Articles | Volume 23, issue 6
Research article
04 Nov 2016
Research article |  | 04 Nov 2016

A local particle filter for high-dimensional geophysical systems

Stephen G. Penny and Takemasa Miyoshi

Abstract. A local particle filter (LPF) is introduced that outperforms traditional ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in accuracy and computational cost. The standard sampling importance resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each grid point. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights to smooth the transition between neighboring points. Gaussian noise is applied with magnitude equal to the local analysis spread to prevent particle degeneracy while maintaining the estimate of the growing dynamical instabilities. The approach is validated against the local ensemble transform Kalman filter (LETKF) using the 40-variable Lorenz-96 (L96) model. The results show that (1) the accuracy of LPF surpasses LETKF as the forecast length increases (thus increasing the degree of nonlinearity), (2) the cost of LPF is significantly lower than LETKF as the ensemble size increases, and (3) LPF prevents filter divergence experienced by LETKF in cases with non-Gaussian observation error distributions.

Short summary
Particle filters in their basic form have been shown to be unusable for large geophysical systems because the number of required particles grows exponentially with the size of the system. We have applied the ideas of localized analyses at each model grid point and use ensemble weight smoothing to blend each local analysis with its neighbors. This new local particle filter (LPF) makes large geophysical applications tractable for particle filters and is competitive with a popular EnKF alternative.