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An ensemble framework for time delay synchronization

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Parlitz,  Ulrich
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Pinheiro, F. R., van Leeuwen, P. J., & Parlitz, U. (2018). An ensemble framework for time delay synchronization. Quarterly Journal of the Royal Meteorological Society, 144(711), 305-316. doi:10.1002/qj.3204.


Cite as: http://hdl.handle.net/21.11116/0000-0001-2698-9
Abstract
Synchronization based state estimation tries to synchronize a model with the true evolution of a system via the observations. In practice, an extra term is added to the model equations which hampers growth of instabilities transversal to the synchronization manifold. Therefore, there is a very close connection between synchronization and data assimilation. Recently, synchronization with time-delayed observations has been proposed, in which observations at future times are used to help synchronize a system that does not synchronize using only present observations, with remarkable successes. Unfortunately, these schemes are limited to small-dimensional problems. In this article, we lift that restriction by proposing an ensemble-based synchronization scheme. Tests were performed using the Lorenz'96 model for 20-, 100- and 1000-dimension systems. Results show global synchronization errors stabilizing at values of at least an order of magnitude lower than the observation errors, suggesting that the scheme is a promising tool to steer model states to the truth. While this framework is not a complete data assimilation method, we develop this methodology as a potential choice for a proposal density in a more comprehensive data assimilation method, like a fully nonlinear particle filter.