Limits of the WTQ method for calculating momentum flux

The acceleration of the large scale circulation by gravity wave is commonly described via the vertical gradient of the vertical flux of horizontal pseudomomentum, or in short of the momentum flux. The momentum flux vector is given by

 (F_px,F_py) = (1-f²/ω²) ( <u'w'>,<v'w'>)

where < > describes the spatial or temporal mean of at least one wavelength or period of the gravity wave. If one is going actually to calculate momentum flux from an observation or high-resolution model, several difficulties arise. First, one has to know the intrinsic frequency ω of the wave, second one tacitly assumes that only a single wave is causing the wind perturbations u', v' and w', and third one needs to find an appropriate averaging interval. One possibility to solve this is to perform spectral analysis. An alternative was introduced by Geller et al. (2013) which, based on the polarization relations, infers ω directly from the perturbation wind temperature quadratics and is hence referred to as WTQ. In a brief study we will investigate the implication of the single wave assumption for the momentum flux calculated from data sets calculating multiple waves.