Approximate Gauss-Newton methods for optimal state estimation using reduced-order models

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 8, 2008, Pages 1367-1373

  Lawless, A S ^a   Nichols, N K ^a   Boess, C ^b   Bunse Gerstner, A ^b  

^a UNIVERSITY OF READING   (United Kingdom)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

Gauss Newton methods; Large scale nonlinear least squares problems subject to dynamical system constraints; Variational data assimilation; Weather, ocean and climate prediction

Indexed keywords

CLIMATOLOGY; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; OCEANOGRAPHY; OPTIMIZATION; RANDOM PROCESSES; WEATHER FORECASTING;

GAUSS-NEWTON METHOD; OPTIMAL STATE ESTIMATION;

ESTIMATION;

CLIMATOLOGY; ESTIMATION; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; OCEANOGRAPHY; OPTIMIZATION; RANDOM PROCESSES; WEATHER FORECASTING;

EID: 40749147172     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1629     Document Type: Conference Paper

References (15)

1. Gill PE, Murray W, Wright MR. Practical Optimization. Academic Press: New York, 1986.
2. Lawless AS, Gratton S, Nichols NK. Approximate Gauss-Newton methods for nonlinear least squares problems. SIAM Journal on Optimization 2007; 18:106-132.
3. Lawless AS, Gratton S, Nichols NK. An investigation of incremental 4D-Var using non-tangent linear models. Quarterly Journal of the Royal Meteorological Society 2005; 131:459-476.
4. Lawless AS, Gratton S, Nichols NK. Approximate iterative methods for variational data assimilation. International Journal for Numerical Methods in Fluids 2005; 47:1129-1135.
5. Courtier P, Thépaut J-N, Hollingsworth A. A strategy for operational implementation of 4D-Var, using an incremental approach. Quarterly Journal of the Royal Meteorological Society 1994; 120:1367-1387.
6. Antoulas AC. Approximation of Large-scale Dynamical Systems. SIAM: Philadelphia, PA, 2005.
7. Farrell BF, Ioannou PJ. State estimation using a reduced-order Kalman filter. Journal of Atmospheric Science 2001; 58:3666-3680.
8. Cao Y, Zhu J, Navon IM, Luo Z. A reduced order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. International Journal for Numerical Methods in Fluids 2007; 53:1571-1583.
9. Lewis JM, Lakshmivarahan S, Dhall S. Dynamic Data Assimilation: A Least Squares Approach. Cambridge University Press: Cambridge, 2006.
10. Laub AJ, Heath MT, Paige CC, Ward RC. Computation of system balancing transformations and other applications of simultaneous diagnolization algorithms. IEEE Transactions on Automatic Control 1987; AC-32:115-122.
11. Chablaoui Y, Van Dooren P. Model reduction of time-varying systems. In Dimension Reduction of Large-scale Systems, Benner P, Mehrmann V, Sorensen D (eds). Springer: Berlin, 2005.
12. Freund RW. Model reduction methods based on Krylov subspaces. Acta Numerica 2003; 12:267-319.
13. Gugercin S, Sorensen DC, Antoulas AC. A modified low-rank Smith method for large-scale Lyapunov equations. Numerical Algorithms 2003; 32:27-55.
14. Lawless AS, Nichols NK, Boess C, Bunse-Gerstner A. Using model reduction methods within incremental 4D-Var. Monthly Weather Review, in press.
15. Katz D, Lawless AS, Nichols NK, Cullen MJP, Bannister RN. A comparison of potential vorticity-based and vorticity-based control variables. Numerical Analysis Report, 8/2006, Department of Mathematics, The University of Reading, 2006.