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An adaptive variational method for data assimilation with imperfect models Cover

An adaptive variational method for data assimilation with imperfect models

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Open Access
|Jan 2000

References

  1. Albert , A. E. and Gardner , L. A. , Jr . 1967 . Stochastic approximation and nonlinear regression . The MIT Press , Cambridge , Mass .
  2. Amodei , L . 1995 . Solution approachée pour un problem d’assimilation de donnees météorologiques avec prise en compte de l’erreur de modele. Comptes Rendus de l’Academie des Sciences 321, serie II a, 1087-1094. Bengtsson, L. 1991. Advances and prospects in numerical weather prediction . Q. J. R. Meteorol. Soc . 117 , 855 902 .
  3. Bennett , A. F . 1992 . Inverse methods in physical oceanography . Cambridge University Press , New York , 346 pp .
  4. Bennett , A. F. , Leslie , L. M. , Hagelberg , C. R. and Powers , P. E . 1993 . Tropical cyclone prediction using a barotropic model initialized by a generalized inverse method. Mon. Wea. Re v . 121 , 1714 1729 .
  5. Bernstein , S. and Hyland , D . 1985 . The optimal projection equations for reduced-order state estimation . IEEE Trans. Autom. Contr . AC-30 , 583 585 .
  6. Blanchet , I. , Frankignoul , C. and Cane , M . 1997 . A comparison of adaptive Kalman filters for a tropical Pacific ocean model. Mon. Wea. Re v . 125 , 40 48 .
  7. Burgers , J. M . 1974 . The nonlinear diffusion equation. D. Reidel Publ. Co., Dordrecht, Holland , 173 pp. Cohn , S. E. 1982 . Methods of sequential estimation for determining initial data in numerical weather prediction. PhD thesis. Courant Institute of Mathematical Sci-ences Report no. CI-6-82, New York University, New York , 183 pp.
  8. Courtier , P . 1997 . Dual formulation of 4-dimensional variational assimilation . Q. J. R. Meteorol. Soc . 123 , 2449 2461 .
  9. Courtier , P. Thepaut , J.-N . and Hollingsworth , A. 1994 . A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc . 120 , 1367 1388.
  10. Daley , R . 1992 . Forecast-error statistics for homogeneous and inhomogeneous observation networks. Mon. Wea. Re v . 120 , 627 647 .
  11. Dee , D. P . 1983 . Computational aspects of adaptive filtering and applications to numerical weather prediction. PhD thesis. Courant Institute of Mathematical Sciences Report no. CI-6-83 , New York University , New York , 150 pp.
  12. Dee , D. P . 1992 . A simple scheme for tuning forecast error covariance parameters. Workshop on Variational assimilation, with special emphasis on three-dimensional aspects. ECMWF, Reading (UK), 191 - 205 .
  13. Dee , D. P . 1995 . On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Re v . 123 , 1128 1145 .
  14. Dee , D. P. , Cohn , S. E. , Dalcher , A. and Ghil , M . 1985 . An efficient algorithm for estimating noise covariance in distributed systems . IEEE Trans. Automat. Control AC-30 , 1057 1065 .
  15. DeMaria , M. and Jones , R. W . 1993 . Optimization of a hurricane track forecast model with the adjoint model equations. Mon. Wea. Re v . 121 , 1730 1745 .
  16. Derber , J. C . 1989 . A variational continuous assimilation technique. Mon. Wea. Re v . 117 , 2437 2446 .
  17. Egbert , G. D. and Bennett , A. F . 1996 . TOPEX/Poseidon tides estimated using a global inverse model . J. Geophys. Res . 99 , 24821-24 852 .
  18. Fukumori , I. and Malanotte-Rizzoli , P . 1995 . An approximate Kalman filter for data assimilation: an example with an idealized Gulf Stream model . J. Geophys. Res . 100 , 6777 6793 .
  19. Gelb , A . 1974 . Applied optimal estimation . The MIT Press, 374 pp.
  20. Gilbert , J. C. and Lemarechal , C . 1989 . Some numerical experiments with variable storage quasi-Newton algo-rithms . Math. Programming B45 , 407 435 .
  21. Ghil , M. , Cohn , S. E. , Tavantzis , J. , Dube K. and Isaacson , E . 1981 . Application of estimation theory to numerical weather prediction. In: Dynamic meteoro-logy: data assimilation methods ( L. Bengtsson , M. Ghil , and E. Källén , eds.). Springer Verlag, New York , 139 - 224 .
  22. Haines , K . 1991 . A direct method for assimilating sea surface height data into ocean model with adjustments to the deep circulation . J. Phys. Oceanogr . 21 , 843 868 .
  23. Hoang , H. S. , De Mey , P. and Talagrand , O . 1994 . A simple adaptive algorithm of stochastic approximation type for system parameter and state estimation. Proc. 33rd Conference on decision and control . Lake Buena Vista, Florida, US. 747-752 (available from Dr. Hoang, SHOM/CMO/GRGS/CNRS, 18 Av. Edouard Belin 31055, Toulouse Cedex, France).
  24. Hoang , H. S. , De Mey , P ., Talagrand , O . and Baraille , R. 1995 . Assimilation of altimeter data in a multilayer quasi-geostrophic ocean model by simple nonlinear adaptive filter. Proc. Second Int. Symp. On Assimilation of observations in meteorology and oceanography, Tokyo, Japan, World Meteor. Org., 521-526 (available from Dr. Hoang, SHOM/CMO/GRGS/CNRS, 18 Av. Edouard Belin 31055, Toulouse Cedex, France).
  25. Hoang , H. S. , Baraille , R ., Talagrand , O. , Carton X. and De Mey , P. 1998 . Adaptive filtering: application to assimilation of satellite data assimilation in oceano-graphy. Dyn. Atmo. and Oceano . 24 , 257 281.
  26. Jazwinsky , A. H . 1969 . Adaptive filtering . Automatika 5 , 475 485 .
  27. Kalman , R. E . 1960 . A new approach to linear filtering and prediction problems . J. Basic Eng . 82D , 35 45 .
  28. LeDimet , F. X. and Talagrand , O . 1986 . Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38 , 97 110 .
  29. Lions , J. L . 1971 . Optimal control system governed by partial differential equations . Springer-Verlag , New York , pp. 396 .
  30. Liu , D. C. and Nocedal , J . 1989 . On the limited BFGS method for large scale optimization . Math. Program-ming B45 , 503 528 .
  31. Mehra , R. K . 1970 . On the identification of variances and adaptive Kalman filtering. IEEE Trans. Automat ., Contr . AC-15 , 175 184 .
  32. Mellor , G. L. and Ezer , T . 1991 . A Gulf stream model and an altimetry assimilation scheme , J. Geophys. Res . 96 , C5 , 8779 8795 .
  33. Menard , R. and Daley , R . 1996 . The application of Kalman smoother theory to the estimation of 4DVAR error statistics . Tellus 48A , 221 237 .
  34. Ngodock , H. E. and LeDimet , F. X . 1998 . Sensitivity studies for geophysical flows. Proceedings of Int. Conf. On Compu. fluid dyn., Brenos Aires (available from Prof. LeDimet, LMC, BP 53X, 38041 Grenoble Cédex, France).
  35. Rauch , H. E. , Tung , F. and Striebel , C. T . 1965 . Maximum likelihood estimates of linear dynamic systems . AIAA Journal 3 , 1445 1450 .
  36. Sasaki , Y . 1970 . Some basic formalisms on numerical variational analysis. Mon. Wea. Re v . 98 , 875 883 .
  37. Stauffer , D. R. and Bao , J.-W . 1993 . Optimal determination of nudging coefficients using the adjoint equations . Tellus 45A , 358 369 .
  38. Talagrand , O. 1998 . A Posteriori evaluation and verification of analysis and assimilation algorithms. Proc. of ECMWF Workshop on Diagnosis of Data Assimilation System. Reading, UK. 17 - 28 .
  39. Uboldi , F. and Kamachi , M . 2000 . Time-space weak-constraint data assimilation for nonlinear models. Tellus 52A , in press.
  40. Wergen , W . 1992 . The effect of model errors in variational assimilation . Tellus 44A , 297 313 .
  41. Wunsch , C . 1996 . The ocean circulation inverse problem , Cambridge Univ. Press , Cambridge , UK , 442 pp .
  42. Zou , X. , Navon , I. M. and LeDimet , F. X . 1992 . An optimal nudging data assimilation scheme using parameter estimation . Q. J. R. Meteorol. Soc . 118 , 1163 1186 .
  43. Zupanski , M . 1993 . Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Wea. Re v . 121 , 2396 2408 .
  44. Zupanski , D . 1997 . A general weak constraint applica-tion to operational 4D-VAR data assimilation system. Mon. Wea. Re v . 125 , 2274 2292 .
Language: English
Page range: 265 - 279
Submitted on: Feb 8, 1999
Accepted on: Oct 18, 1999
Published on: Jan 1, 2000
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2000 Jiang Zhu, Masafumi Kamachi, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.