Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Laroche, Stéphane; Gauthier, Pierre (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
In order to meet current operational limitations, the incremental approach is being used toreduce the computational cost of 4D variational data assimilation (4D-Var). In the incremental4D-Var, the tangent linear (TLM) and adjoint of a simplified lower-resolution model are usedto describe the time evolution of increments around a trajectory defined by a complete fullresolutionmodel. For nonlinear problems, the trajectory needs to be updated regularly byintegrating the full-resolution model during the minimization. These are referred to as outeriterations (or updates) by opposition to inner iterations done with the simpler TLM and adjointmodels to minimize a local quadratic approximation to the actual cost function. In this study,the role of the inner and outer iterations is investigated in relation to the convergence propertiesas well as to the interactions between the large (resolved by both models) and small scalecomponents of the flow. A 2D barotropic non-divergent model on a b-plane is used at twodifferent resolutions to define the complete and simpler models. Our results show that it isnecessary to have a minimal number of updates of the trajectory for the incremental 4D-Varto converge reasonably well. To assess the impact of restricting the gradient to its large scalecomponents, experiments are carried out with a so-called truncated 4D-Var in which the completemodel is used to compute the gradient which is truncated afterwards to retain only thosecomponents used in the incremental 4D-Var. A comparison between the truncated and incremental4D-Var shows that the large-scale components of the gradient are well approximatedby the lower resolution model. With frequent updates to the trajectory, the incremental 4D-Varconverges to an analysis which is close to that obtained with the truncated 4D-Var. Thisconclusion is verified when perfect observations with a complete spatial and temporal coverageare used or when they are restricted to be available at a coarser resolution (in space and time)than that of the model. Finally, unbiased observational error was introduced and the resultsshowed that at some point, the minimization is overfitting the observations and degrades theanalysis. In this context, a criterion related to the level of observational noise is found todetermine when to stop the minimization when the complete 4D-Var is used. This criteriondoes not hold however for the incremental and truncated 4D-Var, thereby indicating that itmay be very difficult to establish in a more realistic context when the error is biased and themodel itself is introducing a biased error. The analysis and forecasts from the incremental4D-Var compare well to those from a full-resolution 4D-Var and are more accurate than thoseobtained from a low-resolution 4D-Var that uses only the simplified model.DOI: 10.1034/j.1600-0870.1998.t01-3-00001.x
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Andersson, E., Pailleux, J., The´paut, J. R. Eyre, A. P. McNally, G. A. Kelly and P. Courtier, 1994. Use of cloud-cleared radiances in 3D and 4D variational data assimilation. Q. J. R. Meteorol. Soc. 120, 627-653.
    • Courtier, P. and O. Talagrand, 1987. Variational assimilation of meteorological observations with the adjoint vorticity equations. Part II: Numerical results. Q. J. R. Meteorol. Soc. 113, 1329-1347.
    • Courtier, P., J.-N. The´paut and A. Hollingsworth, 1994. A strategy for operational implementation of 4D-Var using an incremental approach. Q. J. R. Meteorol. Soc. 120, 1367-1387.
    • Courtier, P., E. Andersson, W. Heckley, J. Pailleux, D. Vasiljevic´, M. Hamrud, A. Hollingsworth, F. Rabier and M. Fisher, 1998. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part I: Formulation. Q. J. R. Meteorol. Soc., in press.
    • Cressman, G. P., 1959. An operative objective analysis scheme. Mon. Wea. Rev. 88, 367-374.
    • Daley, R., 1991. Atmospheric Data Analysis. Cambridge University Press, Cambridge, 457 pages.
    • Eyre, J. R., G. A. Kelly, A. P. McNally, E. Andersson and A. Persson, 1993. Assimilation of TOVS radiances information through one-dimensional variational analysis. Q. J. R. Meteorol. Soc. 119, 1427-1463.
    • Eyre, J. R., 1994. Assimilation of radio occultation measurements into a numerical weather prediction system. ECMW F T echnical Memorandum 199, Reading, U.K, 34 pages.
    • Fisher, M. and P. Courtier, 1995. Estimating the covariance matrices of analysis and forecast error in variational data assimilation. ECMW F T echnical Memorandum 220, Reading, U.K, 26 pages.
    • Gauthier, P. 1992. Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model. T ellus 44A, 2-17.
    • Gauthier, P., L. Fillion, P. Koclas and C. Charette, 1996. Implementation of a 3D variational analysis at the Canadian Meteorological Centre. Proceedings of the 11th AMS Conference on Numerical weather prediction. Norfolk, Virginia, 19-23 August 1996.
    • Gilbert, J. C. and C. Lemare´chal, 1989. Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming 45, 407-435.
    • Mahfouf, J.-F., R. Buizza and R. M. Errico, 1996. Strategy for including physical processes in the ECMWF variational data assimilation system. In: Proceedings of the ECMW F Workshop on Nonlinear aspects of data assimilation. Shinfield Park, Reading, U.K. RG2 9AX, 9-11 September 1996.
    • Orszag, S. A., 1971. Numerical simulation of incompressible flows within simple boundaries (I). Galerkin (spectral ) representations. Stud. in Appl. Math. 50, 293-327.
    • Parrish, D. F. and J. C. Derber, 1992. The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev. 120, 1747-1763.
    • Pires, C., R. Vautard and O. Talagrand, 1996. On extending the limits of variational assimilation in nonlinear chaotic systems. T ellus 48A, 96-121.
    • Rabier, F. and P. Courtier, 1992. Four-dimensional assimilation in the presence of baroclinic instability. Q. J. R. Meteorol. Soc. 118, 649-672.
    • Rabier, F., J. F. Mahfouf, M. Fisher, H. Ja¨rvinen, A. Simmons, E. Andersson, F. Bouttier, P. Courtier, M. Hamrud, J. Haseler, A. Hollingsworth, L. Isaksen, E. Klinker, S. Saarinen, C. Temperton, J. N. The´paut, P. Unde´n and D. Vasiljevic´, 1997. Recent experimentation on 4D-Var and first results from a simplified Kalman filter. ECMW F T echnical Memorandum 240. Reading, U.K, 42 pages.
    • Sun, J., D. W. Flicker and D. K. Lilly, 1991. Recovery of three-dimensional wind and temperature fields from single-Doppler radar data. J. Atmos. Sci. 48, 876-890.
    • Tanguay, M., P. Bartello and P. Gauthier, 1995. Fourdimensional data assimilation with a wide range of scales. T ellus 47A, 974-997.
    • The´paut, J.-N., D. Vasiljevic´, P. Courtier and J. Pailleux, 1993. Variational assimilation of conventional meteorological observations with a multilevel primitiveequation model. Q. J. R. Meteorol. Soc. 119, 153-186.
    • The´paut, J.-N. and P. Courtier, 1991. Four-dimensional data assimilation using the adjoint of a multilevel primitive equation model. Q. J. R. Meteorol. Soc. 117, 1225-1254.
    • Yang, W., M. Navon and P. Courtier, 1996. A new Hessian preconditioning method applied to variational data assimilation experiments using NASA general circulation models. Mon. Wea. Rev. 124, 1000-1017.
    • Zou, X., Y.-H. Kuo and Y.-R. Guo, 1995. Assimilation of atmospheric radio refractivity using a nonhydrostatic adjoint model. Mon. Wea. Rev. 123, 2229-2249.
    • Zupanski, M. 1993. A preconditioning algorithm for large-scale minimization problems. T ellus 45A, 478-492.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article

Collected from