Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential
importance sampling, suited for nonlinear and non-Gaussian filtering
problems. Unless the number of ensemble members scales exponentially with the
problem size, particle filter (PF) algorithms experience weight degeneracy.
This phenomenon is a manifestation of the curse of dimensionality that
prevents the use of PF methods for high-dimensional data assimilation. The
use of local analyses to counteract the curse of dimensionality was suggested
early in the development of PF algorithms. However, implementing localisation
in the PF is a challenge, because there is no simple and yet consistent way
of gluing together locally updated particles across domains. In this article, we review the ideas related to localisation and the PF in
the geosciences. We introduce a generic and theoretical classification of
local particle filter (LPF) algorithms, with an emphasis on the advantages
and drawbacks of each category. Alongside the classification, we suggest
practical solutions to the difficulties of local particle filtering,
which lead to
new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz
40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using
the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms
yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms, even for a mildly nonlinear system.
A modified ensemble Kalman particle filter for non-Gaussian systems with nonlinear measurement functions
