Two Comments on the Surface Quasigeostrophic Model for the Atmospheric Energy Spectrum

Abstract

The horizontal wavenumber spectra of wind and temperature in the upper troposphere and lower stratosphere display a narrow k?3 range at scales on the order of 1000 km and a broad k?5/3 range at mesoscales on the order of 1 to 500 km. Recently, Tulloch and Smith suggested that a surface quasigeostrophic (SQG) turbulence model can explain the observed spectra. Here, it is first argued that the mesoscale spectra are not likely to be explained by any quasigeostrophic model because the Rossby number corresponding to the mesoscale dynamics is on the order of unity or larger. Then it is argued that the SQG model in particular cannot explain the observations because its mesoscale spectrum displays a k?5/3 dependence only in a very thin layer just below the tropopause. The thickness of this layer can be estimated to be of the order of 10 m, whereas aircraft measurements are typically performed several hundred meters away from the tropopause.