### Abstract

In this study, data from three atmospheric models are analyzed to investigate the existence of atmospheric flow regimes despite nearly Gaussian statistics of the planetary waves in these models. A hierarchy of models is used, which describes the atmospheric circulation with increasing complexity. To systematically identify atmospheric regimes, the presence of metastable states in the data is searched for by fitting so-called hidden Markov models (HMMs) to the time series. A hidden Markov model is designed to describe the situation in which part of the information of the system is unknown or hidden and another part is observed. Within the context of this study, some representative variable of planetary-scale flow (e.g., mean zonal flow or leading principal component) is known ("observed"), but its dynamics may depend crucially on the overall flow configuration, which is unknown. The behavior of this latter, "hidden" variable is described by a Markov chain. If the Markov chain possesses metastable (or quasi persistent) states, they are identified as regimes. In this perspective, regimes can be present even though the observed data have a nearly Gaussian probability distribution. The parameters of the HMMs are fit to the time series using a maximum-likelihood approach; well-established and robust numerical methods are available to do this. Possible metastability of the Markov chain is assessed by inspecting the eigenspectrum of the associated transition probability matrix. The HMM procedure is first applied to data from a simplified model of barotropic flow over topography with a large-scale mean flow. This model exhibits regime behavior of its large-scale mean flow for sufficiently high topography. In the case of high topography, the authors find three regimes, two of which correspond to zonal flow and the third to blocking. Next, a three-layer quasigeostrophic model is used as a prototype atmospheric general circulation model (GCM). Its first empirical orthogonal function (EOF) is similar to the Arctic Oscillation (AO) and exhibits metastability. For this model, two regime states are found: one corresponding to the positive phase of the AO with large amplitude and decreased variability of the streamfunction field, and another corresponding to the negative AO phase with small amplitude and increased variability. Finally, the authors investigate a comprehensive GCM. The leading four EOFs of this model show no signs of metastability. The results of the barotropic flow over topography and of the quasigeostrophic model suggest that the observed small skewness of planetary wave probability density functions (PDFs) is an imprint of blocked circulation states.

Original language | English (US) |
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Pages (from-to) | 1740-1757 |

Number of pages | 18 |

Journal | Journal of Climate |

Volume | 21 |

Issue number | 8 |

DOIs | |

State | Published - Apr 15 2008 |

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### ASJC Scopus subject areas

- Atmospheric Science

### Cite this

*Journal of Climate*,

*21*(8), 1740-1757. https://doi.org/10.1175/2007JCLI1751.1

**A hidden Markov model perspective on regimes and metastability in atmospheric flows.** / Franzke, Christian; Crommelin, Daan; Fischer, Alexander; Majda, Andrew J.

Research output: Contribution to journal › Article

*Journal of Climate*, vol. 21, no. 8, pp. 1740-1757. https://doi.org/10.1175/2007JCLI1751.1

}

TY - JOUR

T1 - A hidden Markov model perspective on regimes and metastability in atmospheric flows

AU - Franzke, Christian

AU - Crommelin, Daan

AU - Fischer, Alexander

AU - Majda, Andrew J.

PY - 2008/4/15

Y1 - 2008/4/15

N2 - In this study, data from three atmospheric models are analyzed to investigate the existence of atmospheric flow regimes despite nearly Gaussian statistics of the planetary waves in these models. A hierarchy of models is used, which describes the atmospheric circulation with increasing complexity. To systematically identify atmospheric regimes, the presence of metastable states in the data is searched for by fitting so-called hidden Markov models (HMMs) to the time series. A hidden Markov model is designed to describe the situation in which part of the information of the system is unknown or hidden and another part is observed. Within the context of this study, some representative variable of planetary-scale flow (e.g., mean zonal flow or leading principal component) is known ("observed"), but its dynamics may depend crucially on the overall flow configuration, which is unknown. The behavior of this latter, "hidden" variable is described by a Markov chain. If the Markov chain possesses metastable (or quasi persistent) states, they are identified as regimes. In this perspective, regimes can be present even though the observed data have a nearly Gaussian probability distribution. The parameters of the HMMs are fit to the time series using a maximum-likelihood approach; well-established and robust numerical methods are available to do this. Possible metastability of the Markov chain is assessed by inspecting the eigenspectrum of the associated transition probability matrix. The HMM procedure is first applied to data from a simplified model of barotropic flow over topography with a large-scale mean flow. This model exhibits regime behavior of its large-scale mean flow for sufficiently high topography. In the case of high topography, the authors find three regimes, two of which correspond to zonal flow and the third to blocking. Next, a three-layer quasigeostrophic model is used as a prototype atmospheric general circulation model (GCM). Its first empirical orthogonal function (EOF) is similar to the Arctic Oscillation (AO) and exhibits metastability. For this model, two regime states are found: one corresponding to the positive phase of the AO with large amplitude and decreased variability of the streamfunction field, and another corresponding to the negative AO phase with small amplitude and increased variability. Finally, the authors investigate a comprehensive GCM. The leading four EOFs of this model show no signs of metastability. The results of the barotropic flow over topography and of the quasigeostrophic model suggest that the observed small skewness of planetary wave probability density functions (PDFs) is an imprint of blocked circulation states.

AB - In this study, data from three atmospheric models are analyzed to investigate the existence of atmospheric flow regimes despite nearly Gaussian statistics of the planetary waves in these models. A hierarchy of models is used, which describes the atmospheric circulation with increasing complexity. To systematically identify atmospheric regimes, the presence of metastable states in the data is searched for by fitting so-called hidden Markov models (HMMs) to the time series. A hidden Markov model is designed to describe the situation in which part of the information of the system is unknown or hidden and another part is observed. Within the context of this study, some representative variable of planetary-scale flow (e.g., mean zonal flow or leading principal component) is known ("observed"), but its dynamics may depend crucially on the overall flow configuration, which is unknown. The behavior of this latter, "hidden" variable is described by a Markov chain. If the Markov chain possesses metastable (or quasi persistent) states, they are identified as regimes. In this perspective, regimes can be present even though the observed data have a nearly Gaussian probability distribution. The parameters of the HMMs are fit to the time series using a maximum-likelihood approach; well-established and robust numerical methods are available to do this. Possible metastability of the Markov chain is assessed by inspecting the eigenspectrum of the associated transition probability matrix. The HMM procedure is first applied to data from a simplified model of barotropic flow over topography with a large-scale mean flow. This model exhibits regime behavior of its large-scale mean flow for sufficiently high topography. In the case of high topography, the authors find three regimes, two of which correspond to zonal flow and the third to blocking. Next, a three-layer quasigeostrophic model is used as a prototype atmospheric general circulation model (GCM). Its first empirical orthogonal function (EOF) is similar to the Arctic Oscillation (AO) and exhibits metastability. For this model, two regime states are found: one corresponding to the positive phase of the AO with large amplitude and decreased variability of the streamfunction field, and another corresponding to the negative AO phase with small amplitude and increased variability. Finally, the authors investigate a comprehensive GCM. The leading four EOFs of this model show no signs of metastability. The results of the barotropic flow over topography and of the quasigeostrophic model suggest that the observed small skewness of planetary wave probability density functions (PDFs) is an imprint of blocked circulation states.

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U2 - 10.1175/2007JCLI1751.1

DO - 10.1175/2007JCLI1751.1

M3 - Article

VL - 21

SP - 1740

EP - 1757

JO - Journal of Climate

JF - Journal of Climate

SN - 0894-8755

IS - 8

ER -