Normal-Mode Global Rossby Waves: Theory and Observations

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  • 1 Center for Climatic Research, and Department of Meteorology, University of Wisconsin-Madison 53706
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Abstract

This study addresses first the question of what normal-mode global Rossby waves might exist in the Earth's atmosphere. Then it identifies fourteen of these theoretically predicted waves in the NMC global tropospheric analyses.

Normal modes of linearized global primitive shallow water equations were found given a basic state of latitudinally dependent steady zonal flow. The solutions are free Rossby and gravity waves. Many of the waves' north-south structures are similar to Hough functions, which are the solutions of the simpler problem of free waves in an atmosphere at rest.

By projecting 1200 consecutive days of twice-daily NMC global tropospheric analyses of velocity and geopotential onto idealized three-dimensional, normal-mode Rossby wave structures, time series of wave amplitudes and phases were formed. Spectral analyses of these time series for zonal wavenumbers 1–4 revealed statistically significant peaks at eight out of 25 theoretical Rossby wave frequencies. Six additional woes may exist, but their significance could not be statistically supported because their spectral peaks fell into the red noise portion of the spectra. Periods for the fourteen waves lie between ∼2 and ∼30 days. Excluding the two weakest waves, average amplitudes at the surface range from 0.3 to 2 mb.

Prior to this study, only two normal-mode Rossby waves had been identified with confidence in the troposphere, a zonal wavenumber-1, 5-day wave and a zonal wavenumber-1, 16-day way. This study has identified up to ten more modes which have comparable amplitudes.

Abstract

This study addresses first the question of what normal-mode global Rossby waves might exist in the Earth's atmosphere. Then it identifies fourteen of these theoretically predicted waves in the NMC global tropospheric analyses.

Normal modes of linearized global primitive shallow water equations were found given a basic state of latitudinally dependent steady zonal flow. The solutions are free Rossby and gravity waves. Many of the waves' north-south structures are similar to Hough functions, which are the solutions of the simpler problem of free waves in an atmosphere at rest.

By projecting 1200 consecutive days of twice-daily NMC global tropospheric analyses of velocity and geopotential onto idealized three-dimensional, normal-mode Rossby wave structures, time series of wave amplitudes and phases were formed. Spectral analyses of these time series for zonal wavenumbers 1–4 revealed statistically significant peaks at eight out of 25 theoretical Rossby wave frequencies. Six additional woes may exist, but their significance could not be statistically supported because their spectral peaks fell into the red noise portion of the spectra. Periods for the fourteen waves lie between ∼2 and ∼30 days. Excluding the two weakest waves, average amplitudes at the surface range from 0.3 to 2 mb.

Prior to this study, only two normal-mode Rossby waves had been identified with confidence in the troposphere, a zonal wavenumber-1, 5-day wave and a zonal wavenumber-1, 16-day way. This study has identified up to ten more modes which have comparable amplitudes.

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