A reduced adjoint approach to variational data assimilation

Muhammad Altaf, Mohamad El Gharamti, Arnold W. Heemink, Ibrahim Hoteit

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The adjoint method has been used very often for variational data assimilation. The computational cost to run the adjoint model often exceeds several original model runs and the method needs significant programming efforts to implement the adjoint model code. The work proposed here is variational data assimilation based on proper orthogonal decomposition (POD) which avoids the implementation of the adjoint of the tangent linear approximation of the original nonlinear model. An ensemble of the forward model simulations is used to determine the approximation of the covariance matrix and only the dominant eigenvectors of this matrix are used to define a model subspace. The adjoint of the tangent linear model is replaced by the reduced adjoint based on this reduced space. Thus the adjoint model is run in reduced space with negligible computational cost. Once the gradient is obtained in reduced space it is projected back in full space and the minimization process is carried in full space. In the paper the reduced adjoint approach to variational data assimilation is introduced. The characteristics and performance of the method are illustrated with a number of data assimilation experiments in a ground water subsurface contaminant model. © 2012 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Feb 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications


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