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Original Research Papers

Computation of observation sensitivity and observation impact in incremental variational data assimilation

Author:

Yannick Trémolet

Global Modeling and Assimilation Office, Code 610.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771, US
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Abstract

We discuss the computation of observation sensitivities and observation impact for incremental variational data assimilation (VDA), accounting for the inner and outer loops. To fully account for the outer loops, a second-order adjoint of the data assimilation system is required, which makes it impractical for an operational data assimilation system. However, some approximations can be made that allow useful results to be obtained with multiple outer loop iterations, in particular, for observation impact studies.

Two algorithms are presented to compute the adjoint of the inner loop minimization, and their merits are discussed. Validation results are given for both of these algorithms. We show that one algorithm, based on the adjoint of an approximation of the inverse of the Hessian of the cost function, can also be used to investigate some convergence aspects of the incremental VDA inner loop. Because it is computationally inexpensive, the proposed algorithm could be used to monitor an operational system routinely.We give some numerical results illustrating the impact of observations in successive outer loop iterations.

How to Cite: Trémolet, Y., 2008. Computation of observation sensitivity and observation impact in incremental variational data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 60(5), pp.964–978. DOI: http://doi.org/10.1111/j.1600-0870.2008.00349.x
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  Published on 01 Jan 2008
 Accepted on 20 May 2008            Submitted on 14 Jan 2008

References

  1. Andersson , E. , Fisher , M. , Munro , R. and McNally , A. 2000 . Diagno-sis of background errors for radiances and other observable quan-tities in a variational data assimilation scheme, and the explanation of a case of poor convergence . Q. J. R. Meteorol. Soc . 126 , 1455 – 1472 .  

  2. Baker , N. and Daley , R. 2000 . Observation and background adjoint sensitivity in the adaptative observation targeting problem . Q. J. R. Meteorol. Soc . 126 , 1431 – 1454 .  

  3. Cardinali , C. 2008 . Monitoring the observation impact in the short-range forecast. Q. J. R. Meteorol. Soc . Submitted .  

  4. Cardinali , C. and Buizza , R. 2004 . Observation sensitivity to the analysis and the forecast: a case study during ATreC targeting campaign.In: Proceedings of the First THORPEX International Science Sympo- sium . 6 – 10 December 2004, Montreal, Canada, WMO TD 1237 WWRP/THORPEX No. 6 .  

  5. Courtier , P. , Thepaut , J.-N. and Hollingsworth , A. 1994 . A strategy for operational implementation of 4D-Var, using an incremental ap-proach . Q. J. R. Meteorol. Soc . 120 , 1367 – 1387 .  

  6. Errico , R. 2007 . Interpretations of an adjoint-derived observational im-pact measure . Tellus 59A , 273 – 276 .  

  7. Fisher , M. 2003 . Estimation of Entropy Reduction and Degrees of Free-dom for Signal for Large Variational Analysis Systems. Tech. Memo. 397, ECMWF.  

  8. Fisher , M. , Leutbecher , M. and Kelly , G. 2005 . On the equivalence between Kalman smoothing and weak-constraint four-dimensional variational data assimilation . Q. J. R. Meteorol. Soc . 131 , 3235 – 3246 .  

  9. Gelaro , R. , Zhu , Y. and Errico , R. 2007 . Examination of various-order adjoint-based approximations of observation impact . Meteorol. Z . 16 , 685 – 692 .  

  10. Golub , G. and Van Loan , C. 1996 . Matrix Computations 3rd Edition . Johns Hopkins University Press , Baltimore , USA .  

  11. Langland , R. and Baker , N. 2004 . Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system . Tellus , 56A , 189 – 201 .  

  12. Pellerin , S. , Laroche , S. , Morneau , J. and Tanguay , M. 2006 . Estimation of adjoint sensitivity gradients in observation space using dual (PSAS) formulation of the MSC operational 4D-Var. In: Proceedings of the Seventh International Workshop on Adjoint Applications in Dynamic Meteorology. 9-13 October , 2006 , Obergurgl , Austria .  

  13. Tan , D. , Andersson , E. , Fisher , M. and Isaksen , L. 2007 . Observing sys-tem impact assessment using a data assimilation ensemble technique: application to the ADM-Aeolus wind profiling mission. Tech. Memo. 510, ECMWF.  

  14. Trémolet , Y. 2006. Accounting for an imperfect model in 4D-Var. Q. J. R. Meteorol. Soc . 132 , 2483-250 4 .  

  15. Trémolet , Y. 2007a. First-order and higher-order approximations of ob-servation impact. MeteoroL Z . 16 , 693 - 694 .  

  16. Trémolet , Y. 2007b. Incremental 4D-Var convergence study. Tellus 59A , 706 - 718 .  

  17. Trémolet , Y. 2007c. Model error estimation in 4D-Var. Q. J. R. MeteoroL Soc. 133 , 1267-128 0 .  

  18. Wang , Z. , Navon , I. M. , Le Dimet , E-X. and Zou , X. 1992 . The second order adjoint analysis: theory and applications . MeteoroL Atmos. phys . 50 , 3 – 20 .  

  19. Wu , W.-S. , Purser , J. and Parrish , D . 2002 . Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev . 130 , 2905 - 2916 .  

  20. Xu , L. , Langland , R. , Baker , N. and Rosmond , T . 2006 . Develop-ment and testing of the adjoint of NAVDAS-AR. In: Proceedings of the Seventh International Workshop on Adjoint Applications in Dynamic Meteorology, 9-13 October, 2006, Obergurgl, Austria.  

  21. Zhu , Y. and Gelaro , R. 2008 . Observation sensitivity calculations using the adjoint of the gridpoint statistical interpolation (GSI) analysis system . Mon. Wea. Rev . 136 , 335 – 351 .  

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