Latitudinal-Wavenumber Power Spectra of Stratospheric Temperature Fluctuations

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  • 1 Department of Physics, Iowa State University, Ames 50011
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Abstract

Daily global grids of satellite radiance data over a 24-month period (1973–74) are decomposed into spherical harmonic functions. It is shown that a certain function of the expansion coefficients can be interpreted as the latitudinal wavenumber (k) dependence for global stratospheric temperature variance spectra. Beyond a forcing region, the spectra can be fit to the form km, with m=−4.1±0.6 for the upper and lower stratosphere, respectively. To within the data scatter, no seasonal dependence is found for m. The onset of the inertial subrange occurs at lowers k for the upper stratosphere than for the lower stratosphere. From a theoretical standpoint it is shown that a sufficient condition for isotropy/homogeneity of the fluctuation spectrum for a two-dimensional scalar on the surface of a sphere is that the variance matrix elements be independent of zonal wavenumber. This leads to a prediction of m=−3.6 for the parameters appropriate to the present investigation. The detailed results suggest that the discrepancy between observation and theory is due in part to significant anisotropy effects on large-scale fluctuations. These results are thought to be the first measurements of latitudinal power spectra for large-scale atmospheric motions and, in addition, to represent the first spectral measurements of any kind for the inertial region of large-scale motions in the stratosphere.

Abstract

Daily global grids of satellite radiance data over a 24-month period (1973–74) are decomposed into spherical harmonic functions. It is shown that a certain function of the expansion coefficients can be interpreted as the latitudinal wavenumber (k) dependence for global stratospheric temperature variance spectra. Beyond a forcing region, the spectra can be fit to the form km, with m=−4.1±0.6 for the upper and lower stratosphere, respectively. To within the data scatter, no seasonal dependence is found for m. The onset of the inertial subrange occurs at lowers k for the upper stratosphere than for the lower stratosphere. From a theoretical standpoint it is shown that a sufficient condition for isotropy/homogeneity of the fluctuation spectrum for a two-dimensional scalar on the surface of a sphere is that the variance matrix elements be independent of zonal wavenumber. This leads to a prediction of m=−3.6 for the parameters appropriate to the present investigation. The detailed results suggest that the discrepancy between observation and theory is due in part to significant anisotropy effects on large-scale fluctuations. These results are thought to be the first measurements of latitudinal power spectra for large-scale atmospheric motions and, in addition, to represent the first spectral measurements of any kind for the inertial region of large-scale motions in the stratosphere.

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