## 4 Validation of the Optical Flow Estimates  
The detection of westward-propagating eddies and Rossby waves in satellite altimetry measurements has been based on the analysis of time-longitude or Hovmoller diagrams of SSH anomalies. A time-longitude diagram is a two-dimensional plot that represents a time series of zonal sections. Westward-propagating signals (waves) are clearly seen as tilted crests and troughs of SSH anomalies moving linearly from right to left across the diagram. The speed of these signals can be easily calculated from the slope of the diagonal alignments of crests and troughs. Displayed in Figure 7 are the time-longitude diagrams of SSH anomalies along the zonal sections of 10\({}^{\circ}\)W-10\({}^{\circ}\)E at several latitudes that we use to validate the results obtained with the OF method. The diagrams reveal the westward propagation at 15\({}^{\circ}\)S, 25\({}^{\circ}\)S, and 33\({}^{\circ}\)S, i.e., within the South Atlantic subtropical gyre, and the eastward propagation at 45\({}^{\circ}\)S, where the Sub-Antarctic Front of the ACC is located. We use the two-dimensional Radon transform (2D-RT; e.g., [48]) to objectively estimate the speed of propagating signals in the selected time-longitude plots (Figure 7). The 2D-RT has been widely used in satellite remote sensing for the global analysis of Rossby waves (e.g., [49; 50; 51; 52]). The method consists of projecting the Hovmoller diagram onto a line at a range of angles from 0 to 179\({}^{\circ}\) (the time axis is at 90\({}^{\circ}\)). When the line is perpendicular to the alignment of crests and troughs of the Rossby waves in the diagram, the projected SSH anomalies have the maximum variance (energy). The angle of the perpendicular to the line with the maximum variance yields the speed of propagation. The 2D-RT is best applied to the regions where the speed is reasonably constant within the selected subdomain. This is why the longitudinal extent of the subdomain used in this study was limited to 20\({}^{\circ}\). The zonal eddy propagation velocities between 10\({}^{\circ}\)W-10\({}^{\circ}\)E estimated with the 2D-RT are \(-\)5.3 km/day at 15\({}^{\circ}\)S, \(-\)3.6 km/day at 3.6\({}^{\circ}\)S, \(-\)2.8 km/day at 33\({}^{\circ}\)S, and 2.2 km/day at 45\({}^{\circ}\)S (positive eastward). Figure 7: Time–longitude (Hovmoller) diagrams of the high-pass filtered SSH for the zonal segments between 10\({}^{\circ}\)W–10\({}^{\circ}\)E at 15\({}^{\circ}\)S, 25\({}^{\circ}\)S, 33\({}^{\circ}\)S, and 45\({}^{\circ}\)S (the segments are shown by the white dashed lines in Figure 1). The color shading shows SSH anomalies in cm. The zonal eddy propagation velocities estimated using a Radon transform are shown on top of each panel. In addition, we estimate the eddy propagation velocities using the space-time-lagged cross-correlation analysis similar to [22; 23]. In essence, this method is based on computing correlations between the SSH anomalies at each grid point with the SSH anomalies at all the neighboring locations and at various time lags. At each time lag, the location of the maximum correlation is determined, and a velocity is estimated from the time lag and the distance of the location from the origin. An average velocity vector weighted by the correlation coefficients is ultimately computed from the estimates at various time lags. To focus on the mesoscale eddies, the time lags are limited to less than 100 days. The zonal and meridional dimensions of the box, within which the correlations are computed, are set to latitude-dependent correlation scales from [53], ranging from 100 km at 60\({}^{\circ}\)S to about 270 km at 10\({}^{\circ}\)S.  
Displayed in Figure 8 is a comparison of the eddy propagation velocities between 10\({}^{\circ}\)W-10\({}^{\circ}\)E estimated with the OF method (blue curve), the 2D-RT (red stars), and the space-time-lagged cross-correlation analysis (red curve).