An accurate procedure for estimating the phase speed of ocean waves from observations by satellite borne altimeters

Observations of sea surface height (SSH) fields using satellite borne altimeters were conducted starting in the 1990s in various parts of the world ocean. Currently, a long period of 20 years of calibrated and accurate altimeter observations of Sea Surface Height Anomalies (SSHA) is publically available and ready to be examined for determining the rate of westward propagation of these anomalies, which are interpreted as a surface manifestation of linear Rossby waves that propagate westward in the ocean thermocline or as nonlinear eddies. The basis for estimating the speed of westward propagation of SSHA is time-longitude (Hovmöller) diagrams of the SSHA field at fixed latitude. In such a diagram the westward propagation is evident from a left-upward tilt of constant SSHA values (i.e. contours) and the angle between this tilt and the ordinate is directly proportional to the speed of westward propagation. In this work we use synthetically generated noisy data to examine the accuracy of three different methods that have been separately used in previous studies for estimating this slope (angle) of the time-longitude diagram: The first is the application of Radon transform, used in image processing for detecting structures on an image. The second method is the application of 2D Fast Fourier Transform that yields a frequency-wavenumber diagram of the amplitudes so the frequency and wavenumber where the maximum amplitude occurs determine the phase speed i.e. the slope. The third method constitutes an adaptation of Radon transform to a propagating wave in which structures of minimal variance in the image are identified. The three methods do not always yield the same phase speed value and our analysis of the synthetic data shows that an estimate of the phase speed at any given latitude should be considered valid only when at least two of the methods yield the same value. The relevance of the suggested procedure to observed signals is verified by applying it to observed SSHA signals in the ocean.