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This content will become publicly available on February 23, 2017

Title: Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators

In the context of filtering chaotic dynamical systems it is well-known 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 discrete-time and continuous-time 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 » 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.« less
Authors:
 [1] ;  [1] ;  [1] ;  [2]
  1. Univ. of Warwick, Coventry (United Kingdom)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
OSTI Identifier:
1261535
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 325; Journal Issue: C; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Research Org:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
ORNL LDRD Director's R&D; USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING 3DVAR; Lorenz ’96; filter accuracy; adaptive observations; extended Kalman filter