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.

Current data assimilation methods still face problems in strongly nonlinear cases. A promising solution is a particle filter, which provides a representation of the state probability density function (pdf) by a discrete set of particles. To allow a particle filter to work in high-dimensional systems, the proposal density freedom is explored.We used a proposal density from synchronization theory, in which one tries to synchronize the model with the true evolution of a system using one-way coupling, via the observations. This is done by adding an extra term to the model equations which will control the growth of instabilities transversal to the synchronization manifold. In this paper, an efficient ensemble-based synchronization scheme is used as a proposal density in the implicit equal-weights particle filter, a particle filter that avoids filter degeneracy by construction. Tests using the Lorenz96 model for a 1,000-dimensional system show successful results, where particles efficiently follow the truth, both for observed and unobserved variables. These first tests show that the new method is comparable to, and slightly outperforms, a well-tuned Local Ensemble Transform Kalman Filter. This methodology is a promising solution for high-dimensional nonlinear problems in the geosciences, such as numerical weather prediction. K E Y W O R D Sdata assimilation, ensemble, synchronization, nonlinear, particle filter 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. APPENDIXThis appendix contains the pseudocode algorithms to run the IEWPF using the ensemble-based synchronization as a proposal, as described in Section 2.3.