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Commonly used methods fail to detect known phase speeds of simulated
signals of Sea Surface Height Anomalies

Abstract. This work examines the accuracy and validity of two variants of Radon transform and two variants of the Two-Dimensional Fast Fourier Transform (2D FFT) that have been previously used for estimating the propagation speed of Sea Surface Height Anomalies (SSHA) derived from satellite borne altimeters. The examination employs numerically simulated SSHA 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 ab-initio known, 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 even when its amplitude is 5 times larger than all other modes and that they successfully detect the phase speed of the dominant input mode only when its amplitude is 10 times (or more) larger than the other modes. This requirement is an unrealistic limitation on oceanic SSHA observations. 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 algorithms identify a dominant input mode decreases with the increase in the number of modes in the signal. Our findings cast a doubt on the reliability of phase speed estimates of SSHA observations and the reported “too fast” phase speed of baroclinic Rossby waves in the ocean.
