The impact of high vertical resolution in the Met Office Unified Model

Recent numerical model results suggest that the −5/3 energy spectrum on wavelengths less than about 500 km in the free atmosphere reflects motions where the rotational and divergent kinetic energies are comparable. This can be reproduced by models with sufficient horizontal resolution. This paper examines the sensitivity to vertical resolution. If the small-scale regime is dominated by stratified turbulence with a large Froude number, the appropriate vertical resolution is set by U/N, where U is a horizontal velocity scale and N the Brunt-Vaisala frequency, and thus only depends on the degree of stratification. This is estimated to imply a vertical gridlength of no more than a few hundred metres. In this paper, we use additional diagnostics of the vertical structure to show that the Froude number increases as the vertical resolution is increased. This is consistent with theories of stratified turbulence based on shear instability, while it is not consistent with the idea of layered two-dimensional turbulence. We also show that the treatment of gravity wave breaking is improved by the use of higher vertical resolution. However, the overall character of the model horizontal and vertical spectra does not change much when the vertical gridlength is reduced from 720 m to 180 m in the upper troposphere, with proportional reductions elsewhere. While the model simulates regions where a breakdown to turbulence would be expected, it does not have sufficient resolution to produce explicit turbulence and the horizontal resolution is not sufficient to show a −5/3 spectrum..