Conditions for successful data assimilation

Authors

  • Alexandre J. Chorin,

    1. Department of Mathematics, University of California, Berkeley, California, USA
    2. Lawrence Berkeley National Laboratory, Berkeley, California, USA
    Search for more papers by this author
  • Matthias Morzfeld

    Corresponding author
    1. Department of Mathematics, University of California, Berkeley, California, USA
    2. Lawrence Berkeley National Laboratory, Berkeley, California, USA
    • Corresponding author: M. Morzfeld, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720, USA. (mmo@math.lbl.gov)

    Search for more papers by this author

Abstract

[1] We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically reasonable problems, it can be moderate even when the number of variables is huge. We then analyze several data assimilation algorithms, including particle filters and variational methods. We show that well-designed particle filters can solve most of those data assimilation problems that can be solved in principle and compare the conditions under which variational methods can succeed to the conditions required of particle filters. We also discuss the limitations of our analysis.