Conditioning of incremental variational data assimilation, with application to the Met Office system

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Haben, S. A. ; Lawless, A. S. ; Nichols, N. K. (2011)

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.
  • References (25)
    25 references, page 1 of 3

    Dando, M. L., Thorpe, A. J. and Eyre, J. R. 2007. The optimal density of atmospheric sounder observations in the Met Office NWP system. Q. J. R. Met. Soc. 133, 1933-1943.

    Fisher, M., Nocedal, J., Tre´molet, Y. and Wright, S. J. 2009. Data assimilation in weather forecasting: a case study in PDE-constrained optimization. Optim. Eng. 10, 409-426.

    Gauthier, P., Charette, C., Fillion, L., Koclas, P. and Laroche, S. 1999. Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part 1: the global analysis. Atmos.- Ocean 37, 103-156.

    Gauthier, P., Tanguay, M., Laroche, S., Pellerin, S. and Morneau, J. 2007. Extension of 3DVAR to 4DVAR: implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Rev. 135, 2339- 2354.

    Gauthier, P. and The´paut, J.-N. 2001. Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Me´te´o-France. Mon. Wea. Rev. 129, 2089-2102.

    Golub, G. H. and Van Loan, C. F. 1996. Matrix Computations, 3rd Edition, Johns Hopkins University Press, Baltimore, MD.

    Gratton, S., Lawless, A. S. and Nichols, N. K., Baltimore, MD 2007. Approximate Gauss-Newton methods for non-linear least-squares problems. SIAM J. Optim. 18, 106-132.

    Haben, S. A., Lawless, A. S. and Nichols, N. K. 2009. Conditioning of the 3DVAR data assimilation problem. Mathematics Report 3/2009, Department of Mathematics, University of Reading, U.K. Available from aspx

    Haben, S. A., Lawless, A. S. and Nichols, N. K. 2010. Conditioning and preconditioning of the variational data assimilation problem. Comput. Fluids 46, 252-256.

    Healy, S. B. and White, A. A. 2005. Use of discrete fourier transforms in the 1dvar retrieval problem. Q. J. R. Met. Soc. 131, 63-72.

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