A study of the dynamics of four-dimensional data assimilation

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The problem of four-dimensional data assimilation is investigated on the inviscid linearized shallow-water equations. The conditions under which an assimilation of mass data, performed according to a simple updating scheme, will reconstruct the complete mass and velocity fields are studied. On the basis of a mathematical result proved elsewhere, it is shown that energy conservation ensures exact convergence towards any given solution, irrespective of geostrophy or lack of geostrophy, under the only condition that the available observations define a unique solution of the model equations. For most values of the relevant parameters, the divergent part of the wind field is reconstructed much more rapidly than the rotational part. The effect of a damping of gravity waves is considered, and shown to accelerate the reconstruction of the wind field only for scales which are large compared to the Rossby radius of deformation. These results are generalized to the inviscid linearized multi-level primitive equations. The case of wind observations is also considered, and shown to lead to reconstitution of the complete mass field. Finally, comparison with numerical results obtained with non-linear equations shows that the main features deduced from the linearized theory are preserved, but also suggests that the non-linear advection can, at least in some cases, accelerate the process of reconstruction.DOI: 10.1111/j.2153-3490.1981.tb01729.x
  • References (6)

    Arakawa, A. and Lamb, V. 1977. Computational design global, four-dimensional analysis experiment during of the basic dynamical processes of the UCLA general the GATE period, Part I. J.Atrn. Sci. 33, 561-591. circulation model, in Methods in Computational Morel, P. and Talagrand, 0. 1974. Dynamic approach Ph.vsics Vol. 17. (ed. J. Chang). Academic Press, to meteorological data assimilation. Tellus 26, New York, U.S.A. 334-344.

    Bengtsson, L. 1975. 4-dimensional assimilation of Sadourny, R. 1972. Approximations en differences finies meteorological observations. GARP Publication des equations de Navier-Stokes appliquks a un Series No. 15, World Meteorological Organisation, ecoulement geophysique. Part 111. Ann. Gkophys. 28, Geneva, Switzerland. 789-802.

    Blumen, W. 1975a. An analytical view of updating Sadourny, R. 1975. Description du modele de circulation meteorological variables. Part I: Phase errors. J. generale du LMD, Internal Report, Laboratoire de Atmos. Sci. 32,274-286. Meteorologie Dynamique, Paris, France.

    Blumen, W. 1975b. An analytical view of updating Simmonds, I. 1976. Data assimilation with a one-level, meteorological variables: Part 11: Weighted assimila- primitive equation spectral model. J. Atrn. Sci. 33, tion. J.Atrn. Sci. 32,690-697. 1155-1 17 I.

    Bube, K. 1978. The construction of initial data for Simmonds, 1. 1978. The application of a multi-level hyperbolic systems from nonstandard data. Ph.D. spectral model to data assimilation. J. Atm. Sci. 35, Thesis, Stanford University. Available from University 1321-1339. Microfilms International, Ann Arbor, MI 48 106, Talagrand, 0. 1972. On the damping of high-frequency U.S.A. motions in four-dimensional assimilation of meteoroDavies, H. C. and Turner, R. E. 1977. Updating logical data.J. Arm. Sci. 29, 1571-1574. prediction models by dynamical relaxation: an Talagrand, 0. 1977. Contribution a I'assimilation quadriexamination of the technique. Quart. J. R . Met. Soc. dimensionelle d'observations meteorologiques. 103,225-245. Doctoral Thesis, Universite Pierre-et-Marie Curie, Ghil, M., Shkoller, B. and Yangarber, V. 1977. A Paris, France. Available from the author. balanced diagnostic system compatible with a Varga, R. S. 1962. Matrix iterative analysis. Prenticebarotropic prognostic model. Month. Wea. Rev. 105, Hall, Inc., Englewood Cliffs, New Jersey, U.S.A. 1223- 1238. Williamson, D. and Dickinson, R. 1972. Periodic Lorenc, A., Rutherford, I. and Larsen, G. 1977. The updating of meteorological variables. J. Atm. Sci. 29, ECMWF Analysis and Data-Assimilation Scheme: 19&193. Analysis of Mass and Wind Fields, Technical Report Williamson. D. and Kasahara, A. 1971. Adaptation of No. 6, ECMWF, Reading, U.K. meteorological variables forced by updating. J . Arm.

    Miyakoda, K., Umscheid, L., Lee, D. H., Sirutis, J., Sci. 28, 1313-1324. Lusen, R. and Pratte, F. 1976. The near-real-time,

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