The Agulhas system is the boundary current system of the South Indian Ocean Subtropical Gyre. As the Agulhas Current (AC) flows southwestward to the south tip of Africa, it separates from the Agulhas Bank and becomes a free jet until reaching a turning point termed Agulhas retroflection (AR). Here, roughly 75% of AC (van Sebille et al., 2009a) returns to the Indian Ocean as the Agulhas Return Current (ARC), while the rest may enter the Atlantic as Agulhas leakage (AL). Recent study based on floats data shows that 27.8% of the AC water leaks into the Atlantic (Daher et al., 2020).

The AL is considered a crucial component of the Atlantic Meridional Overturning Circulation (AMOC) upper limb, and can affect the strength and stability of AMOC (Gordon, 1986; Biastoch et al., 2008, 2009; Gunn et al., 2020). The AL consists of Agulhas rings with diameters ranging from 150 km up to more than 300 km (de Ruijter et al., 1999; van Aken et al., 2003), smaller eddies (Wei and Wang, 2023), as well as submesoscale features (Loveday et al., 2015; Cheng et al., 2016). The Agulhas rings can be observed and tracked using altimetry data, and their sizes and translation speed can be inferred as well (Byrne et al., 1995; Schouten et al., 2000; Dencausse et al., 2010b; Backeberg et al., 2012), but its exact mass, heat, and salt transports are difficult to estimate (de Ruijter et al., 1999; van Aken et al., 2003). The mass and buoyancy transport of the total leakage is even harder to derive with in situ or altimeter observations. Therefore, the volume or heat transport associated with AL is often indirectly estimated based on the proportion of AC water entering the South Atlantic (Bryden et al., 2005). It should be noted that the large salinity variability of AC also makes it harder to quantify the AL salt transport (McMonigal et al., 2020).

The relationship between AL, AC, and the AR position remains unclear. On one hand, Rouault et al. (2009) and van Sebille et al. (2009a) have attempted to establish a statistical relationship between AC and AL, but their conclusions contradicted each other. Using a temperature and salinity criteria to determine AL water mass in numerical model, Rouault et al. (2009) found a positive correlation between AC and AL. Although the negative correlation between AC transport and AL (van Sebille et al., 2009a) agrees with most of previous understanding of the retroflection dynamics (Ou and de Ruijter, 1986; Dijkstra and de Ruijter, 2001; Le Bars et al., 2012), other studies using a hierarchy of numerical models have shown that the AL may be decoupled from the AC (Loveday et al., 2014), but responds strongly to the changes in wind stress curl of the westerlies (Durgadoo et al., 2013). On the other hand, the relationship between ring shedding, the AL strength, and the AR longitudinal position has been established (Ou and de Ruijter, 1986; van Sebille et al., 2009b), and the AR position was even used as proxy of the ring shedding events or the AL (Lutjeharms and Van Ballegooyen, 1988; Feron et al., 1992).

Earlier algorithms used to identify the AR position as well as the related ring-shedding processes are mostly based on the specific sea surface height (SSH) or absolute dynamic topography (ADT) contours. For instance, Dencausse et al. (2010a) used the westernmost point from one of the two SSH isolines, depending on the distance between the westernmost points of the two isolines. Usually, the 1.7 m isoline is used to determine retroflection position. At the moment of ring shedding, however, the distance between 1.7 m and 1.9 m SSH contours may be more than 150 km. Then a higher critical value of 1.9 m is applied to avoid ambiguity in definition. Van Sebille et al. (2009b) used the SSH isoline on which the maximum AC velocity was found, and took its westernmost point as the retroflection. Loveday et al. (2014) set a threshold of the mean SSH within the upstream AC area where it is less turbulent, thus obtained an isoline whose westernmost point is considered the retroflection. Based on satellite altimetry data, Zhu et al. (2021) used 0.7 m ADT isoline to detecting the Agulhas retroflection. In addition to the various isoline-related morphological criteria, Russo et al. (2021) further proposed an improved method to ascertain the retroflection, by combining the kinematical feature, i.e., the maximum speed of the current with its associated ADT values. Once the retroflection is determined, its variability on multiple timescales can be analyzed. However, no long-term retroflection longitudinal changes were confirmed during the altimeter era, but seasonality has been noted and the seasonality phases have shown strong interannual variability (Dencausse et al., 2010a).

High eddy kinetic energy has been observed as well as simulated in the vicinity of the retroflection area (Loveday et al., 2014; Cheng et al., 2016), and both cyclonic and anticyclonic eddies can interact with the AR (Lutjeharms et al., 2003). Ring shedding events in infrared images tend to be accompanied by abrupt eastward jump of the retroflection point, usually following an accelerating westward penetration of AC jet (Lutjeharms and Van Ballegooyen, 1988). This phenomenon was also observed by Feron et al. (1992) and Dencausse et al. (2010a) from sea surface ADT, and was subsequently termed as “pulse-like” behavior of the retroflection. Dencausse et al. (2010a) also noted abrupt westward jump of the retroflection, due to re-absorption of a previously detached ring. Cyclonic lee eddies are present west of the Agulhas Bank, and may contribute to the westward elongation of the retroflection through advection (Dencausse et al., 2010a). Lutjeharms et al. (2003) observed a lee eddy splitting into two, and found it instrumental in pinching the Agulhas ring off the retroflection.

Given the wide divergence about the linkage of AL with AC and the complexity of retroflection dynamics, here we propose a new algorithm to detect the retroflection locations so as to reexamine the relationship between retroflection and upstream AC. The impact of the local wind forcing on the AR and the linkage of AR position with ring shedding processes and the AL are also involved. In Section2, the gridded altimeter data and a regional numerical model configurations are described, and the energetics of the Agulhas system is analyzed to identify the AC jet core and the retroflection. The relationship between the AC jet and the AR position is examined in Section 3. Section 4 shows the AR displacements in details, and local wind forcing anomaly associated with displacements is noted. Numerical experiments are designed to test the impact of the local wind anomaly on the AR in Section 5. The ring shedding, occlusion and migration processes are discussed for extreme eastward and westward retroflection events in Section 6. Finally, the results are summarized and discussed in Section 7.

The resultant monthly AC jet axis is shown in Fig. 2. It is found to be more stable upstream (smaller variation) close to the continent and less stable downstream (larger variation) after separating from the southern tip of Africa, roughly divided at 26°E (dashed line in Fig. 2). The mean path orientation turns from southwestward east of 20°E to westward around 18°E, and tilts further northwestward around 16°E (thick black line in Fig. 2). It should be noted that the mean jet path is an average taken at each available longitude. The sample size for the mean latitude calculation decreases towards west, thus the northward slant of AC path west of 17°E may not be robust in statistics. Nonetheless, the mean AC path derived from the dynamical algorithm generally accords with the direction of ADT isolines and fits the route along the maximum ADT gradient, which fully demonstrates the rationality of this method.

The difference between MKE and EKE are integrated along the upstream and downstream sections of the AC jet path to represent the AC strength, and their normalized indices and 13-month running means are shown in Figs 3a and b. It should be noted that the along-path integration is different from that along a vertical section across the AC, which only reflects its strength at a certain point along its path. The correlation coefficients between upstream and downstream jet strength are 0.33, 0.49， and 0.58 (all significant at 95% level of t-test), respectively for monthly, 3-month running average, and the 13-month running average. This shows somewhat consistency between the upstream and downstream flow strengths.

In order to quantify the swing amplitude of the AC downstream path, the distance between each AC paths (the grey lines in Fig. 2) and the mean (the thick black line in Fig. 2) is measured by computing the spatial standard deviation (std) along the AC downstream. The formula is as follows:

where $ {x}_{i} $ and $ \overline{x} $ denote the latitude values at each longitude points for individual and time mean paths respectively, and $ n $ is the total downstream longitude number. The time series is presented in Fig. 3c. At downstream, the jet path alteration is highly correlated with its strength with the correlation coefficients of –0.58, –0.69, and –0.69 (all significant at 95% level of t-test), for monthly, 3-month, and 13-month running means. Therefore, on seasonal to interannual timescales, the stronger the downstream AC jet, the more stable (i.e., the less variable) it is.

A few studies have looked into the relationship between the AC transports and the longitudinal position of retroflection point. On one hand, Ou and de Ruijter (1986) found that a stronger AC has greater inertia, thus it can detach from the continental slope more easily, indicating the eastward shift of retroflection point. Based on (1/10)° numerical simulations, van Sebille et al. (2009a, b) also found that weaker AC corresponds to further westward retroflection displacements. On the other hand, using a series of sensitivity numerical experiments, Loveday et al. (2014) showed that the AL did not respond to increasing AC strength driven by increasing trade wind stress curl, and consequently concluded that AL was decoupled from the AC. They also noted that stronger inertial AC overshoot did not result in more eastward retroflection. In our study, the retroflection point is recognized as the westernmost end-point of the AC jet stream. The normalized retroflection longitudinal position index (Fig. 3d) is compared with the upstream and downstream AC jet strength and its stability. The retroflection longitude is not significantly correlated with the integrated AC jet strength upstream or downstream, and it is not significantly correlated with the downstream jet stability either. Therefore, our results do not support the linear correlation between the AC and the AR position, which is in line with Loveday et al. (2014).

Given decoupling of the retroflection position from the AC strength, composite analysis based on the ±1.5 standard deviation of normalized retroflection position index shown in Fig. 3d is applied to ascertain factors that account for the east-west shift of retroflection. Extreme eastward retroflection displacements (otherwise known as early retroflections), i.e., more than 1.5 standard deviation east of the mean longitude, are found to occur in 24 months out of the total 312 months considered in this study. Similarly, the extreme westward displacements (otherwise known as late retroflections) are found to occur in 21 months. The jet paths for the 21 most westward months and 24 most eastward months are displayed in Figs 4a and b, respectively. In the case of the extreme westward displacements, the jet paths are elongated westward until about 16°E and occasionally tilt northward. For the extreme eastward displacements, the jet paths shoot southward at about 21°E.

The composites of the ADT and geostrophic flow for the extreme eastward and westward retroflections differ from each other (Fig. 5). A weak anticyclonic feature is located to the west of the extreme eastward retroflection point (Fig. 5a), alluding to the ring shedding process associated with the eastward shift of AC. As for the extreme westward cases, it is noteworthy that a remarkable cyclonic feature with low ADT values appears to the north of the elongated AC jet paths (Fig. 5b). Unlike other types of cyclonic eddies, such as those induced by Natal Pulses or shear edge eddies on the east side of the Agulhas Bank (Lutjeharms et al., 2003), this cyclonic feature occurs locally on the west side of the Agulhas Bank and coincides with the elongated AC, and is larger in size than the shear edge eddies.

The approximate area for the cyclonic feature is marked by a black rectangular box (Fig. 5b), within which the spatially averaged ADT is shown from 45 d before to 105 d after the occurrence of extreme retroflection displacements (Fig. 5c). The timing of the changes of the mean ADT within the rectangular box indicates that ADT anomalies develop almost in parallel to the east-west shift of retroflection and persist over 60 d, which fully demonstrates a close connection between the westward extension of the AC and the cyclonic anomaly at the north flank of AC axis. In contrast, the eastward shift of the retroflection is roughly associated with the overall anticyclonic anomalies on the north side. This inspired us to speculate on the other factors that drive the east-west shift of retroflection position than the aforementioned AC jet strength or its stability.

We therefore examined the possible effect of the local wind stress curl in the vicinity of retroflection area. The composite of wind stress curl anomalies for 24 extreme eastward shift retroflection months (Fig. 6a) is generally positive in the whole region. On the contrary, the composite of the wind stress curl anomalies for westward retroflection position is mostly negative (Fig. 6b), especially around the retroflection. To examine the effect of the local wind forcing where the cyclonic feature appears (black rectangular box in Fig. 5b), the 15-d running mean wind stress curl within the box is lead-lag composited for eastward retroflection events (blue line in Fig. 6c) and westward retroflection events (red line in Fig. 6c), respectively. The positive (negative) wind stress curl within the box starts developing about 10 d before the extreme eastward (westward) retroflection occurs, and its magnitude reaches a maximum about 5 d to 6 d before the extreme. The same lead-lag composite analysis is also applied to the region of retroflection (grey box in Fig. 6b), where the differences in wind stress curl composites appears the largest. In contrast, the 15-d running mean wind stress curl anomalies in this area did not exhibit any significant difference for two groups of extreme events until about 8 d after the retroflection point shift (Fig. 6d). Therefore, a wind-driven mechanism is proposed here to interpret the east-west shift of retroflection point. In response to the anomalous negative wind stress curl forcing within the black rectangular box (Fig. 6), a local cyclonic anomaly develops on the north side of the retroflection, which in turn accelerates the westward Agulhas jet stream and results in the westward shift of the retroflection. On the contrary, positive wind stress curl suppresses the anomalous cyclone, resulting in the retreat of jet stream at its southern flank and the eastward shift of retroflection.

In order to verify the above inferred mechanism, a ROMS model was configured in the Agulhas system area and a set of numerical experiments were designed. The detailed choices for numerical schemes and parameters can be found in Section 2.2. Due to the pulse-like behavior of the retroflection related to ring shedding processes, timings of the retroflection positions corresponding to different local wind forcing conditions cannot be compared directly. Instead, mean retroflection longitudes on time scales longer than 1 year are compared to qualitatively verify the local wind forcing effects on the retroflection position. We firstly checked the annual mean ADT during the altimeter era (1993–2018) for the observation data. It turns out that similar patterns of cyclonic features are present in certain years, while absent in others. Here the two contrasting years of 2017 and 2002 are selected (shown in Fig. 7) because the mean retroflection longitudes in these two years are relative eastward (18.4°E) and westward (17.7°E). It is noteworthy that a cyclonic feature is present at the northern flank of the westward extension of the AC in 2002 (Fig. 7b), but not in 2017 (Fig. 7a). In association with the obvious ADT contrast, the annual mean wind stress curl anomalies in these two years also exhibit a great contrast between the positive anomalies in 2017 (Fig. 8a) and the negative anomalies in 2002 (Fig. 8b), particularly in the retroflection region. Therefore, the possible connection between negative wind stress curl anomalies, cyclonic circulation, and the westward extension of retroflection position may work even in annual mean state, i.e., 2002. And the opposite process may occur in other years such as 2017, with positive wind stress curl anomalies corresponding to the inactive cyclone and the eastward shift of retroflection.

In view of the significant differences between these two years (Figs 8a and b), the mean state, the boundary conditions, and the surface forcings in 2017 were used to spin up the model and drive the control run, whereas perturbed local wind stress is used to drive three perturbed runs. Three steps were implemented to generate the perturbe local wind stress. First, the mean wind stress forcing in 2017 was subtracted from the mean wind stress in 2002 (Fig. 8c). Second, the local wind stress anomaly was obtained, by multiplying the difference with a gaussian weighting function W(x, y) varying in space as follows:

where the center (x₀, y₀) is at 18.5°E, 37.25°S, and R is 350 km, and its spatial distribution is shown in Fig. 8d. Third, the wind stress anomaly is added to the mean wind stress in 2017, which is used to force three perturbed runs. The parameters of the weighting function are chosen so that a strong negative wind stress curl anomaly close to that in 2002 is applied roughly within the rectangular box to the north of the retroflection (Fig. 8d), while other area of the domain is still forced by the 2017 mean wind stress.

The model was spun up by applying 2017 mean ERA5 surface wind stress, heat flux, and radiation flux for 10 years, with 2017 mean ORAs5 temperature, salinity, and velocity as boundary conditions. The end of spin-up state is used as initial condition, and the same surface forcings are applied for another 5 years as the “control” run. Then three “perturbed” runs are performed for 5 years, with the same forcing as the control run, except that the local wind stress perturbations are applied with 0, 1, and 2 months dalay after the control run. In this way, we can examine an ensemble of the longitudinal retroflection shift runs, so as to minimize the bias due to intermittent ring shedding and ensure robustness of the results.

The modeled 5-year mean SSH for the control run and the ensemble mean SSH of the three perturbed run are shown in Figs 9a and b. The modeled Agulhas Current transports are calculated by integrating the cross-ACT (Agulhas Current Time-series) instrumental array (Beal and Elipot, 2016) transports within 1000 m depth, and the resulting AC transports are (74.8 ± 11.3) × 10⁶ m³/s for the control run, and (74.7 ± 11.9) × 10⁶ m³/s, (75.6 ± 12.3) × 10⁶ m³/s, (75.3 ± 12.8) × 10⁶ m³/s for the three perturbed runs respectively. The transports are consistent to the AC transport estimated by previous studies, e.g., 73.0 × 10⁶ m³/s in Beal and Bryden (1999). The AC transports are not significantly different between the control run and the perturbed runs, hence cannot be the likely cause of the retroflection shifts. The three perturbed runs are forced with a cyclonic wind stress curl anomaly in an area adjacent to the retroflection (Fig. 8d). Although the model is not able to simulate the cyclonic feature as observed (Fig. 7b), the SSH difference between perturbed runs and the control runs within the cyan box (Fig. 8d) is more than 0.1 m. The absence of the cyclonic eddy is probably because the model resolution cannot resolve the submesoscale processes (Schubert et al., 2021). Nevertheless, a notable discrepancy of retroflection positions between these two cases can be easily detected, i.e., 17.5°E for the control run, and 16.8°E, 17.1°E, and 17.2°E for the perturbed runs. A closer look at the retroflection area shows that the retroflection of the ensembled perturbed runs locate further west than the control run (Figs 9a and b).

Due to the intermittent pulsing of the retroflection associated with ring shedding, a few extreme retroflection events can render a huge shift of the mean retroflection on seasonal to interannual time scales. Therefore, instead of directly examining the retroflection time series, the probability distribution of the retroflection longitudes are compared between the control run and the perturbed runs (Figs 9c and d). The retroflection longitudes for each model run is calculated using the kinematic algorithm proposed in Section 2.3, based on 3-d average horizontal velocity. The total number of occurances of retroflection are counted in bins from 13°E to 25°E with 1° increment, and are divided by the total number of occurances in all bins from 13°E to 25°E to derive the probability distribution of the retroflection longitudes. In the first 3 model years, the most probable retroflection longitudes for the perburbed runs are further west, resulting in more westward mean retroflection longitudes in the perturbed runs than in the control run (Fig. 9c). While for the latter 2 years, the most probable retroflection longitudes for the perturbed runs are not consistently further west than the control run (Fig. 9d). The consistency of the westward retroflection shift is abscent when the local forcing is prolonged than 3 years, indicating that local cyclonic wind stress perturbation may not have a lasting effect. On the contrary, the large-scale westerly changes beyond the retroflection may cause a more sustained shift of retroflection and more profound circulation adjustment (Durgadoo et al., 2013).

Although the local wind stress anomaly in the model did not generate the strong oceanic cyclonic feature to the north of the retroflection, the ocean responses can still lead to the westward retroflection shift. This discrepancy between model and observation results may be interpreted by local negative relative vorticity anomalies to the north of the retroflection in the perturbed runs in contrast with the control run (figure not shown), which corresponds to southwestward advection and possibly leads to prolonged AC and more westward retroflection in the purburbed runs. This analysis indicates that even though the cyclonic feature does not prominently show up in numerical experiment, the local negative wind stress anomaly indeed can induce local negative vorticity anomaly and the westward retroflection shift through ocean advection. The experiment results indicate that in the real ocean, the local wind stress forcing may play an even more important role in determining the retroflection location.

Strong eddy activities have been observed in close proximity to the retroflection, as a result of the retroflection shifting as well as eddy spawning (Fig. 1b). The composite ADT of the extremely westward retroflection clearly show a cyclonic circulation at the north (Fig. 5b), which may play a role in the processes of Agulhas ring shedding and Indian-to-Atlantic Ocean volume transport. To preliminarily examine the possible connection of this cyclonic feature, Agulhas ring shedding and the AL, lead-lag composite analysis of 15-d mean ADT based on the retroflection position index is done and shown in chronological order in Fig. 10 for the westward shift and Fig. 11 for the eastward shift of retroflection events.

A weak cyclonic feature can be identified 30 d before the extreme westward retroflection occurs (Fig. 10a), and it gradually strengthens as the retroflection intrudes westwards (Figs 10b, c， and d). Then the cyclonic feature can last about 60 d on average after the extreme westward retroflection occurs (Fig. 5c). After the retroflection reaches the westernmost longitude, an Agulhas ring develops and sheds as the retroflection retreats back to the Indian Ocean (Figs 10e and f). In the extreme westward retroflection cases, the presence of the long-lasting cyclonic feature as well as the more westward shedding location of the Agulhas ring may make it easier for the rings to propagate further northwestward into the Atlantic, and resulting in higher AL.

Before the occurrence of extreme eastward retroflection events, the similar weak cyclonic feature can also be clearly identified at the north flank of the retroflection region (Figs 11a and b). This cyclone, however, shifts southwestward and decays with time, in association to the retreat of the AC axis and ring shedding event (Figs 11c and d). It seems that the weakened cyclone, on its way southwestward, blocks the movement of the newly formed ring, resulting in the reintegration of the ring into the continuously westward advancing AC jet (Figs 11e and f). Although we cannot definitely conclude that all of rings shedding in the extreme eastward retroflection events are merged back again into the AC, these composite results at least allude less rings propagating into the Atlantic, hence weaker AL for the eastward retroflection months.

It is worth noting that the Agulhas leakage is not merely composed of Agulhas rings, but includes the mean flow, the mesoscale eddies and the filaments. Rühs et al. (2022) integrated multi-source data to examine the long-term change of the AL. They asserted that on the decadal time scale, the AL is attributed less to the Agulhas rings and the EKE, but more to the mean flow. In order to probe possible impact of the retroflection position on the Atlantic water property on monthly scale, the OISST anomaly and ERA5 SST anomaly (SSTa) are composited on the retroflection position index (Fig. 12). With the retroflection shifting westward, the remarkable warming on the South Atlantic side (solid box in Fig. 12, hereafter SA) is in sharp contrasts to the moderate cooling on the Indian Ocean side (dashed box in Fig.12, hereafter IO). The retroflection-related SST anomalies are insensitive to the dataset selection (Figs 12a and b), and can persist to the next month (Fig. 12c). This result is consistent with the study of Zhu et al. (2021), though they applied different method of retroflection identification. According to Biastoch et al. (2015) and Rühs et al. (2022), the SST difference between the SA and the IO can be viewed as a good proxy for the AL variability (hereafter AL_SST). Figure 13 shows the lead-lag composited differences of the AL_SST based on the retroflection index. It is apparent that the westward retroflection events are associated with the positive anomalous AL (red crosses) within two months, while the eastward retroflection cases are followed by the weakening AL (blue circles) in the next month (Fig. 13a). The resultant AL_SST differences between the westward and the eastward retroflection events are significantly beyond the standard error bars in the time lag of zero and one month (Fig. 13b). This lends the support for the monthly to seasonal correspondance of the AL variability with the retroflection position via the Agulhas ring shedding process.

To further verify the inference from the above composite analysis, we selected several extreme cases to check their ring shedding processes one by one. As shown in Fig. 14, left panels are two eastward retroflection cases and right panels are two westward retroflection cases according to our criteria. Their corresponding AC jet paths are plotted as red thick lines. In consistent with the previous studies (Zhu et al., 2021), the 0.7 m ADT isolines (colored contours) are chose to ascertain the time evolution of retroflection. For the eastward retroflection cases, the disruption of isolines occurs at about 19°E for Case 1 (Fig. 14a) and about 21°E for Case 2 (Fig. 14c). The resultant rings, however, keep relatively still and stable for weeks, until they are absorbed into the main flow. This may lead to the abrupt westward jump of retroflection position within the framework of ADT/SSH contour criteria. For the westward retroflection cases, the rings fall off the main flow west of 18°E (Figs 14b and d), and they continuously move westward into the Cape Basin in 30 d. The strong contrast of ring activity between the eastward and the westward cases lend support to the composite results, alluding to the connection of retroflection position and the AL on monthly timescale.

In this study, a kinematic criterion based on the spatial distribution of MKE and EKE is proposed to ascertain the AC strength, its stability as well as the retroflection position within an unified framework. Their linear correlations are examined and the result suggests decoupling of the retroflection position and the AC. Further composite analyses reveal that a cyclonic feature north of the retroflection, possibly induced by the local wind stress curl, is closely associated with the extreme westward retroflection events. Numerical experiments are then designed to test whether and how much local wind stress anomaly can affect the AR displacements. The simulated mean retroflection longitudes, forced by local negative wind stress anomaly, have shifted westward significantly. Furthermore, our results suggest the different fates of detached rings corresponding to the shift of retroflection, i.e., reabsorbed into the mean flow for the easternmost retroflection or migrating persistently towards the Atlantic Ocean for the westernmost retroflection. This also indicates the relevance of AR position to the AL because the passage of Agulhas rings can result in pronounced AL events (Cheng et al., 2016).

Due to the turbulent activities in the retroflection area, especially in the processes of ring generation, migration and dissipation, ambiguity is inevitable for the retroflection identification. Most of previous studies have simply chosen a fixed SSH as a critical value and took the westernmost grid point on the corresponding isoline as the retroflection. The retroflection longitude obtained this way is thus very sensitive to the chosen critical value. For instance, the difference between retroflection locations obtained using 1.7 m and 1.9 m as critical SSH is in the range of 30 km to 150 km most of the time, but can be as large as 600 km (Dencausse et al., 2010a). More importantly, the unstable state of AC jet path downstream makes it difficult to distinguish exact retroflection position from temporary isoline disruptions in a morphological perspective. For example, an extreme eastward retroflection event of 2000/2001 has been noted in previous studies (de Ruijter et al., 2004; Dencausse et al., 2010a). The event lasts nearly half a year, resulting in zero ring shedding and greatly reduced AL. However, none of these months stands out in this study as the easternmost retroflection cases. A detailed probe into the event reveals that the ADT isoline indeed breaks up at about 28°E at the end of November (Fig. 15a). The water body falling off the main flow remains essentially stable for over three months (Figs 15b, c and d), neither westward drifting nor re-merging into the mainstream. Therefore, the controversy about the retroflection point lies in whether this water body belongs to or is independent from the AC mainstream. In consideration of the strong stability and large size of the fractured body, it is rational to regard the body as a part of AC, thus the retroflection point could be set at the west end of fractured body (about 18°–21°E) rather than at its east end (about 27°–28°E). This inference can be further evidenced by a fragmented but extended AC path far beyond 27°E according to our kinematic standard (red thick lines in Fig. 15). In this sense, the 2000/2001 event should not be grouped into the easternmost retroflection events from a dynamical perspective, though in morphology it appears an early retroflection.

The pulsation of the retroflection has been noted previously (Lutjeharms and van Ballegooyen, 1988), and is mostly characterized by a westward progression lasting 25.7 d on average followed by abrupt eastward shift (Dencausse et al., 2010a). In this study, the westernmost retroflection is unstable to form rings, and the subsequent eastward retreat of the retroflection makes it hard to reabsorb the ring but to let it shed. The easternmost retroflection may also form rings as it grows unstable, but it tends to reabsorb the ring during its subsequent westward protrusion. Our study is roughly consistent with findings by Dencausse et al. (2010a) that most complete separations of ring from the AR coincides with the westward extremes in spite of the discrepancy in the AR position estimation. Since AL occurs mostly in the form of Agulhas rings, it can be inferred that the leakage is much larger during the westward retroflection than the eastward cases in monthly and annual timescale, which is partly supported by our numerical experiments. This may set a new theoretical base to investigate the AL variation on multiple time scales. Nonetheless, further statistical and modelling studies are necessary to establish a robust physical connection and quantitative relation between the AR and the AL, which can greatly improve our understanding of inter-basin exchange in the Southern Ocean as well as its role in the AMOC variability and in the global climate change.