Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model

Andrew J. Majda, Christian L. Franzke, Alexander Fischer, Daniel T. Crommelin

Research output: Contribution to journalArticlepeer-review


A controversial topic in the recent climate modeling literature is the fashion in which metastable low-frequency regimes in the atmosphere occur despite nearly Gaussian statistics for these planetary waves. Here a simple 57-mode paradigm model for such metastable atmospheric regime behavior is introduced and analyzed through hidden Markov model (HMM) analysis of the time series of suitable low-frequency planetary waves. The analysis of this paradigm model elucidates how statistically significant metastable regime transitions between blocked and zonal statistical states occur despite nearly Gaussian behavior in the associated probability distribution function and without a significant role for the low-order truncated nonlinear dynamics alone; turbulent backscatter onto the three-dimensional subspace of low-frequency modes is responsible for these effects. It also is demonstrated that suitable stochastic mode reduction strategies, which include both augmented cubic nonlinearity and multiplicative noise, are also capable of capturing the metastable low-frequency regime behavior through a single stochastic differential equation compared with the full turbulent chaotic 57-mode model. This feature is attractive for issues such as long-term weather predictability. Although there have been many applications of HMM in other sciences, this work presents a previously undescribed application of HMM analysis to atmospheric low-frequency variability and points the way for further applications including their use in extended range predictability.

Original languageEnglish (US)
Pages (from-to)8309-8314
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number22
StatePublished - May 30 2006


  • Atmospheric low-frequency variability
  • Hidden Markov models
  • Predictability
  • Stochastic modeling

ASJC Scopus subject areas

  • General


Dive into the research topics of 'Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model'. Together they form a unique fingerprint.

Cite this