Editorial Type:
Article
Article Type:
Research Article

Signatures of Nonlinear Dynamics in an Idealized Atmospheric Model

Dmitri Kondrashov Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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Sergey Kravtsov Department of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin—Milwaukee, Milwaukee, Wisconsin

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Michael Ghil Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California, and Geosciences Department and Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, Paris, France

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Print Publication:
01 Jan 2011
DOI:
https://doi.org/10.1175/2010JAS3524.1
Page(s):
3–12
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Abstract

Signatures of nonlinear dynamics are analyzed by studying the phase-space tendencies of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography. Nonlinear, stochastic, low-order prototypes of the full QG3 model are constructed in the phase space of this model’s empirical orthogonal functions using the empirical model reduction (EMR) approach. The phase-space tendencies of the EMR models closely match the full QG3 model’s tendencies. The component of these tendencies that is not linearly parameterizable is shown to be dominated by the interactions between “resolved” modes rather than by multiplicative “noise” associated with unresolved modes. The method of defining the leading resolved modes and the interactions between them plays a key role in understanding the nature of the QG3 model’s dynamics, whether linear or nonlinear, deterministic or stochastic.

Corresponding author address: Dmitri Kondrashov, Department of Atmospheric and Oceanic Sciences, 405 Hilgard Ave., Box 951565, 7127 Math Sciences Bldg., UCLA, Los Angeles, CA 90095–1565. Email: dkondras@atmos.ucla.edu

Abstract

Signatures of nonlinear dynamics are analyzed by studying the phase-space tendencies of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography. Nonlinear, stochastic, low-order prototypes of the full QG3 model are constructed in the phase space of this model’s empirical orthogonal functions using the empirical model reduction (EMR) approach. The phase-space tendencies of the EMR models closely match the full QG3 model’s tendencies. The component of these tendencies that is not linearly parameterizable is shown to be dominated by the interactions between “resolved” modes rather than by multiplicative “noise” associated with unresolved modes. The method of defining the leading resolved modes and the interactions between them plays a key role in understanding the nature of the QG3 model’s dynamics, whether linear or nonlinear, deterministic or stochastic.

Corresponding author address: Dmitri Kondrashov, Department of Atmospheric and Oceanic Sciences, 405 Hilgard Ave., Box 951565, 7127 Math Sciences Bldg., UCLA, Los Angeles, CA 90095–1565. Email: dkondras@atmos.ucla.edu

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