Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations
By: Philippe Courtier and Olivier Talagrand
References
-
Asselin
, R. 1972. Frequency filter for time integrations. Mon. Wea. Rev. 100, 487– 490. -
Buckley
, A. A.and Lenir, A. 1983. QN-like Variable Storage Conjugate Gradients. Mathematical Program-ming, 155– 175. -
Courtier
, P. 1987. Application du contrôle optimal a la precision numérique en Meteorologie . These de doctorat de l'universite Pierre-et-Marie-Curie, Paris(in French). -
Courtier
, P.and Talagrand, O.. Q. J. R. Meteorol. Soc. 113, 1329-134 7. -
Daley
, R. 1978. Variational non-linear normal mode initialization. Tellus, 201– 218. -
Daley
, R., Wergen, W.and Cats, G. 1986. The objective analysis of planetary-scale flow. Mon. Wea. Rev. 114, 1892– 1908. -
Derber
, J. C. 1987. Variational four dimensional analysis using quasi-geostrophic constraints. Mon. Wea. Rev. 115, 998– 1008. -
Eliasen
, E., Machenhauer, B.and Rasmussen, E. 1970. On a numerical method for integration of the hydro-dynamical equations with a spectral representation of the horizontal fields. Report No. 2, Institute for Theoretical Meteorology , Copenhagen University, Copenhagen. -
Ghil
, M., Cohn, S., Tavantzis, J., Bube, K.and Isaacson, E. 1981. Applications of estimation theory to numerical weather prediction. In:, M.and E.). Springer-Verlag, New York, 139– 224. -
Ghil
, M., Cohn, S. E.and Dalcher, A. 1982.(ed. D.). Proceedings of the Stanstead Seminar, McGill University, Montreal, Canada. -
Gill
, P. E., Murray, W.and Wright, M. H. 1982. Practical optimization . Academic Press, London. -
Hall
, M. C. G., Cacuci, D. G.and Schlesinger, M. E. 1982. Sensitivity analysis of a radiative-convective model by the adjoint method. J. Atmos. Sci. 39, 2038– 2050. -
Hoffman
, R. N. 1986. A Four-Dimensional Analysis Exactly Satisfying Equations of Motion. Mon. Wea. Rev. 114, 388– 397. -
Jazwinski
, A. H. 1970. Stochastic processes and filtering theory . Academic Press, New York. -
Lacarra
, J. F.and Talagrand, O.. Short-range evolution of small perturbations in a barotropic model., 81– 95. -
Le Dimet
, F. X.and Talagrand, O.. Tellus 38A, 97– 110. -
Leith
, C. E. 1980. Nonlinear normal mode initialization and quasi-geostrophic theory. J. Atmos. Sci. 37, 954– 964. -
Lewis
, J. M.and Derber, J. C. 1985. The use of adjoi n t -
equations to solve a variational adjustment problem with advective constraints
. Tellus 37A, 309– 322. -
Lions
, J. L. 1971. Optimal control of systems governed by partial differential equations (English translation) . Springer-Verlag, Berlin. -
Lorenc
, A. C. 1986. Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112, 1177– 1194. -
Lorenc
, A. C. 1988a. Optimal nonlinear objective analysis. Q. J. R. Meteorol. Soc. 114, 205– 240. -
Lorenc
, A. C. 1988b. A practical approximation to optimal four dimensional objective analysis. Mon. Wea. Rev. 116, 730– 745. -
Machenhauer
, B. 1977. On the dynamics of gravity oscillations in a shallow water model with appli-cations to normal mode initialization. Beitr. Phys. Atmos. 50, 253– 271. -
Navon
, I. M.and Legler, D. M. 1987. Conjugate-gradient methods for large-scale minimization in meteorology. Mon. Wea. Rev. 115, 1479– 1502. -
Pailleux
, J., Nuret, M., Durand, Y.and Betout, P. 1982. Developpement et resultats de tanalyse objective operationnelle SAPHIR. Working note no. 26, Etablissement d'Etudes et de Recherches Météor-ologiques, Paris. -
Robert
, A. J., Henderson, J.and Turnbull, C. 1972. An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Rev. 100, 329– 335. -
Sasaki
, Y. 1970. Some basic formalisms in numerical variational analysis. Mon. Wea. Rev. 98, 875– 883. -
Talagrand
, O.and Courtier, P.. Variational assimilation of meteorological observations with the adjoint vorticity equation-Part I. Theory.. 113, 1311– 1328. -
Thacker
, W. C.and Long, R. B. 1988. Fitting Dynamics to Data. J. Geophys. Res. 93, 1227– 1240. -
Urban
, B. 1985. Croissance maximum des erreurs dans les modeles meteorologiques simples. Working report, Ecole Nationale de la Météorologie , Toulouse, France. -
Vautard
, R.and Legras, B. 1988. On the Source of Midlatitude Low-Frequency Variability. Part II: Nonlinear Equilibration of Weather Regimes. J. Atmos. Sci. 45, 2845– 2867. -
Wahba
, G. 1982. Variational methods in simultaneous optimum interpolation and initialization . In: The interaction between objective analysis and initialization(ed. D. Williamson). Proceedings of the Fourteenth Stanstead Seminar., Montreal, Canada.
DOI: https://doi.org/10.3402/tellusa.v42i5.11896 | Journal eISSN: 3035-9554
Language: English
Page range: 531 - 549
Submitted on: Nov 16, 1988
Accepted on: Aug 17, 1989
Published on: Jan 1, 1990
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 1990 Philippe Courtier, Olivier Talagrand, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.