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May  2010, 27(2): 441-486. doi: 10.3934/dcds.2010.27.441

Mathematical strategies for filtering turbulent dynamical systems

Andrew J. Majda 1, , John Harlim 2, and  Boris Gershgorin 1,

1. 

Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute for Mathematical Sciences, New York University, New York, NY 10012-1110, United States, United States
2. 

Depatment of Mathematics, North Carolina State University, Raleigh, NC 27695, United States

Received  October 2009 Revised  February 2010 Published  February 2010

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.
Keywords: stochastic parameter estimation, data assimilation, Kalman filter, filtering turbulent systems, model error..
Mathematics Subject Classification: Primary: 93E11, 62L12; Secondary: 65C2.
Citation: Andrew J. Majda, John Harlim, Boris Gershgorin. Mathematical strategies for filtering turbulent dynamical systems. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 441-486. doi: 10.3934/dcds.2010.27.441
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