### Abstract

The modus operandi of modern applied mathematics in developing very recent mathematical strategies for filtering turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines, exactly solvable nonlinear models with physical insight, and novel cheap algorithms with judicious model errors to filter turbulent signals with many degrees of freedom. A large number of new theoretical and computational phenomena such as "catastrophic filter divergence" in finite ensemble filters are reviewed here with the intention to introduce mathematicians, applied mathematicians, and scientists to this remarkable emerging scientific discipline with increasing practical importance.

Original language | English (US) |
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Pages (from-to) | 441-486 |

Number of pages | 46 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 27 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2010 |

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### Keywords

- Data assimilation
- Filtering turbulent systems
- Kalman filter
- Model error
- Stochastic parameter estimation

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems*,

*27*(2), 441-486. https://doi.org/10.3934/dcds.2010.27.441