Abstract
This paper presents a comparison of two reduced-order, sequential, and variational data assimilation methods: the singular evolutive extended Kalman filter (SEEK) and the reduced 4D-Var (R-4D-Var). A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasilinear regime, both methods produce similarly good results. However, the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more nonlinear regime, when tropical instability waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blayo E, Blum J, Verron J (1998) Assimilation variationnelle de données en océanographie et réduction de la dimension de l’espace de contrôle. Gauthier-Villars, pp 199–219
Courtier P, Thépaut JN, Hollingsworth A (1994) A strategy for operational implementation of 4D-Var using an incremental approach. Q J R Meteorol Soc 120:1367–1387
Durbiano S (2001) Vecteurs caractéristiques de modéles océaniques pour la réduction d’ordre en assimilation de données. Mémoire de Thése de Doctorat, LMC, UJF, Université de Grenoble I, 20 Décembre 2001
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
Greiner E, Arnault S, Morliére A (1998a) Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987: Part 1: method and statistical results. Prog Oceanogr 41:141–202
Greiner E, Arnault S, Morliére A (1998b) Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987: Part 2: oceanographic interpretation. Prog Oceanogr 41:203–247
Ide K, Courtier P, Ghil M, Loreanc AC (1997) Unified notation for data assimilation: operational, sequential and variational. J Meteor Soc Jpn 75:181–189
Lermusiaux PFJ, Robinson AR (1999) Data assimilation via error subspace statistical estimation. Part I: theory and schemes. Mon Weather Rev 127:1385–1407
Madec G, Delecluse P, Imbard M, Levy C (1998) OPA8.1 Ocean General Circulation Model reference manual. Institut Pierre et Simon Laplace (IPSL) technical report, 1998
Menkes C, Boulanger JP, Busalachi JP, Vialard J, Delecluse P, McPhaden MJ, Hackert E, Grima N (1998) Impact of TAO vs. ERS wind stresses onto simulations of the Tropical Pacific Ocean during the 1993–1998 period by the OPA OGCM, climate impact of scale interactions for the Tropical Ocean–Atmosphere system. Euroclivar Workshop Report 13:46–48
Pham DT, Verron J, Roubaud MC (1998) A singular evolutive extended Kalman filter for data assimilation in oceanography. Inverse Probl 14:979–997
Rabier F, Thépaut JN, Courtier P (1998) Extended assimilation and forecast experiments with a four-dimensional variational assimilation system. Q J R Meteorol Soc 124:1861–1887
Robert C, Durbiano S, Blayo E, Verron J, Blum J, Le Dimet F-X (2005) A reduced-order strategy for 4D-Var data assimilation. J Mar Syst 57(1–2):70–82
Testut CE, Brankart JM, Parent L (2001) An integrated system of sequential assimilation modules. SESAM2.0 reference manual. MEOM-LEGI Tech. Rep, Univ. Joseph Fourier
Veersé F, Pham D-T, Verron J (2000) 4D-Var/SEEK: a consistent hybrid variational-smoothing data assimilation method. Rapport de recherche INRIA, No. 3902
Verlaan M, Heemink AW (1997) Tidal flow forecasting using reduced-rank square root filters. Stoch Hydrol Hydraul 11:349–368
Verron J, Gourdeau L, Pham DT, Murtugudde R, Busalacchi AJ (1999) An extended Kalman filter to assimilate satellite altimeter data into a nonlinear numerical model of the tropical Pacific Ocean: method and validation. J Geophys Res 1054:5441–5458 (March)
Vialard J, Menkes C, Anderson DLT, Alonso Balmaseda M (2002) Sensitivity of Pacific Ocean Tropical instability waves to initial conditions. J Phys Oceanogr 33:106–121
Vialard J, Weaver A, Anderson DLT, Delecluse P (2003) Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean, part 2: physical validation. Mon Weather Rev 131:1379–1395
Weaver A, Courtier P (2001) Correlation modelling on the sphere using a generalized diffusion equation. Q J R Meteorol Soc 127:1815–1846
Weaver AT, Vialard J, Anderson DLT (2003) Three- and four-dimensional variational assimilation with a general circulation model of the Tropical Pacific Ocean, part 1: formulation, internal diagnostics and consistency checks. Mon Weather Rev 131:1360–1378
Acknowledgements
J.-M. Brankart and A. Weaver are gratefully acknowledged for supplying, respectively, the SESAM and OPAVAR packages and for providing support in using these tools. This work has been supported by CNES and the MERCATOR project. Idopt is a joint CNRS-INPG-INRIA-UJF research project.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible editor: Lee-Lueng Fu
Rights and permissions
About this article
Cite this article
Robert, C., Blayo, E. & Verron, J. Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean. Ocean Dynamics 56, 624–633 (2006). https://doi.org/10.1007/s10236-006-0079-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-006-0079-9