Search from over 60,000 research works

Advanced Search

Nonlinear error dynamics for cycled data assimilation methods

Full text not archived in this repository.
Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Moodey, A. J. F., Lawless, A. S. orcid id iconORCID: https://orcid.org/0000-0002-3016-6568, Potthast, R. W. E. orcid id iconORCID: https://orcid.org/0000-0001-6794-2500 and Van Leeuwen, P. J. (2013) Nonlinear error dynamics for cycled data assimilation methods. Inverse Problems, 29 (2). 025002. ISSN 0266-5611 doi: 10.1088/0266-5611/29/2/025002

Abstract/Summary

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Altmetric Badge

Item Type Article
URI https://reading-clone.eprints-hosting.org/id/eprint/30559
Item Type Article
Refereed Yes
Divisions Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher Institute of Physics
Download/View statistics View download statistics for this item

University Staff: Request a correction | Centaur Editors: Update this record

Search Google Scholar