Variance power spectra of wind and temperature fluctuations as functions of vertical wave number from several hundred balloon ascents over the very flat terrain of central Illinois are analyzed. Special attention is given to the effects of prewhitening the data prior to spectral analysis, and it is shown that prewhitening should be used when spectral slopes are more negative than about -3. The conclusions of a previous study that did not use prewhitening are reexamined using prewhitening with an expanded set of balloon ascents. The present results confirm the past conclusions that the vertical wave number spectra are inconsistent with the major predictions of saturated gravity wave models in several important respects. The expanded data set used here permits the study of changes from summer to winter, and it is shown that spectral slopes are steeper in winter than in summer and that both spectral slope and amplitude have the most significant correlation with parameters of the large-scale flow during winter. ¿ 2001 American Geophysical Union