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Assimilation techniques: 3dVar
April 2001
By Mike Fisher
European Centre for Medium-Range Weather
Forecasts.
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REFERENCES
Andersson, E. and H. Järvinen, 1998. Variational Quality Control. Quarterly Journal Royal Met. Society, Vol. 125, No. 554, pp 697.
Andersson, E., J. Haseler, P. Undén, P. Courtier, G. Kelly, D. Vasiljevic, C. Brancovic, C. Cardinali, C. Gaffard, A. Hollingsworth, C. Jakob, P. Janssen, E. Klinker, A. Lanzinger, M. Miller, F. Rabier, A. Simmons, B. Strauss, J-N. Thepaut and P. Viterbo, 1998, The ECMWF implementation of three dimensional variational assimilation (3D-Var). Part III: Experimental results. Quarterly Journal Royal Met. Society. Vol. 124, No. 550, pp1831-1860.
Andersson, E., M. Fisher, R. Munro, A. McNally, 2000, Diagnosis of background errors for radiances and other observable quantities in a variational data assimilation scheme, and the explanation of a case of poor convergence. Quarterly Journal Royal Met. Society. Vol. 126, pp1455-1472.
Courtier P., E. Andersson, W. Heckley, J. Pailleux, D. Vasiljevic, M. Hamrud, A. Hollingsworth, F. Rabier and M. Fisher, 1998, The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation. Quarterly Journal Royal Met. Society, Vol 124, No. 550, pp 1783.
Dennis J.E. Jr. and J.J. Moré, 1977, Quasi-Newton Methods, Motivation and Theory. SIAM Review, Vol. 19, No. 1, pp 46-89.
Fisher M. and P. Courtier, 1995, Estimating the covariance matrix of analysis and forecast error in variational data assimilation. ECMWF Technical Memorandum No. 220.
Gilbert J.C. and C. Lemaréchal, 1989, Some numerical experiments with variable storage quasi-Newton algorithms, Math. Prog 45, pp 407-436.
Hollingsworth A. and P. Lönnberg, 1986, The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field. Tellus, 38A, pp 111-136.
Liu D.C. and J. Nocedal, 1989, On the limited memory BFGS method for large scale optimization, Mathematical Programming, 45, pp 503-528.
Nocedal J., 1980, Updating quasi-Newton matrices with limited storage, Mathematics of Computation, 35, No. 151, pp 773-782.
Parrish, D. and J.C. Derber, 1992, The National Meteorological Center's spectral statistical interpolation analysis system. Monthly Weather Review, 120, pp1747-1763.
Rabier F., A. McNally, E. Andersson, P. Courtier, P. Undén, J. Eyre, A. Hollingsworth and F. Bouttier, 1998, The ECMWF implementation of three-dimensional variational assimilation (3D-Var). II: Structure function. Quarterly Journal Royal Met. Society, Vol. 124, No. 550, pp 1809.
Shewchuk J.R. 1994, An introduction to the conjugate gradient method without the agonizing pain. Edition
. http://www.cs.cmu.edu/~jrs/ Wang Z., I. Navon, F.X. Le Dimet and X. Zou, 1992, The second order adjoint analysis: theory and applications. Meteorology and Atmospheric Physics, 1992.
Wang Z., I. Navon and X. Zou and F.X. LeDimet, 1995, A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products, Computational Optimization and Applications, 4, pp 241-262.
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