Performance analysis of local ensemble Kalman filter

Abstract

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only information within a local radius. This paper rigorously analyzes the local EnKF (LEnKF) for linear systems, and shows that the filter error can be dominated by the ensemble covariance, as long as 1) the sample size exceeds the logarithmic of state dimension and a constant that depends only on the local radius; 2) the forecast covariance matrix admits a stable localized structure. In particular, this indicates that with small system and observation noises, the filter error will be accurate in long time even if the initialization is not. The analysis also reveals an intrinsic inconsistency caused by the localization technique, and a stable localized structure is necessary to control this inconsistency. While this structure is usually taken for granted for the operation of LEnKF, it can also be rigorously proved for linear systems with sparse local observations and weak local interactions. These theoretical results are also validated by numerical implementation of LEnKF on a simple stochastic turbulence in two dynamical regimes.

40 pages, 3 figures

References in corpus (5)

• Regularized estimation of large covariance matrices
• Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit
• Localizing the Ensemble Kalman Particle Filter
• Perturbations and projections of Kalman-Bucy semigroups
• A data-driven method for improving the correlation estimation in serial ensemble Kalman filters

Cited by in corpus (4)

• Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
• Analysis of a localised nonlinear Ensemble Kalman Bucy Filter with complete and accurate observations
• Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization
• Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models