Fig. 1

PDT implemented on synthetic data. a Temporal variations of two synthetic wave amplitudes in wind u. These waves are the diurnal and semidiurnal tides with frequency and zonal wavenumbers [f, s] = [1cpd, 1] and [2cpd, and 2], respectively. b Superposition of the waves with a unit of Gaussian noise. c The cross-wavelet spectrum of the time series was sampled along the two horizontal dashed lines, a and b in (b). Through the cross-wavelet spectrum, s can be identified through the PDT, as summarized in “The phase difference technique (PDT) for diagnosing zonal wavenumber” section