Determination of the Brunt-Vaisala frequency from vertical velocity spectra

Recent work on the spectra of vertical velocity oscillations due to gravity waves in the troposphere, stratosphere and the mesosphere has revealed a typical feature which we call the Brunt-Vaisala cutoff. Several observers noticed a spectral peak near the Brunt-Vaisala frequency. This peak often is characterized by a very steep slope at the high frequency part, but a fairly shallow slope towards lower frequencies. Some example spectra of stratosphere observations are given. This distinct spectral shape (most clear at the upper height 22.5 km) can be explained by the fact that the vertical velocity amplitudes of atmospheric gravity waves increase with frequency up to their natural cutoff at the Brunt-Vaisala frequency. The measurement of the frequency of the peak in a vertical velocity spectrum was found to yield most directly the Brunt-Vaisala-frequency profile. Knowing the Brunt-Vaisala frequency profile, one can deduce the potential temperature profile, if one has a calibration temperature at one height. However, even the uncalibrated profile will be quite useful, e.g., to determine fronts (defined by temperature inversions) and the tropopause height. This method fails for superadiabatic lapse rates when the Brunt-Viasala frequency is imaginary. The application of this method will also be difficult when the wind velocity is too high, causing the Doppler effect to smear out the total spectrum and blur the Brunt-Vaisala cutoff. A similar deficiency will also appear if the gravity-wave distribution has a maximum in wind direction.