## Main

A multitude of ice-core and marine records show that the past 800,000 years of Earth’s history were dominated by global-scale alternations between glacial and interglacial conditions with a high degree of nonlinearity in the climatic response to gradual external forcing1,2. This is particularly relevant for glacial terminations, which are thought to be driven by relatively weak insolation forcing due to changes in Earth’s orbital configuration3,4. In this context, it has been proposed that disruptions to circulation patterns in the coupled atmosphere–ocean system might have acted to accelerate Antarctic warming and the outgassing of CO2 from the Southern Ocean (SO) to cross a critical level necessary to maintain interglacial conditions at a global scale5,6,7. A possible mechanism to reach such a point is an abrupt weakening of the Atlantic meridional overturning circulation (AMOC) and a corresponding reduction of northward oceanic heat transport associated with SO and Antarctic warming, according to the bipolar-seesaw concept8,9,10, which has been detected in a wide spectrum of models11,12. However, since abrupt oscillations between relatively weak and strong AMOC states and corresponding SO changes are thought to be a ubiquitous feature of millennial-scale climate variability throughout most glacial periods13,14, it is open to question what facilitates such a strong temperature response during deglaciation (Fig. 1).

## Interglacial and glacial water-mass configurations

The large-scale meridional water-mass distribution in the modern ocean is characterized by deep waters originating in the North Atlantic (North Atlantic Deep Water; NADW) and the SO (Antarctic Bottom Water; AABW). These water masses are connected by mixing processes and wind-driven upwelling within the SO15,16,17,18. AABW represents the densest water mass in the modern ocean due to its low temperature (AABW is relatively fresh and cold compared with the overlying NADW)18,19. Only at great depth does the pressure dependence of the thermal expansion coefficient in the equation of state (the thermobaric effect) mean that the warmth of NADW makes it less dense than AABW20. Thus, a reduction in the temperature contrast between the two water masses will tend to destabilize the water column, ultimately resulting in NADW replacing AABW as the deepest water mass.

With respect to ocean temperature, the most accurate/robust evidence for glacial ocean cooling on a global scale stems from noble gases trapped in ice cores. Bereiter et al.21 show that mean ocean cooling (2.5 ± 0.24 °C) was greater than the maximum possible cooling of AABW, since modern AABW has a temperature of −0.88 °C22 and seawater has a freezing point of about −2 °C. Of particular relevance to our study is the implication that ‘warmer’ water masses such as NADW and intermediate water masses within the Southern Atlantic must have cooled to a greater extent than AABW23. This implies that thermal deep-ocean stratification in the glacial ocean was weaker than it is today. In a hypothetical scenario with no change to the salinity distribution, we can see that such heterogeneous cooling of the glacial ocean could lead to an unstable water column (Extended Data Fig. 1), and yet proxy reconstructions suggest that the glacial version of AABW maintained its position as the deepest water mass at least in the South Atlantic region24,25. Therefore, something probably acted to compensate for the loss of stability from thermal stratification in the glacial ocean.

Indeed, other proxy evidence26,27 suggests that the salinity of glacial AABW could have been much greater than today, even to the point that deep-ocean salinity stratification may have been reversed with respect to the modern26. Such salinity changes could be brought about by enhanced equatorward sea-ice export in the glacial SO28 in combination with reduced melting of Antarctic ice as a consequence of colder NADW20. Analyses of different boundary conditions in atmosphere–ocean general circulation model (AOGCM) equilibrium simulations suggest that especially the interplay of low CO2, low obliquity29 and large Northern Hemisphere ice sheets30 provides favourable conditions for the formation of salty deep waters around Antarctica.

Using the fully coupled Earth system model (COSMOS)29,31 (Methods), Zhang et al. have previously shown29 that the application of glacial boundary conditions can lead to particularly salty deep waters in the SO region compared with pre-industrial conditions. In this study, we augment the glacial (LGMCTRL) and pre-industrial (PIDCTRL) control experiments of Zhang et al.29 to include an intermediate climate state (40kaCTRL, Methods, Figs. 3 and 4 and Extended Data Figs. 29) to investigate any differences in the response to ‘terminal’ and non-terminal AMOC perturbations (which we describe later).

In the glacial ocean simulation LGMCTRL, the strongest temperature decrease (of more than 4 °C with respect to both PIDCTRL and 40kaCTRL) occurs within levels of the southward NADW return flow (Fig. 2 and Extended Data Figs. 2 and 3). The local LGMCTRL cooling maximum at ~2.5 km depth (Fig. 2c) can be linked to a combination of a shoaling (~200 m) of the glacial NADW cell and production of colder NADW (although we note that a model–data comparison for our glacial state with marine calcite δ18O values includes the possibility that NADW formation might actually have been weaker and even shallower32,33,34 than in our simulated LGM state35).

In stark contrast to the changes at intermediate depths, the weakest temperature and strongest salinity differences between the pre-industrial and glacial states are detected in the deep SO (Fig. 2c,d). Here we observe a shift from a purely temperature-controlled stratification to one that is also characterized by a stable haline density gradient (at least within the SO). A similar contrast is observed between glacial and intermediate (40 thousand years ago (ka)) conditions (Extended Data Fig. 2).

We note that the mechanism of deep-ocean salinification proposed by Adkins20 (which calls on the cooling of NADW as a means for reducing the melting of Antarctic land ice and related input of freshwater to the SO) could work in tandem with increased sea-ice export (as observed in our model simulation) to produce highly saline bottom waters.

An overview of simulated salinity structure in LGM states (unperturbed) encompassing the last three Paleoclimate Model Intercomparison Project (PMIP)/Coupled Model Intercomparison Project (CMIP) model generations36,37,38,39,40 shows that a simulation of a salty glacial deep ocean (Extended Data Fig. 10) by AABW on a global scale is a persistent challenge, which partly reflects limits of current models to simulate key processes41,42 that influence AABW characteristics. This also includes the mechanism described by ref. 20, and while the current generation of coupled AOGCMs cannot resolve that mechanism explicitly, we can at least demonstrate its viability using a coupled ice-sheet/ice-shelf cavity model (Methods and Extended Data Fig. 4). However, the precise mechanism by which a salty deep ocean is generated is not important for the following discussion, in which we investigate the theoretical implications of a relative increase in the importance of salinity versus temperature stratification in the glacial ocean. For further discussion, see Methods.

## Salinity gradient and temperature changes with depth

Deep-ocean stratification depends on the interplay between salinity and temperature changes with depth. We therefore derive an analytical expression (which is independent of the model simulations) for the thermal gradient (dT/dz) that accounts for the interplay between thermal and haline contributions to the net density change with depth:

$$\frac{{{\mathrm{d}}T}}{{{\mathrm{d}}z}} = - \frac{{{\mathrm{d}}\rho/{\mathrm{d}}z}}{{\alpha_{\mathrm{T}}\rho _0}}\left( {1 + \frac{{{\mathrm{d}}\rho_{\mathrm{S}}/{\mathrm{d}}z}}{{{\mathrm{d}}\rho_{\mathrm{T}}/{\mathrm{d}}z}}} \right)^{ - 1}$$

Here, dρS/dz and dρT/dz represent the haline and thermally driven density changes with depth and dρ/dz is the combined (net) change in density with depth (which must remain positive to maintain stability). Density and the thermal expansion coefficient are indicated by ρ0 and αT. We now explore the implications of a glacial ocean state in which an increase in salinity stratification accommodates a decrease in the thermal contrast between northern- and southern-sourced deep-water masses. In particular, we are interested in the surface SO temperature response that would result from the upwelling of deeper waters (for example, due to a perturbation of the AMOC) that are relatively warm (not as cold) compared with a non-glacial state.

With the aid of the different terms in the equation, we can evaluate the importance of the stable glacial salinity stratification for the reduced thermal stratification in LGMCTRL. We focus our attention on the deep South Atlantic (zonally averaged at 30° S) to assess the export characteristics out of the Atlantic basin and to avoid effects of intra-basin scale upwelling on Southern Hemisphere communication. In particular, the choice of the depth level influences the thermohaline characteristics of the reference water masses. Therefore, we choose a level at 3,000 m depth, which is within a broader core of waters with similar stratification characteristics that represent an unstable (PIDCTRL, 40kaCTRL) or stable (LGMCTRL) salinity stratification. The first term on the right-hand side of the equation can then be diagnosed from our modelled control runs, enabling us to plot dT/dz versus the ratio of haline to thermally driven density changes ($$\frac{{{\mathrm{d}}\rho_{\mathrm{S}}/{\mathrm{d}}z}}{{{\mathrm{d}}\rho_{\mathrm{T}}/{\mathrm{d}}z}}$$) for a variety of background states (Fig. 3).

For any of the three different background states with a given density structure (dρ/dz, ρ0 and αT), it can be seen that for constant dρ/dz the ratio of haline to thermally driven density stratification must increase to accommodate any decrease in the vertical temperature contrast between northern- and southern-sourced deep-water components in the South Atlantic (coloured curves in Fig. 3). The key difference between our glacial simulation and a pre-industrial or intermediate (40 ka) state is the large increase in salinity stratification (which is actually reversed with respect to the non-LGM states) relative to the thermal stratification. Together with the palaeo-evidence described earlier, this suggests that the cooling potential of upwelled water to the surface SO in a full glacial is relatively much less than for either the pre-industrial or intermediate state. Naturally, this has implications for the oceanic and atmospheric response to a perturbation of the AMOC that might be expected as a necessary ingredient of glacial termination.

## Southern high-latitude response to AMOC weakening

We next perform perturbation simulations to investigate the implications of different glacial–interglacial water-mass configurations with respect to SO and Antarctic temperature responses to an abrupt weakening of the AMOC (Fig. 4 and Extended Data Fig. 5). We use the same model set-up as in the control simulations and apply a freshwater perturbation of 0.15 Sv (1 Sv = 106 m3 s–1) to the North Atlantic ice-rafted debris belt for 800 years (further details are provided in Methods). In summary, we find that warming sea surface conditions and declining sea-ice cover occur as the dominant high-latitude Southern Hemisphere response to an AMOC weakening only under LGM conditions (Fig. 4d,e).

In the following discussion, we focus on the comparison of the perturbation simulations LGMPERT and PIDPERT (the 40kaPERT responses are similar to those of PIDPERT) (Fig. 4). On weakening of AMOC, surface warming at the southern boundary of the Atlantic basin (~30° S) penetrates to a depth of ~2 km irrespective of the background conditions (Fig. 5a,b). This warming response is a common characteristic among NADW perturbation simulations43,44, which can be linked to heat storage45 in the low latitudes and South Atlantic and reduced ventilation of intermediate and deep waters, combined with the downward mixing of heat from the thermocline46. This ‘advection–diffusion balance’ concept is also consistent with the relatively strong LGMPERT warming (Fig. 5) along the perturbed glacial AMOC-return pathway (Extended Data Fig. 7), reflecting the more pronounced vertical temperature contrast across the NADW cell in the unperturbed LGMCTRL state (Fig. 2 and Extended Data Fig. 3).

In all experiments, the Atlantic basin temperature response below ~2 km is one of cooling (Fig. 5 and Extended Data Fig. 8) as the NADW cell weakens (Fig. 4a) and shoals (Extended Data Fig. 7) during the first ~200 years of hosing. Compared with PIDPERT, the more pronounced LGMPERT cooling between 2.0 and 2.5 km (Fig. 5c) reflects the initially shallower NADW cell (Extended Data Fig. 3) as the AMOC is perturbed (Extended Data Fig. 7). Below this depth, however, cooling in LGMPERT is weaker than in the PIDPERT (Fig. 5c). At first glance, this is perplexing since shoaling of the overturning cell (Extended Data Fig. 7) and isopycnals at these depth levels is more pronounced in LGMPERT (the density levels at 3,000 m depth in PIDCTRL and LGMCTRL shoal by ~160 m and ~230 m, not shown). However, the phenomenon is a direct consequence of the build-up of relatively warmer waters in the glacial deep ocean (with respect to intermediate depths) permitted by the increase in salt stratification (Fig. 3 and Extended Data Fig. 6).

As predicted, this fundamental change in deep-ocean stratification (from temperature controlled in PIDCTRL to one that is dependent on a stable haline density gradient in LGMCTRL) leads to a very different SO surface temperature response to North Atlantic freshwater forcing and AMOC perturbation. In PIDPERT, cooling is observed across the surface SO due to the upwelling of cold deep waters when the AMOC is in a perturbed state. By contrast, for LGMPERT between ~100 and 200 years we observe a continuous surface warming across Antarctic circumpolar latitudes south of ~45° S and extending into the Drake Passage (south of ~55° S), reflecting the upwelling of relatively warmer waters that characterize the glacial deep ocean in our simulations (Fig. 5 and Extended Data Figs. 8 and 9). It is important to emphasize that cooling does occur in the deep ocean during LGMPERT (Fig. 5b), but this cooling is reduced relative to PIDPERT (Fig. 5c) and, in combination with warming at intermediate depths, produces a net warming at the SO surface.

The contrasting SO surface temperature responses lead to very different temperature responses over Antarctica (Fig. 4e). In fact, the integrated surface heat flux anomaly south of 55° S is of opposite signs in LGMPERT and PIDPERT. Only in the glacial state does the AMOC perturbation result in atmospheric warming in the southernmost ocean region. When combined with atmospheric heat transport, the positive ocean–atmosphere heat flux observed in LGMPERT produces by far the largest and fastest temperature rise across Antarctica within the first ~200 years when compared with PIDPERT and 40kaPERT (Fig. 4e). After ~200–300 years, NADW strength and geometry have largely adjusted to the persistent freshwater perturbation, and Antarctic warming proceeds at a reduced rate.

## Salty glacial deep ocean and deglaciation

We have demonstrated that a fundamental change in deep-ocean stratification can lead to a greatly enhanced climatic response to AMOC weakening while in a glacial state. The simulated Antarctic seesaw response is amplified by a factor of ~2 on a multicentennial timescale compared with interglacial or subglacial conditions. The surface cooling (as opposed to warming) that we observe in the SO high latitudes under pre-industrial and subglacial conditions might be a model-specific characteristic12, but it is important to note that the key to an amplified seesaw warming is a more pronounced haline to thermal density stratification ratio (which is predicted from proxy reconstructions, as described earlier). Increasing this ratio has the same effect irrespective of the climate background conditions, as shown in the phase space analysis in Fig. 3. The underlying mechanism might also therefore represent a key to understanding the spread of SO high-latitude responses in previous glacial AMOC perturbation experiments using a range of models47. For the specific model used in our study, a damped SO surface temperature response is obtained for LGM experiments using a modern-like salinity stratification29 as employed by Kageyama et al.47.

Our simulations do not include a representation of the global carbon cycle, but several previous studies have called on AMOC-induced stratification changes within the SO as a key player in glacial–interglacial CO2 variability48,49,50,51,52. Furthermore, it has also been suggested that AMOC-induced CO2 changes53 might provide an internal feedback with the potential to promote transitions between different climate states54. Abrupt changes in the mode of AMOC occurred throughout the last glacial period13 and were linked to temperature changes across Antarctica and (on occasion) variations in CO255, and yet only those changes associated with the last termination were sufficient to mark the transition back to an interglacial state. Previous studies have suggested various combinations of ice-sheet size2 and specific orbital configurations1,56 in an attempt to explain why glacial termination occurs only when it does. Our findings provide an alternative explanation: that global-scale water-mass salinity characteristics represent a key player to promote deglaciation once a salty deep-ocean reservoir has been formed at full glacial conditions.

## Methods

### Rate of change in Antarctic temperature records

In Fig. 1, the relatively large rates of change observed in the upper sections of the record (particularly the Holocene, which has not experienced high-amplitude millennial-scale variability) using a 200 yr pre-smooth reflects the much higher temporal resolution of the upper sections of ice cores relative to deeper sections. Using a pre-smoothing of 500 yr alleviates this problem while (in our opinion) preserving an accurate (not overly smoothed) representation of the relative rates of change associated with millennial-scale events.

### Model description

We use the comprehensive fully coupled Earth system model COSMOS (ECHAM5-JSBACH-MPIOM) in this study. The atmospheric model ECHAM558, complemented by a land surface component with dynamic vegetation JSBACH59, is used at T31 resolution (~3.75°), with 19 vertical hybrid sigma-pressure levels. The ocean model MPIOM60, including sea-ice dynamics that are formulated using viscous-plastic rheology61, runs on a bipolar curvilinear Arakawa-C grid. The grid size (120 × 101) corresponds to a formal longitudinal resolution of ~3° (360/120) and a latitudinal resolution of ~1.8° (180/101). The vertical domain is represented by 40 unevenly spaced depth layers. The climate model has already been used to simulate, for example, the past millennium31, the Miocene warm climate62,63, the Pliocene64, the internal variability of the climate system65, the Last Glacial Maximum climate29,47 and glacial millennial-scale variability at intermediate climate conditions54,66. The glacial (LGMCTRL) and pre-industrial (PIDCTRL) states used in our study are experiments LGMW and PI from Zhang et al.29. The glacial state is characterized by a salty deep-ocean reservoir in reasonable agreement with available salinity reconstructions. Note that the generation of an interglacial-to-glacial salinity reversal is expected to be dependent on, for example, the model itself, the model configuration and the experimental set-up (Extended Data Fig. 10). However, for the mechanism described here, a salinity reversal per se is not necessary. The data-based demand that the temperature gradient between northern and southern sources of deep water within the Atlantic was reduced during the LGM compared with today20 implies that a reduction in the thermal deep-ocean stratification was accompanied by a stronger glacial salinity increase of AABW relative to NADW. Were this not the case, then the density stratification of the glacial South Atlantic/SO would necessarily have been weaker than today. A simple evaluation for the importance of a glacial salinity reversal for glacial–interglacial density changes is provided in the corresponding section.

### Experimental design

Besides the pre-industrial (PIDCTRL) and the Last Glacial Maximum (LGMCTRL) control climates from Zhang et al.29, we conduct an equilibrated MIS3 control simulation (40kaCTRL) by imposing fixed boundary conditions for 40 ka. In detail, the three orbital parameters in experiment 40kaCTRL are 0.013146 (eccentricity), 358.17° (precession of the equinoxes, the angle between the Earth’s position during the Northern Hemisphere vernal equinox and the orbit perihelion) and 23.61° (obliquity)67. The greenhouse gas concentrations are 195 ppm (CO2), 413 ppb (CH4) and 231 ppb (N2O)68,69. The ice-sheet configuration is a combination of ice-sheet reconstructions from ICE-5G70 and PMIP3. That is, the topography anomaly between 40 ka and the LGM in ICE-5G is first calculated and then is added to the PMIP3 LGM topography29. Global mean sea level is ~80 m lower at 40 ka than the pre-industrial level. Experiment 40kaCTRL is integrated for 5,000 years to an equilibrated state that serves as the starting point for the perturbation experiment.

Identical hosing experiments are then conducted under the three different climate backgrounds in experiments PIDPERT, LGMPERT and 40kaPERT. A freshwater flux of 0.15 Sv is added to the Ruddiman Belt (40°–55° N, 45°–20° W) for 800 years to ensure a quasi-equilibrated response in the SO. A freshwater perturbation of 0.15 Sv agrees with estimates of deglacial meltwater release during Heinrich Stadial 1 as assessed in different studies71,72,73. Global mean sea-level height is corrected for the input of additional freshwater. Hence, coastlines remain the same during a freshwater perturbation experiment. Averages of 100 years are shown in our results.

### Vertical temperature and salinity changes

On the basis of the linear approximation of the density equation and neglected pressure variations, we can calculate density changes with depth by:

$$\frac{{{\mathrm{d}}\rho }}{{{\mathrm{d}}z}} = \rho _0 \left( { - \alpha_{\mathrm{T}}\frac{{{\mathrm{d}}T}}{{{\mathrm{d}}z}}} \right. + \beta_{\mathrm{S}}\left. {\frac{{{\mathrm{d}}S}}{{{\mathrm{d}}z}}} \right)$$
(1)

where ρ0 is density, T is temperature, S is salinity, αT is the thermal expansion coefficient and βS is the haline contraction coefficient. So that a temperature contribution to density changes with depth equates to:

$$\frac{{{\mathrm{d}}\rho_{\mathrm{T}}}}{{{\mathrm{d}}z}} = - \rho _0 \alpha_{\mathrm{T}}\frac{{{\mathrm{d}}T}}{{{\mathrm{d}}z}}$$
(2)

and a salinity contribution equates to:

$$\frac{{{\mathrm{d}}\rho _{\mathrm{S}}}}{{{\mathrm{d}}z}} = \rho _0 \beta _{\mathrm{S}}\frac{{{\mathrm{d}}S}}{{{\mathrm{d}}z}}$$
(3)

Rearrangement of equation (2) leads to:

$$\frac{{{\mathrm{d}}T}}{{{\mathrm{d}}z}} = - \frac{{{\mathrm{d}}\rho_{\mathrm{T}}/{\mathrm{d}}z}}{{\alpha_{\mathrm{T}} \rho _0}}$$
(4)

Further substituting dρT/dz in equation (4) by:

$$\frac{{{\mathrm{d}}\rho _{\mathrm{T}}}}{{{\mathrm{d}}z}} = \frac{{{\mathrm{d}}\rho }}{{{\mathrm{d}}z}} - \frac{{{\mathrm{d}}\rho_{\mathrm{S}}}}{{{\mathrm{d}}z}}$$
(5)

temperature changes with depth can be expressed as a function of the ratio between the haline and thermal density changes with depth:

$$\frac{{{\mathrm{d}}T}}{{{\mathrm{d}}z}} = - \frac{{{\mathrm{d}}\rho/{\mathrm{d}}z}}{{\alpha_{\mathrm{T}}\rho _0}}\left( {1 + \frac{{{\mathrm{d}}\rho_{\mathrm{S}}/{\mathrm{d}}z}}{{{\mathrm{d}}\rho_{\mathrm{T}}/{\mathrm{d}}z}}} \right)^{ - 1}$$
(6)

### Formation of a salty glacial deep ocean: model limitations

State-of-the-art AOGCMs lack fully interactive ice-sheet components and do not allow to simulate increased glacial melt in response to ocean warming. Furthermore, essential processes such as ice shelf–ice cavity ocean interactions are not included in the current generation of fully coupled AOGCMs74, which limits the ability to investigate a fuller spectrum of relevant processes and interactions such as the ‘pre-freshening’20 of AABW via NADW. Furthermore, the ocean model component in our study and other global climate models is too coarse to represent the northward transport of dense shelf waters across the Antarctic shelf edge and their subsequent sinking to depth74, which represents a fundamental source of abyssal ocean circulation in the modern ocean. However, there is another mode associated with open-ocean convection75 that has been identified as an additional surface to deep-ocean exchange process based on satellite data76,77. This modern mode with notable deep (>2,000 m) open-ocean convection between 90° S and 55° S under pre-industrial conditions has been diagnosed in more than two-thirds of the CMIP5 models. While this polynya-induced mode is not dominant today, it could have been the main source of AABW formation during full glacial conditions with a widely ice-covered continental shelf and a lower sea level than today. This situation might have favoured a glacial open-ocean type convection mode that is free to reach the seafloor75.

In that sense, a dominant glacial production regime of AABW by open-ocean convection, predominantly in the centres of the Weddell and Ross Sea gyres, as modelled in our model set-up78 might capture the actual glacial water-mass conversion much better than under modern conditions.

To test the viability of the mechanism for the generation of a salty glacial deep ocean as proposed by Adkins20, we have evaluated how far our simulated control states are consistent with less melting of Antarctic ice by colder NADW during glacial conditions. In this context, we have applied the Potsdam Ice-Shelf Cavity Model (PICO)79 to quantify changes in the subshelf melt rates. PICO is developed from the ocean box model of Olbers and Hellmer80 and is implemented as a module of the Parallel Ice Sheet Model (PISM)81 to simulate the vertical overturning circulation in ice-shelf cavities and thus enables the computation of subshelf melt rates (Extended Data Fig. 4) consistent with this circulation. We run the simulations at a spatial resolution of 16 × 16 km. The PICO settings are the standard settings that were used by Reese et al.79 to obtain a realistic pre-industrial ice sheet. The PISM settings were taken from Sutter et al.82, and the atmospheric forcing is from regridded yearly RACMO2.3 2 m air temperature and precipitation fields83.

Driving this model set-up with the thermohaline ocean fields of experiment PIDCTRL in equilibrium simulations of 200 kyr we end up with an aggregated melt flux of ~1,400 Gt yr−1 (Extended Data Fig. 4a), which is not far from the observed value 1,500 ± 237 Gt yr−1 for present-day conditions84. Keeping the same experimental set-up but replacing the thermohaline fields by the 40kaCTRL and LGMCTRL fields, results in a reduction of the aggregated melt flux by ~26% and 50%, respectively. This suggests that a reduction of Antarctic ice melt by colder NADW could indeed contribute to the generation and maintenance of a salty deep-ocean reservoir, especially since surface melt rates are negligible in the contribution to Antarctic ice-mass loss for modern climate conditions and colder climates. Hence, attempts should be made to incorporate this mechanism in future Earth system model approaches to explore essential interactions in particular at the ice–ocean interface, and it is open to question how far a fuller representation of the AABW formation mechanism would lead to a different model response. These investigations should be combined with the analysis of, for example, benthic foraminiferal δ18O and Mg/Ca records to discriminate sea-ice-derived versus Antarctic-ice-derived salinity stratification.

### Glacial deep-ocean salinity structure in models of different PMIP/CMIP generations

Currently, there is no collective framework of perturbation experiments for glacial and interglacial conditions that would allow us to test our perturbation experiments within a model intercomparison. Nevertheless, we have generated an overview of simulated glacial deep-ocean salinity structure in LGM states (unperturbed) encompassing the last three PMIP/CMIP model generations (Extended Data Fig. 10).

Using the same model as employed in our study, the glacial deep-ocean salinity structure (including a PMIP2/CMIP436,37 model intercomparison) was investigated in the study of Zhang et al.29. From the six other models in that study, two models (CCSM385 and HadCM3M286) also generated a stable glacial salt stratification (Extended Data Fig. 10). Note that PMIP utilized no specific protocol concerning the initial ocean condition for LGM simulations36,37, and notably the three models (including COSMOS) that were initialized from a previous glacial ocean state were the only ones to simulate a stable glacial deep-ocean salt stratification29. We suggest that this difference is a key to the different outcomes.

In model simulations at hand for the PMIP3/CMIP538,39 and PMIP4/CMIP640 generations, the north–south deep-ocean salinity contrast is dominated by a relatively salty North Atlantic, except within CCSM487. In that model, saltier deep SO conditions are simulated, but these salinity characteristics do not extend into the Atlantic basin. Hence, the simulation of a salty glacial deep ocean via AABW at a global scale is not a coherent characteristic in LGM simulations with current coupled AOGCMs.

Where do we stand now? We think at least three possibilities should be taken into account for further research:

• The inference of a salinity-stratified glacial ocean via AABW has been questioned, and the scarce pore-water chlorinity data availability necessitates an increase in data constraints88.

• The simulation of a salty deep ocean seems to depend on conditions before the LGM, which therefore need to be incorporated into transient simulations rather than initiating models with LGM boundary conditions29. In particular, orbital configurations incorporating low obliquity and low atmospheric CO2 concentrations in combination with Northern Hemisphere ice sheets in a later stage of a glacial cycle (but before the glacial maxima) should be considered as an alternative framework for simulating a salty glacial deep ocean29,30.

• Models need to be improved; accurate formation of AABW via shelf processes is an ongoing challenge41. Furthermore, important processes such as interactive ice sheets and shelf–ice cavity ocean interactions need to be included for detailed studies, and we note that the mechanism of deep-ocean salinification proposed by Adkins20 (Extended Data Fig. 4) could work in tandem with increased sea-ice export to produce highly saline bottom waters. Recently, it has also been suggested that the export of icebergs from the SO to the Atlantic basin might modify interglacial-to-glacial salt balance between NADW and AABW42. As yet, these key processes and mechanisms are missing in coupled climate models, and therefore the conjecture that models that are simulating the salty reservoir might do it for the wrong reason cannot be excluded.

### Glacial deep-ocean salinity constraints

The observation/reconstruction of extremely high glacial SO salinities and abyssal waters is very scarce, and a salinity value of 37.1 ± 0.2 PSU at Shona Rise26 represents a singularity that has been questioned by the analyses of pore fluid chlorinity/salinity data from deep-sea cores using estimation methods deriving from linear control theory88. Similarly to the ‘glacial’ state in Galbraith and Lavergene30, we simulate a lower salinity at this core location (36.04 PSU). Aside from this extreme salinity value, our simulated salinity in the deep Pacific between 3,500 m and 5,500 m is 36.03. This value is within the uncertainty of the reconstructed salinity (36.1 ± 0.1) based on chloride concentrations of deep Pacific bottom waters at five different core locations containing the same depth range27.

### Estimates for the importance of salinity changes

To estimate the importance of interglacial-to-glacial salinity changes for the maintenance of deep-ocean stratification, we suggest two simple criteria. One criterion can help to evaluate the necessity of salinity changes in the evolution of the simulated glacial temperature structure. For example, in the PIDCTRL and LGMCTRL experiment pair (Fig. 2), an unstable glacial situation applies if:

$$\frac{{{\mathrm{d}}\rho _{{\mathrm{T}}\_{\mathrm{LGM}}}}}{{{\mathrm{d}}z}} + \frac{{{\mathrm{d}}\rho _{{\mathrm{S}}\_{\mathrm{PID}}}}}{{{\mathrm{d}}z}} < 0$$
(7)

That is, the glacial temperature decrease with depth is too weak to balance the effect of pre-industrial salinity decrease with depth on density (compare Extended Data Fig. 1).

While the latter criterion can help to assess the necessity of salinity changes, it does not answer the importance of a salinity reversal and the transition from an unstable to a stable salinity structure. Therefore, we additionally suggest to compare the LGMCTRL with a PIDCTRL temperature gradient that would result from the shift of the unstable to a neutral salt stratification. This can be depicted in Fig. 3. Here the glacial cooling with depth (blue dot) is weaker than the intercept of the PIDCTRL solution with the y axis. The corresponding criterion can be expressed as:

$$\frac{{{\mathrm{d}}T_{\_{\mathrm{LGM}}}}}{{{\mathrm{d}}z}} > - \frac{{{\mathrm{d}}\rho /{\mathrm{d}}z}}{{\alpha _{{\mathrm{T}}\_{\mathrm{PID}}}\ \rho _{0\_{\mathrm{PID}}}}}$$
(8)

That is, even if the unstable haline stratification contribution to dρ_PID/dz would be replaced by a neutral haline density stratification (dρS_PID/dz = 0), the reduced thermal stratification along solutions with constant dρ_PID/dz, αT_PID and ρ0_PID still requires a cooling with depth, which is stronger than dT_LGM/dz.