On glacial-interglacial timescales, it is believed that the Southern Ocean strongly impacted the atmospheric carbon dioxide (CO2) inventory owing to its leverage on the communication between the atmosphere and the voluminous ocean carbon reservoir1,2. Several mechanisms are proposed to have curbed CO2 release from the ocean interior during glacial periods, including sea ice expansion3, an increase in Subantarctic phytoplankton export production fueled by higher iron-bearing dust supply to the surface ocean4,5, and isolation of Antarctic Zone (AZ) surface waters from CO2-rich deep water masses6,7,8,9,10,11,12. Regarding the last mechanism, while several proposals exist for the cause of AZ surface isolation, such as changes in surface buoyancy forcing and changes in abyssal mixing over rough seafloor topography, altered wind-driven upwelling is able to provide a holistic explanation for reconstructed changes in high latitude oceans of both hemispheres, for glacial-interglacial changes as well as millennial-scale events (ref. 9 and references within).

Changes in the position and/or strength of Southern Westerly Winds (SWW) are thought to have modulated Antarctic upwelling13,14,15. Surface winds cause divergent Ekman transport south of the wind stress maximum, near the axis of the Antarctic Circumpolar Current (ACC) between 45°S and 55°S, leading to the upwelling of CO2- and nutrient-rich subsurface waters along tilted surfaces of constant density. These isopycnals run poleward and upward across the ACC16, inducing strong meridional gradients in sea surface temperature (SST) and density that define the ACC frontal system17,18. The Polar Frontal Zone (PFZ) and the Subantarctic Zone (SAZ), enveloped by the Antarctic Polar Front (APF) to the south and the Subtropical Front (STF) to the north, mark the transition from the cold Antarctic surface water derived from outcropping deep water masses, to the warm Subtropical Zone (STZ) surface waters. The meridional location of this transition has important implications for Southern Ocean overturning circulation and thus the partitioning of CO2 between ocean and atmosphere and global climate during glacial-interglacial cycles13,19.

Modern oceanographic data and numerical simulations suggest that the ACC fronts are largely steered by seafloor bathymetry due to the depth structure of the frontal jets, but the extent of frontal shift under substantial climate forcing is still under debate20,21. Similarly, model simulations are not consistent in their evaluation of the effect of changing SWW stress on upwelling intensity22,23. On glacial-interglacial timescales, available paleoceanographic reconstructions agree on the direction of latitudinal shifts of the ACC fronts24,25,26,27,28,29 but do not agree on coherent patterns of change in the SWW30. In order to reconstruct changes in Southern Ocean upwelling and identify its drivers, additional quantitative information is needed on the temporal evolution of the ACC fronts on a continuous basis over glacial cycles9,12,13,19.

To shed light on the timing and structure of Southern Ocean frontal movements and connect these with changes in SWW and upwelling dynamics, we report reconstructions of the meridional gradient in surface layer temperature across the ACC in the southern Indian Ocean based on the TEXL86 paleothermometer, using a revised TEXL86 calibration (Supplementary Note 1). TEXL86 is an organic compound-based proxy that records changes in temperature at the sea surface or the shallow subsurface31,32,33 and is thought to be appropriate for polar and subpolar regions (Supplementary Note 2). For simplicity, we refer to both the TEXL86-reconstructed 0–200 m integrated temperature and World Ocean Atlas (WOA) 2009 0–200 m integrated temperature as sea surface temperature (SST) in this study. We analyze the temporal evolution of reconstructed SST difference (ΔSST) between MD11-3357 (44.68°S, 80.43°E, 3,349 m water depth) and MD11-3353 (50.57°S, 68.39°E, 1568 m water depth) in the Subantarctic and Antarctic zones (SAZ and AZ) of the southeast Indian Ocean, respectively (Fig. 1). The meridional ΔSST between the SAZ and AZ sites is used to investigate the temporal evolution of frontal displacements, based on a simple quantitative framework (see “Methods”). Our focus is the steep temperature gradient in the ACC enveloped by the APF and the STF, so the meridional frontal displacements reconstructed in this study refer to the band of transition from Antarctic surface water to subtropical water rather than a strictly defined front. This approach is enabled by applying the same paleothermometric method to core sites across a large latitudinal range. Our analyses produce a temporally continuous reconstruction of the ACC latitude that lends strong support to the hypothesis of meridional frontal migration during the last glacial cycle, with a generally more equatorward position during cold periods and more poleward location during warm intervals. Based on the results, we argue that the mean position of the SWW had a profound impact on the latitudinal position of the Southern Ocean fronts in the study region. In addition, Earth’s axil tilt (obliquity) has been proposed to force changes in atmospheric and oceanic circulation and strongly affects the climate of the middle to high latitude Southern Hemisphere34. Asynchrony between CO2 and Antarctic temperature in late Pleistocene ice core records is found to be associated with obliquity35, and recent reconstruction of Antarctic Zone surface nutrient conditions has provided evidence for a mechanistic link between obliquity and this asynchrony via its modification of Antarctic upwelling and CO2 outgassing during the last glacial cycle12. The quantitative, temporally continuous reconstruction of the ACC latitude in this work allows identification of the effect of obliquity on ACC isotherms, providing additional support for the effect of obliquity on SWW intensity and Antarctic upwelling.

Fig. 1: Maps of modern Southern Ocean 0–200 m annual surface temperature (SST) and 10 m zonal wind.
figure 1

a Annual 0–200 m surface temperature of World Ocean Atlast 200945 (°C) and b 10 m zonal wind strength based on reanalysis data for the period 1951–197878,79. Pink circles indicate core locations of MD11-3353 (50.57°S, 68.39°E) in the Antarctic Zone (AZ) and MD11-3357 (44.68°S, 80.43°E) in the Subantarctic Zone (SAZ). STF Subtropical Front; SAF Subantarctic Front, APF Antarctic Polar Front, after ref. 18.

Results and discussion

Fidelity of TEXL 86 in the Kerguelen region

The TEX86 paleothermometer is based on the relationship between SST and the distribution of archaeal membrane lipids (glycerol dibiphytanyl glycerol tetraethers [GDGTs])31. In polar and subpolar regions, the TEXL86 index has been shown to provide more realistic paleotemperature estimates than the TEX86 index32,33. The main difference between the two indices is that TEXL86 does not include the crenarchaeol regioisomer, which is found only in low abundances at SSTs below 15 °C (Supplementary Fig. 1)33. Numerous studies have applied TEXL86 in the (sub)polar regions for downcore temperature reconstruction12,32,36,37,38,39,40,41. The offset of reconstructed TEXL86-SST (compared to WOA09 SST) for the global core-top compilation42 is ±3.2 °C (Supplementary Note 3), which is likely due to influences from factors such as the depth and seasonality of GDGT export, archaeal community change, and terrestrial GDGT input43, on top of potential interlaboratory variation44. Previous studies postulated that in more restricted localities, the error of TEXL86 SST reconstruction is smaller than that in the global TEXL86 calibration, since these factors are less variable within a given region. Within the Indo-Pacific ACC core-tops, although there is a tendency for TEXL86 to overestimate SSTs in this region, our revised TEXL86 calibration accurately captures the SST difference (ΔSST) between any two sites (Supplementary Note 3). This is likely due to a relatively uniform non-thermal contribution to TEXL86 within the region. The offset of reconstructed TEXL86 ΔSST (compared to WOA09 ΔSST) between any two core-tops within a specific region of the ACC is overall smaller than that between any two core-tops in the whole ACC, supporting the hypothesis of more similar non-thermal factors in more restricted oceanographic settings (Supplementary Note 3).

The overall glacial-interglacial change of TEXL86-SST at the two sites agree well with SST records of other paleothermometry methods from nearby sites (Supplementary Note 4). The youngest (core-top) samples from MD11-3357 and MD11-3353 (with estimated ages of 1.06 ka and 0.79 ka, respectively) provide SST estimates of 12.9 °C and 4.1 °C, respectively (Fig. 2), 3.0 °C and 1.3 °C warmer than the WOA09 SST45 (9.9 °C and 2.8 °C, respectively). These errors lie within ±1 standard deviation for the Indo-Pacific ACC core-tops (Supplementary Note 3). The GDGT indices related to several non-thermal factors fall within the expected range for the two core sites (Supplementary Note 5), suggesting that the tendency to overestimate SST at the two sites may be due to non-thermal contributions not reflected in these GDGT indices. The TEXL86 core-top ΔSST between the two sites is 8.8 °C, 1.7 °C higher than the WOA09 ΔSST. Apart from non-thermal factors mentioned above, this difference between reconstructed core-top ΔSST and modern ΔSST may derive from high frequency SST changes in the Southern Ocean. Millennial-scale SST oscillations of as much as 4 °C have been observed around the Antarctic Peninsula46, which were synchronous with SST oscillations of ~1 °C in the southwest Pacific in the late Holocene47. Given that the surface sediments in the Kerguelen region are often more than one thousand years old12, an offset of 1.7 °C between the core-top TEXL86 ΔSST and WOA09 ΔSST is reasonable. As MD11-3353 and MD11-3357 are close to each other in the Kerguelen region, the factors potentially affecting TEXL86 temperature reconstruction are likely similar at the two sites throughout the time period of interest. If so, the resulting uncertainties in absolute temperature estimation should be of similar amplitude and of the same direction, such that they should not greatly bias the calculated temperature difference between the two sites. We take 1 °C to be the uncertainty of the reconstructed ΔSST, taking both analytical precision and non-thermal archaeal factors into consideration (Supplementary Note 6).

Fig. 2: Sea surface temperature (SST) reconstructions across the last glacial cycle.
figure 2

a GDGT-based (TEXL86) SST reconstruction for core MD11-3357 (red) and core MD11-3353 (blue), compared to the EPICA Dome C (EDC) temperature change48 (gray). b SST difference (ΔSST) between the two cores, SST(MD11-3357) – SST(MD11-3353), interpolated on a 2.5 kyr time step. Blue bars indicate cold periods of MIS 2, 4, and 6 and pink bars indicate warm periods of MIS 5e and the early Holocene. Arrows on the y-axis indicate modern annual temperatures of the shallow subsurface (0–200 m)45. The map shows the location of the core sites with bathymetry in the Kerguelen region80. STF Subtropical Front, SAF Subantarctic Front, APF Antarctic Polar Front, after ref. 18.

Fig. 3: Data-simulation comparison of the relationship between Antarctic air temperature and the sea surface temperature difference (ΔSST) between the two Southern Ocean sediment cores.
figure 3

a The reconstructed ΔSST in comparison with EPICA Dome C (EDC) temperature depicts a horseshoe pattern with its angular point (largest ΔSST) around −4 °C. Red open circles represent data from the late MIS 2 to the end of Termination 1 (10–24 ka), and the red line and arrow represent the temporal progression of ΔSST towards younger ages. Orange open circles represent data from the late MIS 6 to the end of Termination 2 (129–144 ka), and the orange line and arrow represent the temporal progression of ΔSST towards younger ages. b The downcore record of reconstructed ΔSST between MD11-3357 and MD11-3353. c, d Simulated ΔSST between the latitude of MD11-3357 and that of MD11-3353 without ACC shift (green dashed line and solid line) compared with EDC temperature and age. e, f Simulated ΔSST with the best-fitting linear model of ACC shift (dark blue dashed line and solid line) compared with EDC temperature and age. The data in (a) and (b) are plotted semi-transparent in the background of (cf).

SST changes and the link to frontal shifts

SSTs at both MD11-3353 and MD11-3357 are closely correlated with Antarctic ice core-reconstructed air temperature48 (Fig. 2). The records depict a glacial-interglacial SST amplitude of about 9 °C (Fig. 2), in good agreement with multi-proxy SST reconstructions in the area49,50. In WOA09, the steepest slope of longitudinally averaged SST in the Kerguelen region lies north of AZ site MD11-3353 and around three-fifths south of SAZ site MD11-3357 (Supplementary Fig. 15). ΔSST would decrease (SSTs would become more similar) if, as a consequence of frontal shifts, both sites recorded temperatures from more similar water masses. This would occur if the fronts shifted either northward or southward.

The reconstructed ΔSST between the two core sites during the past 150 ka shows a pattern distinct from that of the glacial-interglacial climate evolution (Fig. 2a). This pattern is not a result of uncertainties in the age model (Supplementary Note 7). During peak glacial intervals such as Marine Isotope Stage (MIS) 2, 4, and 6, ΔSST is reduced to 4.5–6 °C. It reaches maximum values of >7.5 °C during intermediate climate intervals, such as MIS 5c and MIS 3, while during peak interglacials, ΔSST drops again to 4–6 °C. A cross-plot between ΔSST and the Antarctic ice-core (EPICA Dome C (EDC)) temperature reconstruction supports the inference that ΔSST decreases as climate approaches peak cold and warm climate states and reaches highest values under intermediate climate conditions (Fig. 3a). This non-monotonic relationship between ΔSST and EDC temperature suggests that the ACC fronts have shifted northward and southward as climate changed.

To understand the impact of frontal shifts on ΔSST between the selected core sites, we use a simple quantitative framework to illustrate the responses of SST at individual sites and ΔSST between sites to latitudinal migrations of the ACC and explore the outputs of different scenarios of coupling between frontal latitude and regional climate under different setups of the framework (Fig. 3; see “Methods”, Supplementary Note 8 & 9). We first simplified the meridional SST profile in the Kerguelen region in WOA09 into three segments, the AZ segment, the Polar Transition Zone (PTZ) segment—which includes the PFZ and SAZ—and the STZ segment, respectively. Then we applied different parameters to alter the three segments, mimicking hypothetical frontal changes, while assuming that the width of the PTZ has been constant. The parameters dictating the response of ΔSST to a certain ACC latitude change in this quantitative framework are the ranges of glacial-interglacial SST change in the AZ and the STZ, respectively, which reflect the extent of polar amplification. For the sensitivity analysis, we explored the changes of ΔSST between our sites compared to Antarctic climate (with EDC temperature taken as representing the latter) under different scenarios of coupling between frontal latitude and regional climate and with different prescribed framework parameters (Supplementary Note 8). In this study, we assume that the relationship between the ACC latitude and Antarctic climate remains linear. This assumption is derived from a linear relationship between global mean temperature and SWW latitude observed in GCM simulations51, overall synchronicity between southern high latitude SST and global mean SST during the last glacial-interglacial cycle52, and strong coupling between the steep SST gradient in the Southern Ocean (which we used to define the ACC) and surface wind stress in both modern observations17 and GCM simulations53. The results show that the non-monotonic relationship observed between ΔSST and EDC temperature only exists when the fronts shift alongside Antarctic climate change (Fig. 3, Supplementary Note 8). Altering either the prescribed framework parameters, namely the ranges of SST change in the AZ and the STZ, or the rate of frontal migration relative to Antarctic air temperature change alters the shape of the non-monotonic pattern (Supplementary Figs. 16 and 17).

Based on an estimated maximum glacial-interglacial SST change of 6 °C in the AZ and 2.5 °C in the STZ (Supplementary Note 9), an optimization algorithm was applied to find the linear model between ACC frontal latitude and Antarctic air temperature that best fits the TEXL86-reconstructed ΔSST between MD11-3357 and MD11-3353: Δlat (degrees) = ΔTEDC (°C) * 0.58 + 4.20 (see “Methods”, Supplementary Fig. 19). When we swap the maximum SST change in AZ and STZ (i.e., hypothetical tropical amplification), the optimization algorithm produces a very similar slope for the best-fitting linear model, suggesting that this linear relationship between ACC frontal latitude and Antarctic air temperature is robust and largely insensitive to changes in the prescribed parameters of the framework (Supplementary Fig. 19). Changes in the width of the ACC play a minor role in controlling the relationship between the simulated ΔSST of the two sites and Antarctic air temperature (Supplementary Note 10).

When the location of the ACC is kept unchanged, the simulated ΔSST decreases when climate warms (Fig. 3), which is the result of prescribed polar amplification in the framework. This trend qualitatively matches that of the reconstructed ΔSST for the warmer climate intervals, but the simulated change in ΔSST is too small (Fig. 3d). In addition, the no-shift simulation cannot reproduce the low ΔSST characteristic of the coldest conditions. In contrast, when ACC frontal latitude increases linearly with Antarctic air temperature, the observed non-monotonic relationship between TEXL86-reconstructed ΔSST and EDC temperature is well-captured (Fig. 3e). This simulation also captures many temporal features in the ΔSST change between the two sites (Fig. 3f) as well as in the glacial-interglacial SST changes at individual core sites (Supplementary Fig. 20). TEXL86 SST data from two additional sites located between the latitudes of MD11-3357 and MD11-3353 also agree with the simulated changes in ΔSST under the best-fitting linear model, albeit with greater uncertainty (Supplementary Note 11), indicating that our framework and the frontal shift model are robust for the southeast Indian Ocean. Within the four sites in the Kerguelen region, MD11-3353 and MD11-3357 likely represent the most appropriate pair to evaluate ΔSST for the effect of ACC migration because they are adequately close for frontal displacements to directly affect the ΔSST between the two sites, while being adequately distant that changes in ΔSST are robust against paleothermometric errors. Thus, our discussion of ACC latitude reconstruction focuses on these two sites.

ACC frontal shifts in the southern Indian Ocean over the last glacial cycle

While bottom topography is an important constraint on the path of barotropic deep ACC currents23,54, large variability of the ACC fronts upstream and downstream of topographic features has been observed to correlate with SWW shifts induced by changes in Southern Annular Modes in the Indian Southern Ocean55. In addition, the warming and freshening trend of the Southern Ocean reflects a southward displacement of isopycnals during the past 40 years21, and the surface hydrographic frontal structure has been observed to shift southward by about 60 km on a circumpolar average from 1992 to 200756. In the Kerguelen region, from 1992 to 2007, the APF has been observed to change its position from passing north of the plateau to passing through Fawn Trough56, suggesting that the ACC fronts can overcome topographic barriers under substantial forcing.

To reconstruct past changes in ACC latitude, using the relationship between ΔSST and ACC latitude inferred from our framework, we include the reconstructed TEXL86-ΔSST between MD11-3353 and MD11-3357 to back-calculate the latitudinal changes of the ACC fronts based on the measured ΔSST (Fig. 4 and Supplementary Fig. 21; see “Methods”). During cold intervals, including MIS 2, MIS 4, and MIS 6, the low ΔSST implies a northward shift of the ACC of ~2° compared to today (Fig. 4d). During the previous interglacial (MIS 5e), SST at MD11-3357 and MD11-3353 were ~2–4 °C warmer compared to pre-industrial, and the reconstructed ΔSST was very low (~4 °C). This suggests that the ACC fronts were as much as 6° further south than today (Fig. 4d), such that the steepest SST gradient moved southward of the AZ core MD11-3353. Our estimated ACC positions for both the LGM and MIS 5e appear to be more poleward than most of frontal shifts estimated in previous studies for the southern Indian Ocean (Supplementary Fig. 24). These studies either assume the same (sub-)isotherm as an ACC front throughout the glacial-interglacial climate change or assume the shift in abundance or size of specific plankton species to be associated with an ACC front. Factors such as homogenous cooling of the deep ocean, response of plankton to glacial-interglacial biogeochemical changes, and season-specific signals may bring uncertainty to frontal shifts based on the above assumptions, explaining the discrepancy in reconstructed frontal shifts between our study and previous studies (Supplementary Note 12). The very southward ACC position during MIS 5e reconstructed by our framework is further consistent with the unusually low biogenic opal flux at MD11-3353 during this interval41, which may be related to silicic acid limitation on diatom growth as a consequence of the more southward location of the APF (Supplementary Note 13 and Supplementary Fig. 25).

Fig. 4: Meridional migrations of the ACC over the last glacial cycle and their connections to climate and CO2 change.
figure 4

a Atmospheric CO272 (black) and EPICA Dome C (EDC) temperature change48 (gray). b Offset between CO2 and predicted CO2 based on a linear relationship between Antarctic ice core temperature and CO212 (dark red). c Compilation of SST at 50°–60°S52 (pink) and global SST change66 (purple). d Changes in ACC latitude calculated from ΔSST (3357−3353) (thick blue solid and dashed lines) and the uncertainty envelope (lighter shading). The dashed line represents where the measured ΔSST corresponds to an uncertainty range of ACC latitude change and the ACC latitude change is estimated as the average of the upper bound and lower bound (see “Methods”). e Changes in the difference between air temperatures at the moisture source (Tsource) and ice core site (Tsite) of Vostok (dark gray) relative to modern conditions reconstructed from ice deuterium excess73, and obliquity81 (yellow). f Offset between Indian AZ diatom-bound δ15N and predicted diatom-bound δ15N based on a linear relationship between Antarctic air temperature and diatom-bound δ15N12 (brown), g Combined record of Indian AZ diatom-bound δ15N as an indicator of upwelling12 (dark green) and predicted diatom-bound δ15N based on a linear relationship between Antarctic air temperature and diatom-bound δ15N12. The numbers at the top indicate Marine Isotope Stages. The vertical gray bars indicate different cooling periods of low obliquity (111.5–116.5 ka in MIS 5d) or lowering obliquity (1.5–6.5 ka in the late Holocene) during warmer conditions, low obliquity during glacial conditions (31.5–36.5 ka in MIS 3), and high obliquity during intermediate conditions (89–94 ka in MIS 5b).

According to our framework, the rising temperatures at MD11-3357 and MD11-3353 during the last two glacial terminations were associated with poleward shifts in the ACC fronts that led to an initial increase followed by a decrease in ΔSST (Figs. 2b and 3a), as the steepest part of the meridional SST profile moved first to a position sandwiched between the two sites and then to a position partially south of both sites (Supplementary Fig. 15). At the end of both terminations, ΔSST progressed to a lower range (Fig. 3a), signaling that the fronts are most poleward at the beginning of interglacials (Fig. 4d). There appears to be an offset between the progressions of ΔSST during the two glacial terminations (Fig. 3a), which suggests that the SST structure within the ACC may be subject to more variations than our framework assumes. Nevertheless, the similar shape of the ΔSST progression when plotted over EDC temperature during the two terminations argues that they experienced similar changes in ACC frontal positions (Figs. 3a and 4d).

At the end of Termination 1 and in the early Holocene, the lower reconstructed ΔSST suggests that the steepest part of the meridional SST profile was partially south of MD11-3353 and the ACC fronts reached as much as ~4° southward of the current position (Fig. 4d). This ACC position agrees with a more southward APF in the Kerguelen region reconstructed previously for this time period25, and is also consistent with the low opal flux observed at MD11-3353 during the last deglaciation and the early Holocene41 (Supplementary Note 13 and Supplementary Fig. 25). During the late Holocene, while Antarctic air temperature remained stable, the reconstructed ΔSST increased from ~6.5 °C to ~8 °C (Fig. 2), suggesting a gradual northward shift of the ACC fronts to place a greater portion of the steepest meridional SST transition between MD11-3353 and MD11-3357 (Fig. 4d). A northward ACC shift should correspond to a declining EDC temperature, yet the EDC temperature remained stable during this interval, resulting in a leftward trend that deviates from the linear relationship when the EDC temperature change is plotted over ACC latitude change (Fig. 5a). Here, we explore possible explanations for this deviation.

Fig. 5: EDC temperature change and atmospheric CO2 compared to temporal changes in the latitude range of the ACC.
figure 5

Gray circles represent interpolated a EDC temperature changes48 and b CO272 compared to changes in the latitudinal position of the ACC relative to today reconstructed from ΔSST between MD11-3353 and MD11-3357. Gray dashed line in (a) represents the best-fitting linear model between EDC temperature and ACC latitude. Gray dashed line in (b) represents a linear regression between atmospheric CO2 and reconstructed ACC latitude change. Filled symbols and lines correspond to the shaded intervals in Fig. 4. Red symbols and arrowed line represent the progression during the late Holocene from 6 ka to 1 ka. Yellow symbols and arrowed line represent the progression during MIS 5d from 116.5 ka to 111.5 ka. Navy symbols and arrowed line represent the progression during MIS 3 from 36.5 ka to 31.5 ka. Open green symbols and arrowed line represent the progression at MIS 5b from 94 ka to 89 ka when obliquity is at maxima. Increased deviation of data from the linear relationship during MIS 2 and MIS 3 in (a) may be due to errors in the reconstructed ACC latitude during millennial scale events which are poorly resolved in the TEXL86 SST records. Increased deviation of data from the linear relationship during MIS 2–4 in (b) may be due to stronger effects of iron fertilization in the SAZ on CO2 during these intervals.

The location of Kerguelen Plateau in the flow path of the ACC (Fig. 2) may have made the fronts more prone to meander upstream and downstream of the plateau55. The modern APF to the west of the Kerguelen Plateau is shown to seasonally meander by as much as 4° because of interaction with local topography57. The large meander of the APF path may have caused sporadic changes in the width of the ACC, which may contribute to higher ΔSST between MD11-3357 and MD11-3353. The southern Kerguelen bathymetry (Fig. 2) may also help to explain the Holocene deviation from the relationship between EDC temperature and ACC latitude. Civel-Mazens et al.25 suggested that during the warmer interglacials such as MIS 5e and MIS 9, the ACC is pushed poleward enough that the APF persistently passes through Fawn Trough, which is ~5° southward of the current APF, while the APF only briefly passed through Fawn Trough at the end of the last deglaciation and returned northward to its path north of the Kerguelen Plateau over the later part of Holocene because of the relatively mild climate. The authors also suggested a similar APF position for MIS 7, which is interpreted to be another more moderate interglacial. These interpretations agree with the idea that the bathymetric thresholds may be persistently surpassed in warmer interglacials such as MIS 5e, whereas during the intermediate interglacials such as the Holocene, this threshold was overcome only temporarily by the APF. Thus, the northward shift of the ACC fronts within the Holocene may be the consequence of a failed attempt to cross the bathymetric threshold.

Another possibility is that Antarctic Ocean surface water temperature is decoupled from EDC temperature during the Holocene. The decrease in summer insolation at 65°N in the last 10 ka is much smaller compared to that of 115–125 ka, and its cooling effect through the albedo feedback is weak, mostly constrained to the extratropical Northern Hemisphere58. The lowering obliquity during the Holocene decreases the insolation received at high latitudes, but it may lead to a relatively weak cooling effect at Antarctica’s inland ice core sites, as high albedo would result in little changes in net absorbed radiation. On the other hand, stronger cooling may occur at Antarctica’s continental margins and the surrounding Antarctic Ocean. Similar to the TEXL86-SST at MD11-3353, diatom-based SST records from the AZ in the Indian and Atlantic sector also show a decline during the Holocene49,59. SST reconstructions at different sites near the Western Antarctic Peninsula as well as the δD record at Taylor Dome also show cooling temperatures for the last 10 ka, tracking the decline in local insolation46. The cooling of the Antarctic Ocean would correspond with a northward shift of the ACC, as predicted by our linear model between Antarctic climate and ACC latitude.

A related explanation, which will be discussed further below, involves the role of obliquity in Southern Ocean upwelling. Declining obliquity over the Holocene is expected to have strengthened the SWW and thus northward Ekman surface water transport and upwelling in the AZ60,61, consistent with diatom-bound nitrogen isotope reconstructions12,62 (Fig. 4f, g). Independent of any change in the meridional position of the SWW, this would have pushed surface isotherms equatorward (i.e., increasing the meridional tilt of isopycnals)63. Thus, decoupling of ACC frontal position from Antarctic air temperature may be a fingerprint of obliquity-driven changes in upwelling.

Controls on ACC front latitudes

As a result of the back-calculation based on the best-fitting linear model, the temporal evolution of the ACC position deduced from ΔSST is generally correlating with changes in both ice core air temperature48 and compiled Southern Ocean SSTs52 (Fig. 4a, c, d). Our results provide quantitative evidence for the connection between Antarctic climate and the position of ACC flow path in the Indian sector of the Southern Ocean over glacial cycles, which allows identification of specific mechanisms that drive changes in the SWW in the Indian sector during climate transitions. ACC shifts during the last glacial cycle reconstructed in the Pacific and Atlantic sector have a similar glacial-interglacial trend as in the Indian sector, but the extents of the shifts appear to be different26. It is proposed that in the Pacific Southern Ocean, tropical forcing of the SWW prevails over mid-to-high latitude forcing, suggesting heterogeneity in the changes of the SWW in different Southern Ocean sectors over orbital timescales64. Thus, the interpretations of frontal latitude change in the Kerguelen region likely reflect the response of the ACC flow in the Indian Ocean, and the mechanisms identified in the following discussions may not be applicable to other sectors, while this quantitative method opens the door for future investigation of sector-specific ACC dynamics.

Variations in the latitude of SWW and the strong SST gradient that defines the ACC are found to be strongly coupled in modern oceanographic observations17,53 (Fig. 1). Applying these relationships to frontal shifts in the Indian Southern Ocean over the last glacial cycle, the northward displacements of the ACC during MIS 5d, MIS 4, and MIS 2 argue for coincident northward (equatorward) shifts of the SWW. These intervals are associated with global cooling driven by changes in Earth’s orbital parameters, which, according to global climate model simulations, should have driven an equatorward shift of the westerly winds as part of a cooling-driven contraction of the Hadley cell60,65. However, the cooling at MIS 5d does not bring global temperature or EDC temperature to LGM levels48,66, while the coinciding equatorward shift of the ACC does (Fig. 4c, d), which results in an upward trend that slightly deviates from the linear relationship between EDC temperature and ACC latitude (Fig. 5a). Thus, some additional driver is needed to explain the extent of ACC equatorward shift at MIS 5d.

As introduced previously, another important factor in the mid-latitude westerly winds is Earth’s obliquity61. As a result of the linear correlation between ACC latitude and Antarctic climate and the strong 40 kyr component in the EDC temperature record, the reconstructed ACC latitude over the last glacial cycle partially covaries with the obliquity cycle, with a more northward position associated with low obliquity (Fig. 4d, e). However, obliquity seems to be playing an additional role through its impact on SWW wind intensity, affecting upwelling in the Antarctic Zone and northward transport of cold water. In global climate model simulations, lower obliquity can enhance the mid-latitude temperature gradient, which in turn drives intensification of the mid-latitude westerly winds60,61,67,68. In model simulations in which changes in eddy fluxes only partially cancel changes in wind-driven Ekman flow, an increase in wind strength would enhance the residual circulation of the Southern Ocean upper cell and increase the transport of cold water northward, leading to surface cooling to the north of the AZ63, corresponding with a northward frontal shift. When we compare the progression of EDC temperature with the reconstructed latitudinal migration of the ACC in the Indian Southern Ocean, MIS 5d and the late Holocene, which are characterized by low or declining obliquity, fall to the left of the linear relationship (Fig. 5a), indicating greater northward ACC shift than predicted by EDC temperature change alone. This pattern becomes evident when comparing to MIS 5b, another relatively well-constrained period in our record that is associated with cooling and northward ACC shift but high obliquity, which plots along the linear relationship between EDC temperature and the latitudinal position of the ACC. The difference in the EDC temperature-ACC location relationship between these time intervals suggests that low obliquity can contribute to northward ACC migration by enhancing Antarctic upwelling. Unlike during the late Holocene when the effect of obliquity sustained strong upwelling in the AZ, during MIS 5d, this enhancement in upwelling by obliquity is a secondary effect which is masked by the dominating impact of equatorward ACC shift on the general Southern Ocean overturning circulation that acts to reduce surface-deep exchange. However, similar patterns in the deviation from the observed relationships between EDC temperature and ACC latitude, and between ACC latitude and atmospheric CO2 during MIS 5d and the late Holocene, point to a uniform link to obliquity, which will be discussed in detail next.

Changes in upwelling and CO2 outgassing

Changes in the latitude range of the ACC and the SWW may have important consequences for the release of carbon from the deep ocean through its communication with the atmosphere in the Southern Ocean14. A northward shift in the SWW would decrease upwelling of deep water in the upper cell of the overturning circulation in the Southern Ocean13, which would promote carbon storage through a combination of mechanisms9. In addition, decreased upwelling of the relatively warmer Circumpolar Deep Water under more equatorward SWW would promote the expansion of quasi-permanent sea ice and shoal the density interface between the lower and upper cells of the Southern Ocean overturning69, decreasing the deep turbulent mixing and isolate Antarctic Bottom Water from the other water masses in the ocean interior, maintaining CO2 in the deep ocean70,71. Our reconstructed temporal changes in the latitudinal position of the ACC shows a generally linear relationship with atmospheric CO272 (Fig. 5b). There is more scatter in the data of MIS 2-4 (towards bottom left in Fig. 5b), which may be due to effects of increased iron-fertilization in the SAZ on atmospheric CO2 during these intervals that may not strictly correspond with ACC latitude change5,12.

Two discrepancies between our reconstructed frontal latitude and the atmospheric CO2 record are worth noting. Specifically, the fronts shifted strongly northward at MIS 5d while CO2 declined only modestly, and the fronts shifted northward through the late Holocene while CO2 rose (Figs. 4a, d and 5b). These discrepancies can be explained by the intensity of AZ upwelling (as reconstructed with diatom-bound δ15N12; Fig. 4g), which does not have a unique relationship with the mean latitude of the westerly winds. As previously discussed, the low obliquity at MIS 5d and the declining obliquity during the late Holocene should have increased the temperature gradient between the middle and high latitudes, which is supported by the increase in temperature difference between moisture source and ice core site of Vostok73. This increase in temperature gradient should have intensified the SWW, compensating for the equatorward displacement of the winds so as to maintain and/or increase upwelling and thus permit CO2 outgassing from the AZ12. The progression of CO2 level compared with that of ACC latitude during MIS 5d and the late Holocene with low(ering) obliquity falls towards the left of the linear trend, in contrast to MIS 5b with high obliquity that closely follows the linear trend (Fig. 5b), suggesting less CO2 drawdown than predicted based on ACC latitude change, supporting a compensation from intensified SWW and strengthened upwelling. In addition, as described above, the strong SWW-driven (Ekman) transport of AZ surface waters northward driven by low(ering) obliquity at MIS 5d and the late Holocene may have worked to push surface isotherms northward (Fig. 5a). Together, these processes can explain the otherwise anomalous conditions of MIS 5d and the late Holocene of a northward frontal position (Fig. 4d), stronger AZ upwelling than expected from ACC latitude (Fig. 4g), and relatively high atmospheric CO2 (Fig. 4a, b).

Two potential issues with this mechanism are noted here. First, the compiled data (Fig. 4) suggest that the role of obliquity on AZ upwelling was muted during the coldest climates of the last glacial cycle, as there is no evident deviation in the progression of Antarctic temperature or atmospheric CO2 compared to ACC latitude during a cooling event at the end of MIS 3 when obliquity was low (Fig. 5). This may be due to greater sensitivity of AZ upwelling to changes in obliquity-driven SWW intensity when the SWW is more poleward. Another issue points to the stronger deviation during the late Holocene compared to MIS 5d, despite relatively higher obliquity of the former. In other words, the diatom-bound N isotope upwelling proxy and atmospheric CO2 suggest that the enhancement of wind strength during the late Holocene was able to overcome the impact of northward ACC latitude to drive a trend of stronger AZ upwelling. Why? It is possible that the effect of obliquity on the strength of the SWW and subsequent effects on AZ upwelling and CO2 outgassing is dependent on some other yet unclear climate components, which might arise in future studies by comparing similar low-obliquity intervals in several glacial-interglacial cycles.

Enabled by the application of the same paleothermometry method across a large latitudinal difference in the Southern Ocean and a framework imitating the impact of ACC migrations on Southern Ocean SST, the approach taken here provides a quantitative, temporally continuous view of how the boundary between the thermally contrasting Antarctic and subtropical surface waters has migrated over a full glacial cycle in the Indian Southern Ocean. The results suggest that cooling was a dominant driver of the equatorward shift of the SWW during the ice ages, with changes in the wind strength driven by obliquity also contributing to reconstructed changes. Through its effects on Southern Ocean upwelling and related vertical circulation, the equatorward shift of the SWW during ice ages should have enhanced the storage of carbon in the deep ocean, helping to explain the lower atmospheric CO2 levels of the ice ages. During MIS 5d and the late Holocene, low obliquity and thus an increased mid-to-high latitude temperature gradient may have strengthened the westerly wind-driven AZ upwelling, compensating for the equatorward SWW location so as to sustain the upwelling in the AZ and thus maintaining/raising atmospheric CO212. At the same time, strong Ekman upwelling forces the ACC northward during these particular time intervals. Thus, the effects of obliquity may explain the deviation of MIS 5d and the late Holocene from the overarching tendency for a more northward ACC to be associated with Antarctic cooling, reduced AZ upwelling, and lower atmospheric CO2 over the last glacial cycle.

The quantitative framework employed in this study is a rather coarse representation of the surface ocean temperature transition across the ACC and has multiple underlying assumptions. However, this approach is diagnostic and allows us to identify a robust connection between ACC latitude and climate in the Indian Southern Ocean, and to investigate its influence on atmospheric CO2. With generation of SST records of higher resolution and refinements in the parameterization of the quantitative framework, this approach promises to provide multiple constraints on the climatic controls on ACC frontal location and circulation in different sectors of the Southern Ocean.


Study area

Marine sediment cores MD11-3353 (50.57°S, 68.39°E, 1568 m water depth) and MD11-3357 (44.68°S, 80.43°E, 3349 m water depth) were recovered by the R.V. Marion Dufresne in 2011 around the Kerguelen Archipelago in the southeast Indian Ocean (Fig. 1). Both cores were recently described elsewhere12,41,62. MD11-3353 is located slightly south of the modern Antarctic Polar Front (APF), whereas MD11-3357 is located in the Subantarctic Zone (SAZ), north of the Subantarctic Front (SAF). The Kerguelen Plateau exerts a strong influence on the ACC flow such that 60% of the current is deflected northwards of the Plateau, followed by a southeastward flow east of the plateau, and the integrated ACC flow is estimated to reach 150 Sv around the Kerguelen Plateau74.

Age models

This study relies on previously published age models for all cores12,41. Briefly, the age model for MD11-3357 relies on graphical alignment of the GDGT-based SST reconstruction with the EDC deuterium record41. The original age model for MD11-335341, aligning GDGT-based SST with the EDC deuterium record, has been updated by adjusting the youngest and oldest tie points and adding two tie points in MIS 3 based on diatom-bound δ15Ν correlation with the diatom-bound δ15N record of MD12-339412.

SST reconstructions

GDGT measurements were performed at the Max Planck Institute for Chemistry (MPIC) following the method proposed in ref. 75. Briefly, the GDGT-fraction was extracted from 3–5 g of freeze-dried sediment and simultaneously separated from other organic biomarkers using an Accelerated Solvent Extractor (ASE 350) and analyzed with a high-pressure liquid chromatograph coupled to a single quadrupole mass spectrometer detector (HPLC-MS; Agilent 1260 Infinity)76. Temperature of the surface ocean was reconstructed using a revised TEXL86 calibration that linearly fits the global core-top TEXL8642 to World Ocean Atlas 200945 0–200 m integrated surface ocean temperature (Supplementary Note 1). Intra-laboratory standard TEXL86-SST error for replicate measurements of a standard sediment sample extracted in each batch of samples (n = 13) was 0.34 °C, similar to literature estimates44. We discuss the uncertainties in absolute SST reconstruction and ΔSST reconstruction by the updated calibration function in the Supplementary Note 3. We discuss potential contribution of non-thermal factors to the estimated TEXL86 temperatures in the Kerguelen region over the last glacial-interglacial cycle using a series of GDGT-based indices in the Supplementary Note 5. We provide an estimate of the uncertainty of the reconstructed ΔSST in Supplementary Note 6.

ΔSST calculation

To calculate past ΔSST, the data from different cores have been interpolated at a time grid of 2.5 kyr, which best resembles the initial resolution in both cores. ΔSST was then determined by subtraction:

$$\Delta {{{{{\rm{SST}}}}}}({{{{{\rm{t}}}}}}_{{{{{{\rm{x}}}}}}})={{{{{\rm{SST}}}}}}({{{{{{\rm{t}}}}}}}_{{{{{{\rm{x}}}}}}})_{{{{{{\rm{core}}}}}}1}-{{{{{\rm{SST}}}}}}({{{{{{\rm{t}}}}}}}_{{{{{{\rm{x}}}}}}})_{{{{{{\rm{core}}}}}}2}$$

with tx describing the same age point in the cores, core 1 being MD11-3357 and core 2 being MD11-3353.

Quantitative framework setup

The initial meridional SST profile is the zonally averaged annual mean temperature of 0–200 m depth of the region 68.5°E to 80.5°E, 34.5°S to 60.5°S from World Ocean Atlas 200945. The initial meridional SST profile is simplified to three segments: the Antarctic Zone (AZ) segment, the Polar Transition Zone (PTZ, i.e., the Polar Frontal Zone (PFZ) and the SAZ combined) segment, and the Subtropical Zone (STZ) segment (Supplementary Fig. 15). From higher to lower latitudes, the AZ-PTZ boundary (denoted \({{{{{\rm{lat}}}}}}1\)) and PTZ-STZ boundary (denoted \({{{{{\rm{lat}}}}}}2\)) are the latitudes with the largest increase and decrease in the slope of the meridional SST profile, respectively. These changes in slope represent the transition from the cold polar surface water mass towards the warm STZ surface water. The SST within each segment was then fitted to a linear line:

$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{AZ}}}}}}}({{{{{\rm{lat}}}}}})={{{{{{\rm{k}}}}}}}_{{{{{{\rm{AZ}}}}}}}* {{{{{\rm{lat}}}}}}+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{AZ}}}}}}},{{{{{\rm{lat}}}}}} \, < \, {{{{{\rm{lat}}}}}}1$$
$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{PTZ}}}}}}}({{{{{\rm{lat}}}}}})={{{{{{\rm{k}}}}}}}_{{{{{{\rm{PTZ}}}}}}}* {{{{{\rm{lat}}}}}}+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{PTZ}}}}}}},{{{{{\rm{lat}}}}}}1\, < \,{{{{{\rm{lat}}}}}}\, < \,{{{{{\rm{lat}}}}}}2$$
$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{STZ}}}}}}}({{{{{\rm{lat}}}}}})={{{{{{\rm{k}}}}}}}_{{{{{{\rm{STZ}}}}}}}* {{{{{\rm{lat}}}}}}+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{STZ}}}}}}},{{{{{\rm{lat}}}}}}\, > \,{{{{{\rm{lat}}}}}}2$$

Two parameters, \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}}\) and \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}}\), represent the maximum glacial-interglacial SST change (i.e., warmest SST minus coldest SST) in the two regions, respectively. EDC relative air temperatures were used as a reflection of Antarctic climate change. Temperature changes at EDC were transferred into different amounts of SST change in the AZ and the STZ due to polar amplification. For any given EDC temperature change at time \(t\), we assume that the SST of the AZ and STZ will increase/decrease a fraction of the maximum SST change of the zone, and we can get the SST lines in the AZ and the STZ at time \(t\) (Supplementary Fig. 15, with the constraint that the lowest SST is −2 °C, the freezing point of sea water, for the AZ):

$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{AZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{no}}}}}}\,{{{{{{\rm{shift}}}}}}}}= \, {{{{{{\rm{k}}}}}}}_{{{{{{\rm{AZ}}}}}}}* {{{{{\rm{lat}}}}}}+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{AZ}}}}}}}\\ +\frac{\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\left({{{{{\rm{t}}}}}}\right)}{\max \left(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\right)-\min (\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}})}* {{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}},\\ {{{{{\rm{lat}}}}}}\, < \,{{{{{\rm{lat}}}}}}1$$
$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{STZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}=\, {{{{{{\rm{k}}}}}}}_{{{{{{\rm{STZ}}}}}}}* {{{{{\rm{lat}}}}}}+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{STZ}}}}}}}\\ +\frac{\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\left({{{{{\rm{t}}}}}}\right)}{\max \left(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\right)-\min (\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}})}* {{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}},\\ {{{{{\rm{lat}}}}}}\, > \,{{{{{\rm{lat}}}}}}2$$

The new SST line of the PTZ segment at time \(t\) is a linear regression between the new SSTs at \({{{{{\rm{lat}}}}}}1\) and \({{{{{\rm{lat}}}}}}2\). (Supplementary Fig. 15):

$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{PTZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}= \frac{{{{{{{\rm{SST}}}}}}}_{{{{{{\rm{STZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}2\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}-{{{{{{\rm{SST}}}}}}}_{{{{{{\rm{AZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}1\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}}{{{{{{\rm{lat}}}}}}2-{{{{{\rm{lat}}}}}}1}* {{{{{\rm{lat}}}}}}+{{{{{{{\rm{m}}}}}}}^{{\prime} }}_{{{{{{\rm{PTZ}}}}}}},\\ {{{{{\rm{lat}}}}}}1\, < \, {{{{{\rm{lat}}}}}}\, < \,{{{{{\rm{lat}}}}}}2$$

We then assume that a change in Antarctic temperature leads to a latitudinal shift of all three SST lines, and the amount of shift is linearly related to the amount of EDC temperature change (note that the slopes of all three SST lines are the same as in the no-shift scenario):

$$\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})=a* \Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}({{{{{\rm{t}}}}}})+b(\Delta {{{{{\rm{lat}}}}}}\, > \, 0\,{{{{{\rm{represents}}}}}}\,{{{{{\rm{a}}}}}}\,{{{{{\rm{poleward}}}}}}\,{{{{{\rm{shift}}}}}})$$

The SST lines after the shift are:

$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{AZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{shift}}}}}}}=\, {{{{{{\rm{k}}}}}}}_{{{{{{\rm{AZ}}}}}}}* \left({{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}\left({{{{{\rm{t}}}}}}\right)\right)+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{AZ}}}}}}}\\ +\frac{\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\left({{{{{\rm{t}}}}}}\right)}{\max \left(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\right)-\min (\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}})}\\ * {{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}},{{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})\, < \,{{{{{\rm{lat}}}}}}1+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})$$
$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{STZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{shift}}}}}}}=\, {{{{{{\rm{k}}}}}}}_{{{{{{\rm{STZ}}}}}}}* \left({{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}\left({{{{{\rm{t}}}}}}\right)\right)+{{{{{{\rm{m}}}}}}}_{{{{{{\rm{STZ}}}}}}}\\ +\frac{\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\left({{{{{\rm{t}}}}}}\right)}{\max \left(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\right)-\min (\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}})}\\ * {{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}},{{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})\, > \,{{{{{\rm{lat}}}}}}2+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})$$
$${{{{{{\rm{SST}}}}}}}_{{{{{{\rm{PTZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}\right)}_{{{{{{\rm{shift}}}}}}} =\, \frac{{{{{{{\rm{SST}}}}}}}_{{{{{{\rm{STZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}2\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}-{{{{{{\rm{SST}}}}}}}_{{{{{{\rm{AZ}}}}}}}{\left({{{{{\rm{t}}}}}},{{{{{\rm{lat}}}}}}1\right)}_{{{{{{\rm{no}}}}}}\,{{{{{\rm{shift}}}}}}}}{{{{{{\rm{lat}}}}}}2-{{{{{\rm{lat}}}}}}1}* \left({{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})\right)\\ +{{{{{{{\rm{m}}}}}}}^{{\prime} }}_{{{{{{\rm{PTZ}}}}}}},{{{{{\rm{lat}}}}}}1+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})\, < \,\left({{{{{\rm{lat}}}}}}+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})\right)\, < \,{{{{{\rm{lat}}}}}}2+\Delta {{{{{\rm{lat}}}}}}({{{{{\rm{t}}}}}})$$

Determination of the optimal parameters

To tune our model to match the reconstructed ΔSST, we need to determine the four variables: the maximum range of SST change in the AZ and STZ, i.e., \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}}\) and \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}}\), and the slope and intercept of the linear model between \(\Delta {{{{{\rm{lat}}}}}}\) and \(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\), i.e., \({{{{{\rm{a}}}}}}\) and \({{{{{\rm{b}}}}}}\). The sensitivity analysis (Supplementary Note 8) shows that \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}}\) and \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}}\) have limited impact on when the maximum ΔSST occurs, thus we tentatively choose 6 °C to be \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}}\) and 2.5 °C to be \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}}\), based on glacial temperature reconstructions77.

The sensitivity analysis shows that with realistic values for \(a\), the maximum ΔSST between the two sites would occur when the ACC is ~2° southward of its current position within the observed maximum ΔSST range (Supplementary Fig. 17). The maximum TEXL86-reconstructed ΔSST occurs when the temperature change at EDC is around −3 °C to −5 °C, and the sensitivity analysis shows that this only agrees with conditions of b > 0 (Supplementary Fig. 17), which means that the ACC should be southward of its current position when EDC temperature is at the current level, inconsistent with the frontal locations inferred from the modern meridional SST profile. This inconsistency leads us to consider the possibility that the modern ACC latitude is an outlier compared to the relationship between frontal movement and EDC temperature from MIS 6 to MIS 2 and we should consider a new initial meridional SST profile.

A straight-forward option is to choose the scenario when the steep PTZ segment is optimally sandwiched in between the core’s locations as the new initial meridional SST profile. This would also be the scenario when ΔSST is the largest. According to the TEXL86-reconstructed data, this scenario would be when the temperature change at EDC is around −4 °C and the ACC is around 2° southward of its current position. However, the exact meridional SST profile of this time is unknown. According to the TEXL86-reconstructed data, when the EDC temperature change was between −3 °C and −5 °C, the frontal shift placed the steep PTZ segment between MD11-3353 and MD11-3357, and the mean value of the ΔSST is ~7.7 °C, which is similar to the SST difference between the two endpoints of the PFZ segment in the current WOA meridional SST profile, which is ~8 °C. Thus, it is a fair estimate that the new initial scenario is the current meridional SST profile shifted 2° southward, at the time when the EDC temperature change was −4 °C. The actual meridional SST profile may be higher or lower than our assumed profile, but for the ΔSST, the difference in the absolute value will be canceled off. We define \(\Delta {{{{{\rm{lat}}}}}}^{\prime}\) as the ACC latitude relative to the new initial SST profile, and the relationship between \(\Delta {{{{{\rm{lat}}}}}}\) and \(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}\) becomes:

$$\Delta {{{{{\rm{la}}}}}}{{{{{{\rm{t}}}}}}}^{{\prime} }={\Delta {{{{{\rm{lat}}}}}}-2=a}^{{\prime} }* \Delta {{{{{{{\rm{T}}}}}}}^{{\prime} }}_{{{{{{\rm{EDC}}}}}}}+{b}^{{\prime} }={a}^{{\prime} }* [\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}-\left(-4\right)]+b^{\prime}$$

We take \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{AZ}}}}}}}\) = 6 °C, and \({{{{{{\rm{range}}}}}}}_{{{{{{\rm{STZ}}}}}}}=2.5\)°C and use sequential least squares programming (SLSQP) optimizer to find \(a^{\prime}\) within [0, +inf] and \(b^{\prime}\) within [−inf, +inf] that best fit the reconstructed data. The resulting \(a^{\prime}\) and \(b^{\prime}\) with realistic values that produce the smallest difference between the modeled results and the actual data is 0.58 and −0.12, respectively (Supplementary Fig. 19):

$$\begin{array}{c}\Delta {{{{{\rm{la}}}}}}{{{{{{\rm{t}}}}}}}^{{\prime} }={\Delta {{{{{\rm{lat}}}}}}-2=a}^{{\prime} }* \Delta {{{{{{{\rm{T}}}}}}}^{{\prime} }}_{{{{{{\rm{EDC}}}}}}}+{b}^{{\prime} }={a}^{{\prime} }* [\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}-\left(-4\right)]+b^{\prime} \\ \Delta {{{{{\rm{lat}}}}}}-2=0.58* \Delta {{{{{{{\rm{T}}}}}}}^{{\prime} }}_{{{{{{\rm{EDC}}}}}}}-0.12=0.58* \left[\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}-\left(-4\right)\right]-0.12\\ \Delta {{{{{\rm{lat}}}}}}=0.58* \Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}+4.20\end{array}$$

With this best-fitting pair of \(a^{\prime}\) and \(b^{\prime}\), the ACC shifts southward(northward) by ~0.58° with every °C of EDC warming(cooling). When EDC temperature change is 0 relative to the modern (\(\Delta {{{{{{\rm{T}}}}}}}_{{{{{{\rm{EDC}}}}}}}=0\)), the ACC is 4.20° south of its current position (\(\Delta {{{{{\rm{lat}}}}}}=4.20\)).

Reconstruction of ACC latitude changes in the past 150 kyr

Based on the relationship between the ΔSST of sites MD11-3357 and MD11-3353 and the change of ACC latitude inferred from our framework, we use the reconstructed TEXL86-SST at the two sites to reconstruct the relative frontal positions of the past 150 kyr. Because the relationship is non-monotonic, within the relevant range, each ΔSST corresponds to two ACC positions, and we select the position that makes more sense for the corresponding EDC temperature in our optimized model: If the EDC temperature is lower than −4 °C, we choose the latitude that is more southward than 2° (the upper part of the curve in Supplementary Fig. 21). When ΔSST is higher than 6.7 °C and lower than 7.7 °C, the lower limit of the confidence interval for reconstructed ACC that is more southward than 2° (i.e., the upper part of the curve) is assumed to deviate the same amount from the reconstructed ACC latitude as the upper limit, and the upper limit of the confidence interval for the lower part of the curve is assumed to deviate the same amount from the reconstructed ACC latitude as the lower limit. When ΔSST is higher than 7.7 °C, the reconstructed ACC latitude is taken to be the mean of the upper and lower limit and is represented by the dashed line in Fig. 4d.