B‐preconditioned minimization algorithms for variational data assimilation with the dual formulation
Tóm tắt
Variational data assimilation problems in meteorology and oceanography require the solution of a regularized nonlinear least‐squares problem. Practical solution algorithms are based on the incremental (truncated Gauss–Newton) approach, which involves the iterative solution of a sequence of linear least‐squares (quadratic minimization) sub‐problems. Each sub‐problem can be solved using a primal approach, where the minimization is performed in a space spanned by vectors of the size of the model control vector, or a dual approach, where the minimization is performed in a space spanned by vectors of the size of the observation vector. The dual formulation can be advantageous for two reasons. First, the dimension of the minimization problem with the dual formulation does not increase when additional control variables are considered, such as those accounting for model error in a weak‐constraint formulation. Second, whenever the dimension of observation space is significantly smaller than that of the model control space, the dual formulation can reduce both memory usage and computational cost.
In this article, a new dual‐based algorithm called Restricted
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Tài liệu tham khảo
Axelsson O., 1996, Iterative Solution Methods
Broquet G, 2009, Ocean state and surface forcing correction using the ROMS‐IS 4DVAR data assimilation system, Mercator Ocean Quarterly Newsletter, 34, 5
Da Silva A, 1995, Proceedings of the 2nd WMO Symposium on assimilation of observations in meteorology and oceanography, 273
El Akkraoui A, 2012, Preconditioning of variational data assimilation and the use of a bi‐conjugate gradient method, Q. J. R. Meteorol. Soc.
Fisher M., 2003, Proceedings of Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, 87
Flather RA., 1976, A tidal model of the northwest European continental shelf, Mem. Soc. R. Sci. Liege, 10, 141
Golub GH, 1996, Matrix Computations
GrattonS TointPL TshimangaJ.2009.‘Inexact range‐space Krylov solvers for linear systems arising from inverse problems’. Technical Report 09/20 Department of Mathematics FUNDP University of Namur: Belgium.
Hickey BM., 1998, Coastal oceanography of western North America from the tip of Baja California to Vancouver Island, The Sea, 11, 345
Horn RA, 1999, Matrix Analysis
MadecG.2008. ‘NEMO ocean engine’. Technical Report 27 Note du Pôle de modélisation Institut Pierre‐Simon Laplace (IPSL) France.http://www.nemo‐ocean.eu.
Mogensen K, 2009, ‘NEMOVAR: A variational data assimilation system for the NEMO model’, ECMWF Newsletter, 120, 17
MogensenK BalmasedaMA WeaverAT.2012. ‘The NEMOVAR ocean data assimilation system as implemented in the ECMWF ocean analysis for System 4’. Tech. Report 668 ECMWF: Reading UK.
Nocedal J, 2006, Numerical Optimization
Nour‐Omid B, 1988, Proceedings of First International Symposium on Domain Decomposition Methods for Partial Differential Equations, 250
Parlett BN., 1980, The symmetric eigenvalue problem
Saad Y., 1996, Iterative Methods for Sparse Linear Systems
Shchepetkin AF, 2003, A method for computing horizontal pressure‐gradient force in an oceanic model with a nonaligned vertical grid, J. Geophys. Res., 108, 10.1029/2001JC001047
Veneziani M, 2009, A central California coastal ocean modeling study: 1. Forward model and the influence of realistic versus climatological forcing., J. Geophys. Res., 114
Veneziani M, 2009, A central California coastal ocean modeling study: 2. Adjoint sensitivities to local and remote forcing mechanisms., J. Geophys. Res., 114