A localized weighted ensemble adjustment Kalman filter for high-dimensional nonlinear data assimilation

Abstract

Particle filters provide a nonlinear Bayesian framework for data assimilation, but global weights often degenerate in high-dimensional geophysical systems. Ensemble Kalman filters are stable with practical ensemble sizes, yet their Gaussian and locally linear updates can be restrictive for nonlinear observations and non-Gaussian forecasts. We propose a localized weighted ensemble adjustment Kalman filter (LWEAKF) that uses a localized ensemble adjustment Kalman filter (EAKF) to generate observation-informed proposal centers and then applies a localized particle-weight correction. The method combines a regularized EAKF-centered proposal, effective-sample-size-controlled likelihood tempering, state-dependent vector weights, and local moment-preserving merging. Lorenz-96 experiments compare LWEAKF with EAKF, the local particle filter, and the localized adaptive particle filter. In the fully observed linear case, LWEAKF reduces the continuous ranked probability score (CRPS) by about 3% relative to EAKF when averaged over ensemble sizes. In sparse model-error experiments, the average reductions relative to EAKF are about 9% for linear observations and 11% for modulus observations. For a representative 80-member modulus case, the reductions relative to EAKF, LPF, and LAPF are approximately 15%, 36%, and 12%, respectively. Under the strongly nonlinear logarithmic operator, LWEAKF maintains average CRPS reductions of about 5%–6% relative to the baselines. Additional land–sea experiments, with one contiguous half of the domain unobserved, show the lowest full-domain CRPS for LWEAKF across all ensemble sizes and operators. RMSE-to-spread ratios remain close to unity, indicating calibrated posterior spread. LWEAKF therefore extends EAKF with localized importance weighting while retaining deterministic square-root robustness.