prediction model . Meteorol. Atmos. Phys . 60 , 165 – 178 .
Search in Google Scholar Back to article
Bennett , A. F. , Chua , B. and Leslie , L . 1997 . Generalized inversion of a global numerical weather prediction model (II). Analysis and implementation . Meteorol. Atmos. Phys . 62 , 129 – 140 .
Search in Google Scholar Back to article
Courtier , P . 1997 . Dual formulation of four-dimensional variational assimilation . Quart. J. Roy. Meteor. Soc . 123 , 2449 – 2461 .
Search in Google Scholar Back to article
Courtier , P. and Talagrand , O . 1987. Variational assim-ilation of meteorological observations with the adjoint vorticity equation (I) . Theory. Quart. J. Roy. Meteor. Soc . 113 , 1311-132 8 .
Search in Google Scholar Back to article
Daley , R. A . 1991 . Atmospheric data analysis . Cambridge University Press, 457 pp.
Search in Google Scholar Back to article
Egbert , G. and Bennett , A. F . 1994 . Topex/Poseidon tides estimated using a global inverse model . J. Geo-phys. Res . 99 , 24821 – 24852 .
Search in Google Scholar Back to article
Eknes , M. and Evensen , G . 1995 . Parameter estimation solving a weak constraint variational problem. Proceedings of WMO’s 2nd International Symposium on Assimilation of observations in meteorology and oceanography, March 1995. Tokyo, Japan; PWPR report series no. 5; WMO/TD-no. 651; Vol. I, pp. 95 - 97 .
Search in Google Scholar Back to article
Ide , K. , Courtier , P. , Ghil , M. and Lorenc , A . 1997 . Unified notation for data assimilation: operational, sequential and variational . J. Meteorol. Soc. Japan 75 , 181 – 189 .
Search in Google Scholar Back to article
Lorenc , A. C . 1986 . Analysis methods for numerical weather prediction . Quart. J. Roy. Meteor. Soc . 112 , 1177 – 1194 .
Search in Google Scholar Back to article
Menard , R . 1994 . Kalman filtering of Burgers’ equation and its application to atmospheric data assimilation. PhD Thesis at McGill University. Stormy Weather Group, Scientific Report MW-100, Montreal, Canada , 210 pp.
Search in Google Scholar Back to article
Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. T . 1992 . Numerical recipes , the art of scientific computing. Cambridge University Press , 702 pp .
Search in Google Scholar Back to article
Rabier , F. , Thépaut , J-N. and Courtier , P . 1998 . Extended assimilation and forecast experiments with a four-dimensional variational assimilation system . Quart. J. Roy. Meteor. Soc . 124 , 1861 – 1887 .
Search in Google Scholar Back to article
Whitham , G. B . 1974 . Linear and nonlinear waves . John Wiley and Sons, 636 pp.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.3402/tellusa.v52i4.12277 | Journal eISSN: 3035-9554

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Language: English

Page range: 412 - 421

Submitted on: Jul 21, 1998

Accepted on: Dec 3, 1999

Published on: Jan 1, 2000

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 2000 Francesco Uboldi, Masafumi Kamachi, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 52 (2000): Issue 4