Abstract/Summary

Synchronisation theory is based on a method that tries to synchronise a model with the true evolution of a system via the observations. In practice, an extra term is added to the model equations that hampers growth of instabilities transversal to the synchronisation manifold. Therefore, there is a very close connection between synchronisation and data assimilation. Recently, synchronisation with time delayed observations has been proposed, in which observations at future times are used to help synchronise a system that does not synchronise using only present observations, with remarkable successes. Unfortunately, these schemes are limited to small-dimensional problems. In this paper, we lift that restriction by proposing ensemble-based synchronisation scheme. Tests were performed using Lorenz96 model for 20, 100 and 1000-dimension systems. Results show global synchronisation errors stabilising 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.