Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators
In the context of filtering chaotic dynamical systems it is wellknown that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both theoretically and numerically, conditions on the observations of chaotic systems under which they can be accurately filtered. In particular, we highlight the advantage of adaptive observation operators over fixed ones. The Lorenz ’96 model is used to exemplify our findings. Here, we consider discretetime and continuoustime observations in our theoretical developments. We prove that, for fixed observation operator, the 3DVAR filter can recover the system state within a neighbourhood determined by the size of the observational noise. It is required that a sufficiently large proportion of the state vector is observed, and an explicit form for such sufficient fixed observation operator is given. Numerical experiments, where the data is incorporated by use of the 3DVAR and extended Kalman filters, suggest that less informative fixed operators than given by our theory can still lead to accurate signal reconstruction. Adaptive observation operators are then studied numerically; we show that, for carefully chosen adaptive observation operators, the proportion of the state vector that needs to bemore »
 Authors:

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 Univ. of Warwick, Coventry (United Kingdom)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Physica. D, Nonlinear Phenomena
 Additional Journal Information:
 Journal Volume: 325; Journal Issue: C; Journal ID: ISSN 01672789
 Publisher:
 Elsevier
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 3DVAR; Lorenz ’96; filter accuracy; adaptive observations; extended Kalman filter
 OSTI Identifier:
 1261535
Stuart, Andrew M., Shukla, Abhishek, SanzAlonso, Daniel, and Law, K. J. H.. Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators. United States: N. p.,
Web. doi:10.1016/j.physd.2015.12.008.
Stuart, Andrew M., Shukla, Abhishek, SanzAlonso, Daniel, & Law, K. J. H.. Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators. United States. doi:10.1016/j.physd.2015.12.008.
Stuart, Andrew M., Shukla, Abhishek, SanzAlonso, Daniel, and Law, K. J. H.. 2016.
"Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators". United States.
doi:10.1016/j.physd.2015.12.008. https://www.osti.gov/servlets/purl/1261535.
@article{osti_1261535,
title = {Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators},
author = {Stuart, Andrew M. and Shukla, Abhishek and SanzAlonso, Daniel and Law, K. J. H.},
abstractNote = {In the context of filtering chaotic dynamical systems it is wellknown that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both theoretically and numerically, conditions on the observations of chaotic systems under which they can be accurately filtered. In particular, we highlight the advantage of adaptive observation operators over fixed ones. The Lorenz ’96 model is used to exemplify our findings. Here, we consider discretetime and continuoustime observations in our theoretical developments. We prove that, for fixed observation operator, the 3DVAR filter can recover the system state within a neighbourhood determined by the size of the observational noise. It is required that a sufficiently large proportion of the state vector is observed, and an explicit form for such sufficient fixed observation operator is given. Numerical experiments, where the data is incorporated by use of the 3DVAR and extended Kalman filters, suggest that less informative fixed operators than given by our theory can still lead to accurate signal reconstruction. Adaptive observation operators are then studied numerically; we show that, for carefully chosen adaptive observation operators, the proportion of the state vector that needs to be observed is drastically smaller than with a fixed observation operator. Indeed, we show that the number of state coordinates that need to be observed may even be significantly smaller than the total number of positive Lyapunov exponents of the underlying system.},
doi = {10.1016/j.physd.2015.12.008},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 325,
place = {United States},
year = {2016},
month = {2}
}