Ensemble data assimilation for hyperbolic systems

Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2013) Ensemble data assimilation for hyperbolic systems. Physica D: Nonlinear Phenomena, 243 1: 128-142. doi:10.1016/j.physd.2012.10.005


Author Gonzalez-Tokman, Cecilia
Hunt, Brian R.
Title Ensemble data assimilation for hyperbolic systems
Journal name Physica D: Nonlinear Phenomena   Check publisher's open access policy
ISSN 0167-2789
1872-8022
Publication date 2013-01-15
Year available 2013
Sub-type Article (original research)
DOI 10.1016/j.physd.2012.10.005
Open Access Status
Volume 243
Issue 1
Start page 128
End page 142
Total pages 15
Place of publication Amsterdam, The Netherlands
Publisher Elsevier
Language eng
Abstract Ensemble based methods are now widely used in applications such as weather prediction, but there are few rigorous results regarding their application. The broad goal of this paper is to provide some theoretical evidence of their applicability in the computational study of dynamical systems in some idealized, yet interesting setting. The specific goal of this paper is to investigate a data assimilation procedure (DAP), an ensemble Kalman filter (EKF), in the context of hyperbolic systems. We show that with appropriate assumptions on observations, for every trajectory on an attractor, the predictions produced by the DAP remain close to the truth for all time provided the ensemble is properly initialized, making the DAP reliable. We deal with the case of a one-dimensional unstable direction first, and later extend to higher dimensional unstable spaces. A feature of this approach is that no model linearizations are involved, making it efficient and potentially of interest for applications in high dimensional systems. Lyapunov exponents are also investigated.
Keyword Data assimilation
Ensemble Kalman filtering
Hyperbolic dynamical systems
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 30 Apr 2015, 10:13:38 EST by Kay Mackie on behalf of Mathematics