A local particle filter for high-dimensional geophysical systems

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.