## 2 Materials and Methods  
### Satellite Altimetry Data  
Satellite altimetry has provided accurate, nearly global, sustained observations of SSH since the launch of the TOPEX/Poseidon mission in August 1992. Here, we use the daily SSH maps above the geoid (absolute dynamic topography) from January 1993 to June 2022 processed and distributed by the Copernicus Marine and Environment Monitoring Service (CMES; [[http://marine.copernicus.eu](http://marine.copernicus.eu)]([http://marine.copernicus.eu](http://marine.copernicus.eu)), accessed on 2 May 2023). The SSH above the geoid is the sum of the MDT-CNES-CLS22 mean dynamic topography [40] over the 1993-2012 period and the sea-level anomaly with respect to the mean sea surface. Prior to mapping, the along-track altimetry records are routinely corrected for instrumental noise, orbit determination error, atmospheric refraction, sea state bias, tides, as well as static and dynamic atmospheric-pressure effects [41].  
The SSH maps are then produced on a global \(1/4^{\circ}\times 1/4^{\circ}\) (longitude \(\times\) latitude) grid by the optimal interpolation of measurements from all the altimeter missions available at a given time. Due to the filtering properties of the optimal interpolation, the SSH maps have an effective spatial resolution ranging from about 400 km at \(10^{\circ}\)S to 100 km at \(60^{\circ}\)S and an effective temporal resolution varying between 14-45 days [42]. Although the number of simultaneously flying altimeter satellites has varied with time, it has been reported that the impact of satellite constellation on the effective spatial resolution is modest, with a globally averaged gain of resolution of \(\sim\)5% in maps constructed with three altimeters compared with two altimeters [42].  
Because the smallest repeat period of altimeter satellites (excluding crossover points) is about 10 days and the effective temporal resolution of SSH maps is even longer, using every single daily SSH map for the OF computation is redundant. Therefore, to reduce the computational cost, we use every 10 th SSH map (1076 maps in total). The SSH anomalies are computed with respect to the record-long mean SSH above the geoid (absolute dynamic  
Figure 1: The map of the study region with the color shading showing the standard deviation of the mesoscale sea surface height variability (in meters) and the contours representing the mean dynamic topography every 0.1 m. The general upper—ocean circulation is sketched by arrows. The Agulhas eddies are schematized by red circles. The white dashed lines show segments along which the time–longitude diagrams are analyzed in Section 4. The blank areas are places with data gaps due to seasonal sea-ice cover. Abbreviations: ACC—the Antarctic Circumpolar Current, BMC—Brazil–Malvinas Confluence, ZR—Zapiola Rise, ZA—Zapiola Anticyclone, AR—Agulhas Retroflection, ARC—Agulhas Return Current, DP—Drake Passage.  
topography). The global mean SSH time series is subtracted from each grid point to obtain the local dynamic SSH anomalies not related to the global mean sea-level rise. The seasonal cycle, which is mostly characterized by standing oscillations, is estimated by fitting both the annual and semi-annual harmonics in a least-squares sense and subtracted from the SSH fields. Furthermore, to focus on the mesoscale variability only, we high-pass filter the time series at each grid point by removing the signals with periods greater than 1.5 years.