Fig. 2

Implementation of the WT &LS method on synthetic data. a Temporal variations of three synthetic wave amplitudes in wind u. The frequency and zonal wavenubmers are [f, s] = [1cpd, 1], [1cpd, − 1] and [2cpd, and 2], respectively. b Superposition of the waves with a unit of Gaussian noise. c The zonal wavenumber s estimation results, using the data sampled along the dashed lines in b through the WT & LS method as summarized in “Wavelet transformation plus least-squares (WT & LS) approaches” section. d–f the wave amplitudes estimated according to the s estimation in c through the WT & LS method. In b, the dashed lines indicate three randomly selected longitudes. In c, s is estimated only when the signal is above the significance level \(\alpha\) = 0.05