We study in this paper a new data assimilation algorithm, called the back and forth nudging (BFN). This scheme has been very recently introduced for simplicity reasons, as it does not require any linearization, or adjoint equation, or minimization process in comparison with variational schemes, but nevertheless it provides a new estimation of the initial condition at each iteration. We study its convergence properties as well as efficiency on a 2D shallow water model. All along the numerical experiments, comparisons with the standard variational algorithm (called 4D-VAR) are performed. Finally, a hybrid method is introduced, by considering a few iterations of the BFN algorithm as a preprocessing tool for the 4D-VAR algorithm. We show that the BFN algorithm is extremely powerful in the very first iterations and also that the hybrid method can both improve notably the quality of th! e identified initial condition by the 4D-VAR scheme and reduce the number of iterations needed to achieve convergence.

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  1. Brivadis, Lucas; Andrieu, Vincent; Serres, Ulysse; Gauthier, Jean-Paul: Luenberger observers for infinite-dimensional systems, back and forth nudging, and application to a crystallization process (2021)
  2. Auroux, Didier: Data assimilation for geophysical fluids (2017)
  3. Auroux, Didier; Blum, Jacques; Ruggiero, Giovanni: Data assimilation for geophysical fluids: the diffusive back and forth nudging (2016)
  4. Béréziat, Dominique; Herlin, Isabelle: Solving ill-posed image processing problems using data assimilation (2011)
  5. Chen, X.; Navon, I. M.; Fang, F.: A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model (2011)
  6. Strunk, Achim; Elbern, Hendrik; Ebel, Adolf: Using satellite observations for air quality assessment with an inverse model system (2011) ioport
  7. Dimitriu, Gabriel; Apreutesei, Narcisa; Ştefănescu, Răzvan: Numerical simulations with data assimilation using an adaptive POD procedure (2010)
  8. Strunk, Achim; Ebel, Adolf; Elbern, Hendrik; Friese, Elmar; Goris, Nadine; Nieradzik, Lars Peter: Four-dimensional variational assimilation of atmospheric chemical data -- application to regional modelling of air quality (2010)
  9. Auroux, D.: The back and forth nudging algorithm applied to a shallow water model, comparison and hybridization with the 4D-VAR (2009)
  10. Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Farrell, P. E.; Allison, P. A.; Goddard, A. J. H.: A POD reduced-order 4D-Var adaptive mesh ocean modelling approach (2009)
  11. Jiang, L.; Douglas, C. C.: An analysis of 4D variational data assimilation and its application (2009)
  12. Jiang, Lijian; Douglas, Craig C.: Analysis of an operator splitting method in 4D-Var (2009)
  13. Korn, Peter: Data assimilation for the Navier-Stokes-(\alpha) equations (2009)