Adjoint to the Hessian derivative and error covariances in variational data assimilation

V. P. Shutyaev, I. Y. Gejadze

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4 Citations (Scopus)


The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The optimal solution error is considered through the errors of input data (background and observation errors). The optimal solution error covariance operator is approximated by the inverse Hessian of the auxiliary (linearized) data assimilation problem, which involves the tangent linear model constraints. We show that the derivative of the inverse Hessian with respect to the exact solution may be treated as the measure of nonlinearity for analysis error covariances in variational data assimilation problems.
Original languageEnglish
Pages (from-to)179-188
Number of pages10
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Issue number2
Publication statusPublished - Apr 2011



  • theoretical aspects
  • adjoint
  • hessian derivative
  • error covariances
  • variational data
  • assimilation

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