Efficiency of a POD-based reduced second-order adjoint model in 4D-Var data assimilation

International Journal for Numerical Methods in Fluids

Volumn 53, Issue 6, 2007, Pages 985-1004

  Daescu, D N ^a   Navon, I M ^b  

^a PORTLAND STATE UNIVERSITY   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Adjoint model; Data assimilation; Model reduction; Optimization

Indexed keywords

DATA REDUCTION; GRADIENT METHODS; MATHEMATICAL MODELS; OPTIMIZATION; STATE SPACE METHODS;

DATA ASSIMILATION; HESSIAN-FREE TRUNCATED-NEWTON MINIMIZATION; PROPER ORTHOGONAL DECOMPOSITION; REDUCED-ORDER CONTROL SPACE; SECOND-ORDER ADJOINT MODEL;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; DATA REDUCTION; GRADIENT METHODS; MATHEMATICAL MODELS; OPTIMIZATION; STATE SPACE METHODS;

EID: 33846693459     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1316     Document Type: Article

References (44)

1. Daley R. Atmospheric Data Analysis. Cambridge University Press: Cambridge, MA, 1991.
2. Bennett AF. Inverse Methods in Physical Oceanography. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press: Cambridge, MA, 1992.
3. Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press: Cambridge, MA, 2002.
4. Le Dimet FX, Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 1986; 38A:97-110.
5. Courtier P, Thepaud JN, Hollingsworth A. A strategy of operational implementation of 4D-Var using an incremental approach. Quarterly Journal of the Royal Meteorological Society 1994; 120:1367-1388.
6. Rabier F, Järvinen H, Klinker E, Mahfouf JF, Simmons A. The ECMWF operational implementation of four-dimensional variational data assimilation. Part I: experimental results with simplified physics. Quarterly Journal of the Royal Meteorological Society 2000; 126:1143-1170.
7. Veersé F, Thépaut JN. Multiple-truncation incremental approach for four-dimensional variational data assimilation. Quarterly Journal of the Royal Meteorological Society 1998; 124:1889-1908.
8. Trémolet Y. Diagnostics of linear and incremental approximations in 4D-Var. Quarterly Journal of the Royal Meteorological Society 2004; 130:2233-2251.
9. Trémolet Y. Incremental 4D-Var Convergence Study. ECMWF Technical Memorandum, vol. 469, European Centre for Medium-range Weather Forecasts (ECMWF), Reading, U.K., 2005.
10. Dee DP. Simplification of the Kalman filter for meteorological data assimilation. Quarterly Journal of the Royal Meteorological Society 1990; 117:365-384.
11. Todling R, Cohn SE. Suboptimal schemes for atmospheric data assimilation based on the Kalman filter. Monthly Weather Review 1994; 122:2530-2557.
12. Cane MA, Kaplan A, Miller RN, Tang B, Hackert EC, Busalacchi AJ. Mapping tropical Pacific sea level: data assimilation via a reduced state space Kalman filter. Journal of Geophysical Research 1996; 101:22599-22617.
13. Hoteit I, Pham DT. Evolution of the reduced state space and data assimilation schemes based on the Kalman filter. Journal of the Meteorological Society of Japan 2003; 81(1):21-39.
14. Antoulas AC. Approximation of Large-Scale Dynamical Systems. Advances in Design and Control, SIAM: Philadelphia, PA, 2005.
15. Gunzburger MD. Perspectives in Flow Control and Optimization. Advances in Design and Control, SIAM: Philadelphia, PA, 2003.
16. Rathinam M, Petzold L. A new look at proper orthogonal decomposition. SIAM Journal on Numerical Analysis 2003; 41(5):1893-1925.
17. Ravindran SS. Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition. SIAM Journal on Scientific Computing 2002; 23(6):1924-1942.
18. Ravindran SS. Reduced-order controllers for control of flow past an airfoil. International Journal for Numerical Methods in Fluids 2006; 50:531-554.
19. Blayo E, Blum J, Verron J. Assimilation variationnelle de donées en océanographie et réduction de la dimension de l'espace de contrôle. In Equations aux Dérivées Partielles et Applications. Gauthier-Villars: Paris, 1998; 199-219.
20. Durbiano S. Vecteurs caractéristiques de modèles océaniques pour la réduction d'ordre en assimilation de données. Ph.D. Thesis, Université Joseph Fourier, Grenoble, France, 2001.
21. Hoteit I, Kohl A, Stammer D. Efficiency of reduced-order time-dependent adjoint data assimilation approaches. Estimating the Circulation and Climate of the Ocean (ECCO) - Project Report Series, Report No. 27, 2004.
22. Robert C, Durbiano S, Blayo E, Verron J, Blum J, Le Dimet FX. A reduced order strategy for 4D-Var data assimilation. Journal of Marine Systems 2005; 57:70-82.
23. Nash SG. Preconditioning of truncated-Newton methods. SIAM Journal on Scientific and Statistical Computing 1985; 6:599-616.
24. Nash SG, Nocedal J. A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization. SIAM Journal on Optimization 1991; 1:358-372.
25. Le Dimet FX, Navon IM, Daescu DN. Second order information in data assimilation. Monthly Weather Review 2002; 130(3):629-648.
26. Shanno DF, Phua KH. Remark on 'Algorithm 500: minimization of unconstrained multivariate functions [E4]'. ACM Transactions on Mathematical Software 1980; 6(4):618-622.
27. Neta B, Giraldo FX, Navon IM. Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates. Journal of Computational Physics 1997; 133(1):102-112.
28. Giraldo FX, Neta B. Software for the staggered and unstaggered Turkel-Zwas schemes for the shallow water equations on the sphere. NPS-MA-95-008, Technical Report Naval Postgraduate School, Monterey, CA, 1995.
29. McDonald A, Bates JR. Semi-Lagrangian integration of a gridpoint shallow water model on the sphere. Monthly Weather Review 1989; 117(1):130-137.
30. Lorenc AC, Ballard SP, Bell RS, Ingleby NB, Andrews PLF, Barker DM, Bray JR, Clayton AM, Dalby T, Li D, Payne TJ, Saunders FW. The Met. Office global three-dimensional variational data assimilation scheme. Quarterly Journal of the Royal Meteorological Society 2000; 126:2991-3012.
31. Golub GH, Van Loan CF. Matrix Computations (3rd edn). John Hopkins University Press: Baltimore, MA, 1996.
32. Giering R, Kaminski T. Recipes for adjoint code construction. ACM Transactions on Mathematical Software 1998; 24(4):437-474.
33. Giering R, Kaminski T, Slawig T. Generating efficient derivative code with TAF: adjoint and tangent linear Euler flow around an airfoil. Future Generation Computer Systems 2005; 21:1345-1355.
34. Rostaing N, Dalmas S, Galligo A. Automatic differentiation in Odyssée. Tellus 1993; 45A:558-568.
35. Griewank A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Frontiers in Applied Mathematics, vol. 19. SIAM: Philadelphia, PA, 2000.
36. Giering R. Tangent Linear and Adjoint Model Compiler. Users Manual 1.4. http://www.autodiff.com/tamc [August 1999].
37. Gilbert JC, Lemarechal C. Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming 1989; 45:407-435.
38. Liu DC, Nocedal J. On the limited memory BFGS method for large scale minimization. Mathematical Programming 1989; 45:503-528.
39. Schlick T, Fogelson A. TNPACK - a truncated Newton minimization package for large-scale problems: I. Algorithm and usage. ACM Transactions on Mathematical Software 1992; 18:46-70.
40. Yang W, Navon IM, Courtier P. A new Hessian preconditioning method applied to variational data assimilation experiments using NASA general circulation models. Monthly Weather Review 1996; 124:1000-1017.
41. Zupanski M. A preconditioning algorithm for four-dimensional variational data assimilation. Monthly Weather Review 1996; 124:2562-2573.
42. Lehoucq RB, Sorensen DC, Yang C. ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Software, Environments, and Tools, vol. 6. SIAM: Philadelphia, PA, 1998.
43. Crommelin DT, Majda AJ. Strategies for model reduction: comparing different optimal bases. Journal of Atmospheric Sciences 2004; 1:2206-2217.
44. Meyer M, Matthies HG. Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods. Computational Mechanics 2003; 31:179-191.