A Minimal Baroclinic Model for the Statistical Properties of Low-Frequency Variability

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  • 1 IBM European Center for Scientific and Engineering Computing, 00147 Roma, Italy, CNR-FISBAT, Bologna,Italy, and Center for the Environment and Man, Hartford, CT, and Yale University, New Haven, CT 06511
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Abstract

A recent analysis of atmospheric observations has shown evidence of bimodality in the statistical distribution of wave amplitude in the ultralong (zonal wavenumber group 2–4), low frequency (period >5 days). Similar analysis of the zonal wind and its average shear shows no clear sign of bimodality. Both are characterized by a very variance (≅ 1 m s−1) and the associated kinetic energy fluctuations are not sufficient to account for the variations in wave amplitudes. Global energetic analysis confirms this finding. maintenance of the waves is dominated by baroclinic processes. On the other hand, from a theoretical point of view, barotropic models for wave generation and maintenance be brought into agreement with observed statistics by introducing nonlinear bending of the stationary resonant response to topographic modulation allowing different values of the equilibrium amplitude to correspond to the same value of the zonal flow. However, because of aforementioned energetic difficulties, in a barotropic model the closure equation (form-drag) for the zonal flow does not select states corresponding to values of the zonal wind within the observed statistics for any realistic value of the external parameters (dissipation and momentum forcing). In this paper we show how the inclusion wave field self interaction produces resonance bending in a minimal baroclinic model. The two resulting equilibrium stable states can be achieved within a realistic range of the zonal flow. Moreover, the equilibrium states are characterized by stability properties which, on a theoretical level, are much more satisfactory than in the linear resonance.

Abstract

A recent analysis of atmospheric observations has shown evidence of bimodality in the statistical distribution of wave amplitude in the ultralong (zonal wavenumber group 2–4), low frequency (period >5 days). Similar analysis of the zonal wind and its average shear shows no clear sign of bimodality. Both are characterized by a very variance (≅ 1 m s−1) and the associated kinetic energy fluctuations are not sufficient to account for the variations in wave amplitudes. Global energetic analysis confirms this finding. maintenance of the waves is dominated by baroclinic processes. On the other hand, from a theoretical point of view, barotropic models for wave generation and maintenance be brought into agreement with observed statistics by introducing nonlinear bending of the stationary resonant response to topographic modulation allowing different values of the equilibrium amplitude to correspond to the same value of the zonal flow. However, because of aforementioned energetic difficulties, in a barotropic model the closure equation (form-drag) for the zonal flow does not select states corresponding to values of the zonal wind within the observed statistics for any realistic value of the external parameters (dissipation and momentum forcing). In this paper we show how the inclusion wave field self interaction produces resonance bending in a minimal baroclinic model. The two resulting equilibrium stable states can be achieved within a realistic range of the zonal flow. Moreover, the equilibrium states are characterized by stability properties which, on a theoretical level, are much more satisfactory than in the linear resonance.

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