Computation of the power spectra of mesoscale atmospheric motions from experimental data has become a way of addressing a number of important dynamical questions. These include whether gravity waves or quasi two-dimensional turbulence (also interpreted as vortical modes) are the more energetic mesoscale fluctuations, and whether the atmospheric gravity wave spectrum is convectively saturated. Yet the variance of these small-scale atmospheric motions varies appreciably in space and time, and so spectra computed from such nonstationary data will generally differ from the stationary shape. A model of the vertical wave number spectrum of horizontal velocity fluctuations produced by saturated gravity wave motions has been developed, and it predicts that the spectral form varies considerably with altitude. The effects on spectral computations of this inherent nonstationarity are examined in depth. It is found that this altitude nonstationarity gives rise to computed spectra of the form m-t, where t lies between the nominal unsaturated and saturated values of 0 and 3 respectively. Many spectral measurements which do not compare favorably with the original model spectrum have this shape, and on inspection appear likely to suffer appreciably from nonstationarity, while other measurements which better compare with the model spectrum appear to do so because the nonstationarity was minimized in these measurements.

Simulations involving observed examples of the temporal nonstationarity of time-fluctuating motions reveal that computed frequency spectra are not significantly altered in shape. However, gravity wave and vortical mode theories both provide models of the ground-based frequency spectrum, and both theories predict that these spectra are also nonstationary if the background wind speed varies with time, due to Doppler--shifting effects. Representative simulations of the problem reveal that limited distortions to the gravity wave spectrum arise, but that the vortical mode spectrum can be modified significantly; on occasions its shape is altered to one more like that of the gravity wave model spectra. This may be a candidate for explaining why a number of studies comparing measured frequency spectra with model predictions, in order to ascertain whether gravity waves or vortical modes (or both) produce this fluctuating variance, have produced conflicting conclusions. Because of this possibility, a more stationary measure, termed the ''polarization ratio'', is derived and presented as an additional independent means of evaluating whether gravity waves or vortical modes are responsible for the horizontal velocity fluctuations measured by ground-based sensors.