The simulated global mean LGM near-surface air temperature (SAT) in our model ensemble is 5.0 to 5.8 K colder than the PI reference state (Fig. a). The simulated cooling pattern shows a strong polar amplification illustrated by the significantly larger cooling in the high northern latitudes (9.1 to 9.8 K) than in the tropics (between 3.0 and 3.5 K; Fig. d and c). In the southern high latitudes, the simulated LGM climate is between 4.6 and 6.3 K (mean: 5.1; median: 4.8) colder (Fig. b). These values lie well within the LGM (21 ka) climate signal from the PMIP4 ensemble (3.7 to 6.8 K). Our estimates also agree well with estimates of LGM SAT anomalies from available reanalysis and reconstruction data sets (see Fig. ). For validation, we use recent products either based entirely on proxy data such as the PalMod reconstructions, based on the methodology and proxy data described insee Appendix  or data assimilation products that use either a single model or an ensemble of models . Globally, our simulated SAT anomalies (mean: -5.2 K; median: -5.1 K) align with the range of reconstructed SAT anomalies of the PalMod reconstructions (Appendix ) of -4.1 and -7.1 K (mean: -5.6 K) and the reanalysis of of -6.5 to -3.5 K (mean: -5.0 K) and of -2.9 to -6.0 K (mean: 4.5 K). The reanalyses of and and to a smaller extent the reconstructions of are consistently colder than our ensemble (-6.3 to -7.4 K, -5.7 to -6.5 K, and -7.5 to -5.1 K, respectively) and the data assimilation product. The same signal is present through regional estimates for the northern and southern extratropics and tropics, where our ensemble mean is slightly colder than but warmer than and . Thereby nearly all ensemble members fall into the uncertainty range of the estimates, except for D1.3 for the tropics and southern extratropics.

Maximum cooling is simulated over the Laurentide and Fennoscandian ice sheets (Fig. ), where the higher surface elevation leads to an additional cooling effect. Also the North Atlantic shows a rather strong cooling, which is related to extended sea-ice cover (Fig. ). In general, the simulated pattern of cooling is rather similar to the ensemble mean pattern from the CMIP6 LGM time-slice simulations their Fig. 1 and the reanalysis product of . The spatial pattern of the reanalysis product by is also very similar to our ensemble, but the amplitude of the cooling is considerably stronger. The bias of the simulated PI SAT and sea-ice edge compared to an observation-based estimate is shown in Fig. .

The simulated sea-ice extent on the Northern Hemisphere for the PI period is fairly close to the extent derived from the HadISST data set for the years 1951 to 1990 (; see isolines in Figs.  and ). The main discrepancy is an underestimation of the sea-ice extent in the Southern Ocean.

For the LGM, the ensemble spread for the winter sea-ice extent in the North Atlantic is considerable. Some simulations show an ice-free northeast Atlantic and others a state with winter sea ice that covers nearly the entire North Atlantic north of 40° N. The northwest Atlantic is seasonally sea ice covered in all simulations. In the North Atlantic, the GLOMAP reconstruction does not show a large difference between the northwest and northeast Atlantic. It is worth noting that simulation D2.1 does not show such a contrast either. The Norwegian Sea is only seasonally covered by sea ice in all simulations, whereas most of the Greenland Sea and Iceland Sea are permanently covered by sea ice. GLOMAP indicates seasonal sea-ice cover in the entire Nordic Seas, with the LGM summer sea-ice margin even being north of its position in the 20th century in the HadISST data set . The simulated Southern Ocean sea-ice cover is seasonal, except for some regions close to the coast of Antarctica. The model generally underestimates the summer sea-ice extent in the Southern Hemisphere, both for PI as well as for LGM. The simulated winter sea-ice extent in the Southern Ocean matches the GLOMAP data set well.

The maximum strength of the NADW cell at 26.5° N, which defines the AMOC strength, varies in our PI ensemble between 18.3 and 24.8 Sv (ensemble median is 20.0 Sv) and is located at a depth slightly deeper than 1000 m (see profile of the AMOC at 26.5° N in Fig. a). From measurements of the RAPID array at the same latitude for the years 2004 to 2017, the strength of the AMOC has been estimated to be 17.0 ± 4.4 Sv . The strength of the Antarctic Bottom Water (AABW) cell at 26.5° N varies between 0.4 and 2.5 Sv for the PI ensemble.

For the LGM, the spread of the AMOC strength is much larger, showing values between 14.7 and 26.3 Sv, with an ensemble median of 16.8 Sv. Except for simulation D1.2, all runs show a shallower and slightly weaker AMOC cell during the LGM than for their PI counterpart. The vertical extent of the NADW cell, for which the lower boundary is defined as the depth below 2000 m where the AMOC strength equals zero, becomes shallower by 250 to 450 m for almost all individual ensemble members. However, both the spread of the maximum strength of the NADW cell as well as that of the depth of its lower margin are about twice as large for the LGM as compared to the PI simulations. The prescribed vertical background mixing in the ocean has a very large effect on the AMOC profile, as can be seen from comparing simulations D1.2, D1.1, and D1.3 (see Fig. a). Lower vertical mixing reduces ocean heat transport to high southern latitudes, which results in a substantial cooling (2.4 K colder LGM SATs south of 60° S in D1.3 compared to D1.1). This enhances sea-ice formation and thus brine release. For the LGM, the integrated brine release in locations with a positive net sea-ice formation in the Southern Ocean is 28 % higher in D1.3 compared to D1.1 (calculated from decadal mean data), resulting in saltier and denser AABW. Glacial NADW becomes colder as well but also fresher. Thus, the effective change in density is much smaller than in the south, similar to the findings of . The reduced vertical mixing enables a prolonged preservation of the density excess of AABW compared to NADW on its path towards the deep North Atlantic. The consequence is a weakening and shallowing of the NADW cell and an enhanced presence of AABW (see Fig. b). Stronger vertical mixing has the opposite effect and leads to a LGM AMOC that is even stronger and deeper than its PI counterpart. Overall, the effect of changes in vertical mixing on the AMOC is larger for the LGM than for PI.

has suggested that the reduced shelf area during LGM leads to stronger tides. applied a tidal model and report an enhanced energy supply from tides to the internal wave field (1.8 to 3 times higher for LGM than at present, depending on the ice-sheet geometries). As we used a time-constant background mixing in our simulations, this effect is not included.

For the PMIP4 ensemble, most LGM simulations show a weak deepening and a substantial strengthening of the AMOC (Fig. b). This is in contrast to estimates based on proxy data that indicate a shallowing of the AMOC core and a reduction of the circulation strength e.g., in line with our results.

For the assessment of the past AMOC changes, we analyse changes in the dye tracer, which indicates the relative contribution of the water masses originating from the surface of the North Atlantic and Arctic. A decreasing dye fraction reflects the larger contribution of water which originates from other source regions, which in the Atlantic below 2000 m is primarily AABW. The dye fraction at 26.5° N shows the core of NADW for PI at depths between 1500 and 3000 m (Fig. c). The depth of 3000 m corresponds to the lower margin of the AMOC cell. Below 3500 m, the intrusion of AABW becomes visible as a thick layer of water that consists of a mix of NADW and AABW. For the LGM, the core of the NADW lies shallower and has a reduced vertical extent. The deep layers are dominated by AABW. Estimated changes in the NADW distribution from proxy data show a qualitatively similar pattern . Note that the reconstruction of the data by is based on neodymium isotopes, which might underestimate changes in NADW at the LGM due to their source being at the continental slope , unlike other proxies and our dye tracer, which have their source solely at the surface. Reduced vertical mixing leads to stronger differences in the dye profile at 26.5° N between LGM and PI (see Fig. b) in line with the AMOC changes.

Figure  illustrates the distribution of the dye fraction and the location and strength of the cells of NADW and AABW at the PI and the LGM for one ensemble member (D2.1). In agreement with the shallowing of the lower boundary of the NADW cell at the LGM, the vertical extension of the dye fraction higher than 0.5 is limited to the upper 2500–3000 m. Qualitatively, the shift of the distribution of water masses between PI and LGM in our ensemble follows the changes derived from proxy data . However, quantitatively, the change in the AMOC geometry is different from the change in the spatial pattern of the dye fraction. If the lower boundary of the NADW cell is confined by AMOC =0, a dye fraction of about 0.5 is found at a very similar depth at the LGM. For the PI, the dye fraction at AMOC =0 is much higher (around 0.7), and NADW is the dominant water mass in the deep Atlantic north of 20° N. Our dye fraction provides the opportunity to compare simulated depth shifts of the lower boundary of the AMOC cell to changes in the location of NADW identified by the dye fraction (Fig. ). As already apparent from D2.1 in Fig. , almost all ensemble members show that the shallowing of the dye fraction for the LGM is more pronounced than the shallowing of the NADW cell. Ensemble member D1.2, in which the AABW cell does not extend to 26.5° N, has been excluded from this analysis. For the ensemble mean, the depth change in the water mass boundary indicated by the dye fraction is about 35% larger than that for the AMOC cell boundary. Note that the dye fraction has no methodological uncertainty and no potential variations in the source function as is the case for proxy data . The simulated temporal and spatial variations of the dye fraction at AMOC =0 are a result of water mass mixing intensity and emphasize how complicated a straightforward assessment of the AMOC geometry is based on proxy data (see a further discussion in Appendix  and Fig. ). The simulated difference therefore provides a cautionary note for a quantitative validation of AMOC changes with proxy-derived changes in water mass boundaries.

The simulated Laurentide ice sheet for the LGM has a similar size as in the GLAC-1D reconstructions and ICE-6G , as shown in Fig. . Similar to other studies , the largest differences occur at the southeastern margin, where the reconstructions extend further south than the Laurentide ice sheet in the simulations. Moreover, the simulated Laurentide ice sheet shows a clear two-dome structure – one dome covering the Cordilleran (western Laurentide) ice sheet and the second, more prominent dome, covering the eastern Laurentide. The latter is not distinctly visible in the reconstructions. However, the reconstructions exhibit considerable uncertainties, especially in the thickness distribution. Differences in ice thickness between the modelled Laurentide ice sheet and reconstructions are most prominent in the Hudson Bay and Mackenzie areas. Both regions frequently exhibit Heinrich event (HE)-like surge events e.g. in our model, which will be discussed in more detail in Sect. . The impression that the Labrador Sea is covered by an ice shelf in our simulations stems from the fact that we average over periods with HE-like surge events, during which a temporary ice shelf forms (Fig. a, e, and m), and more frequent periods without an ice shelf in the central Labrador Sea. The model simulates a Fennoscandian ice sheet that is in good agreement with the reconstructions, with differences restricted to the eastern part of the Fennoscandian ice sheet, where it extends further east in the simulations. All model realizations show an ice mass over northeast Siberia that is not present in the reconstructions. For the PI, our simulations show a realistic Greenland ice sheet and some smaller ice caps over Svalbard, Novaya Zemlya, and other Arctic islands. In general, the size of the ice caps over Norway, Baffin Island, and the Rocky Mountains is overestimated. The largest discrepancy between model and observations occurs in northeast Siberia, where a considerable ice cap survives the deglaciation, containing between 2.4–3.2 m sea-level equivalent.

The comparison of simulated ice-sheet size with ice-sheet reconstructions shows larger discrepancies for Antarctica than for the Northern Hemisphere. In particular, the marine-based regions of the Filchner–Ronne and Ross ice shelves, where the ice sheet retreated significantly during the deglaciation, are different. Similar results were obtained by previous glacial cycle simulations with stand-alone ice-sheet models . All model realizations tend to follow one of the following two scenarios for Antarctica: (i) the ice sheet advances to the continental shelf edge at the LGM but does not retreat far enough during the deglaciation or (ii) the ice sheet does not advance to the continental shelf edge at the LGM but retreats to a position in agreement with present-day observations. This indicates that the parameter space for which our model reproduces the advance and retreat pattern of the Antarctic ice sheet could be narrower than for the Northern Hemispheric counterparts. Therefore, our simulations underline the challenge of successfully simulating the evolution of marine-terminating ice sheets over the course of the last deglaciation

Our simulated SATs show an almost continuous warming (Fig. a) akin to the trajectory of the PalMod reconstructions and those of . Overall, the simulated warming closely follows the prescribed increase in atmospheric greenhouse gas concentrations with the strongest warming between 17 and 10 ka. During the Holocene, our simulations indicate a steady warming trend, which is consistent with the data assimilation product by but in contrast to the PalMod reconstructions, which indicate a slight cooling trend throughout the Holocene. This discrepancy in the Holocene temperature trend is quite typical. For a detailed discussion of the Holocene temperature conundrum see e.g. .

Superimposed on the overall warming trend in our simulations are abrupt millennial- and centennial-scale cooling events (Figs. f, ). This variability is not evident in the proxy-based products due to the lower temporal resolution of the reconstructions, which is a consequence of the methodological design and the quality of the underlying proxy data.

The latitudinal distribution of the deglacial ocean surface warming signal is shown in Fig.  by comparing the sea-surface temperatures (SSTs) over different latitude bands derived from our ensemble to proxy-based estimates. Similar to the global SAT evolution, the SST evolution in the northern extratropics shows a continuous warming throughout the entire simulation, interrupted by several abrupt cooling events. Thereby, the model spread of the transient signal is about 1 K if the abrupt cooling events are excluded (see Fig. ). A slow warming trend is present at all latitudes until 17 ka, after which the warming significantly accelerates. In contrast, both proxy-based data sets show a temperature minimum around 17 to 16 ka, at the time of H1, followed by rapid deglacial warming which tapers off between 14 and 13 ka.

In the proxy data set, the YD cold event peaks between 13 and 12 ka. A similar cooling signal is also modelled in some of the runs (e.g. D1.1, D1.2 and D1.4), albeit with a weaker amplitude than in the reconstructions. In general, the timing of the occurrence of individual abrupt events varies between the model runs. From 12 ka onward, all curves show a strong warming until the beginning of the Holocene. Hereby, the modelled warming rates are lower than suggested by the proxy data. During the Holocene, the model runs indicate a weak warming trend, in accordance with the estimate.

In the tropics, the model simulations show a glacial cooling amplitude that is sandwiched by the proxy data, whereupon the PalMod reconstructions indicate less cold SSTs and the reanalysis of indicates cooler SSTs. The onset of the deglacial warming is overall delayed by approximately 1 kyr. The simulated warming signal at this time is much smoother, and the millennial-scale variability seen in the Northern Hemisphere extratropics is much reduced. While this is in accordance with the reconstructions from PalMod, the reanalysis shows a temporal variability rather similar to the northern extratropics. In addition, during the early phase of the deglacial warming, the model ensemble is slightly colder than the uncertainty range from the PalMod reconstructions.

In the Southern Hemisphere extratropics, the model simulations agree very well with the reanalysis data by and lie within the uncertainty range of the PalMod proxy data. All data sets show a slight warming trend through the glacial period. The deglacial warming starts between 18 and 17 ka. The amplitude of the millennial-scale variability is relatively small compared to the other latitude bands. After 11 ka the mean SST in this latitude belt remains stable, which is also indicated by the proxy data (Fig. c).

At around 25 ka, the simulated Northern Hemispheric ice volume is lower than the ice volume in the ICE-6G and GLAC-1D reconstructions (Fig. b) but matches well with the estimate from the more recent PaleoMIST reconstruction. The discrepancy in ice volume between the simulated and the ICE-6G and GLAC-1D ice sheets originates from the overall thinner simulated ice sheets at the beginning of the simulation, primarily in the central ice-sheet regions. The maximum ice volume for ICE-6G and GLAC-1D occurs around 25 ka, followed by a steady ice-volume decrease. The same time period in our simulations is characterized by an ice-volume gain, as is also shown by the PaleoMIST reconstruction. The long-term mass gain is only interrupted by repeated surge events. The growth of the ice sheet is directly related to the continuously low greenhouse gas concentrations prior to 21 ka, resulting in rather cold climate conditions (Fig. a). In our simulations and the PaleoMIST reconstructions, the simulated maximum ice volume is typically reached at around 18 ka. At this time, the GLAC-1D reconstruction lies also well within our ensemble spread, whereas the ICE-6G reconstruction indicates larger ice volumes than all model realizations. After 18 ka, ice-sheet volume slowly decreases in our simulations, transitioning into the last deglaciation, with the strongest ice-volume loss occurring between 14 and 10 ka. Ice-volume loss tapers off markedly after 8 ka. At PI, our simulations overestimate ice volume in the Northern Hemisphere by 42 %–47 % in comparison to the reconstructions. The main reason for this is the slow melting of the additional ice caps present in eastern Siberia and over Baffin Island (Fig. , second column).

Ocean mixing has a considerable effect on the timing and duration of the deglaciation. Enhanced background mixing in D1.2 leads to a faster decay of the Northern Hemisphere ice sheets compared to D1.1; reduced mixing on the other hand delays the decay (see Fig. b and d). Higher vertical mixing enhances Atlantic heat transport in the North Atlantic (not shown), which in turn leads to a warmer climate (compare experiments D1.3, D1.1, and D1.2 in Fig. ) favouring ice-sheet melt.

As for the Northern Hemisphere, the simulated ice volume in the Southern Hemisphere is lower than indicated by the ice-sheet reconstructions at the beginning of the simulation at 25 ka (see Fig. c). While all reconstruction show either constant ice volume or a slight decrease after 25 ka, our simulations exhibit an ice-volume gain until 12–10 ka. Most of our model simulations show an ice-volume decrease only afterwards. However, the magnitude of the ice-volume loss is not large enough over the remaining simulation period, resulting in an Antarctic ice sheet that is too extensive and for which the grounding-line positions are too advanced for PI. Overall, the simulated and reconstructed ice-volume evolution does not match with reconstructions as well as for the Northern Hemisphere. In particular, the advance and retreat magnitudes of the simulated Antarctic ice sheet are underestimated and do not show enough fidelity. As the signals arising from changes in the Antarctic ice sheet are rather small, they did not have an obvious effect on the simulated climate signals during the deglaciation.

The net water flux into the ocean (Fig. d), which on centennial mean timescales is almost identical to the time derivative of the mass of the terrestrial ice sheets, aligns with the growth of the Northern Hemisphere ice sheets during the last part of the glacial. This growth is interrupted by strong discharge events on millennial timescales. From 17 ka onward, the net water flux remains largely positive as a result of the ongoing decay of the ice sheets, with melt rates (direct meltwater discharge as well as melting icebergs) larger than 0.1 Sv between 14 and 10 ka. At the end of the deglaciation, around 8 ka, the ice-sheet mass loss and hence the net water flux reduces drastically and stays relatively constant through the entire Holocene.

From sea-level reconstructions at Barbados, showed the existence of two meltwater pulses. For the first one, MWP1A, estimated melt rates larger than 0.46 Sv for more than 300 years. MWP1A coincides with the rather warm BA period. Ice-sheet reconstructions such as ICE-6G and GLAC-1D suggest that most of the meltwater was discharged into the North Atlantic or Arctic Ocean. None of our coupled simulations produces an amount of meltwater similar in magnitude to MWP1A around 14 ka. However, meltwater pulses close to 0.4 Sv do occur in our simulations during some of the abrupt events. The existence of the second meltwater pulse, MWP1B, before 11 ka was questioned by based on sea-level reconstructions from the tropical Pacific. It is not simulated by our model either.

The time series of the maximal strength of the AMOC cell at 26.5° N shows marked millennial-scale variability during the glacial period (Fig. e). The spread between the ensemble members is considerable. Most simulations show a strengthening of the AMOC from the glacial to the late Holocene. However, there are also simulations with a rather small change in the AMOC between LGM and PI and one simulation (D1.2) with a stronger AMOC at the LGM than at the PI. During the peak of the deglaciation, all simulations show a weakening of the AMOC, which we explain as the response to meltwater hosing, enhancing vertical stability and reducing the ventilation of the deep-water masses. The slow warming in response to rising greenhouse gas concentrations further amplifies vertical stability. Except for short periods of time, the model AMOC is always in a strong mode.

The first deglacial meltwater peak in D2.1 occurs around 18.0 ka (event 1 in Fig. a). The snapshot maps (see Fig. a) show that the event at this time is caused by a surge event from the Fennoscandian ice sheet, with massive iceberg discharge into the Norwegian Sea. This enhances iceberg melt in the Nordic Seas and the North Atlantic. The meltwater reduces surface salinity, suppresses deep convection, and consequently leads to a weakening of the AMOC and an upward shift of the margin between AABW and NADW (Fig. b). These changes are accompanied by a surface cooling in the North Atlantic (see Figs. c and f). Note that the SST cooling in the subpolar and the subtropical North Atlantic associated with AMOC weakening events is of similar magnitude during the glacial and early deglaciation (Fig. c). The glacial temperature at the subpolar location is already rather close to freezing point, which very effectively limits the potential amplitude of any cooling signal at this location.

The next meltwater peak, occurring around 17.22 ka (marked as 2 and 3 in Fig. a), is caused by surges from the Laurentide ice sheet (Fig. b). The event consists of two almost synchronous surges from two source regions of the Laurentide ice sheet. First, a surge in the western part of the Laurentide towards the Arctic occurs. While this surge slows down, another surge takes place from the eastern Laurentide through the Hudson Strait (Fig. c). This abrupt event is rather strong, with a weakening of the AMOC down to 3.9 Sv at 17.2 ka (as indicated in the 100-year means in Figs. b and e). As a result, the margin between the NADW and the AABW cells shifts upward by approx. 800 m. The depth of the 70 % NADW dye fraction moves upward and reaches a maximal uplift of about 400 m 200 years later. The two surges combined discharge a water equivalent of almost 8 m of global sea level within 450 years. This is within the previously reported range for HEs of 2–20 m over a time period of 500 years .

The next event, at approximately 15.14 ka (marked as 4 in Fig. a), is again caused by a discharge event from the Fennoscandian ice sheet into the Norwegian Sea (Fig. d). It is followed by the last big iceberg discharge event around 13.64 ka (event 5 in Fig. a) from the eastern Laurentide ice sheet through the Hudson Strait (see Fig. e). As the deglacial warming is already ongoing during these two events and the temperature at the subpolar location is now well above the freezing point, the SST cooling signals in the subpolar location are now stronger than in the subtropics, similar to the responses known from typical PI hosing experiments e.g..

After 13.64 ka, the North Atlantic in D2.1 shows two more distinct SST cooling events (marked as 6 and 7 in Fig. ). The first of these events reaches a temperature minimum around 11.83 ka and the other one at 10.4 ka in simulation D2.1 (Fig. c). They coincide with a significant decrease in the maximum AMOC strength (Fig. b). But, unlike the previous events, they cannot directly be associated with an abrupt increase in the total amount of meltwater and/or iceberg discharge from the Laurentide or Fennoscandian ice sheets (Fig. a).

The first of these two cold events takes place during the peak of the deglaciation (event 6 in Fig. a). During this time, the Laurentide and Fennoscandian ice sheets experience significant mass loss in response to the increase in global temperatures and summer insolation. This is indicated by an increase in global meltwater release (Fig. a), which is most pronounced in the Arctic (Fig. b). This meltwater input into the Arctic leads to a regime shift in the net freshwater budget of the Arctic Ocean. This quantity is defined as the balance between the meteoric freshwater input (river runoff, precipitation, and iceberg melt minus evaporation) and the export of sea ice from the Arctic into the adjacent seas, which represents a measure for the integrated net freezing rate of Arctic sea ice and the associated brine release. During the glacial period, the Arctic sea-ice export and thus the brine release dominates over the meteoric freshwater input. Hence, the water leaving the Arctic has a higher salinity and colder temperatures and is therefore denser than the inflowing water of Atlantic origin. As a consequence, it contributes to the formation of NADW. Due to the increase in meltwater input from the Laurentide ice sheet into the Arctic Ocean, the net freshwater budget becomes positive for the first time at about 12.47 ka. This means that the Arctic transitions from a state with an effective net freshwater loss due to sea-ice formation and export to a state with a positive net freshwater budget (Fig. b). While this transition occurs rather gradually and takes until about 11.78 ka to be completed in D2.1, it allows for an abrupt decrease in the surface salinity in the Arctic, as the positive net freshwater input allows for a halocline to develop. This stabilizes the stratification in the Arctic and suppresses deep convection in the Arctic. Furthermore, the water leaving the Arctic is now fresher and less dense than the inflowing water. The resulting reorganization of the NADW formation leads to a decrease in AMOC strength. At first the AMOC weakening is rather gradual and overlaid by large centennial-scale variability. The gradual decrease in Arctic sea-ice export starting at about 12.0 ka results in a further increase in the net freshwater budget and ultimately leads to an abrupt weakening of the AMOC (Fig. c).

The overall increase in sea level and the retreat of the ice sheets result in the opening of the Bering Strait and the Barents Sea Opening at about 11.37 and 11.18 ka, respectively. Here, we use the term Barents Sea Opening for the gateway between Svalbard and continental Europe, enabling throughflow between the Norwegian Sea and the Arctic. The opening of the Bering Strait leads to a considerable reduction of Arctic sea-ice volume (about 20 %) and results in a net export of freshwater into the Pacific (not shown). The opening of the Barents Sea Opening further allows for additional sea-ice export to the Nordic Seas (about 20 %). Hence, the opening of both straits ultimately increases the surface salinity in the Arctic, which decreases the stable stratification, enhances the deep-water formation, and allows for an increase in the AMOC strength to nearly pre-event values. Note that the AMOC recovers slightly before the abrupt salinity increase in the Arctic in response to the opening of the Bering Strait. This increase can likely be attributed to a substantial centennial to millennial variability of the AMOC (see Fig. a and c).

It is noteworthy that the freshwater input into the Nordic Seas increases rather rapidly around the time of the opening of the Barents Sea Opening at 11.18 ka. This increase is associated with a redirection of meltwater from the southern margin of the Fennoscandian ice sheet. Relatively small changes in the land–sea mask and ice-sheet margin allow for a redirection of these waters from the North Sea towards the northeast into the White Sea and eventually into the Barents Sea, causing an abrupt increase in the freshwater input into the Nordic Seas (see Fig. b) and reduction in Nordic Seas surface salinity.

The second of the non-surge-induced cooling events (about 10.4 ka; event 7 in Fig. ) is driven by a redirection of meltwater from the Laurentide ice sheet. At this time, much of the meltwater from the Laurentide ice sheet is routed through the St. Lawrence or Mackenzie rivers and ends its path either in the North Atlantic or Arctic, respectively. The paths of the two rivers follow the southern edge of the Laurentide ice sheet and are separated by a drainage divide located northwest of today's Great Slave Lake (Fig. a). At about 10.49 ka, the continued retreat of the northwestern part of the Laurentide ice sheet in conjunction with changes in the land topography through glacial isostatic adjustment allows for the Mackenzie drainage basin to extend much further southeast, all the way towards the Great Lakes (Fig. b). This rerouting leads to a redirection of approximately 0.08 Sv of meltwater from the St. Lawrence River to the Mackenzie River and results in an abrupt increase in meltwater discharge into the Arctic (Fig. b). The freshwater is transported through the coastal boundary currents of the Arctic Ocean towards the deep-water formation sites in the Greenland and Labrador seas, where it leads to a reduction of the NADW formation and thereby a weakening of the AMOC.

The enhanced discharge of meltwater into the Arctic lasts until about 9.41 ka. At this time, the Laurentide ice sheet collapses and splits into two small ice sheets on Baffin Island and in southeast Canada. The associated changes in sea level and glacial isostatic adjustment lead to the opening of the Hudson Bay (Fig. ) and allow for a rerouting of water into the Hudson Bay (Fig. c). A consequence of the ice-sheet collapse is a short increase in the release of icebergs and their melt into the North Atlantic (Fig. g). In response to these changes in the river routing, the AMOC recovers and slowly increases towards its modern strength.

HE-like surges are caused by internal variability of the Northern Hemisphere ice sheets in our model system , which largely follows the classic binge–purge mechanism suggested by . However, the timing of these events is highly variable as shown by the considerable spread between the ensemble members. As the external forcing (orbital parameters and atmospheric greenhouse gas concentrations and for a subset of our ensemble also the volcanic forcing) is identical in all simulations, it cannot serve as explanation for the difference in the timing of the events. As all asynchronous spin-up simulations started from the same state at 45 ka, model parameters obviously have an effect on the timing of the surge events.

To test the role of initial conditions, two additional sensitivity experiments have been performed. These simulations are identical to D2.1, except for slight differences in the initial fields for the ice-sheet and solid-earth model. Instead of the 26 ka conditions, we used the ice-sheet and solid-earth conditions from 27 ka (D2.1.1) and 28 ka (D2.1.2) in the asynchronous spin-up as the initial state. Together with D2.1, the simulations D2.1.1 and D2.1.2 thus allow us to investigate the effect of the initial state of the ice sheet on the timing of the surge events. Of our three main surge regions, the Hudson Strait tends to show the most regular interval between individual events, suggesting a higher predictability of surge events than the other regions. D2.1.1 and D2.1.2 simulate Hudson Strait surge events that are offset by 1 and 2 kyr (Fig. a), which matches the shift in the initial state of the ice sheets and corroborates a high level of predictability shown in previous studies . In agreement with these studies, the level of predictability is considerably lower for the surges originating from the western Laurentide ice sheet. For this region, the spread in the timing and strength of the events is much more irregular, and the simulated shifts in D2.1, D2.1.1, and D2.1.2 are closer to 1 ky instead of the expected 1 and 2 ky (Fig. b) from the initialization. The predictability for our third surge region, the Fennoscandian ice sheet, lies somewhere in between the predictability of the other two surge regions (Fig. c). Overall, our sensitivity simulations clearly demonstrate the importance of the initial conditions for the timing of the surge-induced abrupt events.

Furthermore, the simulated climate over the ice sheets (especially surface mass balance and surface temperature) has an effect on the timing and frequency of the surge events . Together with the rather chaotic surge behaviour of the Mackenzie ice stream, this further enhances the stochastic contribution in the timing of the surge events. Both the initial conditions and the choice of the model parameters influence the timing of the surge event. In consequence, the exact timing of surge-type variability, as derived from observations, cannot be reproduced by a model with interactive ice sheets.

The last two North Atlantic cooling events in D2.1, which are not associated with the occurrence of HEs, can also be identified in most other ensemble members (Fig. e, f). While the timing of the individual events differs between ensemble members, the processes leading to abrupt events in D2.1 are similar in all ensemble members.

In most of our simulations, the onset of the first event not induced by ice-sheet surges is associated with the transition into a regime in which the net freshwater input into the Arctic becomes larger than the sea-ice export to the North Atlantic. This leads, similar to D2.1, in all simulations to the formation of a halocline in the Arctic and a significant reduction in the AMOC strength. However, the timing of the transition towards a positive net freshwater input into the Arctic varies between simulations. Therefore, the timing at which the AMOC strength significantly reduces also differs across ensemble members. For example, D2.2 and D2.3 show weaker AMOC slowdowns and North Atlantic cooling during the onset of this abrupt cooling event than the other simulations. This is likely related to the Bering Strait being open already before the event, at 16.11 ka in D2.2 and 12.28 ka in D2.3 (see Table ), ultimately influencing the freshwater balance by sea-ice export to and the inflow of saltier water from the North Pacific. This is in line with , who showed that the Arctic gateways can have a different impact on the ocean dynamics in the Arctic, depending on whether the Bering Strait or Canadian archipelago are closed or open. Our findings are also in agreement with findings by , who showed that abrupt AMOC transitions are more likely when the Bering Strait is closed. In accordance with , we find that the simulations that exhibit a late opening of the Bering Strait show stronger variations in the Arctic Ocean and AMOC in response to the shift of the sign in the net freshwater balance than the simulations with an early opening.

In our simulations the Bering Strait also plays a pivotal role towards the end of the abrupt event initiated by the changes in the freshwater budget of the Arctic. As shown for D2.1, the opening of the Bering Strait leads to a recovery of the AMOC through an increase in salinity of the Arctic and, thus, a decrease in the vertical stability (see Sect. ). This is the case for all but one of the ensemble members. In line with , who found that the opening of the Bering Strait leads to a substantial salinity increase in the top 50 m of the Arctic Ocean, our simulations show a substantial increase in surface salinity for D2.1 (Fig. b) and the majority of our simulations (D1.1, D1.2, D1.3, D1.4, D2.3, D2.4, not shown). We find that part of this increase in surface salinity can be attributed to a net export of freshwater through the Bering Strait into the Pacific (not shown), which is in agreement with findings by . As the timing of the Bering Strait opening varies significantly between simulations, the full recovery of the salinity also varies. For the simulations with a late opening of the Bering Strait (D1.1, D1.2, D1.3, D1.4), the Arctic is able to maintain low surface salinity and thereby its stable halocline over several millennia. This leads to an overall weaker AMOC with substantially higher variability throughout the course of the deglaciation, until the Bering Strait finally opens (see Table ).

It is noteworthy that the ocean response to an opening/closing of the Bering Strait differs from other studies in some aspects. For example, argue that the opening/closing of the Bering Strait has a substantial impact on the sign of the freshwater budget in the Arctic. They find that if the Bering Strait is opened under deglacial conditions (15 ka), the Arctic changes from a freshwater sink to a freshwater source. Our simulations do not show such a relationship. Rather, they show a transition from a typical glacial state, where the sea-ice export from the Arctic to the Atlantic is larger than the freshwater input into the Arctic, to a state where the freshwater input is larger. Further, our simulations show that this transition is an inherent transient climate response that occurs in all simulations independent of when the Bering Strait is opening. The main difference between the experiments from and our simulations is that an opening of the Bering Strait in our simulations leads to reduced sea-ice export from the Arctic to the Atlantic, whereas their model simulates an increased export. In our simulations, the reduced ice transport is also a result of a reduced sea-ice volume inside the Arctic. These differences are likely related to not considering the effect of freshwater release by melting ice sheets.

A similar sign shift of the Arctic freshwater budget and transition into a slightly weaker AMOC state is also evident in simulations with prescribed ice sheets from the ICE-6G and GLAC-1D reconstructions starting at about 16.09 and 15.86 ka, respectively (see also Table ). The transition from a state where sea-ice export to the Atlantic is larger than the freshwater input into the Arctic to a state where the freshwater input dominates is accompanied by the development of a halocline in the Arctic Ocean in the simulations with ICE-6G and GLAC-1D reconstructions (see ICE6G_P3 and GLAC1D_P3 in Table ). However, the AMOC response in these simulations is much weaker than in the fully coupled simulations (not shown). This is likely related to a relatively low prescribed meltwater input into the Arctic, which was derived from the ice-sheet reconstructions during this time. Only around the time of MWP1A does the freshwater input significantly increase. In general, the simulations with coupled ice sheets show an earlier and more gradual increase in freshwater during the peak of the deglaciation, while the freshwater input into the ocean in the simulations with prescribed ice sheets is dominated by pulses of meltwater. This likely explains the different response.

The deglacial North Atlantic cooling event that is associated with enhanced river discharge into the Arctic due to changes in the river routing also occurs in all our ensemble members (see Table ). It is, consistent with D2.1, in all simulations associated with an expansion of the drainage basin of the Mackenzie River and accompanied by an AMOC slowdown. It agrees with simulations by , where ice-sheets from the ICE-6G reconstructions were prescribed, as well as studies by and , who indicate that a rerouting of rivers caused the YD cooling. Using a high-resolution ocean–sea-ice model, show that freshwater discharged from the Mackenzie River is transported through the narrow coastal boundary currents towards the deep-water formation sites in the Greenland and Labrador seas, where it disrupts the open-ocean convection and thereby weakens the AMOC. In our simulations, the expansion of the Mackenzie drainage basin, due to a small retreat on the southern edge of the Laurentide ice sheet, leads to an abrupt increase in the freshwater input into the Arctic and, thereby, triggers the simulated AMOC slowdown and accompanying Northern Hemispheric cooling consistent with D2.1. In all simulations, the collapse of the Laurentide ice sheet and the opening of the Hudson Bay, which allow for a rerouting of the meltwater previously entering the Arctic Ocean to the Hudson Bay (Fig. ), lead to a recovery of the AMOC. The freshwater reaching the Labrador Sea through the Hudson Strait flows southeastward in a coastal current and has therefore a relatively small effect on the deep convection in the Labrador Sea. Interestingly, the timing of the change in the river routing occurs in some ensemble members before the opening of the Bering Strait (D1.1, D1.2, D1.3, D1.4), hence in a state where the salinity in the Arctic is already reduced and the stratification is relatively stable. Despite this, all simulations show a distinct AMOC weakening in response to the enhanced Arctic freshwater input, indicating that the process itself is consistent throughout all ensemble members (not shown). The results emphasize that changes in the river routing played a crucial role in initiating the North Atlantic cooling events that occur in our simulations between about 12 and 9 ka (Fig. ). Further, the AMOC recovery that follows the opening of the Hudson Bay indicates the importance of changes in the land–sea mask in response to the ice-sheet collapse and associated deglacial sea-level rise for the occurrence of abrupt events. As the changes in river routing and the opening of the Hudson Strait are in all simulations related to the gradual retreat of the Laurentide ice sheet, they appear to be deterministic and, hence, seem to be an integral part of the deglaciation.