The Radon and Hilbert transforms and their applications to atmospheric waves

The Radon and Hilbert transform and their applications to convectively coupled waves (CCWs) are reviewed. The Hilbert Transform is used to compute the wave envelope, whereas the Radon transform is used to estimate the phase and group velocities of CCWs. Together, they provide an objective method to understand CCW propagation. Results reveal phase speeds and group velocities for fast waves (mixed Rossby-gravity, westward and eastward inertio-gravity, and Kelvin) that are consistent with previous studies and with Matsuno's equatorial wave dispersion curves. However, slowly-propagating tropical depression-like systems and equatorial Rossby waves exhibit wave envelopes that propagate faster than the individual wave crests, which is not predicted by dry shallow water theory.