An investigation of incremental 4D-Var using non-tangent linear models

Quarterly Journal of the Royal Meteorological Society

Volumn 131, Issue 606, 2005, Pages 459-476

  Lawless, A S ^a   Gratton, S ^b   Nichols, N K ^a  

^a UNIVERSITY OF READING   (United Kingdom)

^b CERFACS   (France)

Author keywords

Gauss Newton; Incremental formulation; Tangent linear; Variational data assimilation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; GRADIENT METHODS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; VARIATIONAL TECHNIQUES; WEATHER FORECASTING;

GAUSS-NEWTON ITERATION; INCREMENTAL FORMULATION; PERTURBATION FORECAST MODEL (PFM); TANGENT LINEAR MODEL (TLM); VARIATIONAL DATA ASSIMILATION;

METEOROLOGY;

DATA ASSIMILATION; SHALLOW-WATER EQUATION;

EID: 27744580710     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1256/qj.04.20     Document Type: Article

References (16)

1. Chao, W. C. and Chang, L.-P. 1992 Development of a four-dimensional variational analysis system using the adjoint method at GLA. Part I: Dynamics. Mon. Weather Rev., 120, 1661-1673
2. 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, 1367-1387
3. Dennis, J. E. and Schnabel, R. B. 1996 Numerical methods for unconstrained optimization and nonlinear equations. Society for Industrial and Applied Mathematics
4. Gill, P. E., Murray, W. and Wright, M. H. 1981 Practical optimization. Academic Press
5. Laroche, S. and Gauthier, P. 1998 A validation of the incremental formulation of 4D variational data assimilation in a nonlinear barotropic flow. Tellus, 50A, 557-572
6. Lawless, A. S. 2001 'Development of linear models for data assimilation in numerical weather prediction'. PhD thesis, Department of Mathematics, University of Reading
7. Lawless, A. S., Nichols, N. K. and Ballard, S. P. 2003 A comparison of two methods for developing the linearization of a shallow-water model. Q. J. R. Meteorol. Soc., 129, 1237-1254
8. Lorenc, A. C, Ballard, S. P., Bell, R. S., Ingleby. N. B., Andrews, R L. F., Barker, D. M., Bray, J. R., Clayton, A. M., Dalby, T., Li, D., Payne, T. J. and Saunders, F. W. 2000 The met. Office global 3-dimensional variational data assimilations scheme. Q. J. R. Meteorol. Soc., 126, 2991-3012
9. Navon, I. M. and Legler, D. M. 1987 Conjugate-gradient methods for large-scale minimization in meteorology. Mon. Weather Rev., 115, 1479-1502
10. Navon, I. M., Zou, X., Derber, J. and Sela, J. 1992 Variational data assimilation with an adiabatic version of the NMC spectral model. Mon. Weather Rev., 120, 1433-1446
11. Rivest, C., Staniforth, A. and Robert, A. 1994 Spurious resonant response of serni-Lagrangian discretizations to orographic forcing: diagnosis and solution. Mon. Weather Rev., 122, 366-376
12. Shanno, D. F. 1978 On the convergence of a new conjugate gradient algorithm. SIAM J. Numer Anal., 15, 1247-1257
13. Shanno, D. E. and Phua, K. H. 1980 Remark on algorithm 500 - a variable method subroutine for unconstrained nonlinear minimization. ACM Trans. on Mathematical Software, 6, 618-622.
14. Temperton, C. and Staniforth, A. 1987 An efficient two-time-level semi-Lagrangian semi-implicit integration scheme. Q. J. R. Meteorol. Soc., 113, 1025-1039
15. Veersé, F. and Thépaut, J.-N. 1998 Multiple-truncation incremental approach for four-dimensional variational data assimilation. Q. J. R. Meteorol. Soc., 124, 1889-1908
16. Wedin, R-Å. 1974 'On the Gauss-Newton method for nonlinear least squares problems'. Working Paper 24, Institute for Applied Mathematics, Stockholm, Sweden