Comparison between various methods for detecting phase speed of waves in the ocean using satellite borne altimeter

Observations of sea surface height (SSH) fields using satellite borne altimeters were conducted starting in the 1990s in various parts of the world ocean. Analyses of these observations showed a ubiquitous and pronounced westward migration of small amplitude (order of a few centimeters) SSH anomalies (SSHA). These observations were interpreted as a surface manifestation of Rossby waves that propagate westward in the ocean thermocline. The basis for estimating the speed of westward propagation of SSHA is time-longitude (Hovm�ller) 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., same value contours) and the angle between this tilt and the ordinate is directly proportional to the speed of westward propagation. We use three different methods for estimating this slope (angle). The first is the application of Radon transform to the time-longitude diagram, which is a common transform used in image processing for detecting structures on an image. The second method is the application of 2D Fast Fourier Transform to the time-longitude diagram to yield a frequency-wavenumber diagram and finding its maximum amplitude. The third method constitutes an adaptation of Radon transform in which structures of minimal variance in the image are identified. Since the three methods do not always yield the same phase speed value an estimate of the phase speed at a given latitude is considered valid only when at least two of the methods yield the same value.