On extending the limits of variational assimilation in nonlinear chaotic systems
By: Carlos Pires, Robert Vautard and Olivier Talagrand
References
-
Bennett
, A. F. . Inverse methods in physical oceanography. Cambridge University Press, Cambridge, United Kingdom, -
Bennett
, A. F.and Budgell, W. P. . The Kalman smoother for a linear quasi-geostrophic model of ocean circulation. Dyn. Atmos. Oceans, 219– 267. -
Budgell
, W. P. . Nonlinear data assimilation for shallow water equations in branched channels. J. Geophys. Res. 91 (C9), 10, 633-10, 644. -
Courtier
, P.and Talagrand, O. . Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus, 531– 549. -
Courtier
, P., Derber, J., Errico, R., Louis, J.-F.and Vukicevic, T. . Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology. Tellus, 341– 357. -
Courtier
, P., Thepaut, J.-N.and Hollingsworth, A. . A strategy for operational implementation of 4D-VAR, using an incremental approach . Q. J. R. Meteorol. Soc., in press. -
Daley
, R. . Atmospheric data analysis. Cambridge University Press, Cambridge, U.K., -
Derber
, J. C. . Variational four-assimilation analysis using quasi-geostrophic constrains. Mon. Wea. Rev. 115, 998– 1008. -
Devaney
, R., and Nitecki, Z. . Shift automorphisms in the Hénon mapping. Comm. Math. Phys. 67, 137– 148. -
Errico
, R. M.and Vukicevic, T. . Sensivity analysis using an adjoint of the PSU-NCAR mesoscale model. Mon. Wea. Rev. 120, 1644– 1660. -
Evensen
, G. . Using the extended Kalman filter with a multilayer quasigeostrophic ocean model. J. Geophys. Res. 97 (C11), 17, 905-17, 924. -
Evensen
, G. . Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99 (C5), 10, 143-10, 162. -
Farmer
, J. D., and Sidorovich, J. J. . Optimal shadowing and noise reduction. Physica D, 373– 392. -
Gaspar
, P.and Wunsch, C. . Estimates from altimeter data of barotropic rossby waves in the northwestern atlantic ocean. J. Phys. Oceanogr. 19, 1821– 1844. -
Gauthier
, P. . Chaos and quadri-dimensional data assimilation. A study based on the Lorenz model. Tellus, 2– 17. -
Guckenheimer
, J.and Holmes, P. . Nonlinear oscilla-tions, dynamical systems, and bifurcations of vector fields. Springer-Verlag, New-York, 453 pp. -
Ghil
, M.and Malanotte-Rizzoli, P. . Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141– 266. -
Hénon
, M. . A two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50, 69– 77. -
Hirsch
, M. W.and Pugh, C. C. . Stable manifolds and hyperbolic sets. Proc. Symp. Pure. Math. 14, 133– 163. -
Jazwinski
, A. H. . Stochastic processes and filtering theory. Academic Press , New York, USA. -
Kalman
, R. E. . A new approach to linear filtering and prediction problems. J. Basic Eng. 820, 35– 45. -
Lacarra
, J.-F.and Talagrand, O. . Short-range evolution of small perturbations in a barotropic model. Tellus, 81– 95. -
Le Dimet
, F.-X.and Talagrand, O. . Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 97– 110. -
Legras
, B.and Ghil, M. . Persistent anomalies, blocking, and variations in atmospheric predictability. J. Atmos. Sci. 42, 433– 471. -
Lewis
, J.and Derber, J. C. . The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus, 309– 322. -
Li
, Y. . A Note on the uniqueness problem of variational adjustment approach to four-dimensional data assimilation. J. of the Met. Soc. of Japan. 69, 581– 585. -
Lorenc
, A. C. . A global three-dimensional multi-variate statistical interpolation scheme. Mon. Wea. Rev. 109, 701– 721. -
Lorenc
, A. C. . Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112, 1177– 1194. -
Lorenz
, E. N. . Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130– 141. -
Lorenz
, E. N. . A study of the predictability of a 28-variable atmospheric model. Tellus, 321– 333. -
Lorenz
, E. N. . Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci. 26, 636– 646. -
Miller
, R. N., Ghil, M.and Gauthiez, F. . Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. 51, 1037– 1056. -
Molteni
, F.and Palmer, T. . Predictability and finite-time instability of the northern winter circulation. Quart. J. R. Meteor. Soc. 119, 269– 298. -
Nese
, J. M., Dutton, J. A.and Wells, R. . Calculated attractor dimensions for low-order spectral models. J. Atmos. Sci. 44, 1950– 1972. -
Oseledec
, V. I. . A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19, 197– 231. -
Palmer
, T. . Medium and extended-range predictability and the stability of the Pacific/North American mode. Quart. J. R. Meteor. Soc. 114, 691– 713. -
Palmer
, T. . Extended-range atmospheric prediction and the Lorenz model. Bull. Am. Meteor. Soc. 74, 49– 65. -
Parrish
, D.and Derber, D. . The National Meteorological Center’s Spectral Statistical-Interpola-tion Analysis System. Mon. Wea. Rev. 120, 1747– 1763. -
Rabier
, F.and Courtier, P. . Four-dimensional assimilation in the presence of baroclinic instability, Q. J. R. Meteorol. Soc. 118, 649– 672. -
Robertson
, D. H., Brown, F. B.and Navon, I. M. . Determination of the structure of mixed-xenon clusters using a finite-temperature, lattice-based Monte Carlo method. J. Chem. Phys. 90, 3221– 3229. -
Ruelle
, D. . Chaotic evolution and strange attractors. Cambridge University Press, Cambridge, -
Sheinbaum
, J.and Anderson, D. L. T. . Variational assimilation of XBT data. Part I. J. Phys. Oceanogr. 20, 672– 688. -
Sheinbaum
, J.and Anderson, D. L. T. . Variational assimilation of XBT data. Part II. Sensitivity studies and use of smoothing constraints. J. Phys. Oceanogr. 20, 689– 704. -
Sparrow
, C. . The Lorenz equations. Springer-Verlag, New-York, -
Stensrud
, D. J.and Bao, J. W. . Behaviors of variational and nudging assimilation techniques with a chaotic low-order model. Mon. Wea. Rev. 120, 3016– 3028. -
Talagrand
, O. . Data assimilation problems. In: Proceedings, NATO Advanced Study Institute, Energy and water cycles in the climate system, (Gliicksburg, Germany, October 1991), E.and D., eds.- 213. -
Talagrand
, O.and Courtier, P. . Variational assimilation of meteorological observations with the adjoint vorticity equation (I). Theory. Quart. J. R. Met. Soc. 113, 1311– 1328. -
Thacker
, W. C.and R. B., . Fitting dynamics to data. J. Geophys. Res. 93, 1227– 1240. -
Thépaut
, J.-N., Vasiljevic, D., Courtier, P.and Pailleux, J. , 1993. Variational assimilation of conventional meteorological observations with a multilevel primitive-equation model. Q. J. R. Meteorol. Soc. 119, 153– 186. -
Tibaldi
, S.and Molteni, F. . On the operational predictability of blocking. Tellus, 343– 365. -
Toth
, Z.and Kalnay, E. . Ensemble forecasting at NMC. The generation of perturbations. Bull. Amer. Meteor. Soc. 74, 2317– 2330. -
Toth
, Z.and Kalnay, E. . Ensemble forecasting atNMC. The use of the breeding method for generating perturbations. Proceedings, 10th AMS Conference on Numerical Weather Prediction, Portland, Oregon, USA, July 1994. Published by the American Meteorological Society. -
Vautard
, R.and Legras, B. . On the source of tnidlatitude low-frequency variability. Part II. Non-linear equilibration of weather regimes. J. Atmos. Sci. 45, 2845– 2867. -
Vautard
, R. . Multiple weather regimes over the north Atlantic: analysis of precursors and successors. Mon. Wea. Rev. 118, 2056– 2081. -
Zou, X.
and Le Dimet, F.-X.. Incom-plete observations and control of gravity waves in variational data assimilation., 273- 296.
DOI: https://doi.org/10.3402/tellusa.v48i1.11634 | Journal eISSN: 3035-9554
Language: English
Page range: 96 - 121
Submitted on: Sep 21, 1994
Accepted on: Mar 10, 1995
Published on: Jan 1, 1996
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 1996 Carlos Pires, Robert Vautard, Olivier Talagrand, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.