Baroclinic Stationary Waves in Aquaplanet Models

Giuseppe Zappa Science and Management of Climate Change Program, Ca’Foscari University, Venice, and Centro Euro-Mediterraneo per i Cambiamenti Climatici, Bologna, Italy

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Valerio Lucarini Department of Meteorology, and Department of Mathematics, University of Reading, Reading, United Kingdom

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Antonio Navarra Centro Euro-Mediterraneo per i Cambiamenti Climatici, and Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy

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Abstract

An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions.

Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating.

Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

Current affiliation: Department of Meteorology, University of Reading, Reading, United Kingdom.

Corresponding author address: Giuseppe Zappa, Department of Meteorology, University of Reading, RG6 6BB Reading, United Kingdom. E-mail: g.zappa@reading.ac.uk

Abstract

An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions.

Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating.

Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

Current affiliation: Department of Meteorology, University of Reading, Reading, United Kingdom.

Corresponding author address: Giuseppe Zappa, Department of Meteorology, University of Reading, RG6 6BB Reading, United Kingdom. E-mail: g.zappa@reading.ac.uk
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