Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 27, Issue 2, Pages 441-486Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2010.27.441
Keywords
stochastic parameter estimation; Kalman filter; filtering turbulent systems; data assimilation; model error
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Funding
- National Science Foundation [DMS-0456713]
- Office of Naval Research [N00014-05-1-0164]
- Defense Advanced Research Projects Agency [N00014-07-1-0750, N00014-08-1-1080]
- Department of Mathematics, North Carolina State University
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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.
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