Commonly used methods fail to detect known propagation speeds of simulated signals from time-longitude (Hovmöller) diagrams

This work examines the accuracy and validity of two variants of Radon transform and two variants of the two-dimensional fast Fourier transform (2-D FFT) that have been previously used for estimating the propagation speed of oceanic signals such as sea surface height anomalies (SSHAs) derived from satellite-borne altimeters based on time-longitude (Hovmöller) diagrams. The examination employs numerically simulated signals made up of 20 or 50 modes where one, randomly selected, mode has a larger amplitude than the uniform amplitude of the other modes. Since the dominant input mode is known ab initio, we can clearly define "success" in detecting its phase/propagation speed. We show that all previously employed variants fail to detect the phase speed of the dominant input mode when its amplitude is smaller than 5 times the amplitude of the other modes and that they successfully detect the phase speed of the dominant input mode only when its amplitude is at least 10 times the amplitude of the other modes. This requirement is an unrealistic limitation on oceanic observations such as SSHA. In addition, three of the variant methods detect a dominant mode even when all modes have the exact same amplitude. The accuracy with which the four methods identify a dominant input mode with the increase in the number of modes in the signal. Our findings are relevant to the reliability of phase speed estimates of SSHA observations and the reported "too fast" a phase speed of baroclinic Rossby waves in the ocean.