## 5 Summary and Conclusions  
The pathways of mesoscale eddies are an important informative characteristic of ocean dynamics. The objective of this paper is to introduce an application of the optical flow (OF) technique to satellite altimetry data to estimate the direction and speed of transient eddy propagation in the South Atlantic Ocean. The South Atlantic Ocean and the adjacent segment of the Southern Ocean feature several regions with specific eddy variability, such as the Brazil-Malvinas Confluence, the Zapiola Anticyclone, the Agulhas Retrofllection, and the ACC and, therefore, represent an ideal polygon for testing the OF method. The method does not detect/track individual eddies or other SSH patterns. Instead, it provides a description of eddy motion in the Eulerian frame of reference, similar to the space-time-lagged correlation analysis of SSH fields implemented earlier in [22; 23]. The obtained time-mean pattern of eddy propagation velocities (Figure 3) is in an excellent agreement with the results of [22], obtained for the same region (see Figure 1 in [22]). This pattern illustrates the latitude-dependent westward propagation of Rossby waves, as well as the interaction of eddies with ocean currents and with the bottom topography. For example, the westward propagation of eddies is faster in the northern part of the subtropical gyre, where it is reinforced by the northwestward background flow, and it is much slower in the southern part of the gyre, where the mean flow opposes and, thus, slows down the westward propagation of eddies. The eddy propagation in the Argentine Basin, including the Zapiola Anticyclone, provides a great illustration of the steering effect of bottom topography on eddy motion. Another example of the eddy-mean flow interaction is the generally eastward propagation of eddies in the ACC, where the strong background flow reverses the intrinsic westward propagation and forces eddies to move in the direction of the current. The eddy propagation velocities estimated with the OF method are validated by the 2D-RT of time-longitude diagrams at several latitudes and by carrying out the space-time-lagged correlation analysis of SSH fields (similar to [22]). The obtained estimates agree with each other very well, providing strong evidence for the utility of the OF algorithm in oceanographic applications to study the motion of eddies and other sea-surface patterns. An advantage of the OF over the methods used in earlier studies, such as the Lagrangian tracking of eddies and the space-time-lagged correlation analysis, is that it allows the computation of the time-variable part of the eddy propagation velocity. While it has been reported that changes in the stratification probably have a negligible effect on the phase speed of westward propagating signals [47], the variability of strong currents, such as the ACC, does influence the eddy propagation velocity. Therefore, in the regions of strong background flow, the use of the OF to estimate the time-variable eddy motion might be particularly useful. Note that while changes in the surface geostrophic flow are effectively measured by satellite altimetry, changes in the eddy propagation velocity mainly reflect changes in the deep flow, which are not readily available from existing observations. We find that the \"instantaneous\" velocities calculated by the OF between two consecutive satellite images can be rather noisy, particularly in the regions of strong variability. Therefore, the removal of outliers and some low-pass spatial and temporal filtering of the resulting \((u,v)\) fields might be required. The validation of the time-variable part of the eddy propagation velocity is problematic because there are no relevant observations or estimates that can be used as the ground truth. In this work, to validate the result obtained with the OF, we use the meridional SSH gradient in the ACC region, which is proportional to the surface geostrophic flow.