Abstract
One of the main hypothese made in variational data assimilation is to consider that the model is a strong constraint of the minimization, i.e. that the model describes exactly the behavior of the system. Obviously the hypothesis is never respected. We propose here an alternative to the 4D-Var that takes into account model errors by adding a nonphysical term into the model equation and controlling this term. A practical application is proposed on a simple case and a reduction of the size of control using preferred directions is introduced to make the method affordable for realistic applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
eferences
D'Andrea, F. and Vautard, R., Reducing systematic error by empirically correcting model errors. Tellus 52A (2000) 21–41.
Blayo, E., Blum, J. and Verron, J., Assimilation variationnelle de Données en océanographie et réduction de la dimension de l'espace de controle. In: Equations aux dérivées partielles et applications. Gauthier-Villars, Paris (1998) pp. 199–219.
Le Dimet, F.-X. and Charpentier, I., Methodes du second ordre en assimilation de données. In: Equations aux dérivées partielles et applications. Gauthier-Villars, Paris (1998) pp. 107–125.
Cohn, S.E., An introduction to estimation theory. J. Meteorol. Soc. Japan 75(1B) (1997) 257–288.
Dee, D.P. and Da Silva, A.M., Data assimilation in presence of forecast bias. Quart. J. Roy. Meteorol. Soc. 124 (1998) 269–295.
Griffith, A.K. and Nichols, N.K., Accounting for model error in data assimilation using adjoint methods. In: Computational Differentiation: Techniques, Application and Tools. SIAM, Philadelphia, PA (1996) pp. 195–204.
Ide, K., Courtier, P., Ghil, M. and Lorenc, A.C., Unified notation for data assimilation: Operational, sequential, and variational. J. Meteorol. Soc. Japan 751B (1997) 181–189.
Kalman, R.E., A new approach to linear filtering and prediction problems. ASME, J. Basic Engrg.(1960) 35–45.
Lacarra, J.-F. and Talagrand, O., Short-range evolution of small perturbation in a barotropic model. Tellus 40A (1998) 81–95.
Lorenc, A.C., Analysis methods for numerical weather prediction. Quart. J. Roy. Meteorol. Soc. 112 (1986) 1177–1194.
Lions, J.-L., Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1970).
Piacentini, A. and the PALM group: PALM: A modular data assimilation system. In: Proceedings of the Third WMO Symposium on Data Assimilation, Québec. Technical document WMO/TD40986 (1999) in press.
Talagrand, O., The use of adjoint equation in numerical modeling of the atmospheric circulation. In: SIAM Workshop on Automatic Differentiation of Algorithms: Theory, Implementation and Application. Beckenridge, CO (1991).
Vidard, P., Assimilation de données avec controle de l'erreur modèle. DEA Report, University of Grenoble 1 (1998).
Zou, X., Navon, I.M. and Le Dimet, F.X., An optimal nudging data assimilation scheme using parameter estimation. Quart. J. Roy. Meteorol. Soc. 118 (1992) 1163–1186.
Zupanski, D., A general weak constraint applicable to operational 4DVAR data assimilation system. Mon. Weather Rev. 125 (1993) 2274–2292.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vidard, P., Blayo, E., Le Dimet, FX. et al. 4D Variational Data Analysis with Imperfect Model. Flow, Turbulence and Combustion 65, 489–504 (2000). https://doi.org/10.1023/A:1011452303647
Issue Date:
DOI: https://doi.org/10.1023/A:1011452303647