Use of the 3D radon transform to examine the properties of oceanic Rossby waves

One of the most successful applications of satellite-borne radar altimeter data over the oceans in recent years has been the extraction of information about long-wavelength baroclinic Rossby (or planetary) waves, which play a significant role in ocean circulation and climate dynamics. These waves cross ocean basins from east to west at speeds of few centimetres per second at mid-latitudes. The cross-basin propagation time may therefore be several months or even years and an accurate estimation of the speed of the waves is important. We review the methods for obtaining information on Rossby wave velocity from altimetry data, particularly the two-dimensional Radon transform. Unfortunately the use of longitude-time plots, although it allows the estimation of the zonal phase speeds, does not give any information on the speed vector when the propagation of the waves is not purely zonal (east-west). We show how the two-dimensional Radon Transform can be generalised to three dimensions, enabling not only the true propagation velocity component to be determined, but also the direction of the waves and thus any deviation from the pure-westward case. As examples of the application of this extended technique, we show maps of direction, speed and energy of Rossby waves in the North Atlantic Ocean