We spectrally analyzed high-resolution balloon measurements of vertical profiles of temperature and horizontal wind in the troposphere and lower stratosphere over very flat terrain in Illinois. This paper is principally concerned with spectra in the power law range at vertical wavenumbers m≥10-3 cycle/m. The logarithmic spectral slopes and amplitudes are found to have only insignificant dependencies on meteorological parameters, including time of day, season, wind speed and direction, vertical shear, etc., except that between the troposphere and stratosphere the spectral amplitude scales as (N2)q with q~0.3, where N is the buoyancy frequency. The mean slopes are ≈-3 in the stratosphere and ≈-2.6 in the troposphere. On the average the individual spectra with larger amplitudes have less negative spectral slopes. The wide variation of spectral slopes (&sgr;≈0.5) and amplitudes and the weak dependence on N2 are quite inconsistent with the predictions of theories of saturated spectra. Further, the wind spectra in the troposphere and stratosphere are correlated, which suggests some unsaturated propagation between the regions. The ratio of kinetic to potential energy spectra is constant versus m, consistent with the linear gravity wave polarization relations. The magnitude of the model ratio can be brought into agreement with the observed ratio by assuming a model intrinsic frequency spectrum varying as ω-p with p~5/3 to 2 plus an enhancement of energy near the inertial frequency.¿ 1997 American Geophysical Union