The Five-Day Wave on a Sphere with Realistic Zonal Winds

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  • 1 Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Coral Gables, Fla. 33124
  • | 2 National Center for Atmospheric Research, Boulder, Colo. 80303
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Abstract

A 5-day zonal wavenumber 1 oscillation has been well-documented from analysis of surface pressure data, and it has been suggested that it corresponds to the gravest symmetric low-frequency external normal mode of the atmosphere. Previous discussions of such global normal modes have assumed a basic state atmosphere at rest. In this investigation we solve linearized equations governing this mode in an atmosphere with a realistic distribution of zonal winds and including the surface temperature gradient in the lower boundary condition. Time-dependent solutions are obtained for zonal wavenumber 1 on a sphere using finite differences in the latitude-altitude plane. The frequency of symmetric forcing at the lower boundary is varied to find the resonant frequency of the gravest mode. In the presence of solstice zonal winds there is a large latitudinal asymmetry in the response in the upper stratosphere and in the mesosphere. An important feature of this asymmetry is relatively large amplitudes in the summer mesosphere. The amplitude of the temperature wave in the summer mesosphere is 10 K if the amplitude of the solution is scaled to give agreement with surface pressure observations and dissipation by Newtonian cooling is included in the calculation. The period of the mode is very little changed from its value for a basic state atmosphere at rest due to the fact that zonal winds and the temperature gradient at the lower boundary produce almost equal but opposite changes in period. Cancellation of the effects of zonal winds and lower boundary temperature gradient also appears to be responsible for the absence of a significant hemispheric asymmetry in mode structure in the troposphere and lower stratosphere. The time required for the mode to respond completely to lower boundary forcing is on the order of a month.

Abstract

A 5-day zonal wavenumber 1 oscillation has been well-documented from analysis of surface pressure data, and it has been suggested that it corresponds to the gravest symmetric low-frequency external normal mode of the atmosphere. Previous discussions of such global normal modes have assumed a basic state atmosphere at rest. In this investigation we solve linearized equations governing this mode in an atmosphere with a realistic distribution of zonal winds and including the surface temperature gradient in the lower boundary condition. Time-dependent solutions are obtained for zonal wavenumber 1 on a sphere using finite differences in the latitude-altitude plane. The frequency of symmetric forcing at the lower boundary is varied to find the resonant frequency of the gravest mode. In the presence of solstice zonal winds there is a large latitudinal asymmetry in the response in the upper stratosphere and in the mesosphere. An important feature of this asymmetry is relatively large amplitudes in the summer mesosphere. The amplitude of the temperature wave in the summer mesosphere is 10 K if the amplitude of the solution is scaled to give agreement with surface pressure observations and dissipation by Newtonian cooling is included in the calculation. The period of the mode is very little changed from its value for a basic state atmosphere at rest due to the fact that zonal winds and the temperature gradient at the lower boundary produce almost equal but opposite changes in period. Cancellation of the effects of zonal winds and lower boundary temperature gradient also appears to be responsible for the absence of a significant hemispheric asymmetry in mode structure in the troposphere and lower stratosphere. The time required for the mode to respond completely to lower boundary forcing is on the order of a month.

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