The horizontal spectrum of kinetic energy in the upper troposphere in experiments conducted with the Atmospheric GCM for the Earth Simulator (AFES) global spectral general circulation model is examined. We find that the control version of AFES run at T639 spectral resolution can simulate a realistic kinetic energy spectrum with roughly -3 power-law dependence on horizontal wavenumber for wavelengths between about 5000 and 500 km, transitioning to a shallower mesoscale regime at smaller wavelengths. The results depend to a degree on the magnitude of the parameterized horizontal hyperdiffusion, but the existence of a distinct shallow mesoscale range in the simulations is independent of the hyperdiffusion employed. We present results from a number of AFES integrations with spectral truncations ranging from T39 to T639 and determine the appropriate scaling of the parametrized hyperdiffusion with model numerical resolution so that the kinetic energy spectrum in each case converges to realistic values. The experiment was also repeated in a dry version of the model. This version also simulated a shallow mesoscale range, supporting the view that the mesoscale regime in the atmosphere is energized, at least in part, by a predominantly downscale nonlinear spectral cascade.