Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 28, Issue 4, Pages 1397-1442Publisher
SPRINGER
DOI: 10.1007/s00332-018-9453-2
Keywords
Ensemble Kalman filter; Localization technique; High dimensional problem
Categories
Funding
- NUS Grant [R-146-000-226-133]
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available