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.
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