The NorESM family is based on the Community Climate System Model version 4 CCSM4; but differs from the latter in several aspects : NorESM uses an isopycnic coordinate ocean model that originates from the Miami Isopycnic Coordinate Ocean Model MICOM;. The atmospheric component Community Atmosphere Model 4 (CAM4) has the option to use modified chemistry–aerosol–cloud–radiation schemes developed for the Oslo version of CAM (e.g. CAM4-Oslo). The HAMburg Ocean Carbon Cycle HAMOCC; model is adapted to the isopycnic model framework of NorESM and incorporated as the ocean biogeochemistry component of the model.

The basic evaluation and validation of the Climate Model Intercomparison Project Phase 5 (CMIP5) version of NorESM (NorESM1-M) is documented by . Here, we use a recently developed, computationally efficient variant of NorESM1-M: NorESM1-F , designed for multi-millennial and ensemble simulations while retaining the resolution (2∘ atmosphere–land, 1∘ ocean–sea ice) and overall quality of NorESM1-M.

Compared to NorESM1-M, the model complexity of NorESM1-F is reduced by replacing CAM4-Oslo, which uses emissions of aerosols and explicitly simulates their life cycles, with the standard CAM4 that uses prescribed aerosol concentrations. The coupling frequency between atmosphere–sea ice and atmosphere–land is reduced from half-hourly to hourly, allowing the use of an hourly base time step for the sea ice and land components matching the radiative time step of the model; the dynamic subcycling of the sea ice is reduced from 120 to 80 subcycles. The last two changes result in a model speed-up of ∼30 % with a relatively small effect on the modelled climate. In addition, recent code developments in the ocean, atmosphere, and biogeochemistry components have been implemented as documented in detail by . Of these code developments in NorESM1-F, the updated ocean physics led to improvements over NorESM1-M in simulating the strength of the AMOC and the distribution of sea ice; both are important metrics in simulating past and future climates.

In the MIS3 setup (Table ), the solar constant is kept fixed at the pre-industrial value (1360.9 W m-2), and the orbital parameters are set to values corresponding to 38 kyr BP . In the Northern Hemisphere (NH), the chosen MIS3 time slice shows enhanced insolation in spring (April–May–June) relative to present (Fig. ), followed by reduced summer insolation (July–August–September). In the Southern Hemisphere (SH), changes in insolation are less pronounced, with stronger fall (August–September–October) insolation and weaker winter (November–December–January) insolation.

Concentrations of GHGs are set according to ice core measurements of typical interstadial conditions following : CO2, CH4, and N2O concentrations are specified as 215 ppm, 550 ppb, and 260 ppb, respectively, which are identical to the MIS3 setup by . Chlorofluorocarbon (CFC) levels are set to zero.

The ocean bathymetry is adapted based on an estimated sea level lowering of 70 m below present day . As a consequence, many shallow ocean grid points on the shelf turn into land, thereby modifying the land–sea mask (Fig. ). Most of the modifications occur in the northern high latitudes, e.g. the East Siberian Shelf, Laptev Shelf, and the Bering Strait (which is closed).

The configuration of global ice sheet extent and height (Fig. ) is derived from a data-constrained ice sheet model for 38 kyr BP consisting of the Antarctic , Greenland , North American , and Eurasian (Lev Tarasov, personal communication) ice sheets. NorESM1-F does not include a dynamic land ice component, and the assumed ice sheet extent and elevation for MIS3 are fixed. The altitude of the land surface is kept at pre-industrial values outside the ice sheet areas. In the areas covered by land ice, the maximum value of the original pre-industrial topography and MIS3 reconstructed ice sheet topography is used; this procedure prevents jumps to high topography adjacent to the ice sheet margin. The resulting MIS3 Laurentide Ice Sheet reaches altitudes higher than 2500 m but is significantly smaller, both in terms of ice extent and height, when compared to the LGM ice sheets such as ICE-6G . The southeastern margin of the Laurentide Ice Sheet is further north and the surface is 300–900 m lower than during LGM. Similarly, the Eurasian Ice Sheet is smaller, but there is a significant amount of land ice over Fennoscandia. The Laurentide Ice Sheet is merged with the Cordilleran Ice Sheet in our MIS3 ice sheet configuration. However, the shape of the MIS3 ice sheet is highly uncertain; studies have also shown separated Laurentide and Cordilleran ice sheets before the LGM e.g..

For the configuration of land–sea mask in the Barents Sea, care needs to be taken, as this region is an important pathway allowing warm and saline Atlantic water travelling north; therefore, opening or closing it has significant consequences for Arctic ocean circulation and climate . Unfortunately, there is a lack of reliable geological evidence for the existence of land ice in the Barents Sea before the LGM. However, sparse evidence from the Barents Sea–Svalbard region suggest there was little or no land ice here during MIS3 . Therefore, the Barents Sea is kept free of land ice with a reduced water depth (by 70 m) in the MIS3 configuration of the model. The Canadian Archipelago is covered by land ice, blocking the passage of water between Baffin Bay and the Arctic. In Antarctica, the Ross and Weddell seas are covered by grounded ice rather than floating ice shelves as today.

The land surface vegetation type in the MIS3 configuration is set equal to the pre-industrial values, and the extra land points caused by sea level lowering are assigned as tundra (20 % grass plus 80 % bare ground).

With the adjusted MIS3 land–sea mask and surface topography, a new river-routing map is produced (Fig. S1 in the Supplement). For the ice-free land surfaces, the river routing corresponds to the PI simulation. Where there is new land, due to the lower MIS3 sea level, the river outlets are extended to the ocean. For the ice covered areas, a new map is generated based on the land ice topography, routing the water from the land ice along the steepest gradient, either directly to the ocean or to the nearest river if the ice margin terminates on land.

Salt equivalent to 0.6 g kg-1 is uniformly added to the ocean, to account for the large amount of freshwater stored as ice on land. The vertical coordinate in MICOM is potential density with reference pressure of 2000 dbar and is adapted from a present-day range of 28.202–37.800 to 28.672–38.270 kg m-3 below the mixed layer, in order to account for the change in salinity and thus density. As for the PI experiment, the ocean model is initialised with modern temperature and salinity with the abovementioned salinity increment applied. Note that no specific protocols on ocean initialisation are defined for glacial simulations; e.g. within the Paleoclimate Modelling Intercomparison Project (PMIP), the groups chose to initialise their models either from present-day conditions or from a glacial ocean state. As illustrated by , equilibration time for the deep ocean can be significantly reduced (50 % in their model) if a glacial, rather than present-day, ocean state is utilised for initialisation. Note, however, that MIS3 is not a full glacial state and has a climate in between LGM and PI. The PI experiment, that the MIS3 experiment is evaluated against, is performed with the same model, NorESM1-F, and is documented and assessed in . Model equilibration for the NorESM MIS3 experiment will be addressed and discussed in Sect. .

The MIS3 experiment was run for 2500 years and the PI experiment for 2000 years. When comparing the two simulations, the model years between 1800 and 2000 are averaged.

Both the PI and MIS3 experiments reach a quasi-equilibrium climate state after the multi-millennial integration, as indicated by the time series shown in Fig. . The differences between the global mean MIS3 and PI climate are summarised in Table .

In the following results, the statistical significance of the calculated trends is tested using the Student's t test with the number of degrees of freedom, accounting for autocorrelation, calculated following . Trends with p values <0.05 are considered to be statistically significant.

The MIS3 experiment exhibits a small negative TOA radiation balance (-0.16 W m-2 averaged between model years 1801 and 2000, and -0.08 W m-2 between 2301 and 2500; Fig. a). This results in a negative ocean heat flux at the surface and cooling of the global ocean (Fig. d). The cooling trend is -0.05 ∘C per century over model years 1801–2000 and decreases to -0.02 ∘C per century over model years 2301–2500; both are statistically significant. Averaged between model years 1800 and 2000, the global mean MIS3 ocean temperature is 1.7 ∘C colder than that of the PI experiment.

At the ocean surface, sea surface salinity (SSS) in the MIS3 experiment exhibits negligible drift over the model years 1801–2000 (Fig. b, c), whereas SST shows a small statistically significant cooling trend of 0.04 ∘C per century. For MIS3, the global mean SST and SSS are 1.2 ∘C colder and 0.3 g kg-1 saltier, respectively, compared to the PI experiment. Simulated time evolution of sea ice extent in the Northern and Southern hemispheres shows a small drift towards the end of the evolution (Sect. S1 in the Supplement).

While the simulated MIS3 surface properties reach a quasi-equilibrium state, the ocean interior experiences a multi-millennial cooling trend (Fig. d). The slow adjustment of the deep ocean is considered to be important for the evolution of ocean stratification and overturning circulation . As a consequence, care should be taken, and deep ocean equilibration should be assessed. For the deep ocean, the salinity trend in the Atlantic is found to be smaller than 0.006 g kg-1 per century during the model years 1800–2000 (not shown), which is the threshold proposed by for an ocean state of quasi-equilibrium.

Both experiments exhibit an increasing AMOC at the beginning of the model integration, followed by a gradual equilibration to a weaker state (Fig. e). The simulated pre-industrial AMOC at 26.5∘ N is 20.9 Sv, which is close to present-day observations (∼18 Sv; RAPID data from http://www.rapid.ac.uk/rapidmoc, last access: 21 June 2019). For the first few hundred years of the MIS3 integration, the AMOC is significantly stronger than in the PI (by up to 10 Sv), but the difference between the two experiments is gradually reduced as the integration continues. Averaged between model years 1801 and 2000, the simulated MIS3 AMOC at 26.5∘ N is 22.8 Sv, only 1.9 Sv greater than in the PI experiment. Similarly, the simulated maximum strength of the AMOC during MIS3 is 27.5 Sv, 3.2 Sv stronger than that in the PI (24.3 Sv).

The weakening of the AMOC, after the initial overshoot, occurs concurrently with a shoaling of North Atlantic Deep Water (NADW) and more intrusion of Antarctic Bottom Water (AABW) as a manifestation of an adjustment of the deep ocean. Previous studies relate this behaviour to an expansion of Antarctic sea ice in a colder climate : e.g. as Antarctic sea ice grows (Fig. S2), more brine is rejected, favouring the formation of AABW. These processes will be further discussed in Sect. .

Abrupt climate changes such as D-O events have been shown to involve changes in both the geometry and strength of the AMOC, as indicated by a number of marine proxy reconstructions e.g. see the review by and numerical simulations e.g.. In this study, a stronger and deeper AMOC is simulated during a typical MIS3 interstadial as compared to the PI (Fig. ). Given its crucial role in the climate of MIS3, we further discuss the simulated AMOC and the associated distribution of NADW and AABW in this section.

Previous studies have argued that the increased production of AABW during glacial times is driven by expanded Antarctic sea ice and enhanced brine rejection during sea ice formation in the Southern Ocean . The brine induces a negative buoyancy flux, leading to enhanced formation of highly saline AABW (Fig. d). shows that the changes in the deep ocean stratification and circulation can be interpreted as a direct consequence of atmospheric cooling during glacial times, which induces Antarctic sea ice growth and initiates the processes described above.

The simulated ventilation of AABW is enhanced in our MIS3 simulation compared to the PI (Fig. S7). However, in the Atlantic, the volume of AABW is not comparable with that of the LGM, during which benthic foraminiferal δ13C data suggest that AABW dominated the water column in the Atlantic up to a depth of ∼2 km , together with a shallower NADW production. However, measurements of 231Pa/230Th, in combination with 143Nd/144Nd (ϵNd), indicate that a strong AMOC existed at the LGM despite of a shallow upper cell . also show that an active AMOC, neither weaker nor shallower than the present day, prevailed over the last glacial cycle, including the D-O interstadials (the exceptions are Heinrich stadials exhibiting weaker and shallower NADW). The AMOC during interstadials is accompanied by active deep water formation in the North Atlantic, with persistent contributions from northern sourced water. Our simulated MIS3 interstadial AMOC agrees with these reconstructions based on chemical tracers, and the difference with the AMOC at the LGM can be partly (if not fully) attributed to less Antarctic sea ice formation due to the MIS3 climate being milder than that at the LGM.

While deep water production in the Southern Ocean has the potential to displace and reduce the strength of the NADW production, competing effects are at play in the North Atlantic. For example, the altered surface westerlies in the North Atlantic caused by the elevated Laurentide Ice Sheet (Figs. , ) are shown to be able to induce a deeper and stronger AMOC by transporting more salt northward within an intensified gyre circulation, favouring deep ocean convection e.g.; the closure of Bering Strait leads to an increase of surface salinity in the North Atlantic thereby invigorating deep ocean convection and strengthening the AMOC . To isolate and assess the relative impact of these different processes requires a suite of dedicated sensitivity studies which is beyond the scope of this paper, but it is worth mentioning that the processes that take place in both hemispheres act together to create the AMOC shown in Fig. .

During the last glacial, sea level lowering and the removal of shallow continental shelves (Fig. ) result in enhanced tidal dissipation in the open ocean , implying enhanced deep ocean mixing and a strengthened AMOC. demonstrated that such tidal effects can dominate over surface buoyancy effects and lead to a strengthening of AMOC by ∼40 %. Such tidal effects are not considered in the current study, but once included, the AMOC is expected to strengthen and deepen, potentially displacing the lower AABW cell in the Atlantic.

The NorESM MIS3 simulation presented above is representative of an interstadial climate, i.e. a relatively warm period during the last glacial; in agreement with paleo-reconstructions, this includes Greenland temperatures only 5–8 ∘C colder than PI , a strong and active AMOC , and enhanced sea ice cover in the Nordic Seas . In particular, using a high-resolution benthic Mg/Ca temperature record in the Denmark Strait, inferred that during the baseline interstadial mode, ocean circulation and the associated water mass properties are similar to the present day; furthermore, a high-resolution reconstruction of MIS3 sea ice, based on analysis of biomarkers from a marine sediment core in the south Nordic Seas , finds near-perennial sea ice cover during cold stadials, and ice-free periods during warm interstadials. Both proxy studies support our modelled ocean and sea ice state as simulated for the MIS3 interstadial climate state. However, questions remain as to the state of the cold stadial climates of MIS3, which is characterised by much colder Greenland temperatures, near-completely ice-covered Nordic Seas, and reduced AMOC compared to the present day (based on the same references as above). These changes are reinforced during stadials including Heinrich events, when the AMOC shows a further weakening, due to the massive release of icebergs into the North Atlantic e.g..

It is unclear if the baseline climate during MIS3 should be a stadial or interstadial state, nor is it clear that there is indeed a baseline climate, as the climate states can be inherently oscillatory . To examine the possibility of simulating a cold MIS3 stadial climate with NorESM, an additional experiment is branched off and initialised from the MIS3 interstadial control experiment after 1700 model years. The MIS3 “stadial” experiment is run for 800 years with 40 kyr orbital forcing and reduced GHG levels (e.g. CO2 – 200 ppm, CH4 – 450 ppb, N2O – 220 ppb) according to . The major difference compared to the interstadial experiment is that in the “stadial” experiment, the CO2 is lowered by 15 ppmv.

In the MIS3 “stadial” experiment, the global near-surface temperature cools by 0.4 ∘C relative to the MIS3 interstadial experiment (Fig. S11). Winter sea ice slightly expands southwards in the Nordic Seas and in the northwestern Pacific, whereas in the Labrador Sea, sea ice distribution is nearly identical in the two experiments. Furthermore, there is a negligible change to the AMOC. Together, these results indicate that given the changes to the GHG levels that are typical of a stadial state, a cold Greenland climate with a weak AMOC cannot be reproduced in our MIS3 setup without additional freshwater forcing.

With the multi-millennial long integration of the MIS3 simulation presented in this work, only one stable climate state is found, and the model reaches a quasi-equilibrium with a small drift towards the end of the integration. In this section, we explore the potential for model bi-stability associated with the transition between the warm interstadial and cold stadial climate states of MIS3. We do so by perturbing the model with changes in atmospheric CO2 concentrations and the size of the Laurentide Ice Sheet.

Our NorESM MIS3 simulations agree with that of using the LOVECLIM model: given MIS3 boundary conditions, the interstadial climate is the equilibrium climate state, whereas the stadial climate is a perturbed state. A CO2 change of 15 ppmv (typical of stadial conditions) is not sufficient to induce transitions between the two states (Sect. ). However, reported that a gradual change of CO2 concentrations by 15 ppmv in their experiment with intermediate glacial conditions can be sufficient to trigger transitions between weak/strong AMOC modes and therefore stadial/interstadial states. In contrast, examined the effect of CO2 changes on the AMOC strength and geometry in an LGM setup and found a weakening and shoaling of AMOC with decreasing CO2 (from 284 to 149 ppmv) but without transitioning into a weak AMOC mode. They argued that the presence of LGM ice sheets could enhance the AMOC by impacting the surface wind stress in their model and thus help maintain the stability of the AMOC. Interestingly, later reported that with a PI ice sheet configuration, the AMOC exhibits oscillatory behaviour at a CO2 level of 206 ppmv, above (below) which a strong (weak) AMOC mode persists. In addition, the MIS3 simulation reported by is close to disequilibrium and model bi-stability, as indicated by a series of equilibrium freshwater perturbation experiments.

The studies by and on the sensitivity of climate states to CO2 levels and ice sheet sizes, together with the studies of, e.g. , , and , point to the possibility that there could exist a certain range of CO2 levels and ice sheet sizes in which the model is subject to a mode transition and even excitation of self-oscillatory behaviour in North Atlantic climate. The existence and range of such a “window” of CO2 levels and ice sheet heights, however, is expected to be model dependent. In order to explore the potential for model climate transition with NorESM and the existence of a cold stadial state given MIS3 boundary conditions, we investigate the model response to large variations of CO2 and ice sheet height, using the interstadial simulation as the baseline experiment. Another motivation for seeking a cold climate is that, as discussed by , a cold Heinrich stadial-like state is required to “kick” the system into a self-oscillatory behaviour. Even without the self-oscillation, a cold stadial state would serve as a useful baseline experiment for investigating potential triggers of the abrupt cold-to-warm D-O transitions.

It is not within the scope of this paper to perform a complete examination of the model response to every combination of CO2 and ice sheet changes. Rather, we report the model response in the more extreme cases, with a primary focus on the response of the AMOC and sea ice. For the CO2 sensitivity experiments, we reduce the values from 215 to 160 and 140 ppmv. For the ice sheet sensitivity experiments, we reduce the height of the Laurentide Ice Sheet by 50 % and 100 % (the latter is equal to the pre-industrial orography), while keeping the ice mask unchanged. All the sensitivity experiments are branched off and initialised from the MIS3 interstadial simulation, and all other parameters are kept fixed.

Contrary to the studies cited above, the NorESM MIS3 experiments exhibit surprising stability without any significant changes in Greenland temperature, sea ice, or AMOC (Fig. ). For the low CO2 experiments, there is a slight expansion of winter sea ice in the Nordic Seas (Fig. S13), without any notable changes in the strength and locations of convection. As a consequence, the AMOC, although weakened, still remains strong (Fig. ). For the experiments with a reduced Laurentide ice sheet, surface wind stress fields are altered (mainly shifting northwards in the North Atlantic; not shown), whereas the strength of AMOC is only slightly reduced.

Further analysis of key relevant metrics, e.g. spatial distributions of SSS, winter sea ice extent, and AMOC geometry for the sensitivity experiments, are included in the Supplement (Sect. S4). As the changes are highly related to the strength of the AMOC, which is only weakly reduced in the sensitivity experiments, changes in these metrics are also relatively small.

The results of the sensitivity experiments to CO2 and ice sheet height underscore the question of model dependence on the background climate in simulating AMOC transition/bi-stability, despite the fact that the simulations are limited in length (200 to 1000 years), and we therefore cannot fully exclude that further equilibration could bring the climate into a more unstable regime. In our simulation, where the Labrador and Norwegian seas are the major convection sites, a significant change of ocean circulations is not expected unless the Labrador and Norwegian seas are covered by sea ice, thereby inhibiting convection through its insulating effect. However, the NorESM MIS3 and PI experiments both appear to be in a stable regime with a strong AMOC and strong convection in the Labrador and Norwegian seas (Fig. S6). As a consequence, the model state is relatively distant from a potential threshold, including a bi-stability of the AMOC and sea ice. In addition, the NorESM1-F model features a relatively low climate sensitivity (the equilibrium climate sensitivity in response to a doubling of atmospheric CO2 is 2.3 ∘C) which plays a role in the weak response of the MIS3 climate to a further CO2 decrease.

To trigger a cold stadial-like climate state in the NorESM, other mechanisms including enhanced iceberg calving and freshwater input to the North Atlantic from the Laurentide, Greenland and Fennoscandian ice sheets should be considered. There is a rich literature on applying freshwater flux of different magnitudes and locations to study climate response and transitions e.g.. The prospects of perturbing the MIS3 interstadial climate with freshwater fluxes will be explored in detail in a companion study.