Abstract: In the upper troposphere and the lower stratosphere, the atmospheric kinetic energy spectrum shows a transition characteristic, from dependence at large-scale range to dependence at meso-scale range, which can be used as a basic law to assess the accuracy of numerical models. The rusults of GRAPES-GFS in May 2013 are analyzed in this paper. The accuracy of high-resolution GRAPES-GFS is estimated by computing the kinetic energy spectrum and its vertical distribution.The contributions of rotational and divergent components to the total kinetic energy spectrum are also analyzed. The results show that the slope of model kinetic energy spectrum transforms from large-scale range to meso-scale range, but the slopes both in these two ranges are steeper than that of the observation. During the large-scale range, the rotational component is primary in the total kinetic energy spectrum. But with the increasing of wavenumber (decreasing of wavelength), the divergent component becomes comparable even excesses the rotational component. By introducing the principle of conditional extreme value, a new approach is developed to calculate the location of the slope transform that is also called as changepoint. It is demonstrated that the accuracy of this new approach is comparative with that of the Levenberg-Marquardt approach, and the former approach does not need an initial value during the calculation. By using this new approach, the changepoint and the cross of rotational and divergent components are calculated. The results show that the vertical profile of the changepoint is consistent with that of the cross. In addition, the slopes of the divergent component are analyzed. In the meso-scale range, these slopes are very close to -5/3 at all the altitudes, which implies that the divergent component is dominant in the total kinetic energy during the meso-scale range, but the rotational component is dominant during the large-scale range. The difference of their slope results in the slope change of the kinetic energy spectrum. Furthermore, for the slope of the divergent component is close to -5/3 but the slope of the rotational component is steeper than -3, it is demonstrated that the divergent kinetic energy spectrum is more accurate than the rotational kinetic energy spectrum for the GRAPES-GFS model spectrum. In conclusion, GRAPES-GFS can show the slope transition between large-scale range and meso-scale range; compared with the rotational component, the divergent component error is smaller and the larger error in the rotational component may mainly results in the slope of the total kinetic energy spectrum of the model being steeper than the results of observation.