Single analytical wave benchmark example for our wavelet analysis method. Left : Matsuno-Gill type analytical solution that corresponds to a Rossby wave characterized by n = 1; k = 1. Plotted are the zonal wind components overlaid on the shallow water height field. Right: scalogram of the zonal wave number against dimensionless time. Our method correctly identifies the input zonal wave number, k, and the temporal frequency, ω_R, consistent within the uncertainties, which is due to the Heisenberg-Gabor uncertainty principle.