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Preconditioning Representer-based Variational Data Assimilation Systems: Application to NAVDAS-AR

  • Boon S. Chua
  • Liang Xu
  • Tom Rosmond
  • Edward D. Zaron

Abstract

Assimilation of observations into numerical models has emerged as an essential modeling component in geosciences. This procedure requires the solution of large systems of linear equations. Solving these systems in “real-time” or “near-real-time” in a timely manner is still a computational challenge. This paper shows how new methods in computational linear algebra are used to “speed-up” the representer-based algorithm in a variety of assimilation problems, with particular application to the Naval Research Laboratory (NRL) Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR) system.

Keywords

Outer Loop Naval Research Laboratory Linear Optimal Problem Variational Data Assimilation Lanczos Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bennett AF (2002) Inverse Modeling of the Ocean and Atmosphere. Cambridge University Press, New York NYGoogle Scholar
  2. Bennett AF, Chua BS, Harrison DE, McPhaden MJ (2000) Generalized inversion of Tropical Atmosphere-Ocean (TAO) data and a Coupled Model of the Tropical Pacific. Part II: the 1995–1996 La Nina and 1997–1998 El Nino. J Climate 13: 2770–2785CrossRefGoogle Scholar
  3. Bennett AF, Chua BS, Pflaum BL, Erwig M, Fu Z, Loft RD, Muccino JC (2008) The Inverse Ocean Modeling System. I: Implementation. J Atmos Ocean Tech 25:1608–1622CrossRefGoogle Scholar
  4. Chua BS, Bennett AF (2001) An Inverse Ocean Modeling System. Oc Mod 3: 137–165CrossRefGoogle Scholar
  5. Courtier P (1997) Dual Formulation of Four-dimensional Assimilation. Q.J.R. Meteorol Soc 123: 2449–2461CrossRefGoogle Scholar
  6. Descroziers G, Ivanov S (2001) Diagnosis and Adaptive Tuning of Observation-error Parameters in a Variational Assimilation. Q.J.R. Meteorol Soc 127: 1433–1452CrossRefGoogle Scholar
  7. Erwig M, Fu Z, Pflaum B (2006) Generic Programming in Fortran. ACM SIGPLAN 2006 Workshop on Partial Evaluation and Program Manipulation: 130–139Google Scholar
  8. Fisher M (1998) Minimization Algorithms for Variational Data Assimilation. Proceedings of ECMWF Seminar on Recent Developments in Numerical Methods for Atmospheric Modelling, 7–11 September 1998, pp 364–385Google Scholar
  9. Giraud L, Gratton S (2006) On the Sensitivity of Some Spectral Preconditioners. SIAM. J Matrix Anal Appl 27: 1089–1105CrossRefGoogle Scholar
  10. Golub GH, Van Loan CF (1989) Matrix Computations- 2nd ed. Johns Hopkins University Press, BaltimoreGoogle Scholar
  11. Greenbaum A, Strakos Z (1992) Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations. SIAM. J Matrix Anal Appl 13: 121–137CrossRefGoogle Scholar
  12. Hogan T, Rosmond T (1991) The Description of the Navy Operational Global Atmospheric Prediction System’s Spectral Forecast Model. Mon Wea Rev 119: 1786–1815CrossRefGoogle Scholar
  13. Muccino JC, Hubele NF, Bennett AF (2004) Significance Testing for Variational Assimilation. Quart. J Roy Meteor Soc 130: 1815–1838CrossRefGoogle Scholar
  14. Muccino JC, Arango HG, Bennett AF, Chua BS, Cornuelle BD, Di Lorenzo E, Ebgert GD, Haivogel D, Levin JC, Luo H, Miller AJ, Moore AM, Zaron ED (2008) The Inverse Ocean Modeling System. II: Applications. J Atmos Ocean Tech 25:1623–1637CrossRefGoogle Scholar
  15. Notay Y (2000) Flexible Conjugate Gradients. SIAM. J Sci Comput 22: 1444–1460CrossRefGoogle Scholar
  16. Rosmond T, Xu L (2006) Development of NAVDAS-AR: nonlinear formulation and outer loop tests. Tellus 58A: 45–58Google Scholar
  17. Saad Y (2003) Iterative Methods for Sparse Linear Systems-2nd ed. SIAM, Philadelphia PAGoogle Scholar
  18. Sasaki Y (1970) Some Basic Formalisms in Numerical Variational Analysis. Mon Wea Rev 98: 875–883CrossRefGoogle Scholar
  19. Simoncini V, Szyld DB (2007) Recent Computational Developments in Krylov Subspace Methods for Linear Systems. Number. Linear Algebra Appl 14: 1–59CrossRefGoogle Scholar
  20. Xu L, Daley R (2000) Data Assimilation with a Barotropically Unstable Shallow Water System using Representer Algorithms. Tellus 54A: 125–137Google Scholar
  21. Xu L, Rosmond T, Daley R (2005) Development of NAVDAS-AR: formulation and initial tests of the linear problem. Tellus 57A: 546–559Google Scholar
  22. Xu L, Langland R, Baker N, Rosmond T (2006) Development of the NRL 4D-Var data assimilation adjoint system. Geophys Res Abs 8: 8773Google Scholar
  23. Xu L, Rosmond T, Goerss J, Chua B (2007) Toward a Weak Constraint Operational 4D-Var System: Application to the Burgers’ equation. Meteorologische Zeitschrift 16: 767–776CrossRefGoogle Scholar
  24. Zaron ED (2006) A Comparison of Data Assimilation Methods Using a Planetary Geostrophic Model. Mon Wea Rev 134: 1316–1328CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Boon S. Chua
    • 1
  • Liang Xu
  • Tom Rosmond
  • Edward D. Zaron
  1. 1.SAICMontereyUSA

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