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Validation of Quasigeostrophic Zonal Mean Flow Responses to Torques

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  • 1 Meteorologisches Institut, Universität München, Munich, Germany
  • | 2 Institut für Physik der Atmosphäre, DLR, Oberpfaffenhofen, Germany
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Abstract

The angular momentum balance of quasigeostrophic flows is considered both for the standard and the deep formulation of quasigeostrophic theory (QT) in height coordinates, with main emphasis on the response to mountain torques. The related budget equations are derived. It is demonstrated that mountain torques affect only the wind term in the standard three-dimensional QT for β-plane flow while changes of the mass term are possible in deep QT as well. The situation is similar on the sphere where the standard QT restricts the response to the wind term. On the other hand, the mass term tends to be dominant for spherical barotropic flow with a free surface. Formulations of QT in pressure coordinates are discussed.

ECMWF reanalyses are used to see how torques affect the global angular momentum Mg specified by standard QT in height coordinates as compared to the axial angular momentum M of the atmosphere. If QT were satisfactory, the variations of Mg would be closely linked to those of M. Surprisingly, the wind term Mg of QT is not a good approximation to the observed wind term, which contains an important “turbulent” part. The variance of Mg captures only ∼25% of that of M. The cross-covariance function of Mg with the mountain torque To attains amplitudes that are about one-third of those of M and To. It is the same for the friction torque. On the other hand, the response of the mass term in spherical barotropic QT is too strong for standard choices of the Rossby radius.

Corresponding author address: J. Egger, Meteorologisches Institut, Universität München, Theresienstrasse 37, 80333 Munich, Germany. Email: jegger@lrz.uni-muenchen.de

Abstract

The angular momentum balance of quasigeostrophic flows is considered both for the standard and the deep formulation of quasigeostrophic theory (QT) in height coordinates, with main emphasis on the response to mountain torques. The related budget equations are derived. It is demonstrated that mountain torques affect only the wind term in the standard three-dimensional QT for β-plane flow while changes of the mass term are possible in deep QT as well. The situation is similar on the sphere where the standard QT restricts the response to the wind term. On the other hand, the mass term tends to be dominant for spherical barotropic flow with a free surface. Formulations of QT in pressure coordinates are discussed.

ECMWF reanalyses are used to see how torques affect the global angular momentum Mg specified by standard QT in height coordinates as compared to the axial angular momentum M of the atmosphere. If QT were satisfactory, the variations of Mg would be closely linked to those of M. Surprisingly, the wind term Mg of QT is not a good approximation to the observed wind term, which contains an important “turbulent” part. The variance of Mg captures only ∼25% of that of M. The cross-covariance function of Mg with the mountain torque To attains amplitudes that are about one-third of those of M and To. It is the same for the friction torque. On the other hand, the response of the mass term in spherical barotropic QT is too strong for standard choices of the Rossby radius.

Corresponding author address: J. Egger, Meteorologisches Institut, Universität München, Theresienstrasse 37, 80333 Munich, Germany. Email: jegger@lrz.uni-muenchen.de

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