### Abstract

Meridional dipoles of zonal wind and geopotential height are found extensively in empirical orthogonal function (EOF) analysis and single-point correlation maps of observations and models. Notable examples are the North Atlantic Oscillation and the so-called annular modes (or the Arctic Oscillation). Minimal stochastic models are developed to explain the origin of such structure. In particular, highly idealized, analytic, purely stochastic models of the barotropic, zonally averaged zonal wind and of the zonally averaged surface pressure are constructed, and it is found that the meridional dipole pattern is a natural consequence of the conservation of zonal momentum and mass by fluid motions. Extension of the one-dimensional zonal wind model to two-dimensional flow illustrates the manner in which a local meridional dipole structure may become zonally elongated in EOF analysis, producing a zonally uniform EOF even when the dynamics is not particularly zonally coherent on hemispheric length scales. The analytic system then provides a context for understanding the existence of zonally uniform patterns in models where there are no zonally coherent motions. It is also shown how zonally asymmetric dynamics can give rise to structures resembling the North Atlantic Oscillation. Both the one- and two-dimensional results are manifestations of the same principle: given a stochastic system with a simple red spectrum in which correlations between points in space (or time) decay as the separation between them increases, EOF analysis will typically produce the gravest mode allowed by the system's constraints. Thus, grave dipole patterns can be robustly expected to arise in the statistical analysis of a model or observations, regardless of the presence or otherwise of a dynamical mode.

Original language | English (US) |
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Pages (from-to) | 2102-2118 |

Number of pages | 17 |

Journal | Journal of Climate |

Volume | 18 |

Issue number | 12 |

DOIs | |

State | Published - Jun 15 2005 |

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### ASJC Scopus subject areas

- Atmospheric Science

### Cite this

*Journal of Climate*,

*18*(12), 2102-2118. https://doi.org/10.1175/JCLI3337.1

**A stochastic model for the spatial structure of annular patterns of variability and the North Atlantic Oscillation.** / Gerber, Edwin; Vallis, Geoffrey K.

Research output: Contribution to journal › Article

*Journal of Climate*, vol. 18, no. 12, pp. 2102-2118. https://doi.org/10.1175/JCLI3337.1

}

TY - JOUR

T1 - A stochastic model for the spatial structure of annular patterns of variability and the North Atlantic Oscillation

AU - Gerber, Edwin

AU - Vallis, Geoffrey K.

PY - 2005/6/15

Y1 - 2005/6/15

N2 - Meridional dipoles of zonal wind and geopotential height are found extensively in empirical orthogonal function (EOF) analysis and single-point correlation maps of observations and models. Notable examples are the North Atlantic Oscillation and the so-called annular modes (or the Arctic Oscillation). Minimal stochastic models are developed to explain the origin of such structure. In particular, highly idealized, analytic, purely stochastic models of the barotropic, zonally averaged zonal wind and of the zonally averaged surface pressure are constructed, and it is found that the meridional dipole pattern is a natural consequence of the conservation of zonal momentum and mass by fluid motions. Extension of the one-dimensional zonal wind model to two-dimensional flow illustrates the manner in which a local meridional dipole structure may become zonally elongated in EOF analysis, producing a zonally uniform EOF even when the dynamics is not particularly zonally coherent on hemispheric length scales. The analytic system then provides a context for understanding the existence of zonally uniform patterns in models where there are no zonally coherent motions. It is also shown how zonally asymmetric dynamics can give rise to structures resembling the North Atlantic Oscillation. Both the one- and two-dimensional results are manifestations of the same principle: given a stochastic system with a simple red spectrum in which correlations between points in space (or time) decay as the separation between them increases, EOF analysis will typically produce the gravest mode allowed by the system's constraints. Thus, grave dipole patterns can be robustly expected to arise in the statistical analysis of a model or observations, regardless of the presence or otherwise of a dynamical mode.

AB - Meridional dipoles of zonal wind and geopotential height are found extensively in empirical orthogonal function (EOF) analysis and single-point correlation maps of observations and models. Notable examples are the North Atlantic Oscillation and the so-called annular modes (or the Arctic Oscillation). Minimal stochastic models are developed to explain the origin of such structure. In particular, highly idealized, analytic, purely stochastic models of the barotropic, zonally averaged zonal wind and of the zonally averaged surface pressure are constructed, and it is found that the meridional dipole pattern is a natural consequence of the conservation of zonal momentum and mass by fluid motions. Extension of the one-dimensional zonal wind model to two-dimensional flow illustrates the manner in which a local meridional dipole structure may become zonally elongated in EOF analysis, producing a zonally uniform EOF even when the dynamics is not particularly zonally coherent on hemispheric length scales. The analytic system then provides a context for understanding the existence of zonally uniform patterns in models where there are no zonally coherent motions. It is also shown how zonally asymmetric dynamics can give rise to structures resembling the North Atlantic Oscillation. Both the one- and two-dimensional results are manifestations of the same principle: given a stochastic system with a simple red spectrum in which correlations between points in space (or time) decay as the separation between them increases, EOF analysis will typically produce the gravest mode allowed by the system's constraints. Thus, grave dipole patterns can be robustly expected to arise in the statistical analysis of a model or observations, regardless of the presence or otherwise of a dynamical mode.

UR - http://www.scopus.com/inward/record.url?scp=24644512747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24644512747&partnerID=8YFLogxK

U2 - 10.1175/JCLI3337.1

DO - 10.1175/JCLI3337.1

M3 - Article

VL - 18

SP - 2102

EP - 2118

JO - Journal of Climate

JF - Journal of Climate

SN - 0894-8755

IS - 12

ER -