Regularization and Iterative Resampling for the Local Particle Filter

Particle filters (PFs) are sequential Monte Carlo methods that can solve data assimilation problems characterized by non-Gaussian error distributions for prior variables or measurements. Recent efforts to apply PFs for high-dimensional geophysical models have resulted in localized PFs, which significantly reduce the number of particles required for applications of large spatial dimension. Localization, however, is often insufficient for preventing particle weight collapse for real geophysical problems, like numerical weather prediction. For example, it does not prevent the local collapse of weights when provided with a dense network of accurate, independent measurements or when model error is not well characterized. Both situations can lead to filter divergence even for univariate problems. This presentation introduces several approaches for maintaining filter stability under the above circumstances, which can be characterized broadly as “large sampling error” regimes. The first set of approaches adopts regularization in a manner similar to past particle filtering studies; i.e., by including an extra term in the weight calculations to place a lower-bound on effective ensemble size or maximum particle weights. The second set of strategies extend regularization to factor the posterior density, thus allowing for a sequence of iterative resampling steps – each step using a larger effective ensemble size than if a single resampling were performed. In addition to preventing filter divergence in large sampling error regimes, iterative resampling helps alleviate some of the assumptions used to derive the Poterjoy (2016), Poterjoy et al. (2019) local PF algorithms. In the absence of localization or other particle mixing parameters, the iterative resampling converges to the Bayesian solution as sample size increases, thus maintaining this property of the original local PF. Results will be presented for a set of low-dimensional applications, including one that mimics feature displacement errors in weather models.

References:

Poterjoy, J., 2016: A localized particle filter for high-dimensional nonlinear systems. Mon. Wea. Rev., 144, 59 – 76.

Poterjoy, J., L. J. Wicker, and M. Buehner, 2019: Progress in the development of a localized particle filter for data assimilation in high-dimensional geophysical systems., Mon. Wea. Rev. 147, 1107 – 1126.