Contributions of biological and physical dynamics to deglacial CO₂ release from the polar Southern Ocean

Abstract

As a critical region regulating air-sea gas exchanges, the polar Southern Ocean has important implications for deglacial atmospheric CO₂ rises. However, proxy data evidence is sparse to evaluate the respective roles of Southern Ocean biological and physical dynamics in affecting past air-sea CO₂ exchanges due to longstanding challenges in obtaining carbonate materials to reconstruct surface conditions in this region. Here, we circumvent these challenges by constraining polar Southern Ocean surface-water conditions based on preformed deep-water properties derived from paired carbonate ion-phosphate-oxygenation reconstructions during the last deglaciation. We show that polar Southern Ocean carbon losses coincided with increased deep-ocean preformed nutrient concentrations, highlighting reduced biological carbon utilization as a key process for deglacial CO₂ outgassing. By comparing total carbon losses with those attributable to biological processes, we further show that enhanced physically-driven air-sea gas exchanges in the polar Southern Ocean strongly drove CO₂ outgassing towards the end of the last deglaciation.

Introduction

Ice core measurements show rapid atmospheric CO₂ increases during the Late Pleistocene glacial-interglacial transitions^1,2,3. These deglacial atmospheric CO₂ increases are thought to be linked to strengthened release of carbon previously stored in the deep ocean through the Polar Antarctic Zone (PAZ)^4,5,6. Climate models suggest that changes in the PAZ enhanced the release of carbon previously sequestered via both biological and physical processes and thus raised atmospheric CO₂ during deglaciations^{7,8,9,10,11,12,13}. However, mechanisms controlling past atmospheric CO₂ fluctuations remain elusive due to the lack of paleoclimate proxy records in the PAZ. This presents as an obstacle to confidently link PAZ processes to changes in deep-ocean carbon storage and atmospheric CO₂. Given the critical role of the Southern Ocean in governing atmospheric CO₂ on various timescales in the past and future^4,14,15, it is imperative to fully evaluate the respective roles of PAZ biological and physical processes in affecting atmospheric CO₂ using marine paleoclimate archives. Nevertheless, a longstanding challenge to investigate the PAZ is the difficulty to obtain sufficient carbonate materials for paleoclimate reconstructions.

Here, we circumvent this challenge by constraining PAZ conditions using two quasi-conservative properties of deep waters^7,15,16: PO₄* (refs. ^16,17,18) and air-sea exchange signature of carbonate ion concentration ([CO₃^2-]_as)^19,20,21,22. Following deep water formation, signatures of surface source waters can be preserved as “preformed” properties that are quasi-conservative in the ocean interior. PO₄*, derived from concentrations of phosphate and oxygen ([PO₄^3-] and [O₂], respectively), has long been employed to infer the biological nutrient utilization efficiency and surface-water oxygen saturation in deep-water formation regions (Methods)^16,17,18. PO₄* is quasi-conservative because phosphate regeneration is stoichiometrically linked to oxygen consumption during biogenic matter decomposition in the ocean interior. For a given water mass, higher PO₄* largely indicates less efficient nutrient utilization^7,16,17,23. Recently, [CO₃^2-]_as has been developed to constrain CO₂ exchanges between surface waters and the atmosphere^19,20,21,22. [CO₃^2-]_as is quasi-conservative in the ocean interior and represents changes in seawater carbonate ion concentration ([CO₃^2-]) due to the net air-sea CO₂ exchange when source waters leave the surface ocean, after correcting for anthropogenic carbon influences^19,20. In addition to air-sea CO₂ exchanges in source-water regions, the distribution of deep-water [CO₃^2-] is driven by changes in physical conditions in the ocean (salinity, temperature, and pressure), remineralization of sinking organic matter, and dissolution of carbonate. To reveal the effect of air-sea exchanges on [CO₃^2-], calculation of [CO₃^2-]_as accounts for [CO₃^2-] changes driven by (1) physical conditions, (2) redistributions of dissolved inorganic carbon (DIC) and alkalinity related to regeneration of biogenic organic matter and carbonate, which can be estimated by [PO₄^3-] variations, and (3) when considering temporal evolutions, global ocean DIC and alkalinity changes due to imbalances between riverine inputs and marine carbonate burial (Methods). Higher deep-water [CO₃^2-]_as values reflect more net CO₂ losses through air-sea gas exchanges in source regions of the deep water^19,20.

Seawater PO₄* and [CO₃^2-]_as in the deep ocean is largely determined by mixing between southern sourced waters (SSWs) formed in the Southern Ocean and northern sourced waters (NSWs) formed in the North Atlantic (Fig. 1). In the preindustrial ocean, SSWs have higher PO₄* than NSWs, reflecting less efficient nutrient utilization in the Southern Ocean^7,16,17. Preindustrial SSWs have higher [CO₃^2-]_as than NSWs because CO₂ tends to be released in the PAZ due to upwelling of high-DIC deep waters and inefficient biological utilization of nutrients and carbon^4,15,22. Consequently, SSWs are less efficient to sequester atmospheric CO₂ than NSWs¹⁹. Given known water-mass mixing proportions, PO₄* and [CO₃^2-]_as reconstructed in the deep ocean away from polar regions can be used to infer water-mass endmember compositions and thereby surface conditions in deep-water formation regions. By contrast, nonconservative tracers such as [PO₄^3-], [CO₃^2-], and [O₂] can vary substantially due to organic matter respiration within the ocean interior. The advantage of using PO₄* and [CO₃^2-]_as is illustrated by preindustrial ocean hydrography. For example, deep waters in the Pacific show large meridional gradients in [PO₄^3-], [CO₃^2-], and [O₂], largely due to biogenic matter respiration on their northward transport route (Fig. 1 and Supplementary Fig. 1). By contrast, PO₄* and [CO₃^2-]_as in this ocean basin display nearly stable values, reflecting mixing of NSWs and SSWs at relatively fixed proportions (Fig. 1 and Supplementary Fig. 1).

Fig. 1: Preindustrial ocean biogeochemical properties.

a [CO₃^2-]; (b), [PO₄^3-]; (c), [O₂]; (d), [CO₃^2-]_as; (e), PO₄*; (f), Hydrographic sites used to generate transect profiles in (a–e) where the B-C distance is scaled down to better show meridional spans of the Atlantic (A-B) and Pacific (C-D). Note different colour shading scales in a and d, and in b and e. Red circles in (a–f) show the location of site MD97-2106. Data from GLODAPv2^61,62 are used to generate these transect profiles. Preindustrial DIC, derived by removing the anthropogenic component carbon from the total DIC^61,62, are used to calculate [CO₃^2-] and [CO₃^2-]_as. Deep-water [CO₃^2-], [PO₄^3-], and [O₂] (a–c) are non-conservative and affected by biogenic matter respiration, which would complicate inferring source water conditions base on these properties. By contrast, [CO₃^2-]_as and PO₄* in the ocean interior (d, e) are quasi-conservative^{16,17,19,20,21,22}, largely determined by the endmember values of northern sourced waters (NSWs), southern sourced waters (SSWs), and their mixing proportions (see Supplementary Fig. 1 for more details).

It is worth noting that PO₄* and [CO₃^2-]_as are related to different aspects of the marine carbon cycle. While biologically-driven air-sea CO₂ exchange would be accompanied by PO₄* changes, purely physically-driven CO₂ outgassing is largely independent of PO₄*. Seawater [CO₃^2-]_as changes are not tied to any specific mechanisms but the integrate net CO₂ air-sea exchange effects from both biological and physical processes. Therefore, combinational use of PO₄* and [CO₃^2-]_as may allow for distinguishing the respective roles of biological and physical processes in controlling atmospheric CO₂ changes.

In this study, we reconstruct deep-water PO₄* and [CO₃^2-]_as during the last deglaciation (18.0–11.7 ka) using sediment core MD97-2106 (45.15°S, 146.28°E, 3310 m water depth) from the Southwest Pacific (Fig. 1). Based on previous work²³, deep waters at site MD97-2106 are composed of about 30% NSWs and 70% SSWs in the preindustrial ocean (Methods). Due to the dominant influence from SSWs, our core is ideal to constrain preformed conditions of the PAZ surface waters, albeit possible past changes in NSW-SSW mixing ratio must also be considered. We reconstruct deep-water [CO₃^2-] from B/Ca in benthic foraminifera²⁴, [PO₄^3-] from Cd/Ca in benthic foraminifera^25,26, and [O₂] from the carbon isotope gradient between epifaunal and deep infaunal benthic foraminifera²⁷ (Fig. 2 and Supplementary Fig. 2; Methods). Deep-water PO₄* is derived from [PO₄^3-] and [O₂] (refs. ^16,17), and [CO₃^2-]_as is calculated using [CO₃^2-], [PO₄^3-], physical conditions, and modelled global alkalinity changes¹⁹ (Fig. 3; Methods). These two preformed tracers were derived only when underlying proxy reconstructions were available from the same sediment depths. The fully propagated average uncertainties of PO₄* and [CO₃^2-]_as are 0.15 and 7.7 µmol/kg (1σ), respectively, and uncertainties on derived properties are given at 1σ throughout this work. The chronology of our core during the last deglaciation is constrained by 8 planktic radiocarbon dates and 4 age tie-points to Antarctic temperature as previously reported^28,29 (Fig. 2a and Supplementary Fig. 3). See Methods for reconstruction details.

Fig. 2: Deglacial reconstructions at site MD97-2106.

a Sea surface temperature (SST)²⁸. b EPICA Dome C (EDC) δD, a proxy for Antarctic temperature⁷². Triangles at the bottom are age tie points based on SST at site MD97-2106 and EDC δD, and crosses represent ¹⁴C dates^28,29. c Deep-water [CO₃^2-]; (d) Deep-water [O₂]; (e) Deep-water [PO₄^3-]. In (c–e) curves show LOESS smoothed probability maximum trends with envelopes representing ±1σ error ranges including uncertainties from analytical measurements, calibrations, and the age model. In (c–e), empty circles with error bars on the y-axes show the averages and ±1 standard deviations for the late Holocene data derived from core-top sediment samples. Grey vertical shadings highlight the Younger Dryas (YD) and Heinrich Stadial 1 (HS1), which are interrupted by the Antarctic Cold Reversal (ACR). The vertical dashed line marks the boundary between the early and late stages of HS1.

Fig. 3: Deriving PO₄* and [CO₃^2-]_as at site MD97-2106.

Upper panel shows changes in [PO₄^3-] (a) and [O₂]/175 (b) relative to the LGM averages. PO₄* (c) is determined by the sum of [PO₄^3-] and [O₂]/175. Lower panel shows reconstructed [CO₃^2-] (d) alongside expected changes in [CO₃^2-] relative to the LGM values (e), due to temperature-salinity-pressure variations (grey curve), DIC-alkalinity redistributions linked to [PO₄^3-] variations (green curve), and temporal global ocean alkalinity-DIC changes linked to CaCO₃ input/output imbalance (orange curve). All curves shown in (e) assume no air-sea CO₂ exchange. f calculated [CO₃^2-]_as. In (c–f) empty circles with error bars on the y-axes show the averages and ±1 standard deviations for the late Holocene data. Envelopes associated with curves represent ±1σ error ranges incorporating uncertainties from analytical measurements, calibrations, and the age model. The deglacial PO₄* pattern is dominantly driven by [O₂] changes, while millennial-timescale [CO₃^2-]_as variabilities are mainly driven by changes in [CO₃^2-] with secondary contributions from DIC-alkalinity variations linked to [PO₄^3-] fluctuations. Grey vertical shadings highlight the Younger Dryas (YD) and Heinrich Stadial 1 (HS1), which are interrupted by the Antarctic Cold Reversal (ACR). The vertical dashed line marks the boundary between the early and late stages of HS1.

Results

Increased PAZ air-sea CO₂ sequestration at the Last Glacial Maximum

Figure 2 shows reconstructed deep-water [PO₄^3-], [O₂], and [CO₃^2-] during the last deglaciation and their late Holocene (LH; 4.2–0 ka) averages (Supplementary Data 1). From the Last Glacial Maximum (LGM; 18–22 ka) to the LH, our reconstructions show that deep-water [PO₄^3-] declined by 0.10±0.04 µmol/kg (aggregated 1 standard deviation of two compared periods), and [O₂] increased by 75±21 µmol/kg, which is similar to previous records³⁰ (Supplementary Fig. 4). Combining [PO₄^3-] and [O₂], the calculated PO₄* shows an increase by 0.3±0.1 µmol/kg from the LGM to the LH (Fig. 2). During the same time interval, deep-water [CO₃^2-] at our site increased by 16±6 µmol/kg (Fig. 2). In the absence of CO₂ exchanges, warmer temperature, lower salinity, and deeper water depth together would lower [CO₃^2-] at our site by ~2 µmol/kg during the LH compared to the LGM (Fig. 3). Also, assuming no CO₂ exchanges, DIC and alkalinity decreases caused by regeneration of biogenic organic matter and carbonate that are linked to the [PO₄^3-] decrease of 0.10±0.04 µmol/kg would raise [CO₃^2-] by 5±2 µmol/kg from the LGM to the LH (Fig. 3). Global ocean DIC and alkalinity declines associated with CaCO₃ input/output imbalances would lower [CO₃^2-] by 26 µmol/kg (Fig. 3). Because the magnitude of the global alkalinity change cannot yet be reconstructed by proxies, we here rely on model simulations to calculate its effect on [CO₃^2-]_as³¹. However, different choices of modelled deglacial glacial alkalinity change only marginally affects the structure of the deglacial [CO₃^2-]_as changes (Supplementary Fig. 5). The offset between the reconstructed [CO₃^2-] change and the expected [CO₃^2-] changes without air-sea CO₂ exchange is attributed to air-sea CO₂ exchange signals, that is, [CO₃^2-]_as. Based on our calculations, we derive an LGM-to-LH [CO₃^2-]_as increase of 39±6 µmol/kg. Past changes in stoichiometry compositions of remineralized biogenic matter would introduce uncertainties in our calculated PO₄* and [CO₃^2-]_as, but they minimally affect our conclusion as shown by sensitivity tests (Supplementary Figs. 5, 6).

To infer LGM SSW PO₄* and [CO₃^2-]_as from reconstructions at site MD97-2106, SSW-NSW mixing ratios (represented by SSW% and NSW% hereafter; SSW% + NSW% = 100%) at our site and the LGM NSW endmember values need to be constrained. In the preindustrial ocean, SSW% at site MD97-2106 is about 70%, based on PO₄*of 1.36 µmol/kg at our site with SSW and NSW PO₄* endmember values being 1.64±0.06 and 0.73±0.06 µmol/kg, respectively (Fig. 4; Table 1). The preindustrial [CO₃^2-]_as of 6.7 µmol/kg at our site is consistent with 70% SSWs with [CO₃^2-]_as of 10±3 µmol/kg and 30% NSWs with [CO₃^2-]_as of -17±5 µmol/kg (Fig. 4, Table 1). During the LGM, SSW% in the deep South Pacific was higher than the LH as indicated by neodymium isotopes (ε_Nd) records^32,33, due to shoaling of the upper limb of the global overturning circulation^15,34,35,36. We thus assume the LGM SSW% at our site to be 80%. LGM NSW PO₄* has not been reconstructed based on proxies but is expected to be less variable than the LGM SSW PO₄* (refs. ^7,8,15,37). We assume the LGM NSW PO₄* to be 0.58±0.06 µmol/kg, which is 80% of the modern level, following ref. ³⁷. LGM NSW [CO₃^2-]_as is inferred to be -43±5 µmol/kg from a reconstruction in the North Atlantic (Supplementary Fig. 7). Considering the above SSW% and NSW endmember values along with our reconstructions at site MD97-2106, the LGM PO₄* and [CO₃^2-]_as of SSWs are estimated to be 1.18±0.13 and -34±10 µmol/kg, respectively (Table 1). Additional sensitivity tests show that uncertainties associated with SSW% and NSW endmembers only marginally affect our final SSW PO₄* and [CO₃^2-]_as results during the LGM (Supplementary Fig. 8). We find that LGM SSW PO₄* and [CO₃^2-]_as were lower than their LH levels (Fig. 4), suggesting enhanced carbon sequestration in the PAZ during the LGM.

Fig. 4: Mixing between northern and southern sourced waters during the preindustrial era (PI) and the Last Glacial Maximum (LGM).

PI data are hydrographic data from the GLODAPv2 dataset with anthropogenic carbon deducted^61,62. Hydrographic data defining northern sourced water (NSW) and southern sourced waters (SSW) endmembers are shown by blue and red circles, respectively, with darker colour emphasizing higher distribution density. Grey dots are hydrographic data from global ocean deeper than 2 km (excluding the Arctic Ocean). The black line is the NSW-SSW mixing curve. The yellow circle indicates PO₄* and [CO₃^2-]_as reconstructions derived from late Holocene sediment samples at site MD97-2106, which are consistent with the hydrographic data. LGM data are shown by circles with dashed edges. During the LGM, PO₄* and [CO₃^2-]_as reconstructed at site MD97-2016, together with NSW endmember values, are used to deduce SSW endmember values, assuming 80% of glacial SSWs at our site. Any increase of SSW% at MD97-2106 would lower SSW endmember [CO₃^2-]_as and PO₄* values. For the LGM ocean, sizes of the endmember circles indicate the ±1σ variabilities of PO₄* and [CO₃^2-]_as.

Table 1 PO₄* and [CO₃^2-]_as values of NSW, SSW, and at site MD97-2106 during the preindustrial era, the Late Holocene, and the Last Glacial Maximum

The reduced LGM SSW PO₄* compared to the LH could be driven by lower preformed [PO₄^3-] and/or lower preformed [O₂]. Lower LGM preformed [PO₄^3-] would indicate declines in surface-water phosphate and associated DIC in the PAZ^7,8 that were driven by biological processes. For lower LGM preformed [O₂], insufficient O₂ air-sea exchange imposed by physical barriers such as sea ice that would retain O₂ deficiencies of upwelled-and-then-downwelled waters in the PAZ³⁸. However, purely physically-driven component of the lowered PAZ preformed [O₂] is deemed to be relatively small between LGM and LH based on model simulations³⁸. Therefore, declines in PAZ preformed [O₂] must largely originate from previous organic matter remineralization that consumed O₂ and produced CO₂ in tandem. Such a biologically-driven PAZ preformed [O₂] decline must be accompanied by surplus CO₂ that is retained in the newly formed deep waters, because of the longer air-sea exchange equilibration time of CO₂ than O₂ (refs. ^39,40). Therefore, lowered LGM SSW PO₄*, regardless of relative contributions of preformed [PO₄^3-] and preformed [O₂], is stoichiometrically linked to an more DIC sequestered by biological processes in the PAZ. If completely driven by more efficient nutrient utilization, an LGM-LH change in SSW PO₄* of 0.46±0.14 µmol/kg would be associated with a DIC decrease of 58±18 µmol/kg due to enhanced biological CO₂ uptake in the PAZ during the LGM. Such a change in biologically-driven DIC uptake may be slightly overestimated due to a potential but minor contribution of physically-driven disequilibrium to the lowered LGM SSW PO₄*. Our LGM PO₄* reconstruction shows that more phosphate and DIC supplied from the subsurface was biologically utilized in the PAZ, despite lower glacial export productivities in the region^6,41. The associated biological processes would draw down surface-water CO₂ partial pressure, with an effect to strengthen carbon sequestration in the ocean by a maximum amount of 58±18 µmol/kg.

Our SSW PO₄* reconstruction provides new evidence for increased carbon uptake during the LGM caused by more efficient nutrient utilization in the surface Southern Ocean as revealed by published nitrogen isotope (δ¹⁵N) records^42,43,44,45. Importantly, our PO₄* reconstruction reflects an integrated influence of biological processes on the Southern Ocean biogeochemistry and thus can complement surface-ocean δ¹⁵N records, which are presumably biased towards spring-summer seasonality of phytoplankton blooms that are offset from wintertime deep water formation. Moreover, our PO₄* reconstruction demonstrates that reduced preformed nutrient concentrations in the PAZ, driven by more complete utilization of nutrient and carbon supplied to the surface Southern Ocean in spite of lowered export productivity^6,41,45, was propagated downstream to great water depths during the LGM. Our PO₄* reconstructions thus lend strong support for an enhanced biological pump in the PAZ to lower atmospheric CO₂ during the LGM^5,7,8,15.

Lower LGM SSW [CO₃^2-]_as also more directly demonstrates that atmospheric CO₂ was more efficiently sequestered via the PAZ. The sensitivity of [CO₃^2-]_as change to DIC change is previously shown to depend on [CO₃^2-]_as (ref. ¹⁹) and is estimated to be -0.4 on average over the range of [CO₃^2-]_as values reconstructed at our site¹⁹. Based on this sensitivity, the reconstructed LGM-LH change in SSW [CO₃^2-]_as change (-44±10 µmol/kg) corresponds to 110±25 µmol/kg more CO₂ sequestration in the PAZ during the LGM that includes CO₂ sequestration caused by both biological and physical processes. This carbon sequestration during the LGM in the PAZ derived from [CO₃^2-]_as, although dependent on the global alkalinity derived from model simulations, is larger than the upper limit of the biologically-driven air-sea CO₂ uptake of 58±18 µmol/kg estimated from PO₄*. The large difference between CO₂ uptake changes based on [CO₃^2-]_as and PO₄* suggests that in addition to biological processes, physical dynamics such as fluctuations associated with sea-ice extent^10,11, Southern Ocean overturning circulation^34,43, and southern hemisphere westerlies^44,46,47 are an essential contributor to enhanced carbon sequestered in the PAZ during the LGM.

Biologically driven PAZ CO₂ outgassing during Heinrich Stadial 1

High sedimentation rates and tightly constrained chronology in our core allow us to generate detailed deglacial reconstructions (Fig. 5; Methods). During Heinrich Stadial 1 (HS1; 18.0–14.6 ka), PO₄* at our site remained stable during the first 2 ka and rapidly increased by 0.4±0.1 µmol/kg towards the end of HS1 (Fig. 5d). [CO₃^2-]_as at our site displayed a similar pattern, showing minimal change during early HS1 and an increase of 19±3 mol/kg during late HS1 (Fig. 5c). During HS1, SSW% at our site likely increased due to substantially decreased NSW production as indicated by proxy data⁴⁸ (Fig. 5b). Everything else being equal, an SSW% increase from an LGM level of 80% to the extreme but unlikely level of 100% would raise PO₄* and [CO₃^2-]_as at our site by 0.11 and 5 µmol/kg, respectively. Any deglacial NSW PO₄* increase likely occurred after HS1, making little contribution to the reconstructed PO₄* change at our site during HS1⁴⁹. NSW [CO₃^2-]_as increased by 7 µmol/kg as shown by previous reconstructions²⁰ (Supplementary Fig. 7), which could raise [CO₃^2-]_as by at most 2 µmol/kg at site MD97-2106 assuming no SSW% increase (a condition that maximizes the NSW-endmember influence at our site). Therefore, we conclude that PO₄* and [CO₃^2-]_as increases observed at our site during HS1 can be largely attributed to changes in the SSW endmember values.

Fig. 5: Deglacial records indicating deep South Pacific carbon losses.

a Greenland NGRIP ice-core δ¹⁸O (ref. ⁷³). b Northern sourced water (NSW) production strength indicated by ²³¹Pa/²³⁰Th in the North Atlantic⁴⁸. c MD97-2106 [CO₃^2-]_as. d Deep-water PO₄* at MD97-2106, largely reflecting preformed nutrient concentration in the Polar Antarctic Zone (PAZ). e ¹⁴C ventilation ages at site MD97-2106²⁸. f deep-sea coral-bound nitrogen isotopes from the Drake Passage reflecting nutrient utilization efficiency in the Open Antarctic Zone (OAZ)^42,43. g Opal flux from the Atlantic-Sector Southern Ocean indicating the OAZ upwelling strength⁴¹. h Ice-core atmospheric CO₂². i, Ice-core sea-salt sodium concentrations, a proxy for the Southern Ocean sea-ice extent⁴⁶. Note the log scale of y-axis. j EDC ice δD, a proxy for Antarctic temperature⁷². In (c–e) Envelopes associated with curves represent ±1σ error ranges incorporating uncertainties from analytical measurements, proxy calibrations, and the age model. Grey vertical shadings highlight the Younger Dryas (YD) and Heinrich Stadial 1 (HS1), which are interrupted by the Antarctic Cold Reversal (ACR). The vertical dashed line marks the boundary between the early and late stages of HS1.

During early HS1, both PO₄* and [CO₃^2-]_as remained invariant at our site, suggesting that changes in air-sea CO₂ sequestration in the PAZ were too small to be resolved beyond our reconstruction uncertainties. The roughly stable SSW PO₄* during early HS1 coincided with minor nutrient utilization changes shown by opal flux⁴¹ and δ¹⁵N records^42,43,44,45 in the Open Antarctic Zone (OAZ) (Supplementary Fig. 9), the latter of which is well dated in deep-sea coral samples (Fig. 5f). Thus, our new and literature data suggest that PAZ biological processes changed little during early HS1. Nearly constant early-HS1 SSW [CO₃^2-]_as further suggests little changes in air-sea CO₂ exchanges in the PAZ during this period, including those may be caused by physical processes. This seems to contradict with other proxy records, which indicate favourable physical conditions for CO₂ outgassing during early HS1. During this period, Antarctic ice-core sea-salt sodium concentrations suggest Southern Ocean sea-ice extent possibly retreated⁴⁶, and sediment core radiocarbon data indicate improved deep Southern Ocean ventilation at multiple locations including our site^28,30,50. According to model simulations^9,51, enhanced deep Southern Ocean radiocarbon ventilation might be partially driven by changing geometry of the global overturning circulation that is strongly modulated by the sea-ice extent³⁴. Although retreating sea ice itself would promote air-sea gas exchange, the lack of strong CO₂ outgassing resolvable by our [CO₃^2-]_as reconstruction might be related to minor warming in the PAZ and deep Southern Ocean during early HS1⁵², which has been shown by model simulations to be crucial to modulate physically-driven CO₂ outgassing^9,13. Nevertheless, further investigations are needed to better understand how physically-driven air-sea exchanges in the PAZ affected deep-ocean radiocarbon and carbon storage during early HS1.

During late HS1, increased PO₄* suggests more biologically unutilized nutrients relative to the supply and thus a weaker biological pump in the PAZ. This is corroborated by δ¹⁵N records in the OAZ^42,43,44,45 (Fig. 5f and Supplementary Fig. 9), which show prominent decreases in nutrient utilization efficiency over the same period. Ignoring the minor contribution of purely physically driven preformed [O₂] to PO₄*, PO₄* that was raised by 0.4±0.1 µmol/kg at our site suggests 44±10 µmol/kg of DIC became unutilized by biological processes during late HS1. Rising SSW [CO₃^2-]_as during late HS1 also suggests that CO₂ released through air-sea exchange in the PAZ during this period (Fig. 5c). Based on the [CO₃^2-]_as increase of 19±3 mol/kg, 46±11 µmol/kg DIC was released from deep waters at site MD97-2106 during late HS1. Comparable DIC changes estimated based on PO₄* and [CO₃^2-]_as demonstrate that increased DIC related to biologically unutilized nutrients can largely account for CO₂ outgassing in the PAZ during late HS1. Physical processes must have facilitated outgassing of these biology-related DIC during late HS1. For example, given the rising export productivity in the OAZ during this period⁴¹ (Fig. 5g), declines in deglacial nutrient utilization efficiency during HS1 must be driven by more nutrient supplied by enhanced deep water upwelling^5,15,41. However, direct contribution of physical processes to promoting CO₂ outgassing independent of biological processes appears to be small during late HS1.

Reduced PAZ CO₂ outgassing during the Antarctic Cold Reversal

During the Antarctic Cold Reversal (ACR; 14.6–12.8 ka), PO₄* and [CO₃^2-]_as declined at site MD97-2106 by 0.22±0.08 and 11±5 µmol/kg, respectively (Fig. 5). During this period, reinvigorated production of low-PO₄* and low-[CO₃^2-]_as NSWs⁴⁸ would reduce SSW% and thereby lower PO₄* and [CO₃^2-]_as at our site (Figs. 1, 4 and Supplementary Fig. 1). Without changes in NSW and SSW endmember values, the reconstructed PO₄* and [CO₃^2-]_as declines could be largely explained by 30% reduction in SSW% from 100% (highest possible HS1 level) to 70% (ACR level). However, this would require no NSWs at our site during HS1 that is inconsistent with deep Southern Ocean ε_Nd records^32,33. A large SSW% reduction would also raise [O₂] during the ACR, opposite to the reconstructed trends at our site (Fig. 2d) and the Drake Passage⁵³. Therefore, SSW% decline is inadequate to explain all the reconstructed PO₄* and [CO₃^2-]_as changes at our site. A moderate SSW% decline by 15% from HS1 would lower PO₄* and [CO₃^2-]_as, respectively, by 0.12 and 4 µmol/kg, which are too small to account for our reconstructed changes. Hence, we conclude that SSW PO₄* and [CO₃^2-]_as endmember values likely decreased during the ACR.

Our inferred SSW PO₄* reduction suggests a decrease in the preformed nutrient and DIC due to more efficient nutrient utilization in the PAZ during the ACR, in line with OAZ δ¹⁵N records^{41,42,43,44,45} and enhanced marine productivity deduced from marine-derived aerosols recorded by ice cores⁵⁴. The biologically-driven air-sea CO₂ sequestration is also registered by the reconstructed  [CO₃^2-]_as decline  (Fig. 5c). In addition to biological changes, the enhanced CO₂ sequestration may be linked to physical processes including readvancing Antarctic sea ice⁴⁶ that limited air-sea gas exchange and northward shift of the Southern Hemisphere westerlies^44,53. We suggest that both biological and physical changes contributed to enhanced air-sea CO₂ sequestration during the ACR.

Strong physically driven PAZ CO₂ outgassing during the Younger Dryas

During the Younger Dryas (YD; 12.8–11.7 ka), deep-water PO₄* and [CO₃^2-]_as increased by 0.10±0.11 µmol/kg and 16±5 µmol/kg at our site, respectively (Fig. 5c, d). Proxy data suggest that SSW% in the deep Southern Ocean during the YD declined towards the Holocene level^32,35. Any decline in SSW% tends to lower PO₄*, opposite to the reconstructed increasing PO₄* at our site. The NSW PO₄* possibly increased by ~0.15 µmol/kg during the YD⁴⁹, with an effect of raising PO₄* by 0.04 µmol/kg, assuming Holocene SSW% level of 70% at our site (a condition that maximizes the impact of NSW endmember changes). The remaining PO₄* increase of 0.06±0.11 µmol/kg at our site must be due to an increase in SSW endmember PO₄*. We estimate that SSW PO₄* was increased by 0.08±0.17 µmol/kg with SSW% level of 70% at our site. For [CO₃^2-]_as, an NSW endmember [CO₃^2-]_as increase of 15±7 µmol/kg (Supplementary Fig. 7) could account for at most 5±2 µmol/kg [CO₃^2-]_as increase at site MD97-2106, assuming an SSW% of 70%. The remaining 11±6 µmol/kg increase in [CO₃^2-]_as at our site must be caused by an SSW endmember [CO₃^2-]_as increase of 16±9 µmol/kg. Therefore, both PO₄* and [CO₃^2-]_as increases at MD97-2106 are strongly driven by increases in their SSW endmember values during the YD.

Our inferred SSW PO₄* increase during the YD agrees with OAZ δ¹⁵N records^{41,42,43,44,45}, indicative of lowered nutrient utilization efficiency in the OAZ. The 0.08±0.17 µmol/kg increase in SSW PO₄* suggests 8±18 µmol/kg increase in DIC, which could cause a maximum magnitude of 8±18 µmol/kg CO₂ outgassing, due to biological changes in the PAZ during the YD. Meanwhile, the 16±9 µmol/kg increase SSW [CO₃^2-]_as indicate a total air-sea CO₂ loss of 40±23 µmol/kg. Thus, the PAZ CO₂ outgassing during the YD must be mainly attributed to physical processes including substantial sea ice retreat⁴⁶, Southern Ocean circulation changes⁴³, and southward shift of Southern Hemisphere westerlies^44,46,47.

Discussion

Using paired reconstructions of deep-water biogeochemical variables in the deep Southern Ocean, we have derived quasi-conservative tracers, PO₄* and [CO₃^2-]_as, to quantify carbon cycle changes in the PAZ during the last deglaciation. Our reconstructions show that the partitioning of carbon between the deep Southern Ocean and the atmosphere via air-sea CO₂ exchanges in the PAZ were mediated by biological and physical processes both between the LGM and Holocene and on millennial timescales during the deglaciation. PAZ CO₂ outgassing is more strongly associated with biological processes during HS1 and can be largely attributed to physical processes during the YD.

Our reconstructed variabilities in PAZ air-sea CO₂ exchanges are broadly consistent with deglacial atmospheric CO₂ changes², supporting the key role of the PAZ in regulating past atmospheric CO₂ (refs. ^4,5,6). Nevertheless, our reconstructions also show that PAZ air-sea CO₂ exchanges at times deviated from atmospheric CO₂ fluctuations, implying complex mechanisms affecting deglacial atmospheric CO₂. For example, enhanced PAZ CO₂ outgassing during late HS1 diagnosed here appears to lag the atmospheric CO₂ rise that started from early HS1 (ref. ²). Also, our identified CO₂ outgassing reduction during the ACR coincided with an atmospheric CO₂ plateau². These deviations between Southern Ocean outgassing and atmospheric CO₂ evolutions imply critical influences of other ocean volumes (e.g., upper oceans²⁹) and/or regions (e.g., Atlantic sector of the Southern Ocean and the North Atlantic^20,55) on past atmospheric CO₂ changes. Investigations of broader oceanic regions are warranted to better understand ocean-atmosphere carbon interactions, and quasi-conservative tracers such as PO₄* and [CO₃^2-]_as employed here provide useful tools for future studies.

Methods

Trace element and stable isotope analyses

We examined sediment samples from 0–17 cm and 54–225 cm at site MD97-2106. For each sample, the >212 μm fractions of sediments were examined for benthic foraminifera Cibicidoides wuellerstorfi (sensu stricto)⁵⁶, Hoeglundina elegans, and Globobulimina affinis. C. wuellerstorfi can be continuously found throughout the section. H. elegans is abundant above 158 cm, but absent below 207 cm. G. affinis can be found below 96 cm, but is absent above this level, except in 0–17 cm of the core. For trace element analyses, 4–20 C. wuellerstorfi shells and 2–8 H. elegans shells were picked from each sample. When the number of C. wuellerstorfi shells was larger than 15 or the number of H. elegans was larger than 6, uncrushed shells were split into two subsamples and treated separately in further steps.

Foraminifera shells were first gently crushed between glass slides. C. wuellerstorfi shells were cleaned following the modified Mg-cleaning protocol^57,58 and H. elegans samples were cleaned following the Cd-cleaning protocol including the reductive step⁵⁹. The cleaned samples were dissolved in 0.1 M HNO₃ and trace element-to-calcium ratios were measured on an ICP-MS at the Australian National University following the method of ref. ⁶⁰. Analytical uncertainties (1 standard deviation) are >2% for B/Ca and Cd/Ca. Relative standard deviations of replicated C. wuellerstorfi B/Ca and H. elegans Cd/Ca are 1.5-2.6% (3 samples) and 1.0–3.1% (6 samples), respectively. These replicated subsamples are plotted separately in Supplementary Fig. 2.

For carbon and oxygen isotope analyses, 2–5 C. wuellerstorfi shells and 2–5 G. affinis shells were picked from each sample from the same sediment depths. The analyses were performed at the Institute of Earth Environment, Chinese Academy of Sciences. The precision is better than 0.08‰ for δ¹³C and δ¹⁸O analyses, based on repeated measurements of an in-house dolomite standard (TTB1).

Estimating seawater biogeochemistry

Modern hydrographic data near site MD97-2106 (temperature, salinity, DIC, alkalinity, silicate, phosphate, oxygen, and anthropogenic carbon) are retrieved from the GLODAPv2 gridded database^61,62. The anthropogenic carbon is deducted from the measured DIC to obtain the preindustrial DIC levels. Carbonate chemistry parameters are calculated from hydrological data using CO2sys2.1⁶³.

Down-core in-situ deep-water [CO₃^2-] ([CO₃^2-]_in-situ) is reconstructed from B/Ca in benthic foraminifera C. wuellerstorfi. [CO₃^2-]_in-situ can be defined by calcite saturation state (Δ[CO₃^2-]) and calcite saturation values ([CO₃^2-]_sat):

$${[{{{{\rm{CO}}}}}_{3}^{2-}]}_{{{{\rm{in\; situ}}}}}=\Delta [{{{{\rm{CO}}}}}_{3}^{2-}]+{[{{{{\rm{CO}}}}}_{3}^{2-}]}_{{{{\rm{sat}}}}}.$$

(1)

Δ[CO₃^2-] can be estimated from C. wuellerstorfi B/Ca using the calibration from Yu, et al.⁶⁴:

$${{{\rm{B}}}}/{{{\rm{Ca}}}}=(1.14{{\pm }}0.04)*\Delta [{{{{\rm{CO}}}}}_{3}^{2-}]+176.6{{\pm }}1.0.$$

(2)

We adopt the modern [CO₃^2-]_sat for the deglacial reconstruction, because [CO₃^2-]_sat is insensitive to past temperature, salinity, and pressure changes which would only cause ~0.1 μmol/kg variations in [CO₃^2-]_sat at Site MD97-2106 on glacial-interglacial timescales. We use a Monte-Carlo approach to combine the uncertainties in both proxy data and the age model. To combine these uncertainties,  10,000 iterations of the record were firstly randomly generated considering uncertainties associated with the B/Ca-[CO₃^2-] calibration, B/Ca measurements, and the age model. Secondly, the 10,000 iterations were smoothed by a LOESS function. The 1σ uncertainty is defined as half of the difference between the 84th and 16th percentile of the smoothed curves. The combined ±1σ uncertainty of [CO₃^2-] is, on average, ±4.5 μmol/kg for the range of B/Ca observed in core MD97-2106.

Past deep-water [PO₄^3-] is derived from seawater Cd concentration (Cd_w) reconstructed from Cd/Ca in benthic foraminifera H. elegans. Cd_w is estimated by the following equation⁶⁵:

$${{{{\rm{Cd}}}}_{{{{\rm{w}}}}}({{{\rm{nmol}}}}/{{{\rm{kg}}}})=[{({{{\rm{Cd}}}}/{{{\rm{Ca}}}})}_{{{{\rm{foram}}}}}/{{{{\rm{D}}}}}_{{{{\rm{Cd}}}}}}]{*}10,$$

(3)

where D_Cd is the partition coefficient of Cd between foraminifera carbonate and seawater. For H. elegans, D_Cd is 1.0 and independent of water depth^25,66. We apply 5% uncertainty to D_Cd when estimating the uncertainty of seawater [PO₄^3-]. Cd_w is used to estimate [PO₄^3-] based on the relationship between Cd_w and [PO₄^3-] for sites from the GEOTRACES transect GIPY06 located at the South of Tasmania⁶⁷:

$${{{{\rm{Cd}}}}}_{{{{\rm{w}}}}}= {1.23}{*}[{{{{\rm{PO}}}}}_{4}^{3-}]\,+\,1.30\,([{{{{\rm{PO}}}}}_{4}^{3-}]\, > \, 1.5{{{\rm{\mu mol}}}}/{{{\rm{kg}}}},\,\\ {{{{\rm{r}}}}}^{2}=0.76,{{{\rm{n}}}}=294,{{{\rm{RMSE}}}}=0.117).$$

(4)

Using different Cd_w-[PO₄^3-] relations (e.g., a linear correlation for data from the entire GIPY06 transect and a quadratic relation based on the whole GEOTRACES dataset, 2021v2⁶⁸) would result in different absolute [PO₄^3-] values, but downcore [PO₄^3-] patterns remain similar (Supplementary Fig. 10). We choose the local calibration because it yields a late Holocene [PO₄^3-] estimation of 2.23 μmol/kg that is consistent with the modern hydrographic data. Combining uncertainties of D_Cd, RMSE of the Cd_w-[PO₄^3-] relation, Cd/Ca measurements, and the age model using the Monte-Carlo approach similar to that used for [CO₃^2-] reconstructions, the average uncertainty of our [PO₄^3-] reconstructions is ±0.11 μmol/kg (±1σ). Due to the relatively long phosphorus residence time in the ocean (~20–100 ka)⁶⁹, we assume little change in the global oceanic [PO₄^3-] inventory during the last deglaciation.

Past bottom water [O₂] is estimated from the δ¹³C gradient (Δδ¹³C) between epifaunal species C. wuellerstorfi and deep infaunal species G. affinis using the following equation²⁷:

$${\Delta {{{\rm{\delta }}}}}^{13}{{{\rm{C}}}}={0.0077}{*}[{{{{\rm{O}}}}}_{2}]\,+\, 0.41.$$

(5)

The total uncertainty of the [O₂] reconstruction is ±17 μmol/kg (±1σ), which includes both calibration and δ¹³C analytical errors²⁷.

Calculating quasi-conservative tracers

Deep-water PO₄* is derived from in-situ [O₂] and [PO₄^3-] based on the following equation^16,17:

$${{{{{\rm{PO}}}}}_{4}}{*}=[{{{{{\rm{PO}}}}}_{4}}^{3-}]+[{{{{\rm{O}}}}}_{2}]/175-1.95.$$

(6)

The average ±1σ uncertainty in PO₄* is 0.15 μmol/kg, derived from errors in [PO₄^3-], [O₂], and chronology using an iterated LOESS smoothing method. By definition^16,17, calculation of PO₄* employs a ${{\rm{R}}}_{{{\rm{-O}}}_2:{{\rm{P}}}}$ value of 175. Using other ${{\rm{R}}}_{{{\rm{-O}}}_2:{{\rm{P}}}}$ values (e.g., 160 or 180) to calculate PO₄* changes absolute PO₄* values, but with little effect on its deglacial structure (Supplementary Fig. 6). By definition and due to its conservativeness in the ocean, deep-water PO₄* incorporates preformed [PO₄^3-] and preformed [O₂], that is,

$${{{{{\rm{PO}}}}}_{4}}{*}={[{{{{{\rm{PO}}}}}_{4}}^{3-}]}_{{{{\rm{pre}}}}}+{[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{pre}}}}}/175-1.95.$$

(7)

Thus, their relative changes are linked by the following equation:

$${{\Delta {{{\rm{PO}}}}}_{4}} \ast=\Delta {[{{{{\rm{PO}}}}}_{4}^{3-}]}_{{{{\rm{pre}}}}}+{\Delta {[{{{{\rm{O}}}}}_{2}}]}_{{{{\rm{pre}}}}}/175.$$

(8)

Following ref. ³⁸, Δ[O₂]_pre can be further divided into two components related to physical and biological changes:

$$\Delta \left[{{{{\rm{O}}}}_{2}}\right]_{{{\rm{pre}}}}=\Delta \left[{{{{\rm{O}}}}_{2}}\right]_{{{\rm{pre}}}}^{{{\rm{phy}}}}\,+\, \Delta \left[{{{{\rm{O}}}}_{2}}\right]_{{{\rm{pre}}}}^{{{\rm{bio}}}}.$$

(9)

Δ[O₂]_pre^phy is determined by surface O₂ solubility, mainly driven by temperature and air-sea gas exchange disequilibrium not related to biological nutrient utilization.

Calculation of [CO₃^2-]_as is based on the carbonate system sensitivities to changes in physical conditions, remineralization of biogenic organic matter and CaCO₃, and air-sea CO₂ gas exchanges, which are derived from hydrographic data in the preindustrial ocean¹⁹. The carbonate system sensitivities are shown to be similar in preindustrial and LGM conditions¹⁹. We calculate deglacial [CO₃^2-]_as changes at site MD97-2106 in four steps following refs. ^19,20. In step 1, downcore deep-water [CO₃^2-] is normalized to a reference condition (T = 3 °C, S = 35, P = 2500 dbar), using [CO₃^2-]-T-S-P sensitivities from ref. ¹⁹. At site MD97-2106, we estimate deglacial changes in salinity based on global sea level changes, temperature based on benthic foraminiferal δ¹⁸O, and water depth based on global sea level changes, following methods described in ref. ¹⁹. In step 2, seawater [CO₃^2-] changes linked to within-ocean DIC-alkalinity redistributions are calculated by changing in-situ [PO₄^3-] to the global average of 2.22 µmol/kg, following the sensitivity of [CO₃^2-] change to [PO₄^3-] constrained in ref. ¹⁹. [CO₃^2-] changes are driven by DIC and alkalinity changes related to [PO₄^3-] via Redfield Ratio (R_C:P = 127) and rain ratio (the ratio between organic and inorganic carbon in remineralized biogenic matter, C_org:${{\rm{C}}}_{{{\rm{CaCO}}}_3}$ = 4). Using sensitivities of [CO₃^2-] change to [PO₄^3-] defined by different R_C:P and C_org:${{\rm{C}}}_{{{\rm{CaCO}}}_3}$ minimally affects deglacial patterns of [CO₃^2-]_as (Supplementary Fig. 5). In step 3, deep-water [CO₃^2-] changes linked to the global ocean DIC and alkalinity inventory changes due to CaCO₃ input/output imbalance over time is calculated following refs. ^19,20. Global DIC changes associated with this process are half of the global alkalinity changes, which are the offsets between in-situ alkalinity estimated from model simulations³¹ and a reference alkalinity of 2385 µmol/kg. Effects of global DIC-alkalinity changes on [CO₃^2-] are derived using the sensitivity of [CO₃^2-] to DIC constrained in ref. ¹⁹. CaCO₃ input/output imbalance mainly contributes to long-term [CO₃^2-]_as changes. Choosing different modelled deglacial global alkalinity changes leads to varying magnitudes of deglacial [CO₃^2-]_as changes but minimally affects millennial-timescale structure of [CO₃^2-]_as, as shown by sensitivity tests employing different modelled global alkalinity changes (Supplementary Fig. 5). In step 4, [CO₃^2-] changes calculated in Steps 2 and 3 are removed from the [CO₃^2-] normailized to a reference condition in Step 1 to obtain the corrected [CO₃^2-], whose variabilities are attributed to air-sea CO₂ exchange effects. To derive [CO₃^2-]_as, a constant of 78 µmol/kg is deducted from the corrected [CO₃^2-]. Deducting this constant brings the late Holocene [CO₃^2-]_as values close to 0 µmol/kg, which are similar to hydrographic results in the pre-industrial ocean (Figs. 1, 3).

The uncertainty of [CO₃^2-]_as is also derived using the Monte-Carlo approach. Each [CO₃^2-]_as was calculated 10,000 times following the abovementioned methods using [CO₃^2-], [PO₄^3-], temperature, salinity, pressure, and age randomly generated from their averages and standard deviations. The combined ±1σ uncertainty of [CO₃^2-]_as is derived from the 16th and 84th percentiles of the iterated LOESS-smoothed curves, and our calculation yields an average 1σ-uncertainty of 7.7 μmol/kg for [CO₃^2-]_as.

To reliably infer millennial-timescale changes in PO₄* and [CO₃^2-]_as, which are derived by combining different proxies, changes in these proxies underlying the preformed tracers need to be synchronized on the same timescale. To ensure synchroneity of these proxies, only reconstructions of [PO₄^3-], [CO₃^2-], and [O₂], derived from different foraminifera found at the same sediment horizons were combined to calculate PO₄* and [CO₃^2-]_as. Although the benthic foraminifera that we utilized dwell at varying depths within sediments, they were homogenized by bioturbation within sediments after deposition. This is evident by similar deglacial structures of oxygen isotopes in epifaunal and deep infaunal species in our core (Supplementary Fig. 2). Meanwhile, bioturbation does not prevent millennial-timescale deglacial changes being resolved, due to relatively high sediment rates (15 cm/ka) at our site during the last deglaciation. Finally, from the perspective of tracer calculation, millennial-timescale changes in PO₄* and [CO₃^2-]_as are mainly driven by [O₂] and [CO₃^2-] with a minor contribution from [PO₄^3-] (Fig. 3). For example, the concomitant increases in PO₄* and [CO₃^2-]_as during the early HS1 are independent of [PO₄^3-] changes.

Calculation of SSW endmember values and sensitivity test

We follow ref. ²³ to select hydrographic data (GLODAPv2 dataset)^61,62 to derive NSW and SSW endmember values in the preindustrial ocean. The NSW properties are derived from the North Atlantic sites north of 50°N and deeper than 1500 m, with CFC-11 concentrations >0.5 pmol/kg. The SSW properties are derived from the Southern Ocean sites south of 45°S, and deeper than 1500 m, with CFC-11 concentrations >0.5 pmol/kg and neutral density higher than 28.3 kg/m³ (Supplementary Fig. 1). Following these selection criteria, SSWs defined here are mainly ventilated in the PAZ and reside at deep (~>1500 m) depths in the Pacific Basin. A minor component of SSWs at deep depths is ventilated via the Subantarctic Zone⁷⁰, but its contribution during the last deglaciation is smaller than the late Holocene (LH) due to the shallower upper-cell overturning circulation³⁴, and hence considered to be negligible here.

PO₄* and [CO₃^2-]_as levels during the LH, reconstructed from the top part of core MD97-2106, are consistent with estimations based on preindustrial hydrographic data. As both PO₄* and [CO₃^2-]_as are quasi-conservative, LH PO₄* and [CO₃^2-]_as at site MD97-2106 are determined by linear mixing between NSW and SSW endmembers based on the following equations:

$${{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LH}}}}}}^{{{{\rm{MD}}}}97-2106}={{{\rm{NSW}}}}\% \times {{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LH}}}}}}^{{{{\rm{NSW}}}}}+{{{\rm{SSW}}}}\% \times {{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LH}}}}}}^{{{{\rm{SSW}}}}}$$

(10)

$${{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LH}}}}}}^{{{{\rm{MD}}}}97-2106}={{{\rm{NSW}}}}\%\, \times \, {{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LH}}}}}}^{{{{\rm{NSW}}}}}+{{{\rm{SSW}}}}\%\, \times \, {{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LH}}}}}}^{{{{\rm{SSW}}}}}$$

(11)

$${{{\rm{NSW}}}}\%\,+{{{\rm{SSW}}}}\%=1$$

(12)

Similarly, for the LGM, we have:

$${{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LGM}}}}}}^{{{{\rm{MD}}}}97-2106}={{{\rm{gNSW}}}}\% \times {{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LGM}}}}}}^{{{{\rm{NSW}}}}}+{{{\rm{gSSW}}}}\% \times {{{{{{{\rm{PO}}}}}_{4}}{*}}_\_{{{{\rm{LGM}}}}}}^{{{{\rm{SSW}}}}}$$

(13)

$${{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LGM}}}}}}^{{{{\rm{MD}}}}97-2106}={{{\rm{gNSW}}}}\%\, \times \, {{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LGM}}}}}}^{{{{\rm{NSW}}}}}\,+\,{{{\rm{gSSW}}}}\%\, \times \, {{[{{{{{\rm{CO}}}}}_{3}}^{2-}]}_{{{{\rm{as}}}}\_{{{\rm{LGM}}}}}}^{{{{\rm{SSW}}}}}$$

(14)

$${{{\rm{gNSW}}}}\%+{{{\rm{gSSW}}}}\%=1$$

(15)

Equations (13)-(15) can be used to derive PO₄*_{_LGM}^SSW and [CO₃^2-]_{as_LGM}^SSW from PO₄*_{_LGM}^MD97-2106 and [CO₃^2-]_{as_LGM}^MD97-2106, if NSW-SSW mixing ratio and NSW endmembers during the LGM are known. The LGM water mass mixing and NSW endmember values are either not firmly quantified or associated with some uncertainties, but their influences on the LGM SSW endmember estimations can be quantified by sensitivity tests.

Based on paleo circulation reconstructions, SSW% in the deep South Pacific was higher during the LGM than the LH^32,33. We therefore use 80% for the LGM SSW%, compared to 70% for the LH. For PO₄*, there currently lacks coupled [PO₄^3-] and [O₂] reconstructions to constrain PO₄*_{_LGM}^NSW. [PO₄^3-] reconstructions show that LGM NSW was slightly more nutrient depleted than the modern ocean^19,20,66, while the only published LGM reconstruction suggests similar NSW [O₂] during the LGM and the LH⁷¹. We thus assume PO₄*_{_LGM}^NSW to be 80% of the LH level following ref. ³⁷ for our preferred calculations (Table 1), and use PO₄*_{_LGM}^NSW the same as the LH level for sensitivity tests. We adopt LGM [CO₃^2-]_as reconstructed at a North Atlantic site NEAP4K (61.5°N, 24°W, 1.6 km) as the [CO₃^2-]_{as_LGM}^NSW (-43 ± 5 µmol/kg)²⁰. However, glacial deep waters at this site may contain a small fraction of SSWs during the LGM due to the shoaling of NSWs⁶⁶. We thus use [CO₃^2-]_{as_LGM}^NSW derived from 90% NSWs and 10% SSWs at site NEAP4K for sensitivity tests. [CO₃^2-]_{as_LGM}^NSW can be solved from [CO₃^2-]_{as_LGM} at sites NEAP4K and MD97-2106, with assumed SSW-NSW mixing ratios at both sites. As shown in Supplementary Fig. 8, our calculated LGM SSW PO₄* and [CO₃^2-]_as employing different SSW% at our site and different NSW endmember levels are well within the ±1σ uncertainties associated with tracer reconstructions, supporting the robustness of our estimates of the LGM SSW endmembers.