1 Introduction

The Dansgaard-Oeschger (DO) events represent 25 abrupt warming perturbations centred around the North Atlantic that occurred throughout the last glacial-interglacial cycle (Dansgaard et al. 1993). The mechanism that drives these events remains uncertain. The prevailing theory is that they are a response to changes in the strength of the Atlantic Meridional Overturning Circulation (AMOC; Li and Born 2019; Lynch-Stieglitz 2017), which itself is strongly linked to salinity fluctuations in the North Atlantic (Ganopolski and Rahmstorf 2001; Peltier and Vettoretti 2014; Hu et al. 2008; Kageyama et al. 2012). Broecker et al. (1990) proposed the idea that these fluctuations were a response to a ‘salt oscillator’ within the North Atlantic, which postulates that Atlantic salinity fluctuations shift the AMOC between a strong and weak state, which drives the DO events. The driver of this was originally thought to be a response to external forcings, such as freshwater perturbations from continental sources and/or sea ice (Birchfield et al. 1994; Broecker et al. 1985; Ganopolski and Rahmstorf 2001). However, the hypothesis of a freshwater-flux forcing has been criticised (Sakai and Peltier 1997; Peltier and Sakai 2001). More recent studies have put forward different theories, such as an origin in the Southern Ocean (Banderas et al. 2015; Knorr and Lohmann 2003), or changes in atmospheric CO2 which modulates moisture transport in Central America (Zhang et al. 2014).

An alternative hypothesis is that the DO events represent unforced or spontaneous oscillations, reflecting periodic stochastic processes reliant on the internal dynamics of the system (Birchfield and Broecker 1990; Broecker et al. 1990; Drijfhout et al. 2013; Kleppin et al. 2015; Li and Born 2019; Peltier and Vettoretti 2014). Alley et al. (2001) and Ganopolski and Rahmstorf (2002) however suggested that the DO events were due to the action of ‘stochastic resonance’. This combines a weak external forcing with the role of internal variability leading to noise. They employed the CLIMBER-2 model with periodic additions of freshwater forcing into the North Atlantic of unknown origin. This weak-amplitude external forcing was then amplified in the presence of noise, which shifted the AMOC between two different modes. In this case, the AMOC transitions when it is pushed towards a bifurcation point due to the noise in the system. However, there is no explanation as to the origin of this forcing or evidence of this in the observations (Wunsch 2003). Cimatoribus et al. (2013) concluded that the DO events take place close to a bifurcation point and represent the climate system switching between two states in response to either stochastic resonance, or to an external forcing.

Although the direct mechanism remains uncertain, previous studies tend to agree that the DO events are driven by coupled interactions within the atmosphere-ice-ocean system operating under glacial background conditions (see Li and Born 2019). Recently, Vettoretti et al. (2022) showed that the existence of internal oscillations in the CCSM4 model depends on a glacial-level background atmospheric CO2 concentration of between 190 and 225 ppm. Furthermore, a key feature of the glacial climate was the presence of large continental ice sheets, enhanced wind strength and a more intense, less wobbly and shifted jet stream, which may have permitted the climate to support such oscillations and abrupt events (Armstrong et al. 2019a; Cook and Held 1988; Li and Born 2019; Merz et al. 2015; Ullman et al. 2014). Indeed, Wunsch (2006) concluded that DO events were reliant on the presence of continental ice sheets and their influence on wind patterns. Similarly, Zhang et al. (2014) showed that only minor changes in the height of Laurentide ice sheet triggered DO events in the COSMOS model. Ice sheet height shifted wind patterns, which altered the atmosphere–ocean-ice system and impacted sea-ice/freshwater export from the Arctic and advection of salt. This increased AMOC strength and initiated an oscillation.

Problematically, understanding the drivers of DO events is hindered because many complex climate models do not simulate similar oscillations without external forcing, such as freshwater hosing. This issue may be due to models lacking the correct sensitivity to the boundary conditions (Li and Born 2019; Valdes 2011). Saying that, several unforced modelling studies have demonstrated variability similar to the DO events, however these were run with pre-industrial (PI) boundary conditions and events are typically short-lived and weak (Drijfhout et al. 2013; Kleppin et al. 2015; Martin et al. 2015; Sidorenko et al. 2015). More persistent spontaneous DO-like oscillations have been identified in the MPI-ESM model (Klockmann et al. 2018, 2020) using PI ice sheet configuration and glacial CO2 concentrations (190–217 ppm). These oscillations are a response to coupled ocean-ice-atmosphere feedbacks and subpolar gyre (SPG) dynamics. The stadial/interstadial events are characterised by a shift in circulation from the SPG to the Greenland-Iceland-Norwegian (GIN) Seas, driven by wind and density-driven feedbacks and the salinity gradient between the subtropical gyre (STG) and SPG. Similarly, the low resolution CM2Mc model has also shown evidence of DO-like oscillations (Brown and Galbraith 2016). They used a similar configuration of PI ice sheets and a glacial CO2 concentration (180 ppm), and the advection of salt between the STG and SPG was also shown to play an important role.

To our knowledge, the only fully glacial simulations that exhibit persistent and systematic variability have been performed using the University of Toronto version of the CCSM4 model (UofT-CCSM4; Peltier and Vettoretti 2014; Vettoretti and Peltier 2015, 2016, 2018; Peltier et al. 2020) and more recently with the University of Tokyo MIROC model (MIROC4m; Kuniyoshi et al. 2022). The DO-type oscillations identified in UofT-CCSM4 were linked to the ‘salt oscillator’ hypothesis, with transitions between a stadial and interstadial driven by instability in the water column within the Irminger Sea. This opens an extensive polynya in the region during a stadial, which then initiates a rapid warming into an interstadial. These simulations are unique as they provide an accurate representation of the timescale and pulse shape of the DO oscillations. Furthermore, they accurately reproduce the magnitude of the temperature signal associated with individual stadial to interstadial transitions as inferred on the basis of both Greenland and Antarctic ice core records. More recently, aspects of the DO mechanism identified in the UofT-CCSM4 model, including the spatial location of the polynya that opens in the Irminger Sea to mark the stadial-interstadial transition, have been identified in MIROC4m (Kuniyoshi et al. 2022), which has an equivalent resolution to UofT-CCSM4.

In this study, we add an additional model to UofT-CCSM4 and MIROC4m with results from the HadCM3B model (Valdes et al. 2017), which demonstrates DO-scale unforced millennial oscillations in fully glacial simulations. We give a detailed explanation of the coupled ocean–atmosphere-sea-ice feedbacks that drive this oscillation utilising a full set of salinity diagnostics. The aim of this study is to (1) identify the feedbacks that maintain this millennial-scale oscillation and initiate the cooling (stadial) and warming (interstadial) phases, and (2) identify what pushes the glacial climate system into an oscillatory state.

2 Methods

2.1 The HadCM3B model

The Hadley Centre Coupled Model 3 Bristol (HadCM3B) is a coupled climate model and version of the more commonly known HadCM3, which was originally developed at the Hadley Centre/UK Meteorological Office and has been adapted at the University of Bristol. The specific version of the model we use is HadCM3B-M2.1D which is outlined in detail in Valdes et al. (2017) and is only briefly discussed here. HadCM3B been shown to produce an accurate representation of climate and remains competitive with other more modern models used in CMIP5.

The atmosphere model (Pope et al. 2000) has a resolution of 3.75° × 2.75° and 19 vertical levels with a 30-min timestep. It utilises a number of boundary conditions, including the land-sea mask, orography, and a number of soil and vegetation parameters. The ocean model (Gordon et al. 2000) has a resolution of 1.25° × 1.25°, 20 vertical levels and a 1 h timestep. It utilises a rigid lid approach, so there is no variation in ocean volume. HadCM3B incorporates the MOSES 2 land surface scheme (Cox et al. 1999) which simulates physiological processes and fluxes of energy and water. It also incorporates the fractional coverage of nine different surface types, simulated by the dynamic global vegetation model (DGVM) TRIFFID.

The model does not include an interactive land-ice model or carbon and methane cycle so these boundary conditions have been imposed (see below). The river runoff is instantaneously transferred to outflow grid points following a prescribed runoff map. Sea ice is simulated using a zero layer model (Semtner 1976) calculated on top of the ocean with movement controlled by upper-ocean currents. Ice is formed predominantly in leads and by snowfall, with continuous removal from the base through the year and from the surface during summer melts. Sea-ice salinity is assumed to be constant with the flux into the ocean depending on ice formation or melt.

2.2 Experimental set-up

We performed a set of glacial simulations with 30kyr BP (before present) boundary conditions (Table 1), which have previously been shown to exhibit millennial-scale variability in Armstrong et al. (2019b). The boundary conditions include prescribed orbital parameters which are very well constrained and taken from Berger et al. (1998). The concentration of atmospheric CO2 is from the Vostok Ice core (Loulergue et al. 2008; Petit et al. 1999), whilst N2O and CH4 concentrations are from the EPICA Dome C ice core (Spahni et al. 2005).

Table 1 Boundary conditions for the 28 and 30kyr simulations
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HadCM3B does not have an ice-sheet model, so the elevation and extent of the Greenland, Laurentide, Fennoscandian and Antarctic ice sheets have been prescribed. For this, we utilise the ICE-5G model (Peltier 2004) which simulates the evolution of ice thickness, extent, and isostatic rebound. This is used in HadCM3B to calculate orographic height, bathymetry, ice fraction, and the land-sea mask. However, ICE-5G only simulates ice up to the last glacial maximum (LGM; which is at 26kyr BP in the model), so we calculate the pre-LGM ice sheet from the equivalent sea level, and therefore ice volume, during the deglaciation. For example, the sea level at 30 kyr BP is compared to the sea level during the deglaciation (post-LGM), where they are the same, the ice extent is inferred to be the same as that simulated by ICE-5G but for 30kyr BP. This is the same approach used in Armstrong et al. (2019b) and Davies-Barnard et al. (2017). There are limitations as ice sheets show different structures during decay and growth phases, but it provides a better approximation of the ice area than other trialled methodologies, such as in Singarayer and Valdes (2010).

The boundary conditions have been incorporated into a 6000-year base simulation, labelled 30kyrBASE. A full set of salinity diagnostics were output for a 4000-year period. The key salinity tendencies are; advection, convection, sub-grid scale processes which includes both diffusion and the Gent and McWilliams parameterisation of isopycnal advection by eddies (Gent and Mcwilliams 1990), surface fluxes which includes the P-E balance and river runoff, sea-ice processes which is associated with brine rejection from sea-ice formation and meltwater, and mixed layer physics. A more detailed overview of the tendencies is given in Valdes et al. (2017) and references within. The tendencies are plotted as a rate of change of salinity (PSU/yr), and when combined, are equivalent to the change in overall salinity between each year. These are discussed in detail in Sect. 4. The 30kyrBASE simulation has been initiated from a spin up experiment that has been run for more than 6000 years and therefore very long-term trends are small.

This 30kyr BP set-up was originally performed as part of an ensemble study of simulations covering 0 to 60kyr BP outlined in Armstrong et al. (2019b) which also incorporated a 28kyr BP experiment (see their Table 1). These were used to construct a continuous monthly climate dataset for this period (see their Fig. 9). The 30kyr BP experiment from that study exhibits millennial variability, however the 28kyr BP experiment does not show comparable variability despite similar boundary conditions (Table 1). Between the 28kyr and 30kyr experiments there is a decrease in the height and extent of the ice sheets (Fig. 1a) which alters the orographic height (Fig. 1b), greenhouse gas changes are very small with identical CO2 and a 11ppbv and 25 ppbv decrease in CH4 and N2O respectively (Table 1). There is a shift in the orbital parameters (Table 1) and a very small change in the bathymetry (specifically a 50 m deepening in the Iceland-Scotland Ridge, Figure S1), which reflects the flexing of the crust due to ice-sheet change. To investigate what pushes the climate system into an oscillatory state at 30kyr BP, we performed a range of additional 30kyr BP experiments with perturbed boundary conditions emulating those used for the 28kyr experiment (Table 2, Fig. 1). These are 3000-year long simulations with 28kyr orbital parameters (30kyrORB), greenhouse gases (30kyrGHG) and ocean bathymetry (30kyrBATHY) respectively.

Fig. 1
figure 1

The ice sheet boundary conditions for the 28 and 30kyr simulations and anomaly between the two, a ice sheet fractional extent, and b orography which refers to ice-sheet height (m). The specific regions used in the altered ice sheet simulations are identified in the boxes; Fennoscandian (green), East Laurentide (red) West Laurentide (blue) and entire Laurentide (purple)

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Table 2 Overview of all simulations used in this study
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To investigate the role of ice-sheet configuration, we performed a further five simulations with 28kyr BP boundary conditions but with varying 30kyr BP ice sheet configuration (regional height and extent) in order to test if this initiates an oscillation. The difference in fractional extent and height of the ice sheets between the 28kyr and 30kyr BP experiments (Fig. 1a, b) reflects the methodology used to build the ice-sheet configuration. We ran five 3000-year simulations with 28kyr BP boundary conditions with (1) a 30kyr Fennoscandian ice sheet (28kyrFEN), (2) Fennoscandian and east Laurentide ice sheets (28kyrELAU), (3) Fennoscandian, east and west Laurentide ice sheets (28kyrEWLAU), (4) Fennoscandian and the entire Laurentide ice sheets (28kyrLAU), and finally (5) 50% of all the ice sheets (28kyr50). The specific regions are outlined in Fig. 1b. For all of the perturbed boundary simulations, the analysis excludes the initial 1000 years of the simulation to permit a model spin-up.

3 The oscillation in HadCM3B

The timeseries for the AMOC index (mean AMOC strength between 40° and 50° N at 800 m, which reflects peak AMOC flow in HadCM3B) and a range of climate variables for the 30kyrBASE simulation (Fig. 2a) demonstrates an oscillation with a dominant timescale of approximately 1500 years. Stadial (interstadial) periods are characterised by a weaker (stronger) AMOC, cooler (warmer) North Atlantic SATs, an increase (decrease) in sea ice cover, and a decrease (increase) in North Atlantic salinity. The oscillation frequency is compatible with the DO events in the ice core record, which have a characteristic periodicity of between 1000 and 5000 years (Dansgaard et al. 1993), and similarly shows longer stadials than interstadials. The average AMOC strength (at 30° N) at 30kyr is 13.12 ± 2.47 Sv, which compares to the current observed strength of 17.4 Sv (Duchez et al. 2014) and approximately 16.5 Sv in the pre-industrial simulation of HadCM3B. This is consistent with observations that indicate a weaker glacial AMOC (Gebbie 2014; Lippold et al. 2012), although many climate models show the opposite due to enhanced wind stress (Muglia and Schmittner 2015).

Fig. 2
figure 2

a Timeseries of normalised climate variables averaged over the North Atlantic (0:90 N, − 90:20 E) and the AMOC index (defined as the mean AMOC strength between 40° and 50°N at 800 m) for the 30kyrBASE simulation. b Timeseries of the modelled SAT over central Greenland (72:78 N, − 45: − 39 E) and the temperature reconstruction from the NGRIP ice-core (Kindler et al. 2014) spanning two 6 kyr periods either side of 30kyr BP (35.6 to 23.6kyr), the numbers refer to the five DO-events over this period. A 100-year low pass Lanczos filter has been applied to the model data to remove high frequency variability

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A comparison of the modelled central Greenland SATs against two 6kyr sections covering 35.6–23.6 kyr BP (DO events 7 to 3) of the NGRIP ice core record (Kindler et al. 2014) is shown in Fig. 2b. The modelled Greenland temperatures are on average too warm, and despite a comparable timescale, the temperature change between the interstadial and stadial events is of smaller magnitude in the modelled oscillation, which is of between 6.5–8.5 °C compared to 9.5–15.5 °C for DO events 7 to 3 (Kindler et al. 2014). Note that the oscillation in Greenland SAT leads North Atlantic SATs (Fig. 2a), indicating that the climate impacts of the oscillation are instigated at higher latitudes before extending throughout the North Atlantic. More strikingly, the oscillation does not exhibit a ‘sawtooth’ waveform pattern that is shown for many of the DO events in the ice core record, characterised by rapid warming followed by slower cooling (Seager and Battisti 2007). Instead it shows a more symmetric rapid warming/rapid cooling shape. This lack of abrupt change may be due to inadequate representation of physical processes, such as the simulation and response time of sea ice, the parameterisation of vertical diffusion and/or sensitivity to meltwater. This is considered further in the discussion. Saying this, some of the shorter DO events in observations are more symmetric (Buizert and Schmittner 2015) which are more consistent with the results presented here.

The long-term mean climate patterns and their anomalies (Figs. 3, 4) during periods of strong AMOC (AMax; interstadials) and weak AMOC (AMin; stadials) show climatological patterns that are consistent with proxy data (Voelker 2002). Interstadials are characterised by periods of strong AMOC and an enhanced North Atlantic deep-water (NADW) cell, warming in the North Atlantic (NA) and a northward shift in the ITCZ (Fig. 3a–c). Precipitation change impacts the precipitation-evaporation (P-E) balance particularly in the tropics, in response to the shift in the ITCZ (Fig. 3c). Surface air temperature (SAT) anomalies in the NA are in phase with AMOC variability, concentrated over the GIN Seas and SPG (Fig. 3b). The anomalies during stadials are broadly opposite. There is widespread evidence that the DO events were characterised by large changes in sea-ice cover in the NA (Masson-Delmotte et al. 2005; Li et al. 2005, Sadatzki et al. 2019). In HadCM3B, sea-ice fraction oscillates up to 30% within the SPG and the GIN seas (Fig. 3d), with widespread coverage across these regions during stadials.

Fig. 3
figure 3

Long term mean climate variables for the 30kyrBASE simulation (Ltm; left panels), and the anomalies relative to this baseline during periods of strong AMOC (AMax-Ltm; middle panels) and weak AMOC (AMin-Ltm; right panels). AMax (interstadials) and AMin (stadials) are defined as when the AMOC index is one standard deviation above and below the mean

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Fig. 4
figure 4

The same as Fig. 3 but for ocean variables. These are averaged over 0–666 m water depths

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Ocean salinity (Figs. 4a, S2) shows a prominent NA dipole pattern centred on the SPG and Greenland-Iceland-Norwegian (GIN) Seas, and the tropics. The contrasting pattern between these regions during stadials and interstadials is consistent with the salt oscillator hypothesis (Broecker et al. 1990) and the oscillations in both UofT-CESM4 and MPI-ESM (Klockmann et al. 2020; Peltier and Vettoretti 2014). This dipole therefore indicates a similar oscillator mechanism may be present in HadCM3B, with build-up and collapse of the salinity gradient between these two regions being an important component of the oscillation. Ocean temperatures (Figs. 4b, S3) show a more complex pattern, with interstadials characterised by warmer temperatures in the Norwegian Sea and Northern subpolar Gyre and cooler temperatures in the tropics, with opposing anomalies during stadials. The meridional cross sections (Figs. S2 and S3) indicate that tropical salinity/temperature anomalies are predominately in the subsurface, whereas at high latitudes they extend throughout the water column. The anomalies in the mixed later depth (MLD, Fig. 4c) indicate enhanced convection and deep-water formation during interstadials, predominantly in the Nordic Seas and across the Scotland-Iceland ridge.

Anomalies in the ocean currents (Fig. 4d) are largely characterised by fluctuations in the strength of the eastern North Atlantic Current (NAC) indicative of varying AMOC strength During interstadials when the AMOC is strong the NAC increases in strength, accompanied by an increase in current strength across the GIN Seas. Li and Born (2019) postulated that changes to both AMOC and SPG strength were positively correlated throughout the DO events, however Klockmann (2020) showed the opposite to be the case in the MPI-ESM. The barotropic streamfunction averaged over the SPG gyre (not shown) indicates that the SPG strength is positively correlated to AMOC strength in HadCM3B. This overall increase in gyre strength during interstadials reflects the overall increase in transport in the NA. This is discussed further in Sect. 4.

4 The oscillator mechanism

In order to understand the mechanism that drives the oscillation we need to determine what governs the strength of the AMOC. In HadCM3B, AMOC variability is dominated by salinity fluctuations (Figure S4). Therefore we need to understand the balance of surface salinity and how this varies through time. Salinity tendency diagnostics (PSU/yr) were output for a 4000-year period of the 30kyrBASE simulation; positive/negative values indicate where salinity increases/decreases due to that process. Figure 5 shows the composite spatial patterns of the terms contributing to the tendencies during AMin (stadials), AMax (interstadials) and the anomaly (AMax-AMin). To highlight key sites of spatial variability, Fig. 6 shows the first EOF and corresponding PC1 timeseries for the tendencies (additional EOFs do not further clarify the mechanism and are not shown).

Fig. 5
figure 5

Composite spatial patterns for the salinity tendencies (PSU/yr) averaged over 0-666 m for the 30kyrBASE simulation during periods of AMin (stadials; left panels), AMax (interstadials; middle panels) and the difference between the phases (AMax-AMin; right panels). Convection is averaged over 0–300 m to highlight changes more clearly. Positive/negative values indicate where salt is added/removed. AMax (interstadials) and AMin (stadials) are defined as when the AMOC index is one standard deviation above and below the mean

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Fig. 6
figure 6

The first EOF and the corresponding PC1 timeseries (PSU) for the salinity tendencies averaged over 0–666 m from the 30kyrBASE simulation. Convection is averaged over 0–300 m to highlight variability more clearly. The amount of variance explained by EOF1 is stated. Note the change in scale between the left and right panels

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Within the NA, horizontal salinity advection is the main contributor that transports salt northwards along the NAC from the saline tropics to the subpolar regions, driven by the salinity gradient (Figs. 5a, b, 6a, b). The horizontal advective tendency (Fig. 5a) is broadly negative in the tropics as salt is removed via advection, and broadly positive at higher latitudes, particularly the eastern SPG, reflecting the direction of the NAC. The key area of variability is the eastern edge of the NAC and the subpolar gyre (Fig. 6a, b), with interstadials showing an increase in horizontal advection into the Nordic Seas (Fig. 5a) implying increased AMOC strength. This indicates an expansion of the key advective regions into the Nordic Seas during periods of AMax.

The sub-grid scale tendencies (Figs. 5c, 6c) include horizontal and vertical diffusion and the Gent McWilliams scheme (Gent and Mcwilliams 1990), which parameterises isopycnal eddy advection. These broadly counter salinity advection as they remove the salinity gradient developed via advective processes. As such, variability in these processes largely opposes advection. Sub-grid scale variability is an order of magnitude smaller than advection (Fig. 6c), indicating the dominant role that advection plays. The combined advection and diffusion tendencies (Fig. 5e) highlight the changing role of the SPG and Nordic Seas. The composite anomaly indicates that during interstadials these tendencies are more positive in the Nordic Seas and negative across the SPG, particularly the Eastern SPG and southwest of Greenland. This negative anomaly indicates a broader inflow of salty water along the eastern flank of the SPG, with increased transport of salt into the Nordic Seas.

Convection (Figs. 5d, 6d) is a comparatively small tendency and is primarily present in surface (0–300 m) waters, yet it is crucial in forming deep water and driving overturning. During stadials, convection is limited to the Iceland Basin. During interstadials, convection increases across the Norwegian Sea, Iceland-Scotland ridge, the Irminger Sea and across the central SPG. This indicates a widespread increase in deep-water formation during AMax and expansion across the SPG and the Nordic Sea region.

The surface flux tendency (Figs. 5f, 6e) is determined by freshwater fluxes associated with the P-E balance and river runoff at the coastlines. In the tropics, this tendency is positive primarily due to the negative precipitation-evaporation (P-E) balance which increases salinity; this is key in maintaining the tropics/SPG salinity gradient. In the tropics, variability in the P-E balance reflects the changing position of the ITCZ (Fig. 6e). Interstadials show a negative anomaly due to increased freshening from a northward shifted ITCZ and vice versa, which is a response to changes in the meridional temperature gradient. The surface tendency is largely positive at higher latitudes during interstadials due to increased evaporation associated with warmer temperatures (Fig. 5f).

The surface flux tendency plays an important role in influencing the salinity gradient between the topics and the SPG/Nordic Seas region. This subsequently impacts advection and therefore the strength of the AMOC. This mechanism has previously been identified as the driver of centennial oscillations of the AMOC in HadCM3 (Vellinga and Wu 2004). Figure 7 shows the timeseries for tropical and SPG/Nordic Sea salinity, the salinity gradient between the two regions, and the AMOC index. It shows that AMOC strength, and therefore the oscillation, is determined by the salinity gradient between the regions. A high salinity gradient is a precursor for the transition from a stadial into an interstadial, in part driven by high tropical salinity. In contrast, the transition from an interstadial to a stadial is driven by the collapse of the salinity gradient. The position of the ITCZ plays an important role in determining tropical salinity and therefore in driving the oscillation, as was also shown by Vellinga and Wu (2004). This is discussed in more detail in the following subsections.

Fig. 7
figure 7

Timeseries of salinity in the tropics (PSU), the combined subpolar gyre and Nordic Sea (PSU), the salinity gradient between the two regions (PSU), and the AMOC index (SV; defined as the mean AMOC strength between 40° and 50° N at 800 m) for the 30kyrBASE simulation. See Fig. 7 for the map of these regions. The vertical red lines indicate where AMOC strength decreases at the end of an interstadial and the horizontal red lines the corresponding salinity gradient range (Sv). A 100-year low pass Lanczos filter has been applied to remove high frequency variability

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The impact of sea ice on salinity is complex and its role differs depending on location (Figs. 5g, 6f). Note that the model does not incorporate an interactive ice-sheet module and prognostic ice sheet calving. In the Arctic and eastern GIN Seas, sea-ice formation removes freshwater and so increases salinity in these regions (Fig. 5g). However, in areas of the GIN Seas and SPG sea ice freshens during both stadials and interstadials (Fig. 5g). This is due to the seasonal nature of sea-ice; with build up during the winter from freezing of sea water and accumulation from precipitation, which melts in the summer flushing out both frozen sea water and accumulated freshwater. The net impact is a freshening effect. During interstadials, this freshening effect of SPG sea-ice is reduced (Fig. 5g) due to the northward retreat of the sea-ice edge (Figs. 3d, 6f). This contributes to an increase in salinity in the SPG and therefore the decrease in the salinity gradient between the SPG and the tropics (Fig. 7). However, in the Nordic and Irminger seas, the tendency becomes more negative due to a decrease in sea ice cover and consequent release of freshwater (Fig. 5g), which acts to counter the increase in regional salinity during an interstadial (Fig. 4a).

The tendencies show that advection plays a dominant role in driving the AMOC, which itself is determined by the salinity gradient between the tropics and SPG/Nordic Seas region (Fig. 7). The build up and collapse of this salinity gradient is the key mechanism which drives the oscillation. Furthermore, the key site of downwelling expands from the SPG across to the Nordic Sea region during an interstadial. In the following subsections we will explore in more detail what controls this salinity gradient and what triggers the transition between the stadials and interstadials.

4.1 Stadial period

The changing regional roles of the tendencies are key in driving the oscillation. In order to identify what triggers the transitions between stadials and interstadials, Fig. 8 shows the timeseries for key regional tendencies and climate variables. Additional regional tendencies are shown in Figure S5.

Fig. 8
figure 8

Regional timeseries for the 30kyrBASE simulation of the salinity tendencies (PSY/yr), salinity and the vertical density gradient (as standardised values) averaged over 0–666 m water depth, note the change in scale. Convection is averaged over 0–300 m to highlight variability more clearly. Timeseries for sea level pressure and wind stress curl (as standardised values) are shown for the Nordic Sea. For the tropics, the solid and dashed black lines represent advection averaged over 0–300 and 300–666 m respectively. The relevant regions are shown on the map. A 100-year low pass Lanczos filter has been applied to remove high frequency variability

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During stadials, temperatures are cold, sea ice extent is widespread, and the NAC and AMOC are weak (Figs. 2, 3, 4). Salinity and ocean temperature in the northern NA are at a minimum due to reduced transport of warm, saline waters from the tropics (Fig. 4a, b). In the Nordic Seas (Fig. 8a) advection is at a minimum, but it remains high in the Irminger Sea (Fig. 8b) and across the SPG (Fig. 8c), indicating that advection is predominantly into this region during stadials. However, the transport of salt is too small to maintain substantial deep-water formation, and the increased vertical density gradient across the SPG (Fig. 8c) indicates a more stratified water column, and so convection is at a minimum across the Northern North Atlantic (Fig. 8a–c).

In the Nordic Seas (Fig. 8a), colder conditions increase sea-ice formation, which adds salt and acts as a negative feedback, countering the reduced advection during the stadial. In the SPG (Fig. 8c), the seasonal nature of sea ice means it freshens these regions as discussed above. Therefore, sea ice acts to freshen more during the stadial as sea ice is more widespread (Fig. 5g). However, in the Irminger Sea its role is less negative as colder conditions reduce seasonal sea ice fluctuations (Fig. 8b).

The tropics exhibit an opposing salinity anomaly during the stadial (Figs. 4a, 8d) due in part to an increase in the surface salinity flux. This reflects the southward shift of the ITCZ (Fig. 3c) due to the increased meridional temperature gradient. This enhances the negative P-E balance and so the tendency is more positive during the stadial (Fig. 8d). Additionally, the advective tendency is more negative within surface water (0-300 m, Fig. 8d), in contrast to being more positive in intermediate depths (300–666 m, dashed black line, Fig. 8d). This indicates that during a stadial, more salt is advected from the surface waters into intermediate depths within the tropics, instead of being advected northward. These factors cause an accumulation of salt in the tropics (Figs. 7, 8d) and an increase in the salinity gradient between the tropics and the Northern North Atlantic (the SPG and Nordic Seas) during the stadial (Fig. 7). As stated above, the build-up and collapse of this salinity gradient is crucial in maintaining the oscillation. Note that across the Northern North Atlantic, salinity and AMOC strength increases steadily throughout the stadial (Fig. 7). This could in part be due to the reduced freshening effect of sea ice in the SPG as the stadial progresses (Fig. 8c), indicating sea-ice retreat. In contrast, sea ice growth and associated brine rejection in the Nordic Seas (Fig. 8a) could also play a role in driving this increase. This gradual build up of salinity is likely to be important in priming the system to shift to a strong AMOC state.

4.2 Transition into an interstadial

The transition into an interstadial is characterised by an increase in AMOC strength and NA salinity/temperature (Figs. 2, 7, 8). Advection decreases within the SPG and Irminger Seas (Fig. 8b, c) and increases into the Nordic Seas (Fig. 8a), indicating a shift in circulation. This shift may be a response to increasing temperatures, so water needs to move further north to lose enough heat to sink. Convection increases in all these regions however (Fig. 8a–c), despite reduced advection. In the Nordic Seas sea ice volume decreases (Fig. 8a), this freshens the region, which acts as a negative feedback to increased advection.

In the Nordic Seas the increase in convection and temperature, and decrease in the density gradient (Fig. 8a), lead AMOC change by approximately 50 years (Fig. 9). This indicates that this region is important in triggering the interstadial as we do not see a similar lead for any of the other regions (Figure S6). The driver of this may be a wind-driven positive feedback in response to a decrease in sea-ice cover and an increase in sea-level pressure (SLP) across the Nordic Sea (Fig. 8a). As regional salinity increases, circulation and temperatures increase, and sea ice cover decreases. Consequently, a negative SLP anomaly develops (Fig. 8a), which occurs with the same lead-time as convection and temperature (Fig. 9). This strengthens the Icelandic low and increases regional wind stress curl (Fig. 8a). This wind-driven feedback may be the trigger that invigorates convection and circulation in the Nordic Seas, a similar mechanism to that proposed by Klockmann et al. (2020) in the MPI-ESM. This in turn accelerates deep-water formation, which flushes the anomalously saline waters from the tropics into the Nordic Seas, which causes a rapid increase in salinity and active deep-water formation (Fig. 8a) and the AMOC accelerates. Consequently, there is a rapid decline in the salinity gradient between these regions during the transition (Fig. 7).

Fig. 9
figure 9

Lead lag analysis for the Nordic Sea for convection and a range of ocean and atmosphere variables with the AMOC index (defined as the mean AMOC strength between 40° and 50°N at 800 m) for the 30kyrBASE simulation. The climate variables have been averaged over 0–666 m water depth and convection is averaged over 0-300 m. The data has been filtered with a low pass Lanczos filter prior to correlation analysis

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4.3 Interstadial period

The interstadial events are comparatively short-lived, characterised by elevated salinity, warm temperatures, a limited sea-ice extent, and a strong AMOC (Figs. 2, 3, 4, 8). Advection is high into the Nordic Seas (Fig. 8a) but at a minimum in the Irminger Sea (Fig. 8b) and reduced in the central SPG (Fig. 8c). Despite this, salinity and convection remain high across all regions indicating widespread deep-water formation (Fig. 8a–c). In the Irminger Sea, reduced advection is replaced by an increase in diffusive processes, responsible for the increase in regional salinity that maintains convection (Fig. 8b). In the central SPG however, salinity increases due to a decrease in the freshening role of sea-ice processes due to the retreat of the sea-ice margin (Fig. 8c).

In the tropics, salinity is at a minimum due to a decrease in surface fluxes and an increase in advection out of the basin (Fig. 8d). The former reflects a northward shift in the ITCZ (Fig. 3c), which increases precipitation and the P-E balance. As such, the salinity gradient between the Northern NA (SPG and Nordic Seas) and the tropics decreases to a minimum (Fig. 7).

4.4 Transition into a stadial

The transition into a stadial is triggered by the collapse of the salinity gradient (Fig. 7) between the tropics and northern NA during the interstadial. Figure 7 shows that the rapid decline in AMOC strength occurs when the salinity gradient falls from a high of between 1.30 and 1.35 PSU (gkg−1) during the stadial to between 0.43 and 0.51 PSU (gkg−1). Between these critical values, the salt required to drive convection and deep-water formation cannot be sustained and so the AMOC rapidly diminishes. This is comparable to the MPI-ESM (Klockmann et al. 2020), in which a gradient of approximately 0.5 gkg-1 was shown to trigger a stadial.

In response, salt transported via advection is reduced in the Nordic Seas and increases in the Irminger Sea and across the SPG, and convection decreases across the Northern North Atlantic (Fig. 8a–c). In the Nordic Seas, sea ice formation accelerates as temperatures decrease, which shifts the Icelandic low southward causing an increase in regional SLP and decrease in wind stress curl (Fig. 8a). In the tropics, the ITCZ is once again shifted southward (Fig. 3c), this decreases the P-E balance and the surface flux salinity tendency increases (Fig. 8d). Salinity therefore begins to accumulate (Figs. 7, 8d). The oscillation can then start again.

5 The role of continental ice sheets

The 30kyr BP simulations are unique as they demonstrate an oscillation, however simulations with 28kyr boundary conditions do not exhibit variability. In order to determine what pushes the AMOC into an oscillating mode, we performed a range of experiments with perturbed glacial boundary conditions modified to those used for the 28kyr experiments (see Methods; Tables 1, 2). Altered greenhouse gases, orbital parameters, land-sea mask and bathymetry had no impact on the oscillation. Next, we successively decreased the height and extent of the continental ice sheets within a 28kyr non-oscillating simulation to match the configuration of the 30kyr simulation (see Methods; Table 2). An oscillation in the AMOC is initiated following a decrease in the height and extent of the West and East Laurentide ice sheet in the 28kyrEWLAU and 28kyrLAU simulations (Fig. 10c, d). This initiation indicates that AMOC oscillations are sensitive to the configuration of the Laurentide ice sheet in HadCM3B, the height and extent of which triggers the region to be able to oscillate.

Fig. 10
figure 10

The same as Fig. 7 but for the simulations with altered ice sheets (see Table 2)

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The mechanism for this appears to be linked to a northward shift in the position of the jet stream following a decrease in the height and extent of the Laurentide ice sheet (Fig. 11a). Due to the reduced topographic forcing, there is an increase in cold continental air drawn in from over the ice sheet, decreasing SATs over much of the SPG (Fig. 11b). This enhances sea ice growth in the SPG, which has a freshening regional effect due to its seasonal nature as discussed in Sect. 4 and shown in Figs. 5g, 8c. Consequently, there is a decrease in salinity and density (Fig. 11c) despite the colder temperatures. This spins down the SPG (Fig. 11d), reducing deepwater formation and northward heat transport. This weakening is indicated by a decrease in average AMOC strength from 8.98 Sv for the non-oscillating simulations (28kyrFEN, 28kyrELAU and 28kyr50) to 8.16 Sv for the oscillating simulations (28kyrEWLAU and 28kyrLAU). There is also an increase in temperature across the STG/SPG boundary at approximately 40° N (Fig. 11b) and a northward expansion and slowdown of the STG (Fig. 11d). This expansion and slowdown permits a greater salinity anomaly to develop in the tropics, as more water is kept with the region and subject to enhanced evaporation for a longer period. Czaja (2009) similarly showed that a more northerly jet expanded/contracted the subtropical and subpolar gyres.

Fig. 11
figure 11

Composite spatial patterns for the non-oscillating and oscillating simulations with altered ice sheet configurations (see Table 2) and the anomaly (oscillating-non-oscillating). The non-oscillating simulations are the 28kyrFEN, 28kyrELAU and 28kyr50, and the oscillating simulations are the 28kyrEWLAU and 28kyrLAU. Potential Density is averaged over 0–666 m

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The result of this is reduced advection out of the tropics and so a salinity anomaly can build up in the region whilst salinity decreases in the SPG, as shown in the regional timeseries (Fig. 10c, d). Furthermore, the increased meridional temperature gradient due to SPG cooling shifts the ITCZ to an average position further south in the oscillating experiments (not shown), which reduces the P-E balance and contributes to developing a more saline tropics. This build up of salinity initiates the set of feedbacks associated with the stadial identified in Sect. 4. Again, the salinity gradient between the two regions is shown to be key in determining the timing of the interstadial/stadial transition.

6 Discussion and summary

This study presents results from a set of glacial simulations using the HadCM3B coupled climate model with 30kyr BP boundary conditions that demonstrates stochastic oscillations on a 1500-year timescale, comparable in timescale to the DO events observed in the ice core record (Dansgaard et al. 1993). To our knowledge, this is the third GCM to demonstrate such variability utilising fully glacial boundary conditions, the first being the UofT-CESM4 model (Peltier et al. 2020; Peltier and Vettoretti 2014; Vettoretti and Peltier 2016) followed by MIROC4m (Kuniyoshi et al. 2022). We utilise a set of salinity diagnostics to provide a comprehensive mechanism for the oscillation, including the triggers between the phases, and what conditions the North Atlantic to be able to oscillate. In summary:

  • The oscillation represents a complex coupled ocean–atmosphere-sea-ice feedback system within the North Atlantic (NA).

  • This system is strongly linked to the build-up and collapse of the salinity gradient between the tropics and northern NA. This determines the level of advection between the two regions, which governs AMOC strength and consequent climatic impacts.

  • Surface freshwater fluxes and sea ice processes are crucial in developing this salinity gradient. In the tropics, the position of the ITCZ regulates the P-E balance, which acts as a positive feedback in increasing/decreasing regional salinity. Sea-ice feedbacks are location dependant. In the Nordic Seas, sea-ice acts as a negative feedback and may contribute in pushing the oscillation into an opposing phase.

  • The key site of advection and deep-water formation moves from the SPG during stadials to the Nordic Sea during interstadials.

  • The interstadial may be initiated by an atmospheric forcing; this is a wind-driven atmospheric feedback in the Nordic Seas in response to an increase in regional temperature, a decrease in sea ice cover and a consequent increase in SLP, which invigorates wind stress and subsequently convection.

  • A stadial is initiated by an ocean forcing; this involves the collapse of the salinity gradient between the tropics and Northern NA. This collapse weakens advection into the Nordic Seas and diminishes deep-water formation.

  • This oscillation of the AMOC is sensitive to the configuration of the Laurentide ice-sheet. A reduction in ice-sheet height shifts the jet stream northward, causing regional cooling and an increase in seasonal sea ice concentration in the SPG. This freshens the region and reduces deep-water formation, which restricts and weakens the SPG. In contrast, the STG expands northward.

  • Weaker STG/SPG transport and a shift in the ITCZ permits a salinity anomaly to develop in the tropics. This initiates the first interstadial and associated feedbacks that maintain the oscillation.

The oscillation therefore reflects a salt oscillator mechanism in the NA, similar to that initially proposed by Broecker et al. (1990), and also identified in the UofT-CESM4 model (Peltier and Vettoretti 2014; Vettoretti and Peltier 2016, 2018). The salinity gradient between the tropics and Northern North Atlantic (SPG & GIN Seas) is integral in maintaining this salt oscillator, as identified by Brown and Galbraith (2016). The wind-driven trigger of an interstadial is comparable to the mechanism identified in Drijfhout et al. (2013) and Kleppin et al. (2015), and analogous to that identified by Klockmann et al. (2020) in the MPI-ESM. The ocean-driven return to a stadial is also analogous to the MPI-ESM (Klockmann et al. 2020). The height of the Laurentide ice sheet influences the position of the Jet stream, which in addition to the background state of the glacial climate plays a crucial role in priming the system to oscillate, a similar conclusion to Zhang et al. (2014), Wunsch (2006) and Li and Born (2019).

The results here particularly highlight the importance of the dynamics between the tropics and SPG in generating the oscillation. The different roles of surface fluxes (sea ice processes and freshwater flux) within each region are crucial for initiating the transitions between the phases. The SPG and its associated sea-ice dynamics and freshwater fluxes tend to be the common focus when investigating DO events (e.g., Dokken et al. 2013; Gildor and Tziperman 2003; Li et al. 2005; Li and Born 2019; Menviel et al. 2014). Sea ice evidently plays an important role in conditioning (i.e., freshening and weakening) the SPG and in triggering the interstadials. However, the model does not demonstrate the strong connection between sea-ice and the onset of an interstadial as is shown in the UofT-CCSM4 model, specifically the opening of a polynya in the Irminger Sea (Peltier et al. 2020). In HadCM3B, the tropical P-E balance, which reflects the position of the ITCZ, is shown to be of critical importance for maintaining the oscillation. Evidence for such ITCZ shifts on DO time scales are apparent in a wide range of observational studies using tropical speleothem and sediment records (Deplazes et al. 2013; Kanner et al. 2012; Peterson et al. 2000; Dupont et al., 2010; Wang et al., 2004), and a number of modelling studies (e.g., Brown and Galbraith 2016; Chiang and Bitz 2005; Zhang and Delworth 2005). Indeed Vellinga and Wu (2004) and Armstrong et al. (2017) showed that the position of the ITCZ was important in driving centennial AMOC variability in HadCM3, these results also highlight its important role on millennial timescales.

An important difference between the modelled oscillation and the DO events in the ice-core record is the lack of the characteristic sawtooth waveform. It may be that HadCM3B lacks the sensitivity to the wind-driven forcing mechanism that triggers the interstadial. Alternatively, other mechanisms may be involved that are not correctly represented in the model. Peltier et al. (2020) identified the important role of sea-ice and the vertical diapycnal diffusivity parameterisation in the Irminger sea in driving the rapid onset of an interstadial in the UofT‐CCSM4 model, which does exhibit a sawtooth waveform. The parameterisation determines the opening of a polynya in the region due to the onset of vertical mixing that triggers the rapid transition, and is referred to as the ‘fast physics’ component of the DO oscillation (Peltier et al. 2020). A very similar mechanism has subsequently been identified in MIROC4m, which also demonstrates a sawtooth waveform (Kuniyoshi et al. 2022). Both the response of the sea-ice model and this parameterisation may be inaccurately represented in HadCM3B. Indeed HadCM3B incorporates a more primitive sea-ice model compared to the UofT-CCSM4 model, which may be the reason why the rapid transition into an interstadial is not properly represented. Further experiments with varied phase space, including ocean diffusivity, are required to fully investigate the impact these factors may have on the oscillation waveform.

Furthermore, the mechanism that initiates the oscillation differs to those previously proposed. Zhang et al. (2014) increased the height of the Laurentide ice sheet, which increased North Atlantic SATs, accelerating SPG circulation and instigating an oscillation. In contrast Madonna et al. (2017) showed that an equator-ward shift in the jet stream freshens and weakens the SPG via Greenland blocking, which reduces heat transport and initiates an oscillation. We show that a pole-ward shift of the jet weakens both Atlantic gyres and permits a salinity anomaly to develop to drive the interstadial. Therefore it is clear that the impact of the Laurentide ice sheet on the jet stream and the role this plays in driving AMOC oscillations remains unclear within models. The mechanism we identify is evidently linked to the seasonal and freshening role of sea ice in the SPG, which is likely to be a highly model-dependent characteristic of this region, in contrast to other models. It is worth noting that wind stress is directly applied to the surface current in HadCM3B through sea-ice cover. Therefore the increase in sea-ice cover does not decouple the surface currents from the wind forcing, such as in the real world (Valdes et al. 2017). Therefore increased sea-ice cover does not contribute to weakening gyre strength, so density change is the leading factor.

We must also consider why such oscillations are not prevalent in other glacial simulations with very similar ice-sheet configurations. In Armstrong et al. (2019b), a number of glacial simulations performed using HadCM3B incorporated the same 30kyr BP ice-sheet configuration but had different boundary conditions (representing 14, 44, 46, 48, 50, 58 and 60 kyr BP, see Armstrong et al. 2019b and their Table 2). These simulations did not demonstrate an oscillation, which indicates the important role of the background climate state. This validates an idea discussed by Li and Born (2019) of a ‘sweet spot’ in model simulations, where the system is more prone to spontaneous oscillatory behaviour within a specific range of conditions. Indeed, Vettoretti et al. (2022) recently showed that the existence of internal oscillations in CCSM4 is sensitive to the background atmospheric CO2 levels. It might be that the configuration of the ice sheet pushes the system across a transition point, but the background climate is important in permitting a salt oscillator mode to develop, at which point feedbacks within the system can maintain the oscillation.