Multi-wave analytical benchmark example for our wavelet analysis method. Left : Matsuno-Gill type analytical solution that corresponds to a combination of Rossby waves characterized by n = 1, 1; k = 1, 3. Plotted are the wind fields 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 numbers, k, and the temporal frequencies, ω_r, within the uncertainties, which is due to the Heisenberg-Gabor uncertainty principle.