Efficient nonlinear data assimilation using synchronisation in a particle filter

Abstract

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 synchronisation theory, in which one tries to synchronise 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 that will control the growth of instabilities transversal to the synchronisation manifold. In this paper, an efficient ensemble-based synchronisation 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 1000-dimensional system show successful results, where particles efficiently follow the truth, both for observed and unobserved variables. These first test 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