Start Submission Become a Reviewer

Reading: Three-dimensional variational data assimilation for a limited area model

Download

A- A+
Alt. Display

Original Research Papers

Three-dimensional variational data assimilation for a limited area model

Authors:

N. Gustafsson ,

Swedish Meteorological and Hydrological Institute, S-60176 Norrköping, SE
X close

L. Berre,

Swedish Meteorological and Hydrological Institute, S-60176 Norrköping Sweden; Météo-France, Toulouse, FR
X close

S. Hörnquist,

Swedish Meteorological and Hydrological Institute, S-60176 Norrköping Sweden; ABB Corporation, Copenhagen, DK
X close

X.-Y. Huang,

Danish Meteorological Institute, Copenhagen, DK
X close

M. Lindskog,

Swedish Meteorological and Hydrological Institute, S-60176 Norrköping, SE
X close

B. Navascués,

National Meteorological Institute of Spain, Madrid, ES
X close

K. S. Mogensen,

Danish Meteorological Institute, Copenhagen, DK
X close

S. Thorsteinsson

Swedish Meteorological and Hydrological Institute, S-60176 Norrköping Sweden; Icelandic Meteorological Office, Reykjavik, IS
X close

Abstract

A 3-dimensional variational data assimilation (3D-Var) scheme for the High Resolution Limited Area Model (HIRLAM) forecasting system is described. The HIRLAM 3D-Var is based on the minimisation of a cost function that consists of one term, Jb, which measures the distance between the resulting analysis and a background field, in general a short-range forecast, and another term, Jo, which measures the distance between the analysis and the observations. This paper is concerned with Jo and the handling of observations, while the companion paper by Gustafsson et al. (2001) is concerned with the general 3D-Var formulation and with the Jb term. Individual system components, such as the screening of observations and the observation operators, and other issues, such as the parallelisation strategy for the computer code, are described. The functionality of the observation quality control is investigated and the 3D-Var system is validated through data assimilation and forecast experiments. Results from assimilation and forecast experiments indicate that the 3D-Var assimilation system performs significantly better than two currently used HIRLAM systems, which are based on statistical interpolation. The use of all significant level data from multilevel observation reports is shown to be one factor contributing to the superiority of the 3D-Var system. Other contributing factors are most probably the formulation of the analysis as a single global problem, the use of non-separable structure functions and the variational quality control, which accounts for non-Gaussian observation errors.

How to Cite: Gustafsson, N., Berre, L., Hörnquist, S., Huang, X.-Y., Lindskog, M., Navascués, B., Mogensen, K.S. and Thorsteinsson, S., 2001. Three-dimensional variational data assimilation for a limited area model. Tellus A: Dynamic Meteorology and Oceanography, 53(4), pp.425–446. DOI: http://doi.org/10.3402/tellusa.v53i4.12198
  Published on 01 Jan 2001
 Accepted on 6 Feb 2001            Submitted on 17 Mar 2000

References

  1. Berre , L . 1997 . Non-separable structure functions for the HIRLAM 3DVAR. HIRLAM Technical report 30 , November 1997 , 40 pp.  

  2. Berre , L . 2000 . Estimation of synoptic and meso scale forecast error covariances in a limited area model . Mon. Wea. Rev . 128 , 644 – 667 .  

  3. Boer , G. J . 1983 . Homogeneous and isotropic turbulence on the sphere . J. Atm. Sci . 40 , 154 – 163 .  

  4. Bouttier , F . 1996 . Application of Kalman filtering to numerical weather prediction. Proceedings 1996 ECMWF Seminar on Data assimilation and Workshop on Non-linear aspects of data assimilation. ECMWF, Reading, UK, pp. 61 - 90 .  

  5. Cohn , S. E. , Da Silva , A. , Guo , J. , Sienkiewicz , M. and Lamich , D . 1998 . Assessing the effects of data selection with the DAG physical-space statistical analysis system . Mon. Wea. Rev . 126 , 2913 – 2926 .  

  6. Courtier , P. , Thépaut , J.-N. and Hollingsworth , A . 1994 . A strategy for operational implementation of 4D-Var using an incremental approach . Q. J. Roy. Meteorol. Soc . 120 , 1367 – 1388 .  

  7. Courtier , P., Andersson, E., Heckley, W., Pailleux, J., Vasiljevic, D., Hamrud, M., Hollingsworth, A., Rabier, F. and Fisher, M. 1998 . The ECMWF imple-mentation of three dimensional variational assimila-tion (3D-Var). Part I: Formulation . Q. J. Roy. Meteorol. Soc . 124 , 1783– 1808 .  

  8. Daley , R . 1985 . The analysis of synoptic scale divergence by a statistical interpolation procedure . Mon. Wea. Rev . 113 , 1066 – 1079 .  

  9. Daley , R . 1991 . Atmospheric data analysis . Cambridge University Press , Cambridge , UK , 460 pp .  

  10. Derber , J. and Bouttier , F . 1999 . A reformulation of the background error covariance in the ECMWF global data assimilation system . Tellus 51A , 195 – 221 .  

  11. Fisher , M. and Courtier , P . 1995 . Estimating the covari-ance matrix of analysis and forecast errors in variational data assimilation. ECMWF Res. Dep. Technical Memorandum, No. 220.  

  12. Gauthier , P. , Charette , C. , Fillion , L. , Koclas , P. and Laroche , S . 1999 . Implementation of a 3D variational data assimilation system at the Canadian Meteorolo-gical Centre. Part I: the global analysis . Atmosphere-Ocean . 37 , 103 – 156 .  

  13. Gilbert , J. C. and Lemaréchal , C . 1989 . Some numerical experiments with variable storage quasi-Newton algo-rithms . Math. Prog. B 25 , 407 – 435 .  

  14. Gustafsson , N . 1999 . The numerical scheme and lateral boundary conditions for the spectral HIRLAM and its adjoint. ECMWF Seminar Proceedings. Recent developments in numerical methods for atmospheric modelling. ECMWF, Reading, UK, 7-11 September 1998, pp. 335 - 363 .  

  15. Gustafsson , N. and Huang , X.-Y . 1996 . Sensitivity experi-ments with the spectral HIRLAM and its adjoint . Tellus 48A , 501 – 517 .  

  16. Gustafsson , N. , Lönnberg , P. and Pailleux , J . 1997 . Data assimilation for high resolution limited area models . J. Meteorol. Soc. Japan 75 , 367 – 382 .  

  17. Gustafsson , N. , Källén , E. and Thorsteinsson , S . 1998 . Sensitivity of forecast errors to initial and lateral boundary conditions . Tellus 50A , 167 – 185 .  

  18. Haugen , J.-E. and Machenhauer , B . 1993 . A spectral limited-area model formulation with time-dependent boundary conditions applied to the shallow-water equations . Mon. Wea. Rev . 121 , 2618 – 2630 .  

  19. Hollingsworth , A. and Lönnberg , P . 1986 . The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: the wind field . Tellus 38A , 111 – 136 .  

  20. Houtekamer , P. L. , Lefaivre , L. , Derome , J. , Ritchie , H. and Mitchell , H. L . 1996 . A system simulation approach to ensemble prediction . Mon. Wea. Rev . 124 , 1225 – 1242 .  

  21. Huang , X.-Y. , Gustafsson , N. and Källén , E . 1997 . Using an adjoint model to improve an optimum interpola-tion based data assimilation system . Tellus 49A , 161 – 176 .  

  22. Laroche , S. , Gauthier , P. , St-James , J. and Morneau J . 1999 . Implementation of a 3D variational data assim-ilation system at the Canadian Meteorological Centre, Part II: the regional analysis . Atmosphere-Ocean 37 , 281 – 307 .  

  23. Le Dimet , F. X. and Talagrand , O. 1986 . Variational algorithms for analysis and assimilation of meteorolo-gical observations. Theoretical aspects. Tellus 38A , 97 - 110 .  

  24. Lewis , J. M. and Derber , J. C . 1985 . The use of adjoint equations to solve a variational adjustment problem with advective constraints . Tellus 37A , 309 – 327 .  

  25. Lindskog , M. , Gustafsson , N. , Navascués , B. , Mogensen , K. S. , Huang , X.-Y. , Yang , X. , Andrx , U. , Berre , L. , Thorsteinsson , S. and Rantakokko , J . 2001 . Three-dimensional variational data assimilation for a limited area model. Part II: observation handling and assim-ilation experiments. Tellus 53A , this issue.  

  26. Lorene , A . 1981 . A global three-dimensional multivariate statistical interpolation scheme . Mon. Wea. Rev . 109 , 701 – 721 .  

  27. Lorenc , A . 1986 . Analysis methods for numerical weather prediction . Q. J. R. Meteor. Soc . 112 , 1177 – 1194 .  

  28. Lorenc , A . 1988 . Optimal nonlinear objective analysis . Q. J. Roy. Meteor. Soc . 114 , 205 – 240 .  

  29. Lorenc , A . 1997 . Development of an operational vari-ational assimilation scheme . J. Meteorol. Soc. Japan 75 , 339 – 346 .  

  30. Lorenc , A. C. , Ballard , S. P. , Bell , R. S. , Ingleby , N. B. , Andrews , P. L. F. , Barker , D. M. , Bray , JR. ., Clayton , A. M. , Dalby , T. , Li , D. , Payne , T. J. and Saunders , F. W. 2000 . The Met. Office Global 3-Dimensional Variational Data Assimilation Scheme . Q. J. Roy. Meteor. Soc. , 26 , 2991 – 3012 .  

  31. Machenhauer , B . 1977 . On the dynamics of gravity oscil-lations in a shallow water model, with application to normal mode initialization . Beitr. Phys. Atmos . 50 , 253 – 271 .  

  32. Parrish , D. F. and Derber , J. C . 1992 . The National Meteorological Centre’s spectral statistical interpola-tion analysis system . Mon. Wea. Rev . 120 , 1747 – 1763 .  

  33. Rabier , F. , McNally , A. , Andersson , E. , Courtier , P. , Undén , P. , Eyre , J. , Hollingsworth , A. and Bouttier , F . 1998a . The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part II: structure functions . Q. J. Roy. Meteorol. Soc . 124 , 1809 – 1830 .  

  34. Rabier , F. , Thépaut , J.-N. and Courtier , P . 1998b . Extended assimilation and forecast experiments with a four-dimensional variational assimilation system . Q. J. Roy. Meteorol. Soc . 124 , 1861 – 1888 .  

  35. Sadiki , W. , Fischer , C. and Geleyn , J.-F . 2000 . Mesoscale background error covariances: recent results obtained with the limited-area model ALADIN over Morocco . Mon. Wea. Rev . 128 , 3927 – 3935 .  

  36. Sasaki , Y . 1958 . An objective analysis based on the vari-ational method . J. Meteorol. Soc. Japan 36 , 77 – 88 .  

  37. Simmons , A. J. and Burridge , D. M . 1981 . An energy and angular momentum conserving vertical finite-difference scheme and hybrid vertical coordinates . Mon. Wea. Rev . 109 , 758 – 766 .  

  38. Thiébaux , H. J. , Mitchell , H. L. and Shantz , D. W . 1986 . Horizontal structure of hemispheric forecast error cor-relations for geopotential and temperature . Mon. Wea. Rev . 114 , 1048 – 1066 .  

  39. Zupanski , M . 1993 . Regional four-dimensional vari-ational data assimilation in a quasi-operational forecasting environment . Mon. Wea. Rev . 121 , 2396 – 2408 .  

comments powered by Disqus