Data assimilation: the Back and Forth Nudging (BFN) algorithm

This chapter summarizes the work presented in [16,21,17,20,19,29,22].

• Introduction
• ``Back and Forth Nudging'' (BFN) algorithm
  • Forward nudging
  • Backward nudging
  • BFN algorithm
  • Choice of the nudging matrices and interpretation
    • Variational interpretation of the nudging
    • Sequential interpretation
    • Pole assignment method and backward nudging matrix
  
  
• Numerical experiments
  • Numerical choice of the nudging matrices
  • Experimental approach
  • Physical models
    • Lorenz equations
    • 1-D viscous Burgers' equation
    • Shallow water model
    • Layered quasi-geostrophic ocean model
  • Conclusions emerging from the numerical experiments
  
  
• Theoretical convergence results
  • Linear case
  • Transport equations
    • Linear viscous transport
    • Viscous Burgers
    • Inviscid linear transport
    • Inviscid Burgers
      • Remark:
    • Remarks on the theoretical results
  
  
• Nudging and observers
  • Observers for a shallow water model
  • Invariant correction terms
  • Convergence study on a linearized simplified system
  • Numerical experiments
  
  
• Conclusion