A path integral method for data assimilation

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14 Scopus citations

Abstract

Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization. Speedup in the Monte Carlo sampling process is essential if the path integral method has any chance of being a viable estimator on moderately large problems. Here a variety of strategies are proposed and compared for their relative ability to improve the sampling efficiency of the resulting estimator. Provided as well are details useful for its implementation and testing. The method is applied to a problem in which standard methods are known to fail, an idealized flow/drifter problem, which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be a useful assimilation tool in oceanic studies.

Original languageEnglish
Pages (from-to)14-27
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Volume237
Issue number1
DOIs
StatePublished - Jan 1 2008
Externally publishedYes

Funding

The author is most thankful to F. Alexander: his comments and suggestions had a great deal of impact in the writing of this paper. The anonymous reviewers’ help was considerable in making the paper more friendly to the geophysics audience. I also gratefully acknowledges the helpful discussions on the topic of Lagrangian data assimilation with C.K.R.T. Jones and K. Ide. This work was performed while JMR was a visiting fellow at SAMSI; its staff’s kind hospitality is acknowledged. This work was funded by NSF DMS0327642 and ONR N00014-04-1-0215.

Keywords

  • Data assimilation
  • Hybrid Monte Carlo
  • Lagrangian data assimilation
  • Markov Chain Monte Carlo
  • Sampling

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