Concrete ensemble Kalman filters with rigorous catastrophic filter divergence
Abstract
Understanding ensemble-based data assimilation methods, including their performance when applied to high-dimensional nonlinear models with low ensemble size, is a crucial problem in science and engineering. Catastrophic filter divergence is a well-documented but mechanistically mysterious phenomenon whereby ensemble-state estimates explode to machine infinity despite the true state remaining in a bounded region. We provide breakthrough insight into the phenomenon by proposing a simple forecast model that experiences catastrophic filter divergence under all ensemble-based methods. This is the first instance to our knowledge of a forecast model that plainly and rigorously illustrates that simple mechanisms can lead to such a drastic filter malfunction and thereby sheds light on when catastrophic filter divergence should be expected and how it can be avoided.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 10, 2015
- Source ID
- 10.1073/pnas.1511063112
Entities
People
- Andrew J. Majda
- David Kelly
- Xin T. Tong
Organizations
- New York University
- Office of Naval Research