On the Dynamics of Planetary Flow Regimes. Part I: The Role of High-Frequency Transients

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  • 1 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom, and Space and Atmospheric Physics Group, Imperial College, London, United Kingdom
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Abstract

The role of high-frequency transients in the maintenance of planetary-scale flow regimes is investigated using a generalization of the neutral vector approach developed by Marshall and Molteni. Given a nonlinear dynamical model of the atmospheric motion, neutral vectors were defined as the axes with the smallest linear time derivative, computed by linearizing the equations of motion around the time-mean state of the system. If the nonlinear model possesses (at least) two steady states associated with nearly equally populated regimes, then the anomaly fields corresponding to the steady states strongly project onto the subspace spanned by the neutral vectors.

The study of the simple nonlinear models with multiple steady solutions suggests that the nonlinear self-interactions of the high-frequency transients within each regime can shift the phase-space position of the regime mean state (or centroid) from the position of the corresponding steady state. If the feedback of high-frequency transients onto the large scales could be parametrized as a linear function of the large-scale flow itself, then a “generalized” linear time-derivative operator (including the parametrization term) could be defined, and its neutral vectors would correspond more closely to quasi-stationary states associated with regime centroids. Although such a parametrization is difficult to formulate analytically, generalized neutral vectors can be defined through a statistical–dynamical method combines cluster analysis with a dynamical estimate of the linear balance between large-scale-flow tendencies and the “forcing” by high-frequency transients.

This methodology is applied to the analysis of flow regimes in an 80-winter integration of a three-level quasigeostrophic model. Using a hierarchical clustering algorithm, the author finds that those “fine scale” clusters associated with the leading generalized neutral vectors act as nuclei of aggregation in the formation of larger clusters, which define a coarser partition of phase space. For quasi-stationary states corresponding to generalized neutral vectors, the anomalous forcing by high-frequency transients primarily balances the dissipative tendencies in the lower troposphere and the advective tendencies in the upper troposphere. This type of dynamical balance is analogous to the one diagnosed for atmospheric blocking anomalies in previous observational and modeling studies.

Abstract

The role of high-frequency transients in the maintenance of planetary-scale flow regimes is investigated using a generalization of the neutral vector approach developed by Marshall and Molteni. Given a nonlinear dynamical model of the atmospheric motion, neutral vectors were defined as the axes with the smallest linear time derivative, computed by linearizing the equations of motion around the time-mean state of the system. If the nonlinear model possesses (at least) two steady states associated with nearly equally populated regimes, then the anomaly fields corresponding to the steady states strongly project onto the subspace spanned by the neutral vectors.

The study of the simple nonlinear models with multiple steady solutions suggests that the nonlinear self-interactions of the high-frequency transients within each regime can shift the phase-space position of the regime mean state (or centroid) from the position of the corresponding steady state. If the feedback of high-frequency transients onto the large scales could be parametrized as a linear function of the large-scale flow itself, then a “generalized” linear time-derivative operator (including the parametrization term) could be defined, and its neutral vectors would correspond more closely to quasi-stationary states associated with regime centroids. Although such a parametrization is difficult to formulate analytically, generalized neutral vectors can be defined through a statistical–dynamical method combines cluster analysis with a dynamical estimate of the linear balance between large-scale-flow tendencies and the “forcing” by high-frequency transients.

This methodology is applied to the analysis of flow regimes in an 80-winter integration of a three-level quasigeostrophic model. Using a hierarchical clustering algorithm, the author finds that those “fine scale” clusters associated with the leading generalized neutral vectors act as nuclei of aggregation in the formation of larger clusters, which define a coarser partition of phase space. For quasi-stationary states corresponding to generalized neutral vectors, the anomalous forcing by high-frequency transients primarily balances the dissipative tendencies in the lower troposphere and the advective tendencies in the upper troposphere. This type of dynamical balance is analogous to the one diagnosed for atmospheric blocking anomalies in previous observational and modeling studies.

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