## 3 Results
### Time-Variable Eddy Propagation  
As noted earlier, the OF method estimates apparent motion between two consecutive images. By computing the OF between each pair of SSH maps (1075 pairs in total), we can investigate the temporal evolution of the eddy propagation velocity. Changes in the eddy propagation velocity can occur due to changes in the background flow and/or changes in the stratification. [PERSON] et al. [47] concluded that the effects of temporal variations of the stratification can be neglected for the purposes of estimating the phase speed of Rossby waves. They noted, however, that the lack of hydrographic time series at fixed locations make the quantitative estimates of the importance of temporal variability of the stratification difficult to obtain. In the following, we evaluate the temporal evolution of the eddy propagation velocity estimated with the OF method in the ACC region considered above (Figure 5). The region was selected because of the significant influence of the background flow that reverses the intrinsic westward eddy propagation. Therefore, by comparing the variability of the eddy propagation velocity with the variability of the SSH gradient or the geostrophic flow in the region, it is possible to analyze how robust the time-dependent part of the eddy propagation velocity is. It appears that \"instantaneous\" velocities are rather noisy and some spatial and temporal filtering is required. The noise can be due to the measurement and optimal interpolation errors of SSH maps, as well as due to the local violation of the brightness-constancy assumption in highly energetic regions. Displayed in Figure 6a is the time-latitude diagram of the zonal component of the eddy propagation velocity averaged between 10\({}^{\circ}\)W and 10\({}^{\circ}\)E and low-pass filtered with a Lowess filter with a cutoff period of 3 months. Overlaid are the contours of the largest meridional SSH gradients. In the zonal segment considered, both the eastward eddy propagation velocity and the SSH gradient exhibit two distinct bands between about 44-46\({}^{\circ}\)S and 48-50\({}^{\circ}\)S associated with the SAF and the PF, respectively. Here, the eastward eddy propagation velocities are 2-4 km/day  
Figure 5: The Southern Ocean segment of the study domain: (color shading) zonal (eastward) eddy propagation velocity (km/day) and the time–mean SSH (contours). The approximate locations of the SAF and the PF are shown by the red (-0.2 m) and blue (-0.6 m) contours, respectively. and the meridional SSH gradients often exceed 0.2 m per 100 km. Further downstream, these two fronts converge at 30-40\({}^{\circ}\)E (Figure 5). The meridional position of the two fronts has remained rather stationary during the period of observations, but both the SAF and the PF have intensified over the observational period, as suggested by the SSH gradients. What is interesting is that in some periods the intensity of the fronts is correlated with the eastward eddy propagation velocity. The time series of the eddy propagation velocity and the meridional SSH gradient averaged zonally between 10\({}^{\circ}\)W-10\({}^{\circ}\)E and meridionally between 44-46\({}^{\circ}\)S for the SAF and 48-50\({}^{\circ}\)S for the PF are shown in Figures 6b and 6c, respectively. The correlations between the eddy propagation velocity and the SSH gradient are 0.27 for the SAF and 0.46 for the PF, both significant at 95% confidence. Particularly good agreement between the eddy propagation velocity and the SAF intensity is observed in 2001-2009 and in 2015-2021 (Figure 6b). The agreement between the eddy propagation velocity and the PF intensity is more pronounced at interannual time scales, showing the general tendency for the intensification of both the SSH gradient and the eastward-propagation velocity (Figure 6c).