On optimal solution error covariances in variational data assimilation problems

I.Y. Gejadze, F.X. Le Dimet, V. Shutyaev, Scottish Founding Council via GRPE (Funder)

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection-diffusion model.
LanguageEnglish
Pages2159-2178
Number of pages20
JournalJournal of Computational Physics
Volume229
Issue number6
DOIs
Publication statusPublished - 20 Mar 2010

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assimilation
newton
operators
preconditioning
optimal control
Covariance matrix
tangents
iteration
Mathematical operators
convection
Boundary conditions
boundary conditions
coefficients
approximation

Keywords

  • variational data assimilation
  • parameter estimation
  • optimal solution error covariances
  • hessian
  • preconditioning
  • mathematics

Cite this

Gejadze, I. Y., Le Dimet, F. X., Shutyaev, V., & (Funder), S. F. C. V. GRPE. (2010). On optimal solution error covariances in variational data assimilation problems. Journal of Computational Physics, 229(6), 2159-2178. https://doi.org/10.1016/j.jcp.2009.11.028
Gejadze, I.Y. ; Le Dimet, F.X. ; Shutyaev, V. ; (Funder), Scottish Founding Council via GRPE. / On optimal solution error covariances in variational data assimilation problems. In: Journal of Computational Physics. 2010 ; Vol. 229, No. 6. pp. 2159-2178.
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Gejadze, IY, Le Dimet, FX, Shutyaev, V & (Funder), SFCVGRPE 2010, 'On optimal solution error covariances in variational data assimilation problems' Journal of Computational Physics, vol. 229, no. 6, pp. 2159-2178. https://doi.org/10.1016/j.jcp.2009.11.028

On optimal solution error covariances in variational data assimilation problems. / Gejadze, I.Y.; Le Dimet, F.X.; Shutyaev, V.; (Funder), Scottish Founding Council via GRPE.

In: Journal of Computational Physics, Vol. 229, No. 6, 20.03.2010, p. 2159-2178.

Research output: Contribution to journalArticle

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