An adaptive variational method for data assimilation with imperfect models

References

• Albert, A. E. and Gardner, L. A., Jr. 1967. Stochastic approximation and nonlinear regression. The MIT Press, Cambridge, Mass.
   Google Scholar
• 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.
   Google Scholar
• Bennett, A. F. 1992. Inverse methods in physical oceanography. Cambridge University Press, New York, 346 pp.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Bernstein, S. and Hyland, D. 1985. The optimal projection equations for reduced-order state estimation. IEEE Trans. Autom. Contr. AC-30, 583–585.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Courtier, P. 1997. Dual formulation of 4-dimensional variational assimilation. Q. J. R. Meteorol. Soc. 123, 2449–2461.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Daley, R. 1992. Forecast-error statistics for homogeneous and inhomogeneous observation networks. Mon. Wea. Re v. 120, 627–647.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• 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.
   Google Scholar
• Dee, D. P. 1995. On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Re v. 123, 1128–1145.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Derber, J. C. 1989. A variational continuous assimilation technique. Mon. Wea. Re v. 117, 2437–2446.
   Web of Science ®Google Scholar
• Egbert, G. D. and Bennett, A. F. 1996. TOPEX/Poseidon tides estimated using a global inverse model. J. Geophys. Res. 99, 24821-24 852.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Gelb, A. 1974. Applied optimal estimation. The MIT Press, 374 pp.
   Google Scholar
• Gilbert, J. C. and Lemarechal, C. 1989. Some numerical experiments with variable storage quasi-Newton algo-rithms. Math. Programming B45, 407–435.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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).
   Google Scholar
• 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).
   Google Scholar
• 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.
   Google Scholar
• Jazwinsky, A. H. 1969. Adaptive filtering. Automatika 5, 475–485.
   Web of Science ®Google Scholar
• Kalman, R. E. 1960. A new approach to linear filtering and prediction problems. J. Basic Eng. 82D, 35–45.
   Google Scholar
• LeDimet, F. X. and Talagrand, O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38, 97–110.
   Google Scholar
• Lions, J. L. 1971. Optimal control system governed by partial differential equations. Springer-Verlag, New York, pp. 396.
   Google Scholar
• Liu, D. C. and Nocedal, J. 1989. On the limited BFGS method for large scale optimization. Math. Program-ming B45, 503–528.
   Web of Science ®Google Scholar
• Mehra, R. K. 1970. On the identification of variances and adaptive Kalman filtering. IEEE Trans. Automat., Contr. AC-15, 175–184.
   Google Scholar
• Mellor, G. L. and Ezer, T. 1991. A Gulf stream model and an altimetry assimilation scheme, J. Geophys. Res. 96, C5, 8779–8795.
   Web of Science ®Google Scholar
• Menard, R. and Daley, R. 1996. The application of Kalman smoother theory to the estimation of 4DVAR error statistics. Tellus 48A, 221–237.
   Google Scholar
• 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).
   Google Scholar
• Rauch, H. E., Tung, F. and Striebel, C. T. 1965. Maximum likelihood estimates of linear dynamic systems. AIAA Journal 3, 1445–1450.
   Web of Science ®Google Scholar
• Sasaki, Y. 1970. Some basic formalisms on numerical variational analysis. Mon. Wea. Re v. 98, 875–883.
   Web of Science ®Google Scholar
• Stauffer, D. R. and Bao, J.-W. 1993. Optimal determination of nudging coefficients using the adjoint equations. Tellus 45A, 358–369.
   Google Scholar
• 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.
   Google Scholar
• Uboldi, F. and Kamachi, M. 2000. Time-space weak-constraint data assimilation for nonlinear models. Tellus 52A, in press.
   Google Scholar
• Wergen, W. 1992. The effect of model errors in variational assimilation. Tellus 44A, 297–313.
   Google Scholar
• Wunsch, C. 1996. The ocean circulation inverse problem, Cambridge Univ. Press, Cambridge, UK, 442 pp.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Zupanski, M. 1993. Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Wea. Re v. 121, 2396–2408.
   Web of Science ®Google Scholar
• Zupanski, D. 1997. A general weak constraint applica-tion to operational 4D-VAR data assimilation system. Mon. Wea. Re v. 125, 2274–2292.
   Web of Science ®Google Scholar