Concrete ensemble Kalman filters with rigorous catastrophic filter divergence

David Kelly, Andrew J. Majda, Xin T. Tong

Research output: Contribution to journalArticlepeer-review

Abstract

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter.The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.

Original languageEnglish (US)
Pages (from-to)10589-10594
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume112
Issue number34
DOIs
StatePublished - Aug 25 2015

Keywords

  • Data assimilation
  • Ensemble kalman filter
  • Filter divergence

ASJC Scopus subject areas

  • General

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