Localization in the mapping particle filter

Abstract. Data assimilation involves sequential inference in geophysical systems with nonlinear dynamics and observational operators. Particle filters are a promising approach for data assimilation because they are able to represent non-Gaussian densities.

The mapping particle filter incorporates the Stein variational gradient descents to produce a particle flow that transforms state vectors from prior to posterior densities, aiming to minimize the Kullback-Leibler divergence. However, for applications in geophysical systems, challenges persist in high dimensions, where sample covariance underestimation leads to filter divergence. This work proposes two localization methods, one in which a local kernel function is defined and the particle flow is global. The second method, given a localization radius, physically partitions the state vector and performs local mappings at each grid point. Gaussian and Gaussian mixtures are evaluated as a prior density. The performance of the proposed Local Mapping Particle Filters (LMPFs) is assessed in synthetic experiments. Observations are produced with a two-scale Lorenz-96 system, while a single-scale Lorenz-96 is used as a surrogate model, introducing model error in the inference. The methods are evaluated with full and partial observations and with different linear and non-linear observational operators. The LMPFs with Gaussian mixtures perform similarly to Gaussian filters such as ETKF and LETKF in most cases, and in some scenarios, they provide competitive performance in terms of analysis accuracy.