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Original Research Papers

Data assimilation with a barotropically unstable shallow water system using representer algorithms

Authors:

Liang Xu ,

Naval Research Laboratory, 7 Grace Hopper Avenue, Monterey, CA 93943-5502, US
About Liang
Deceased August 2001.
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Roger Daley

Naval Research Laboratory, 7 Grace Hopper Avenue, Monterey, CA 93943-5502
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Abstract

The cycling representer algorithm of Xu and Daley (2000) is a weak constraint four-dimensional variational data assimilation algorithm. It was successfully applied to a one-dimensional transport problem and was able to successfully extract the signal from noisy and sparse observations. The algorithm, however, has not previously been applied to a multivariate, multidimensional system with dynamic instability. The algorithm is also very computationally demanding and awaits considerable enhancement in computer power before being practical for operational forecast models. We have two objectives in this paper. The first is to apply the cycling representer algorithm to a two-dimensional, multivariate barotropically unstable linear shallow water system. The second objective is to formulate and test an accelerated representer algorithm that is much more computationally tractable than the cycling representer algorithm itself. A linear shallow water system with a barotropically unstable basic state was used as a test bed to conduct data assimilation experiments. The evolution of a ‘neutral’ eastward-propagating singular vector was selected as the ‘truth’, against which all data assimilation experiments were to be evaluated. The results indicated that the cycling representer algorithm was capable of providing satisfying state estimates for a multivariate, multidimensional system. The results from the accelerated representer algorithm were very encouraging because it is sufficiently computationally tractable to be used on present day multi-processor machines for operational applications.

How to Cite: Xu, L. and Daley, R., 2002. Data assimilation with a barotropically unstable shallow water system using representer algorithms. Tellus A: Dynamic Meteorology and Oceanography, 54(2), pp.125–137. DOI: http://doi.org/10.3402/tellusa.v54i2.12135
  Published on 01 Jan 2002
 Accepted on 16 Oct 2001            Submitted on 14 May 2001

References

  1. Anderson , E. , Bai , Z. , Bischof , C. , Demmel , J. , Dongarra , J. , Du Croz , J. , Greenbaum , A. , Hammar-ling , S. , McKenney , A. , Ostrouchov , S. and Sorensen , D. 1995 . LAPACK users’ guide , 2nd edn . Society for Industrial and Applied Mathematics , Philadelphia . 325 pp.  

  2. Amodei , L. 1995 . Solution approchee pour un problem d’assimilation de donnees meteorologiques avec prise en compte de l’erreur de modele . C. R. Acad. Sci., Ser. ha 321 , 1087 – 1094 .  

  3. Bennett , A. F. 1997 . Inverse methods and data assimilation , 1997 Summer School Lecture Notes , Oregon State University , Corvallis, Oregon .  

  4. Bennett , A. F. and McIntosh , P. C. 1982 . Open ocean modeling as an inverse problem: tidal theory . J. Phys. Ocean . 12 , 1004 – 1018 .  

  5. Bennett , A. F. and Thorburn , M. A. 1992 . The generalized inverse of a nonlinear quasigeostrophic ocean circulation model . J. Phys. Ocean . 22 , 213 – 230 .  

  6. Chua , B. S. and Bennett , A. F. 2001 . An inverse ocean modeling system . Ocean Modeling 3 , 137 – 165 .  

  7. Cohn , S. E. and Parrish , F. P. 1991 . The behavior of forecast error covariance for a Kalman filter in two dimensions . Mon. Wea. Rev . 119 , 1757 – 1785 .  

  8. Courtier , P. 1998 . Dual formulation of four dimensional variational assimilation . Q. J. R. Meteorol. Soc . 123 , 2449 – 2461 .  

  9. 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 .  

  10. Courtier , P. and Talagrand , O. 1990 . Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus 42A , 531 – 549 .  

  11. Daley , R. and Barker , E. 2000 . The NAVDAS source book , Defense Printing Office for the Naval Research Laboratory , Washington , DC . 217 pp .  

  12. Daley , R. and Barker , E. 2001 . NAVDAS — formulation and diagnostics . Mon. Wea. Rev . 129 , 869 – 883 .  

  13. Egbert , G. , Bennett , A. and Foreman , M. 1994 . TOPEX/POSEIDON tides estimated using a global inverse method. J. Geophys. Res . 99 , 24 , 821 – 24 , 852 .  

  14. Evensen , G. 1997 . Advanced data assimilation for strong nonlinear dynamics . Mon. Wea. Rev . 125 , 1342 – 1354 .  

  15. Evensen , G. and van Leeuwen , P. J. 2000 . An ensemble Kalman smoother for nonlinear dynamics . Mon. Wea. Rev . 128 , 1852 – 1867 .  

  16. Golub , G. H. and Van Loan , C. F. 1996 . Matrix computa-tions , 3rd edn . The Johns Hopkins Press , Baltimore and London . 694 pp.  

  17. Hodur , M. R. 1997 . The Naval Research Laboratory’s coupled ocean/atmosphere mesoscale prediction system (COAMPS) . Mon. Wea. Rev . 125 , 1414 – 1430 .  

  18. Hogan , T. and Rosmond , T. 1991 . The description of the Navy Operational Global Atmospheric Prediction System’s spectral forecast system . Mon. Wea. Rev . 119 , 1786 – 1815 .  

  19. Kuo , H. L. 1949 . Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere . J. Meteorol . 6 , 105 – 122 .  

  20. Menard , R. 1994 . Kalman filtering of Burgers’ equation and its application to atmospheric data assimilation . Ph.D. Thesis , Department of Atmospheric and Ocean Sciences, McGill University, Montreal, Canada .  

  21. Reynolds , C. A. and Palmer , T. N. 1998 . Decaying singular vectors and their impact on analysis and forecast correction . J. Atmos. Sci . 55 , 3005 – 3023 .  

  22. Strang , G. 1986 . Introduction to applied mathematics . Wellesley-Cambridge Press , 758 pp.  

  23. Todling , R. and Ghil , M. 1994 . Tracking atmospheric instabilities with the Kalman filter. Part I: Methodology and one-layer results . Mon. Wea. Rev . 122 , 183 – 204 .  

  24. Xu , L. 1995 . The study of mesoscale land-air-sea inter-action processes using a nonhydrostatic model. Ph.D. Dissertation, North Carolina State University, Raleigh, 336 pp. (Available from Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC).  

  25. Xu , L. and Daley , R. 2000 . Towards a true four dimensional data assimilation algorithm: application of a cycling representer algorithm to a simple transport problem . Tellus 52A , 109 – 128 .  

  26. Zupanski , D. 1997 . A general weak constraint applicable to operational 4DVAR data assimilation systems . Mon. Wea. Rev . 125 , 2274 – 2292 .  

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